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Understanding Mathematics Instruction in Kindergarten

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Title: Understanding Mathematics Instruction in Kindergarten
Language: English
Authors: Danielle Shaw Attaway, Mimi Engel, Robin Jacob, Anna Erickson, Amy Claessens
Source: Elementary School Journal. 2025 125(3):518-547.
Availability: University of Chicago Press. Journals Division, P.O. Box 37005, Chicago, IL 60637. Tel: 877-705-1878; Tel: 773-753-3347; Fax: 877-705-1879; Fax: 773-753-0811; e-mail: subscriptions@press.uchicago.edu; Web site: http://www.press.uchicago.edu
Peer Reviewed: Y
Page Count: 30
Publication Date: 2025
Document Type: Journal Articles
Reports - Research
Education Level: Early Childhood Education
Elementary Education
Kindergarten
Primary Education
Descriptors: Kindergarten, Mathematics Instruction, Low Income Students, Socioeconomic Status, Large Group Instruction, Teaching Methods, Manipulative Materials, Scaffolding (Teaching Technique), Individualized Instruction, Urban Schools, Interdisciplinary Approach
DOI: 10.1086/734379
ISSN: 0013-5984
1554-8279
Abstract: Kindergartners' math skills predict later academic outcomes. However, we know little about kindergarten mathematics instruction. Using data from 182 classroom observations in a large urban district, we explore time spent on mathematics and math content coverage. We also examine two underinvestigated aspects of kindergarten math instruction: (1) whether math is incorporated into other subjects and (2) math pedagogy. We focus on schools serving students from households with lower income and include a small higher-income comparison sample. We find that kindergartners in schools serving students from households with lower income experience more whole-group math instruction and have fewer opportunities to use manipulatives in math. Kindergartners in schools serving students from households with higher incomes are exposed to more math during other subjects. In math, kindergartners across contexts experience cursory reviews of key ideas, rarely have scaffolded instruction, and instruction is not differentiated for students based on their performance or skills.
Abstractor: As Provided
Entry Date: 2025
Accession Number: EJ1464634
Database: ERIC
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  Value: <anid>AN0184105568;esj01mar.25;2025Apr01.05:46;v2.2.500</anid> <title id="AN0184105568-1">Understanding Mathematics Instruction in Kindergarten </title> <p>Kindergartners' math skills predict later academic outcomes. However, we know little about kindergarten mathematics instruction. Using data from 182 classroom observations in a large urban district, we explore time spent on mathematics and math content coverage. We also examine two underinvestigated aspects of kindergarten math instruction: (<reflink idref="bib1" id="ref1">1</reflink>) whether math is incorporated into other subjects and (<reflink idref="bib2" id="ref2">2</reflink>) math pedagogy. We focus on schools serving students from households with lower income and include a small higher-income comparison sample. We find that kindergartners in schools serving students from households with lower income experience more whole-group math instruction and have fewer opportunities to use manipulatives in math. Kindergartners in schools serving students from households with higher incomes are exposed to more math during other subjects. In math, kindergartners across contexts experience cursory reviews of key ideas, rarely have scaffolded instruction, and instruction is not differentiated for students based on their performance or skills.</p> <p>Kindergartners are typically in the midst of major social-emotional, motivational, cognitive, and self-regulatory developmental changes (Sameroff & Haith, [<reflink idref="bib59" id="ref3">59</reflink>]; Skinner, [<reflink idref="bib63" id="ref4">63</reflink>]). Further, kindergarten marks a major transition in that it is very different from preschool or home care (Abry et al., [<reflink idref="bib1" id="ref5">1</reflink>]; Engel et al., [<reflink idref="bib30" id="ref6">30</reflink>]; Justice et al., [<reflink idref="bib42" id="ref7">42</reflink>]). Learning in kindergarten can set the foundation for future success; kindergarten math skills consistently predict later academic outcomes (Duncan et al., [<reflink idref="bib25" id="ref8">25</reflink>]; Ritchie & Bates, [<reflink idref="bib56" id="ref9">56</reflink>]; Watts et al., [<reflink idref="bib74" id="ref10">74</reflink>]).</p> <p>Despite its importance, we know little about kindergarten mathematics instruction. Most research on early math instruction has focused on preschool (Bachman et al., [<reflink idref="bib2" id="ref11">2</reflink>]; Hindman, [<reflink idref="bib38" id="ref12">38</reflink>]). Research on kindergarten math instruction has often used the two Early Childhood Longitudinal Study—Kindergarten (ECLS-K) cohorts, relying on a teacher survey in the spring of kindergarten. A benefit of the ECLS-K is that the data have allowed researchers to explore differences across key subgroups such as historically minoritized student populations, the main sample for the current study. Although the ECLS-K teacher survey provides a nationally representative snapshot of kindergarten instruction, it has several drawbacks. First, it relies on teachers' recall of their classroom environment and teaching across the entire year, which is likely inaccurate and could be biased (Rowan et al., [<reflink idref="bib58" id="ref13">58</reflink>]). Second, individual teachers may interpret survey questions differently (Mayer, [<reflink idref="bib46" id="ref14">46</reflink>]). Third, the survey focuses on content coverage and classroom organization, failing to capture what kindergarten mathematics instruction looks like in terms of pedagogical practices. Pedagogy includes the use of hands-on materials, student grouping, and other measures of instructional quality, a multifaceted construct with definitions that vary across studies. The current study uses widely accepted indicators of quality for young learners, including differentiation, use of materials, instructional grouping, and classroom management (Boston, [<reflink idref="bib9" id="ref15">9</reflink>]; Mu et al., [<reflink idref="bib48" id="ref16">48</reflink>]; Senden et al., [<reflink idref="bib62" id="ref17">62</reflink>]; Stipek & Chiatovich, [<reflink idref="bib66" id="ref18">66</reflink>]). Finally, the most recently available ECLS-K data are from 2010–2011, well over a decade ago. Classroom observations with trained observers help ensure that reporting is consistent and comparable across observations. In addition, classroom observations provide a more comprehensive depiction of instruction, capturing a more nuanced picture of classroom practice. Using classroom observations, the current study provides an updated and detailed picture of kindergarten math instruction.</p> <p>Using data from 182 kindergarten classroom observations conducted over 3 years in a large urban district, we explore time spent on mathematics and math content coverage. We also examine two aspects of kindergarten math that have received little attention. First, we explore how much math is incorporated into other subject areas and activities. Theory indicates that incorporating math into play can expand children's math skills (Sarama & Clements, [<reflink idref="bib61" id="ref19">61</reflink>]), and empirical evidence documents the importance of interdisciplinary learning (Hassinger-Das et al., [<reflink idref="bib35" id="ref20">35</reflink>]; McGuire et al., [<reflink idref="bib47" id="ref21">47</reflink>]; Vetter et al., [<reflink idref="bib72" id="ref22">72</reflink>]).</p> <p>Second, we examine kindergarten math pedagogy. High-quality mathematical pedagogy for young learners includes small groups where children engage with peers (Herrera et al., [<reflink idref="bib37" id="ref23">37</reflink>]; Stright & Supplee, [<reflink idref="bib67" id="ref24">67</reflink>]), use hands-on materials (Carbonneau et al., [<reflink idref="bib13" id="ref25">13</reflink>]), and experience differentiated instruction (Deunk et al., [<reflink idref="bib22" id="ref26">22</reflink>]; Smale-Jacobse et al., [<reflink idref="bib64" id="ref27">64</reflink>]). However, we do not know whether these practices are enacted for kindergartners. We also compare how kindergarten math instruction varies across schools serving students from lower- versus higher-income households. Below we review relevant theory and prior research.</p> <hd id="AN0184105568-2">Theory and Prior Research</hd> <p></p> <hd id="AN0184105568-3">Kindergarten Mathematics</hd> <p>In 2010, the National Council of Teachers of Mathematics (NCTM) and the National Association for the Education of Young Children (NAEYC) published a joint statement emphasizing the need for high-quality, challenging, and accessible mathematics education for 3- to 6-year-olds, noting that this lays the foundation for future mathematics learning (NCTM & NAEYC, [<reflink idref="bib51" id="ref28">51</reflink>]). Kindergarten mathematics learning is important, and the mathematics content kindergartners are exposed to matters (Claessens & Engel, [<reflink idref="bib18" id="ref29">18</reflink>]; Clements & Sarama, [<reflink idref="bib19" id="ref30">19</reflink>]; Engel et al., [<reflink idref="bib28" id="ref31">28</reflink>]). Studies find consistent, long-term associations between early math and later student outcomes. Math achievement measured at kindergarten entry is predictive of school outcomes through eighth grade (Bailey et al., [<reflink idref="bib3" id="ref32">3</reflink>]; Claessens & Engel, [<reflink idref="bib18" id="ref33">18</reflink>]; Claessens et al., [<reflink idref="bib17" id="ref34">17</reflink>]; Duncan et al., [<reflink idref="bib25" id="ref35">25</reflink>]; Jordan et al., [<reflink idref="bib41" id="ref36">41</reflink>]; Watts et al., [<reflink idref="bib74" id="ref37">74</reflink>]) and adult socioeconomic status (Ritchie & Bates, [<reflink idref="bib56" id="ref38">56</reflink>]). Growth in mathematical ability is a strong predictor of adolescent mathematics achievement (Watts et al., [<reflink idref="bib75" id="ref39">75</reflink>]).</p> <p>Studies using the nationally representative ECLS-K cohorts find that devoting additional days per month to basic counting and shapes is negatively associated with end-of-kindergarten mathematics gains, whereas spending additional days per month on more advanced content such as addition and subtraction is positively associated with end-of-kindergarten mathematics gains (Engel et al., [<reflink idref="bib27" id="ref40">27</reflink>], [<reflink idref="bib28" id="ref41">28</reflink>]). Other studies also find that advanced mathematics content is positively associated with achievement (Guarino et al., [<reflink idref="bib33" id="ref42">33</reflink>]), whereas emphasis on basic numbers/shapes predicts smaller gains (Bodovski & Farkas, [<reflink idref="bib7" id="ref43">7</reflink>]; Ribner, [<reflink idref="bib55" id="ref44">55</reflink>]). While prior research documents that early mathematics is important and the math content kindergartners are exposed to is associated with achievement, less is known about other aspects of kindergarten math instruction.</p> <hd id="AN0184105568-4">Kindergarten Mathematics Content</hd> <p>Studies using the ECLS-K cohorts find that teachers report more emphasis on basic content (e.g., simple counting and shapes) than more advanced content (e.g., addition and subtraction) (Engel et al., [<reflink idref="bib27" id="ref45">27</reflink>]; Ribner, [<reflink idref="bib55" id="ref46">55</reflink>]). Other studies use factor analysis and find that the dimensions of kindergarten mathematics content are basic numbers and shapes, advanced counting, writing numbers, applied math, single- and double-digit operations, and math through music and movement (Bodovski & Farkas, [<reflink idref="bib7" id="ref47">7</reflink>]; Chiatovich & Stipek, [<reflink idref="bib16" id="ref48">16</reflink>]). Using both ECLS-K cohorts to describe changes in kindergarten math content over time, research using these data finds that average time on math, including both basic and more advanced math content, increased between 1999 and 2011 (Bassok et al., [<reflink idref="bib6" id="ref49">6</reflink>]; Engel et al., [<reflink idref="bib28" id="ref50">28</reflink>]). Using data from other kindergarten teacher surveys, Cohen-Vogel et al. ([<reflink idref="bib20" id="ref51">20</reflink>]) find that numeracy is a major focus of kindergarten mathematics instruction, and Abry et al. ([<reflink idref="bib1" id="ref52">1</reflink>]) find that kindergarten teachers emphasize counting aloud and calendar-related activities. Although past surveys document the mathematics content kindergarten teachers cover, to our knowledge there is no recent observational evidence describing math in kindergarten.</p> <hd id="AN0184105568-5">Math Outside of the Math Lesson</hd> <p>Typical elementary school schedules divide the day to focus on single subjects (e.g., literacy, math, science). However, within a single subject or during other parts of the day, interdisciplinary learning, where children explore concepts from multiple subjects concurrently, can also occur. Interdisciplinary learning is often more collaborative and playful, and it supports children's cognitive development (Casey et al., [<reflink idref="bib15" id="ref53">15</reflink>]; Frye et al., [<reflink idref="bib32" id="ref54">32</reflink>]; Vetter et al., [<reflink idref="bib72" id="ref55">72</reflink>]).</p> <p>Vygotsky ([<reflink idref="bib73" id="ref56">73</reflink>]) theorized that play is important for children's cognitive growth because it allows children to use cultural tools, create and follow rules, and think abstractly. Sarama and Clements ([<reflink idref="bib61" id="ref57">61</reflink>]) also emphasize the value of interdisciplinary, playful learning for children's cognitive development. They argue that math learning can be supported through "mathematization," the process through which children build upon and expand their math skills by incorporating math with play (e.g., counting to understand a story or using shapes to build a structure). To this end, the joint statement by NCTM and NAEYC highlights the need for teachers to provide time and materials to support young children's engagement in play in which they can explore mathematical ideas (NCTM & NAEYC, [<reflink idref="bib51" id="ref58">51</reflink>]). One interdisciplinary learning avenue is integrating mathematics instruction with gross motor activities like physical education. Experiments find that children who engaged in playful, physically active learning experiences designed to teach math content had significantly larger mathematics learning gains (Bustamante et al., [<reflink idref="bib12" id="ref59">12</reflink>]; Vetter et al., [<reflink idref="bib72" id="ref60">72</reflink>]). These effects persisted for at least 7 to 9 months (Mullender-Wijnsma et al., [<reflink idref="bib49" id="ref61">49</reflink>]).</p> <p>Research also finds benefits from integrating math and literacy instruction. Building children's mathematics vocabulary supports their mathematical thinking (Purpura & Reid, [<reflink idref="bib53" id="ref62">53</reflink>]). Experimental studies find that children exposed to storybook reading interventions that targeted mathematics vocabulary significantly outperformed the control group on measures of mathematical language (Hassinger-Das et al., [<reflink idref="bib35" id="ref63">35</reflink>]; Purpura et al., [<reflink idref="bib52" id="ref64">52</reflink>]). Other studies find that children who were read picture books that introduced mathematics concepts such as numbers and geometry outperformed the control group in quantifying, measurement, and geometry (Casey et al., [<reflink idref="bib15" id="ref65">15</reflink>]; McGuire et al., [<reflink idref="bib47" id="ref66">47</reflink>]; van Den Heuvel-Panhuizen et al., [<reflink idref="bib70" id="ref67">70</reflink>]). While theory and evidence support integrating mathematics with other subjects and activities (Bustamante et al., [<reflink idref="bib12" id="ref68">12</reflink>]; Frye et al., [<reflink idref="bib32" id="ref69">32</reflink>]; McGuire et al., [<reflink idref="bib47" id="ref70">47</reflink>]; Sarama & Clements, [<reflink idref="bib61" id="ref71">61</reflink>]), to our knowledge, there is no evidence describing how much kindergarten mathematics instruction occurs outside of the math lesson, what other subject areas and activities include math, and whether this varies across settings.</p> <hd id="AN0184105568-6">Math Pedagogy</hd> <p>Theory, expert advisory panels, and empirical evidence support the importance of high-quality mathematical pedagogy. Bioecological theory underscores the importance of the environment, because children acquire skills through interactions with their environments (Bronfenbrenner & Morris, [<reflink idref="bib10" id="ref72">10</reflink>]). Vygotsky ([<reflink idref="bib73" id="ref73">73</reflink>]) posited that children learn best when supported by adults or advanced peers who scaffold and guide children's exploration and learning. NAEYC and NCTM advocate for math instruction that maximizes student discourse through collaborative projects and opportunities to engage with peers and adults. They encourage teachers to use questioning, multiple representations, and hands-on learning opportunities to stimulate children's thinking (Copple & Bredekamp, [<reflink idref="bib21" id="ref74">21</reflink>]; NCTM, [<reflink idref="bib50" id="ref75">50</reflink>]).</p> <p>Theory and expert recommendations are supported by studies showing that student grouping and hands-on learning matter. Small-group instruction in early grades provides more opportunities to give and receive help from peers, engage in collaborative dialogue, and participate in hands-on activities; and small-group instruction positively affects student achievement (Herrera et al., [<reflink idref="bib37" id="ref76">37</reflink>]; Jacob et al., [<reflink idref="bib40" id="ref77">40</reflink>]; Klingner & Vaughn, [<reflink idref="bib43" id="ref78">43</reflink>]; Ramani et al., [<reflink idref="bib54" id="ref79">54</reflink>]). Materials also matter. Instructional contexts for young children that include hands-on experiences allow students to learn through play (Carbonneau et al., [<reflink idref="bib13" id="ref80">13</reflink>]; Manches & O'Malley, [<reflink idref="bib45" id="ref81">45</reflink>]; Skinner, [<reflink idref="bib63" id="ref82">63</reflink>]). Everyday objects, manipulatives, and images that resemble everyday objects can help children connect abstract mathematical concepts to the world around them (Brown et al., [<reflink idref="bib11" id="ref83">11</reflink>]). Additionally, differentiated instruction, which supports all children's learning by adapting various elements of the curriculum to tailor to students' needs (Hall et al., [<reflink idref="bib34" id="ref84">34</reflink>]), improves student learning and achievement (Deunk et al., [<reflink idref="bib22" id="ref85">22</reflink>]; Hattie, [<reflink idref="bib36" id="ref86">36</reflink>]; Smale-Jacobse et al., [<reflink idref="bib64" id="ref87">64</reflink>]).</p> <p>Finally, classroom management, which is integral to pedagogy, also predicts children's mathematics achievement (van Dijk et al., [<reflink idref="bib71" id="ref88">71</reflink>]). Students in classrooms taught by teachers with higher value-added model (VAM) scores, differentiated only by better classroom-management skills, perform better in math (Stronge et al., [<reflink idref="bib68" id="ref89">68</reflink>]). Although theory and research highlight grouping, materials, differentiation, and classroom management for children's math learning, most studies that investigate kindergarten math pedagogy do not explore pedagogy separately from mathematics content (Bodovski & Farkas, [<reflink idref="bib7" id="ref90">7</reflink>]; Guarino et al., [<reflink idref="bib33" id="ref91">33</reflink>]) or investigate kindergarten math pedagogy within the context of a specific curriculum (Doabler et al., [<reflink idref="bib24" id="ref92">24</reflink>]).</p> <hd id="AN0184105568-7">Variation in Pedagogy across Educational Contexts</hd> <p>Research finds that pedagogy differs between schools serving children from lower- versus higher-income households and between schools serving historically marginalized populations compared with their more privileged peers. For example, several studies find that teachers who teach children of color or from households with lower income often use more didactic pedagogical techniques (Bassok et al., [<reflink idref="bib6" id="ref93">6</reflink>]; Early et al., [<reflink idref="bib26" id="ref94">26</reflink>]; Stipek, [<reflink idref="bib65" id="ref95">65</reflink>]). In addition, young children from marginalized populations experience fewer scaffolded teaching interactions (Early et al., [<reflink idref="bib26" id="ref96">26</reflink>]) and have less access to center-based, hands-on learning experiences or exposure to mixed instructional content (Bassok et al., [<reflink idref="bib6" id="ref97">6</reflink>]). Conversely, White children are more likely to have supportive teacher interactions (Tonyan & Howes, [<reflink idref="bib69" id="ref98">69</reflink>]), and children in schools serving children from households with higher income spend more time in free-choice activities (Early et al., [<reflink idref="bib26" id="ref99">26</reflink>]). While prior research documents how pedagogy differs between schools serving students from lower- versus higher-income households, these studies focus on instruction in general. Less is known about variation in kindergarten math instruction.</p> <hd id="AN0184105568-8">The Current Study</hd> <p>The current study aims to address these gaps in knowledge about kindergarten mathematics instruction by exploring math time, content, and pedagogical approaches, including information on math taught outside the math lesson, and exploring variation across educational contexts. The current study provides an updated and nuanced description of kindergarten math instruction from a 3-year observational study in a large urban district conducted by trained observers using a validated observation protocol. Building on prior theory and research, we address the following questions:</p> <p></p> <p>• 1.</p> <p></p> <ulist> <item> How much time do kindergarten teachers in schools serving students from households with lower income spend teaching math and what content do they cover? (RQ1)</item> <p></p> <item> <emph>a</emph>)</item> <p></p> <item> How much mathematics instruction occurs within the designated math instructional lesson?</item> <p></p> <item> <bold> _I</bold>i_)</item> <p></p> <item> How much math instruction occurs outside of math lessons, during which activities, and along with what other content areas?</item> <p></p> <item> <emph>c</emph>)</item> <p></p> <item> Does this differ systematically in schools serving students from households with higher income?</item> <p></p> </ulist> <p>• 2.</p> <p></p> <ulist> <item> What does kindergarten mathematics instruction look like in terms of pedagogy, including instructional grouping, materials used, and measures of instructional quality including differentiation and classroom management? (RQ2)</item> <p></p> <item> <emph>a</emph>)</item> <p></p> <item> Does this differ systematically in schools serving students from households with higher income?</item> </ulist> <hd id="AN0184105568-9">Data and Method</hd> <p></p> <hd id="AN0184105568-10">Sample</hd> <p></p> <hd id="AN0184105568-11">Schools</hd> <p>Our primary school sample, where we collected data across all study years, consists of 24 schools in a large urban district serving students from households with lower income (see Table 1). These schools were part of a larger study for which participating schools were selected because at least 70% of students were free or reduced-price lunch (FRPL) eligible.[<reflink idref="bib2" id="ref100">2</reflink>]</p> <p>Table 1. Study Timeline, Number of Schools, Observations, and Classes by Year</p> <p> <ephtml> <table><thead><tr><th align="left" style="border-bottom: solid thin black" rowspan="2" valign="bottom" scope="col" colspan="1">Wave</th><th align="center" style="border-bottom: solid thin black" rowspan="2" valign="bottom" scope="col" colspan="1">Year</th><th align="center" style="border-bottom: solid thin black" rowspan="2" valign="bottom" scope="col" colspan="1">Observation Type</th><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1">SSLI Schools (<italic>n</italic> = 24)</th><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1">SSHI Schools (<italic>n</italic> = 8)</th><th align="center" style="border-bottom: solid thin black" rowspan="2" valign="bottom" scope="col" colspan="1">Total Observations</th><th align="center" style="border-bottom: solid thin black" rowspan="2" valign="bottom" scope="col" colspan="1">Classes</th></tr><tr><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1">Observations</th><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1">Observations</th></tr></thead><tbody><tr><th rowspan="3" valign="bottom" scope="rowgroup" colspan="1">Wave 1</th><td rowspan="3" valign="bottom" colspan="1">2015–2016</td><td valign="bottom" rowspan="1" colspan="1">Math lesson</td><td valign="bottom" rowspan="1" colspan="1">45</td><td valign="bottom" rowspan="1" colspan="1">–</td><td rowspan="3" valign="bottom" colspan="1">75</td><td rowspan="3" valign="bottom" colspan="1">42</td></tr><tr><td style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">Full-day</td><td style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">30</td><td style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">–</td></tr><tr><td valign="bottom" rowspan="1" colspan="1">Fall</td><td valign="bottom" rowspan="1" colspan="1">36</td><td valign="bottom" rowspan="1" colspan="1">–</td></tr><tr><td style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1" /><td style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1" /><td style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">Spring</td><td style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">39</td><td style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">–</td><td style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1" /><td style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1" /></tr><tr><th rowspan="3" valign="bottom" scope="rowgroup" colspan="1">Wave 2</th><td rowspan="3" valign="bottom" colspan="1">2016–2017</td><td valign="bottom" rowspan="1" colspan="1">Math lesson</td><td valign="bottom" rowspan="1" colspan="1">24</td><td valign="bottom" rowspan="1" colspan="1">–</td><td rowspan="3" valign="bottom" colspan="1">40</td><td rowspan="3" valign="bottom" colspan="1">24</td></tr><tr><td style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">Full-day</td><td style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">16</td><td style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">–</td></tr><tr><td valign="bottom" rowspan="1" colspan="1">Fall</td><td valign="bottom" rowspan="1" colspan="1">18</td><td valign="bottom" rowspan="1" colspan="1">–</td></tr><tr><td style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1" /><td style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1" /><td style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">Spring</td><td style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">22</td><td style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">–</td><td style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1" /><td style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1" /></tr><tr><td style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1" /><td style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">2017–2018</td><td style="border-bottom: solid thin black" colspan="5" valign="bottom" rowspan="1">No data collection</td></tr><tr><th rowspan="3" valign="bottom" scope="rowgroup" colspan="1">Wave 3</th><td rowspan="3" valign="bottom" colspan="1">2018–2019</td><td valign="bottom" rowspan="1" colspan="1">Math lesson</td><td valign="bottom" rowspan="1" colspan="1">14</td><td valign="bottom" rowspan="1" colspan="1">16</td><td rowspan="3" valign="bottom" colspan="1">67</td><td rowspan="3" valign="bottom" colspan="1">36</td></tr><tr><td style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">Full-day</td><td style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">20</td><td style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">17</td></tr><tr><td valign="bottom" rowspan="1" colspan="1">Fall</td><td valign="bottom" rowspan="1" colspan="1">17</td><td valign="bottom" rowspan="1" colspan="1">19</td></tr><tr><td style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1" /><td style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1" /><td style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">Spring</td><td style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">17</td><td style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">14</td><td style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1" /><td style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1" /></tr><tr><th align="left" colspan="2" valign="bottom" scope="row" rowspan="1">Total math lesson observations and classes</th><td valign="bottom" rowspan="1" colspan="1" /><td valign="bottom" rowspan="1" colspan="1">83</td><td char="." valign="bottom" rowspan="1" colspan="1">16</td><td char="." valign="bottom" rowspan="1" colspan="1">99</td><td char="." valign="bottom" rowspan="1" colspan="1">55</td></tr><tr><th align="left" colspan="2" valign="bottom" scope="row" rowspan="1">Total full-day observations and classes</th><td valign="bottom" rowspan="1" colspan="1" /><td valign="bottom" rowspan="1" colspan="1">66</td><td char="." valign="bottom" rowspan="1" colspan="1">17</td><td char="." valign="bottom" rowspan="1" colspan="1">83</td><td char="." valign="bottom" rowspan="1" colspan="1">47</td></tr><tr><th align="left" colspan="2" valign="bottom" scope="row" rowspan="1">Total observations and classes</th><td valign="bottom" rowspan="1" colspan="1" /><td valign="bottom" rowspan="1" colspan="1">149</td><td char="." valign="bottom" rowspan="1" colspan="1">33</td><td char="." valign="bottom" rowspan="1" colspan="1">182</td><td char="." valign="bottom" rowspan="1" colspan="1">102</td></tr></tbody></table> </ephtml> </p> <p>Graph</p> <p>1 Note. SSLI = school serving students from households with lower income; SSHI = school serving students from households with higher income. There was no data collection during the 2017–2018 school year due to a gap in funding. Fall and spring observation totals are relevant for math content. Ninety teachers were observed. Twenty teachers were observed once, 60 teachers were observed twice, 2 teachers were observed 3 times, 6 teachers were observed 4 times, and 2 teachers were observed 6 times. In Wave 1, 42 new teachers were observed; in Wave 2, 17 new teachers were observed (7 were not new); and in Wave 3, 31 new teachers were observed (5 were not new).</p> <p>In year 3 of the study, we collected data in 8 additional schools in the same district serving a large majority of students from households with higher income. Adding a small higher-income sample allows us to conduct a within-district comparison of math instruction across school contexts. Ten schools where fewer than 33% of students were FRPL eligible were randomly selected. We used this cutoff to ensure that we had a sharp contrast in terms of populations served. We conducted observations in a total of 8 of the 10 schools after 2 principals opted out.</p> <p>We refer to our primary sample as schools serving students from households with lower income (SSLI) and to our smaller comparison sample as schools serving students from households with higher income (SSHI). Although the percentage of students eligible for FRPL was the criterion used to select SSLI and SSHI schools, income and race/ethnicity are highly correlated in this district. Table 2 shows that SSLIs served a much larger proportion of students of color.</p> <p>Table 2. School-, Teacher-, and Classroom-Level Descriptives for Sample Schools</p> <p> <ephtml> <table><thead><tr><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1" /><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1">SSLI Schools</th><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1">SSHI Schools</th></tr></thead><tbody><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">School-level student demographics (%):</th><td valign="bottom" rowspan="1" colspan="1">(<italic>n</italic> = 24)</td><td valign="bottom" rowspan="1" colspan="1">(<italic>n</italic> = 8)</td></tr><tr><th align="left" colspan="3" valign="bottom" scope="row" rowspan="1"> Race/ethnicity:</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Asian</th><td char="." valign="bottom" rowspan="1" colspan="1">2</td><td char="." valign="bottom" rowspan="1" colspan="1">16</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Black</th><td char="." valign="bottom" rowspan="1" colspan="1">41</td><td char="." valign="bottom" rowspan="1" colspan="1">5</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Hispanic<xref ref-type="table-fn" rid="tfn3">a</xref></th><td char="." valign="bottom" rowspan="1" colspan="1">50</td><td char="." valign="bottom" rowspan="1" colspan="1">14</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> White</th><td char="." valign="bottom" rowspan="1" colspan="1">5</td><td char="." valign="bottom" rowspan="1" colspan="1">55</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> More than one</th><td char="." valign="bottom" rowspan="1" colspan="1">1</td><td char="." valign="bottom" rowspan="1" colspan="1">9</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> English-language learners</th><td char="." valign="bottom" rowspan="1" colspan="1">14</td><td char="." valign="bottom" rowspan="1" colspan="1">3</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Special education</th><td char="." valign="bottom" rowspan="1" colspan="1">22</td><td char="." valign="bottom" rowspan="1" colspan="1">17</td></tr><tr><th style="border-bottom: solid thin black" valign="bottom" scope="row" rowspan="1" colspan="1"> FRPL eligible</th><td char="." style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">93</td><td char="." style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">14</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Sample teacher and classroom demographics (%):</th><td valign="bottom" rowspan="1" colspan="1">(<italic>n</italic> = 149)</td><td valign="bottom" rowspan="1" colspan="1">(<italic>n</italic> = 33)</td></tr><tr><th align="left" colspan="3" valign="bottom" scope="row" rowspan="1"> Race/ethnicity:</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Black</th><td char="." valign="bottom" rowspan="1" colspan="1">26</td><td char="." valign="bottom" rowspan="1" colspan="1">3</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Hispanic<xref ref-type="table-fn" rid="tfn3">a</xref><sup>,</sup><xref ref-type="table-fn" rid="tfn4">b</xref></th><td char="." valign="bottom" rowspan="1" colspan="1">21</td><td char="." valign="bottom" rowspan="1" colspan="1">3</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> White</th><td char="." valign="bottom" rowspan="1" colspan="1">42</td><td char="." valign="bottom" rowspan="1" colspan="1">70</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Other<xref ref-type="table-fn" rid="tfn5">c</xref></th><td char="." valign="bottom" rowspan="1" colspan="1">10</td><td char="." valign="bottom" rowspan="1" colspan="1">24</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Female</th><td char="." valign="bottom" rowspan="1" colspan="1">93</td><td char="." valign="bottom" rowspan="1" colspan="1">88</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> 6+ years teaching experience</th><td char="." valign="bottom" rowspan="1" colspan="1">87</td><td char="." valign="bottom" rowspan="1" colspan="1">94</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Average number of students per class</th><td char="." valign="bottom" rowspan="1" colspan="1">19</td><td char="." valign="bottom" rowspan="1" colspan="1">23</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Average number of adults in the classroom</th><td char="." valign="bottom" rowspan="1" colspan="1">1.6</td><td char="." valign="bottom" rowspan="1" colspan="1">1.9</td></tr></tbody></table> </ephtml> </p> <p>Graph</p> <ulist> <item>2 Note. SSLI = school serving students from households with lower income; SSHI = school serving students from households with higher income; FRPL = free or reduced-price lunch. School-level student demographics reported for the 2018–2019 school year. Sample teacher and classroom demographics are calculated at the observation level and are averaged across the 2015–2016 to 2018–2019 school years.</item> <item>3 a We use the term "Hispanic" because it is the term used in our data sources.</item> <item>4 b Teachers who identified as Hispanic were placed into this category. This category is mutually exclusive from White, Black, and Other, although teachers in our data set reported more complex identities (e.g., Black and Hispanic).</item> <item>5 c Teacher race/ethnicity Other = Asian or more than one race/ethnicity.</item> </ulist> <hd id="AN0184105568-12">Timeline and classroom observations</hd> <p>Table 1 provides information on the study timeline, number of schools, observations, and classes by study year. Over 3 years, the study team conducted 182 observations in 102 kindergarten classes. We define a class as a teacher and their students in an academic year. Observers conducted math lesson (identified by the teacher) or full-day observations. We refer to the primary math instructional time (a math block) from observations as the math lesson. Math lesson observations lasted approximately 90 minutes, continuing until observers were certain the lesson had ended. Full-day observations documented mathematics instruction that occurred throughout the school day in addition to the math lesson that was observed.</p> <p>As shown in Table 1, 75 observations were conducted in SSLIs in 2015–2016, 40 in 2016–2017, and 34 in 2018–2019. Thirty-three observations were conducted in SSHIs in 2018–2019. We conducted 83 math lesson and 66 full-day observations totaling 149 SSLI observations, along with 16 math lesson and 17 full-day observations totaling 33 SSHI observations. Due to a gap in funding, we did not conduct observations in 2017–2018. In each year of data collection, about half of the total observations were conducted in the fall and half in the spring, and when possible, the same teachers were observed in both fall and spring. When teachers were unavailable in the spring, we recruited additional teachers.</p> <hd id="AN0184105568-13">Sample school composition</hd> <p>Table 2 provides school-, teacher-, and classroom-level descriptive statistics. In SSLIs, 91% of students identified as Hispanic[<reflink idref="bib3" id="ref101">3</reflink>] or Black. On average, 14% of students were English-language learners, and across the SSLI schools, 93% of students were FRPL eligible. In contrast, in SSHIs 55% of students identified as White, 16% as Asian, and 14% as Hispanic. On average, 3% were English-language learners, and 14% of students were FRPL eligible.</p> <hd id="AN0184105568-14">Classroom selection</hd> <p>Across all schools, all kindergarten classes, except classrooms designated special education and/or where instruction was conducted entirely in a language other than English,[<reflink idref="bib4" id="ref102">4</reflink>] were recruited to participate. Researchers met with teachers to explain the study, obtain consent, and gather classroom schedules. Consent rates were above 70%. Schools in the district could choose from approved math curricula that align with the Common Core and state learning standards. In the classrooms we observed, all SSLIs used Go Math! whereas SSHIs used a range of mathematics curricula.</p> <hd id="AN0184105568-15">Teachers</hd> <p>As shown in Table 2, in SSLIs most teachers were White (42%), Black (26%), or Hispanic[<reflink idref="bib5" id="ref103">5</reflink>] (21%). Sample SSLI classrooms averaged 19 students, 4 fewer than the average of 23 students in SSHI classrooms. In SSHIs, most of the teachers were White (70%). Teachers in SSHIs were more likely than SSLI teachers to have 6 or more years of teaching experience. Sample SSHI classrooms averaged 1.9 adults per classroom, compared with 1.6 in SSLIs. We observed a total of 90 individual teachers. Of those, 20 were observed once, 60 twice, 2 teachers were observed 3 times, 6 were observed 4 times, and 2 teachers were observed 6 times. The study was not designed to do within-teacher comparisons, and although 60 teachers were observed twice, these observations were not necessarily sequential (fall to spring within the same year). Thus, we do not conduct analyses exploring instruction with subsamples of teachers who were observed two times or more; these samples are idiosyncratic, determined only by availability for observations.</p> <hd id="AN0184105568-16">Observer Training</hd> <p>Trained observers, including the study's principal investigators, research associates, postdoctoral researchers, and graduate students, conducted observations. All observers completed a 2-day training that provided extensive guidance and practice using the observation protocol. At the end of the 2-day training, observers were required to pass a certification test that involved using the study protocol to code videos of a class completing math activities. Around 10% of field observations were double coded, with observations conducted by two certified observers to ensure fidelity in implementing the observation protocol.</p> <hd id="AN0184105568-17">Measures</hd> <p>Observers used an adapted version of the <emph>Classroom Observation of Early Mathematics—Environment and Teaching Protocol</emph> (COEMET; Sarama & Clements, [<reflink idref="bib60" id="ref104">60</reflink>]). The COEMET is designed to measure the quantity and quality of mathematics instruction. Its primary purpose is to capture detailed information about specific math activities (SMAs). Unless referring to SMAs in a technical sense (e.g., counting the number of SMAs), we use the term "math instruction." SMAs are math activities that last for at least 1 minute with a discernible topic, goal, and task. SMAs can be planned or incidental. A new SMA is recorded every time mathematics instruction lasts 1 minute or longer or there is a change in (<emph>a</emph>) student grouping (e.g., moving from whole-group instruction to independent seat work), (<emph>b</emph>) materials (e.g., switching to a new worksheet that involves addition), or (<emph>c</emph>) topic (e.g., shifting from counting to shapes). SMAs record the amount of instructional time spent on math in minutes. When a teacher stopped focusing on math for at least 1 minute, the SMA ended. Thus, all noninstructional time during the math lesson is excluded from this count. Observers completed a COEMET protocol for each SMA. The COEMET items per SMA are detailed in Table 3 and are ordered by research question. For example, to address RQ1 we used start time, end time, and primary math practice. Observers prioritized the lead teacher's activities and instruction, and moved when needed to hear the lead teachers' interactions with students (e.g., when students were working individually and the teacher was moving around the classroom). In rare instances, the lead teacher left the room or engaged in other noninstructional or nonmath activity and another adult in the room provided instruction. In those cases, observers focused on what the assistant teacher, aide, or other adult was doing with the children. If students were in multiple settings, the observer followed the majority of the class.</p> <p>Table 3. Classroom Observation of Early Mathematics—Environment and Teaching Protocol: Items per Specific Math Activity (SMA)</p> <p> <ephtml> <table><thead><tr><th align="left" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1">Item Name</th><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1">Full Item Text</th><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1">Response Options</th></tr></thead><tbody><tr><th valign="top" scope="row" rowspan="1" colspan="1">Start time</th><td valign="top" rowspan="1" colspan="1">Start time</td><td valign="top" rowspan="1" colspan="1">Minutes: Seconds. AM/PM</td></tr><tr><th valign="top" scope="row" rowspan="1" colspan="1">End time</th><td valign="top" rowspan="1" colspan="1">End time</td><td valign="top" rowspan="1" colspan="1">Minutes: Seconds. AM/PM</td></tr><tr><th valign="top" scope="row" rowspan="1" colspan="1">Primary math practice</th><td valign="top" rowspan="1" colspan="1">What is the primary math practice of the SMA?</td><td valign="top" rowspan="1" colspan="1">Observers selected from more than 40 different primary math practices (see Table B1). For SMAs during the math lesson or outside of the math lesson, primary math practices were collapsed into the categories included in Tables B2 and B3, respectively</td></tr><tr><th valign="top" scope="row" rowspan="1" colspan="1">Classroom organization</th><td valign="top" rowspan="1" colspan="1">What classroom organization was used during the SMA?</td><td valign="top" rowspan="1" colspan="1">Whole group, small group, individual with teacher, seat work, small groups with other students</td></tr><tr><th valign="top" scope="row" rowspan="1" colspan="1">Instructional delivery:</th></tr><tr><th valign="top" scope="row" rowspan="1" colspan="1"> Materials</th><td valign="top" rowspan="1" colspan="1">What materials were used by a majority of children during the SMA?</td><td valign="top" rowspan="1" colspan="1">Worksheet/workbook, worksheet/workbook with manipulatives, manipulatives only, whiteboard or a math journal, computer only, other, no materials (select all that were used)</td></tr><tr><th valign="top" scope="row" rowspan="1" colspan="1">Open-ended questions</th><td valign="top" rowspan="1" colspan="1">Throughout the SMA, the teacher asks open-ended questions to get children to share, clarify, or justify their math ideas. The children respond thoughtfully to the open-ended questions.</td><td valign="top" rowspan="1" colspan="1">5: Throughout the SMA, the teacher asks open-ended questions to get children to share, clarify, or justify their math ideas. 3: Teacher sometimes asks open-ended questions to get children to share, clarify, and/or justify their math ideas. 1: Teacher asks no open-ended math questions. N/A: Teacher was not involved in the SMA</td></tr><tr><th valign="top" scope="row" rowspan="1" colspan="1">Encouraged mathematical reflection</th><td valign="top" rowspan="1" colspan="1">The teacher encourages mathematical reflection.</td><td valign="top" rowspan="1" colspan="1">5: Teacher summarizes/reviews key ideas from the SMA often by engaging students in the discussion and highlighting their strategies. 3: Teacher summarizes/reviews key ideas from the SMA but in a brief or cursory way. 1: Teacher does not summarize/review any key ideas from the SMA. N/A: Teacher was not involved in the SMA</td></tr><tr><th valign="top" scope="row" rowspan="1" colspan="1">Scaffolded instruction</th><td valign="top" rowspan="1" colspan="1">The teacher scaffolds children to help them extend their math skills, providing "just enough" support.</td><td valign="top" rowspan="1" colspan="1">5: Teacher is responsive throughout the SMA, often scaffolding most children. 3: Teacher sometimes scaffolds most children, providing a "skeletal" level of support, but involvement may be partial or overly controlling. 1: Teacher never scaffolds children or gives the same kind of help to all children. N/A: Teacher was not involved in the SMA</td></tr><tr><th valign="top" scope="row" rowspan="1" colspan="1">Differentiation</th><td valign="top" rowspan="1" colspan="1">Throughout all SMAs over the entire observation, did the teacher(s) change the math materials, content, or activity for any child based on the child's performance or skill level?</td><td valign="top" rowspan="1" colspan="1">Yes, no</td></tr><tr><th valign="top" scope="row" rowspan="1" colspan="1">Teacher involvement</th><td valign="top" rowspan="1" colspan="1">A teacher is actively involved in the teaching and learning math aspects of the SMA for what percentage of time beyond setup?</td><td valign="top" rowspan="1" colspan="1">0%, 1–25%, 26–50%, 51–76%, 76–100%</td></tr><tr><th valign="top" scope="row" rowspan="1" colspan="1">Student engagement</th><td valign="top" rowspan="1" colspan="1">Students were engaged in mathematics for what percentage of the SMA?</td><td valign="top" rowspan="1" colspan="1">0%, 1–25%, 26–50%, 51–76%, 76–100%</td></tr><tr><th valign="top" scope="row" rowspan="1" colspan="1">Activity delivered clearly</th><td valign="top" rowspan="1" colspan="1">Was the SMA delivered clearly?</td><td valign="top" rowspan="1" colspan="1">Almost all of the time, most of the time, somewhat, not at all</td></tr><tr><th valign="top" scope="row" rowspan="1" colspan="1">Teacher made mathematical errors</th><td valign="top" rowspan="1" colspan="1">Did the teacher make any mathematical errors during the SMA?</td><td valign="top" rowspan="1" colspan="1">Yes, no, N/A: A teacher was not involved in the SMA</td></tr><tr><th valign="top" scope="row" rowspan="1" colspan="1">Classroom management</th><td valign="top" rowspan="1" colspan="1">The classroom-management strategies used hinder the SMA (e.g., the teacher interrupts the flow of the SMA multiple times to address behavior problems).</td><td valign="top" rowspan="1" colspan="1">Yes, no</td></tr></tbody></table> </ephtml> </p> <p>Graph</p> <p>Graph</p> <hd id="AN0184105568-18">Analysis</hd> <p>Data from the 182 kindergarten observations were compiled into a quantitative data set to allow for descriptive analysis. To answer RQ1, we calculated summary statistics separately for time spent on math during and outside the math lesson in SSLIs, and the percentage of math lesson instruction in SSLIs that included each primary math practice. To understand math instruction outside of the math lesson in SSLIs, we qualitatively coded the SMA narrative descriptions and used the classroom organization and start and end times of SMAs.[<reflink idref="bib6" id="ref105">6</reflink>] We calculated the percentage of non-math-lesson math instruction in SSLIs that included each derived code, and we conducted the same analysis for SSHIs. For RQ2, we conducted three different analyses. To explore instructional grouping and materials, we calculated the percentage of math lesson instruction in SSLIs that included each grouping and material type. We also calculated the degree to which teachers in SSLIs asked open-ended questions, encouraged reflection, scaffolded, or differentiated. Finally, we calculated the percentage of math lesson instruction in SSLIs where teachers were actively involved, students were engaged in math, instruction was delivered clearly, and classroom management hindered instruction. We also conducted these RQ2 analyses for SSHIs.</p> <hd id="AN0184105568-19">Results</hd> <p></p> <hd id="AN0184105568-20">Time on Math</hd> <p>Table 4[<reflink idref="bib7" id="ref106">7</reflink>] provides detailed information on the time per day (in minutes) on math instruction. We only find substantive differences, by which we mean differences that are observably large enough that we would expect them to affect children's classroom experiences, between fall and spring for our math content results. Therefore, for the rest of our results, we report averages across the kindergarten year.[<reflink idref="bib8" id="ref107">8</reflink>] We report findings first for SSLIs (our primary sample with more than 80% of our observations), followed by a comparison with SSHIs.</p> <p>Table 4. Time per Day (Minutes) on Math Instruction during the Math Lesson versus outside the Math Lesson by Classroom Type</p> <p> <ephtml> <table><thead><tr><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1" /><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1">Mean</th><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1"><italic>SD</italic></th><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1">25th Percentile</th><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1">50th Percentile</th><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1">75th Percentile</th><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1">Min</th><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1">Max</th><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1"><italic>N</italic></th></tr></thead><tbody><tr><th align="left" colspan="9" valign="bottom" scope="row" rowspan="1">Math lesson:</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> SSLI classrooms</th><td valign="bottom" rowspan="1" colspan="1">49</td><td valign="bottom" rowspan="1" colspan="1">20</td><td valign="bottom" rowspan="1" colspan="1">36</td><td valign="bottom" rowspan="1" colspan="1">48</td><td valign="bottom" rowspan="1" colspan="1">57</td><td valign="bottom" rowspan="1" colspan="1">12</td><td valign="bottom" rowspan="1" colspan="1">164</td><td valign="bottom" rowspan="1" colspan="1">149</td></tr><tr><th style="border-bottom: solid thin black" valign="bottom" scope="row" rowspan="1" colspan="1"> SSHI classrooms</th><td style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">40</td><td style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">20</td><td style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">29</td><td style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">40</td><td style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">47</td><td style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">2</td><td style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">110</td><td style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">32</td></tr><tr><th align="left" colspan="9" valign="bottom" scope="row" rowspan="1">Outside of the math lesson:</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> SSLI classrooms</th><td valign="bottom" rowspan="1" colspan="1">16</td><td valign="bottom" rowspan="1" colspan="1">20</td><td valign="bottom" rowspan="1" colspan="1">5</td><td valign="bottom" rowspan="1" colspan="1">11</td><td valign="bottom" rowspan="1" colspan="1">17</td><td valign="bottom" rowspan="1" colspan="1">1</td><td valign="bottom" rowspan="1" colspan="1">97</td><td valign="bottom" rowspan="1" colspan="1">45</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> SSHI classrooms</th><td valign="bottom" rowspan="1" colspan="1">37</td><td valign="bottom" rowspan="1" colspan="1">20</td><td valign="bottom" rowspan="1" colspan="1">26</td><td valign="bottom" rowspan="1" colspan="1">38</td><td valign="bottom" rowspan="1" colspan="1">51</td><td valign="bottom" rowspan="1" colspan="1">10</td><td valign="bottom" rowspan="1" colspan="1">83</td><td valign="bottom" rowspan="1" colspan="1">17</td></tr></tbody></table> </ephtml> </p> <p>Graph</p> <p>6 Note. Time reported in minutes. SSLI = school serving students from households with lower income; SSHI = school serving students from households with higher income. N = 181. 1/182 classroom observations did not include math instruction.</p> <hd id="AN0184105568-21">SSLI classrooms (primary sample)</hd> <p>In SSLIs, on average per day, teachers spent 49 minutes on math lessons and 16 minutes teaching math outside of the math lesson.</p> <hd id="AN0184105568-22">SSHI classrooms (comparison sample)</hd> <p>In SSHIs, math lessons were 9 minutes shorter (40 vs. 49 minutes in SSLIs) on average. However, teachers in SSHIs spent an average of 37 minutes per day teaching math outside of the math lesson, over double what was observed in SSLIs (37 vs. 16 minutes, respectively).</p> <hd id="AN0184105568-23">Math Outside of the Math Lesson</hd> <p>Due to the substantial observed differences in the average time spent on math outside of the math lesson between SSLI and SSHI classrooms, we conducted additional analyses to better understand the nature of this instruction. Table 5 documents the percentage of math teaching that occurred outside the math lesson and the concurrent activities and content.</p> <p>Table 5. Math Instruction outside of the Math Lesson, Concurrent Activity, or Content by Classroom Type</p> <p> <ephtml> <table><thead><tr><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1" /><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1">SSLI Classrooms (%)</th><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1">SSHI Classrooms (%)</th></tr></thead><tbody><tr><th align="left" colspan="3" valign="bottom" scope="row" rowspan="1">Activity:<sup>a</sup></th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Morning meeting</th><td char="." valign="bottom" rowspan="1" colspan="1">56.5</td><td char="." valign="bottom" rowspan="1" colspan="1">32.8</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Whole group<sup>b</sup></th><td char="." valign="bottom" rowspan="1" colspan="1">23.1</td><td char="." valign="bottom" rowspan="1" colspan="1">31.3</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Centers</th><td char="." valign="bottom" rowspan="1" colspan="1">8.3</td><td char="." valign="bottom" rowspan="1" colspan="1">26.9</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Special</th><td char="." valign="bottom" rowspan="1" colspan="1">6.5</td><td char="." valign="bottom" rowspan="1" colspan="1">3.0</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Seat work<xref ref-type="table-fn" rid="tfn9">b</xref></th><td char="." valign="bottom" rowspan="1" colspan="1">3.7</td><td char="." valign="bottom" rowspan="1" colspan="1">3.0</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Meal time</th><td char="." valign="bottom" rowspan="1" colspan="1">1.9</td><td char="." valign="bottom" rowspan="1" colspan="1">1.5</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Outdoor</th><td char="." valign="bottom" rowspan="1" colspan="1">.0</td><td char="." valign="bottom" rowspan="1" colspan="1">1.5</td></tr><tr><th align="left" colspan="3" valign="bottom" scope="row" rowspan="1">Content:<xref ref-type="table-fn" rid="tfn8">a</xref></th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Math</th><td char="." valign="bottom" rowspan="1" colspan="1">76.9</td><td char="." valign="bottom" rowspan="1" colspan="1">76.1</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Gross motor and math</th><td char="." valign="bottom" rowspan="1" colspan="1">8.3</td><td char="." valign="bottom" rowspan="1" colspan="1">.0</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Art/music and math</th><td char="." valign="bottom" rowspan="1" colspan="1">6.5</td><td char="." valign="bottom" rowspan="1" colspan="1">3.0</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Literacy and math</th><td char="." valign="bottom" rowspan="1" colspan="1">5.6</td><td char="." valign="bottom" rowspan="1" colspan="1">16.4</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Science and math</th><td char="." valign="bottom" rowspan="1" colspan="1">.9</td><td char="." valign="bottom" rowspan="1" colspan="1">3.0</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Social studies and math</th><td char="." valign="bottom" rowspan="1" colspan="1">.9</td><td char="." valign="bottom" rowspan="1" colspan="1">.0</td></tr><tr><th style="border-bottom: solid thin black" valign="bottom" scope="row" rowspan="1" colspan="1"> Social emotional and math</th><td char="." style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">.9</td><td char="." style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">1.5</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Total number of classroom observations</th><td char="." valign="bottom" rowspan="1" colspan="1">45</td><td char="." valign="bottom" rowspan="1" colspan="1">17</td></tr></tbody></table> </ephtml> </p> <p>Graph</p> <ulist> <item>7 Note. SSLI = school serving students from households with lower income; SSHI = school serving students from households with higher income. Columns sum to 100 (taking into account rounding).</item> <item>8 a These analyses are from the qualitative coding described in the analysis section.</item> <item>9 b Whole group and seat work are defined as when other activity types were not occurring and children were in a whole-group or seat-work grouping engaged in instruction that involved math or math and another content area outside of the math lesson.</item> </ulist> <hd id="AN0184105568-24">SSLI classrooms</hd> <p>Students in SSLIs experienced the majority of non-math-lesson mathematics instruction in morning meetings (57%) and during whole-group time (23%). In SSLIs, math instruction outside of the math lesson typically focused solely on math (77%). The most frequently observed concurrent content areas were gross motor (8%), art/music (7%), and literacy (6%).</p> <hd id="AN0184105568-25">SSHI classrooms</hd> <p>Students in SSHI classrooms also engaged in math instruction outside the math lesson, most often during morning meetings (33%) and whole-group time (31%). However, they experienced math instruction frequently during center time (27%, compared with 8% in SSLIs). The percentage of non-math-lesson instruction that focused exclusively on math was similar across SSLIs and SSHIs. However, in SSHIs, literacy was the primary concurrent content area (16%).</p> <hd id="AN0184105568-26">Math Content</hd> <p></p> <hd id="AN0184105568-27">SSLI classrooms</hd> <p>Table 6 summarizes the percentage of math lesson instruction dedicated to each primary math practice by classroom type and semester. In the fall of kindergarten in SSLIs, five primary math practices constituted most of the observed math lesson instruction. The majority of math lesson instruction focused on counting forward by 1s (27%), comparing and ordering (27%), and composing numbers (23%). Less math lesson instruction (8%) was devoted to adding single/double-digit numbers, subtracting single/double-digit numbers, and shapes. In spring, 10 math practices constituted the majority of math lessons. The most frequently observed math practice, as in the fall, was counting forward by ones (27%). Teachers also focused on adding single/double-digit numbers (12%) and subtracting single/double-digit numbers (13%). Primary math practices that were covered in spring but not in fall included missing addend or subtrahend problems (7%) and writing equations (4%). Table B4 provides the average minutes per classroom observation dedicated to each primary math practice in the math lesson.</p> <p>Table 6. Percentage of Math Lesson Instruction Dedicated to Each Primary Math Practice, by Classroom Type and Kindergarten Semester</p> <p> <ephtml> <table><thead><tr><th align="center" style="border-bottom: solid thin black" rowspan="2" valign="bottom" scope="col" colspan="1" /><th align="center" style="border-bottom: solid thin black" colspan="3" valign="bottom" scope="colgroup" rowspan="1">SSLI Classrooms (%)</th><th align="center" style="border-bottom: solid thin black" colspan="3" valign="bottom" scope="colgroup" rowspan="1">SSHI Classrooms (%)</th></tr><tr><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1">Year</th><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1">Fall</th><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1">Spring</th><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1">Year</th><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1">Fall</th><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1">Spring</th></tr></thead><tbody><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Numeral recognition or writing</th><td char="." valign="bottom" rowspan="1" colspan="1">5.5</td><td char="." valign="bottom" rowspan="1" colspan="1">7.0</td><td char="." valign="bottom" rowspan="1" colspan="1">4.1</td><td char="." valign="bottom" rowspan="1" colspan="1">6.1</td><td char="." valign="bottom" rowspan="1" colspan="1">9.4</td><td char="." valign="bottom" rowspan="1" colspan="1">1.6</td></tr><tr><th align="left" colspan="7" valign="bottom" scope="row" rowspan="1">Counting:</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Counting forward by 1s</th><td char="." valign="bottom" rowspan="1" colspan="1">27.1</td><td char="." valign="bottom" rowspan="1" colspan="1">27.4</td><td char="." valign="bottom" rowspan="1" colspan="1">26.9</td><td char="." valign="bottom" rowspan="1" colspan="1">28.6</td><td char="." valign="bottom" rowspan="1" colspan="1">44.7</td><td char="." valign="bottom" rowspan="1" colspan="1">6.5</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Complex counting</th><td char="." valign="bottom" rowspan="1" colspan="1">2.9</td><td char="." valign="bottom" rowspan="1" colspan="1">2.1</td><td char="." valign="bottom" rowspan="1" colspan="1">3.6</td><td char="." valign="bottom" rowspan="1" colspan="1">.7</td><td char="." valign="bottom" rowspan="1" colspan="1">1.2</td><td char="." valign="bottom" rowspan="1" colspan="1">.0</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Comparing and ordering</th><td char="." valign="bottom" rowspan="1" colspan="1">16.5</td><td char="." valign="bottom" rowspan="1" colspan="1">27.4</td><td char="." valign="bottom" rowspan="1" colspan="1">6.6</td><td char="." valign="bottom" rowspan="1" colspan="1">7.5</td><td char="." valign="bottom" rowspan="1" colspan="1">8.2</td><td char="." valign="bottom" rowspan="1" colspan="1">6.5</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Composing numbers</th><td char="." valign="bottom" rowspan="1" colspan="1">16.5</td><td char="." valign="bottom" rowspan="1" colspan="1">22.8</td><td char="." valign="bottom" rowspan="1" colspan="1">10.7</td><td char="." valign="bottom" rowspan="1" colspan="1">23.8</td><td char="." valign="bottom" rowspan="1" colspan="1">11.8</td><td char="." valign="bottom" rowspan="1" colspan="1">40.3</td></tr><tr><th align="left" colspan="7" valign="bottom" scope="row" rowspan="1">Adding and subtracting:</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Add single/double-digit numbers</th><td char="." valign="bottom" rowspan="1" colspan="1">8.8</td><td char="." valign="bottom" rowspan="1" colspan="1">5.8</td><td char="." valign="bottom" rowspan="1" colspan="1">11.5</td><td char="." valign="bottom" rowspan="1" colspan="1">4.8</td><td char="." valign="bottom" rowspan="1" colspan="1">3.5</td><td char="." valign="bottom" rowspan="1" colspan="1">6.5</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Subtract single/double-digit numbers</th><td char="." valign="bottom" rowspan="1" colspan="1">7.2</td><td char="." valign="bottom" rowspan="1" colspan="1">.9</td><td char="." valign="bottom" rowspan="1" colspan="1">12.9</td><td char="." valign="bottom" rowspan="1" colspan="1">4.1</td><td char="." valign="bottom" rowspan="1" colspan="1">4.7</td><td char="." valign="bottom" rowspan="1" colspan="1">3.2</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Missing addend or missing subtrahend problems</th><td char="." valign="bottom" rowspan="1" colspan="1">4.0</td><td char="." valign="bottom" rowspan="1" colspan="1">.3</td><td char="." valign="bottom" rowspan="1" colspan="1">7.4</td><td char="." valign="bottom" rowspan="1" colspan="1">.0</td><td char="." valign="bottom" rowspan="1" colspan="1">.0</td><td char="." valign="bottom" rowspan="1" colspan="1">.0</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Writing and interpreting equations</th><td char="." valign="bottom" rowspan="1" colspan="1">2.0</td><td char="." valign="bottom" rowspan="1" colspan="1">.3</td><td char="." valign="bottom" rowspan="1" colspan="1">3.6</td><td char="." valign="bottom" rowspan="1" colspan="1">2.7</td><td char="." valign="bottom" rowspan="1" colspan="1">.0</td><td char="." valign="bottom" rowspan="1" colspan="1">6.5</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Multiplying or dividing</th><td char="." valign="bottom" rowspan="1" colspan="1">1.6</td><td char="." valign="bottom" rowspan="1" colspan="1">1.2</td><td char="." valign="bottom" rowspan="1" colspan="1">1.9</td><td char="." valign="bottom" rowspan="1" colspan="1">.0</td><td char="." valign="bottom" rowspan="1" colspan="1">.0</td><td char="." valign="bottom" rowspan="1" colspan="1">.0</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Shapes</th><td char="." valign="bottom" rowspan="1" colspan="1">4.6</td><td char="." valign="bottom" rowspan="1" colspan="1">1.2</td><td char="." valign="bottom" rowspan="1" colspan="1">7.7</td><td char="." valign="bottom" rowspan="1" colspan="1">15.6</td><td char="." valign="bottom" rowspan="1" colspan="1">10.6</td><td char="." valign="bottom" rowspan="1" colspan="1">22.6</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Measuring</th><td char="." valign="bottom" rowspan="1" colspan="1">.0</td><td char="." valign="bottom" rowspan="1" colspan="1">.0</td><td char="." valign="bottom" rowspan="1" colspan="1">.0</td><td char="." valign="bottom" rowspan="1" colspan="1">2.7</td><td char="." valign="bottom" rowspan="1" colspan="1">3.5</td><td char="." valign="bottom" rowspan="1" colspan="1">1.6</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Patterning</th><td char="." valign="bottom" rowspan="1" colspan="1">1.0</td><td char="." valign="bottom" rowspan="1" colspan="1">1.5</td><td char="." valign="bottom" rowspan="1" colspan="1">.5</td><td char="." valign="bottom" rowspan="1" colspan="1">1.4</td><td char="." valign="bottom" rowspan="1" colspan="1">1.2</td><td char="." valign="bottom" rowspan="1" colspan="1">1.6</td></tr><tr><th style="border-bottom: solid thin black" valign="bottom" scope="row" rowspan="1" colspan="1">Other<xref ref-type="table-fn" rid="tfn11">a</xref></th><td char="." style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">2.3</td><td char="." style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">2.1</td><td char="." style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">2.5</td><td char="." style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">2.0</td><td char="." style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">1.2</td><td char="." style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">3.2</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Total number of classroom observations</th><td char="." valign="bottom" rowspan="1" colspan="1">149</td><td char="." valign="bottom" rowspan="1" colspan="1">71</td><td char="." valign="bottom" rowspan="1" colspan="1">78</td><td char="." valign="bottom" rowspan="1" colspan="1">32</td><td char="." valign="bottom" rowspan="1" colspan="1">19</td><td char="." valign="bottom" rowspan="1" colspan="1">13</td></tr></tbody></table> </ephtml> </p> <p>Graph</p> <ulist> <item>10 Note. SSLI = school serving students from households with lower income; SSHI = school serving students from households with higher income. Columns sum to 100 (taking into account rounding). o.3% of the math lesson SSLI fall math instruction is missing a primary math practice. 3.1% of the math lesson SSHI spring math instruction is missing a primary math practice.</item> <item>11 a "Other" includes recognizing quantity without counting (subitizing), money, place value, computer, and classifying.</item> </ulist> <hd id="AN0184105568-28">SSHI classrooms</hd> <p>In the fall, kindergarten teachers in SSHIs placed greater emphasis on counting forward by ones than those teaching in SSLIs (45% vs. 27%, respectively). A larger percentage of SSHI fall math lessons focused on subtracting single/double-digit numbers (5% vs. 1%), shapes (11% vs. 1%), and measuring (4% vs. 0%). In spring, the most frequently observed math practices in SSHIs were composing numbers and shapes (40% and 23%, respectively). This contrasts with SSLIs in spring, which most frequently focused on counting forward by ones (27%), adding single/double-digit numbers (12%), and subtracting single/double-digit numbers (13%). Otherwise, teachers in SSHIs, as compared with SSLIs, in spring focused on shapes (23% vs. 8%), adding single/double-digit numbers (7% vs. 12%), writing equations (7% vs. 4%), and subtracting single/double-digit numbers (3% vs. 13%). We share results and discussion on outside the math lesson math content coverage in Appendix A.</p> <hd id="AN0184105568-29">Math Pedagogy</hd> <p></p> <hd id="AN0184105568-30">Instructional grouping</hd> <p></p> <hd id="AN0184105568-31">SSLI classrooms</hd> <p>In SSLIs, students spent more than half of math lessons with the whole group (58%) and an additional 27% of math time doing individual seat work. As shown in Table 7, small-group instruction and one-on-one work with the teacher were observed infrequently, accounting for 15% and 1% of math instruction in SSLIs, respectively.</p> <p>Table 7. Instructional Grouping during Math Lessons by Classroom Type</p> <p> <ephtml> <table><thead><tr><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1" /><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1">SSLI Classrooms (%)</th><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1">SSHI Classrooms (%)</th></tr></thead><tbody><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Whole group</th><td char="." valign="bottom" rowspan="1" colspan="1">57.5</td><td char="." valign="bottom" rowspan="1" colspan="1">39.6</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Seat work</th><td char="." valign="bottom" rowspan="1" colspan="1">26.5</td><td char="." valign="bottom" rowspan="1" colspan="1">30.2</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Small groups with other students</th><td char="." valign="bottom" rowspan="1" colspan="1">9.9</td><td char="." valign="bottom" rowspan="1" colspan="1">22.8</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Small group with teacher</th><td char="." valign="bottom" rowspan="1" colspan="1">5.2</td><td char="." valign="bottom" rowspan="1" colspan="1">6.7</td></tr><tr><th style="border-bottom: solid thin black" valign="bottom" scope="row" rowspan="1" colspan="1">Individual with teacher</th><td char="." style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">.9</td><td char="." style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">.7</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Total number of classroom observations</th><td char="." valign="bottom" rowspan="1" colspan="1">149</td><td char="." valign="bottom" rowspan="1" colspan="1">32</td></tr></tbody></table> </ephtml> </p> <p>Graph</p> <p>12 Note. SSLI = school serving students from households with lower income; SSHI = school serving students from households with higher income.</p> <hd id="AN0184105568-32">SSHI classrooms</hd> <p>We observed notable differences across SSLIs and SSHIs in terms of the percentage of math lessons that occurred in whole- versus small-group settings. Students in SSHIs spent only 40%, compared with 58% in SSLIs, in whole-group instruction. Further, students in SSHIs spent double the amount of math instruction in small groups (30%) compared with SSLIs (15%).</p> <hd id="AN0184105568-33">Materials</hd> <p></p> <hd id="AN0184105568-34">SSLI classrooms</hd> <p>Table 8 describes the types of materials and the frequency of their use during math lessons. The modal category for materials, observed in 38% of math lessons in SSLI classrooms, was none, or no materials. When materials were used, a worksheet or a workbook was most common (28%), or a worksheet/workbook was used in tandem with manipulatives (16%). Manipulatives (alone) were used in 10% of lessons. Individual whiteboards or math journals and computers were used infrequently (3% and 1%, respectively). Table B5 provides more detail on low-incidence materials combinations.</p> <p>Table 8. Materials Used during Math Lessons by Classroom Type</p> <p> <ephtml> <table><thead><tr><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1" /><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1">SSLI Classrooms (%)</th><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1">SSHI Classrooms (%)</th></tr></thead><tbody><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">No materials</th><td char="." valign="bottom" rowspan="1" colspan="1">37.5</td><td char="." valign="bottom" rowspan="1" colspan="1">35.6</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Worksheet/workbook only</th><td char="." valign="bottom" rowspan="1" colspan="1">27.8</td><td char="." valign="bottom" rowspan="1" colspan="1">9.4</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Worksheet/workbook with manipulatives</th><td char="." valign="bottom" rowspan="1" colspan="1">15.6</td><td char="." valign="bottom" rowspan="1" colspan="1">29.5</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Manipulatives only</th><td char="." valign="bottom" rowspan="1" colspan="1">9.7</td><td char="." valign="bottom" rowspan="1" colspan="1">16.1</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Other<xref ref-type="table-fn" rid="tfn14">a</xref></th><td char="." valign="bottom" rowspan="1" colspan="1">5.2</td><td char="." valign="bottom" rowspan="1" colspan="1">8.1</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Whiteboard or math journal</th><td char="." valign="bottom" rowspan="1" colspan="1">3.2</td><td char="." valign="bottom" rowspan="1" colspan="1">1.3</td></tr><tr><th style="border-bottom: solid thin black" valign="bottom" scope="row" rowspan="1" colspan="1">Computer only</th><td char="." style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">1.2</td><td char="." style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">.0</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Total number of classroom observations</th><td char="." valign="bottom" rowspan="1" colspan="1">149</td><td char="." valign="bottom" rowspan="1" colspan="1">32</td></tr></tbody></table> </ephtml> </p> <p>Graph</p> <ulist> <item>13 Note. SSLI = school serving students from households with lower income; SSHI = school serving students from households with higher income.</item> <item>14 a "Other" was most frequently cards with numbers or images, number lines, or 10 frames. "Other" is also low-incidence materials combinations. These combinations were most frequently other items and manipulatives or other items and a worksheet/workbook.</item> </ulist> <hd id="AN0184105568-35">SSHI classrooms</hd> <p>Although the percentage of math lessons where no materials were used was similar across SSLIs and SSHIs (38% vs. 36%, respectively), we observed differences across these school contexts in terms of the frequency with which materials were used. Although math lessons in SSLI classes most often incorporated a worksheet/workbook (28%), math lessons in SSHI classrooms most frequently used a worksheet/workbook in tandem with manipulatives (30%). The second most frequently used materials in SSHI math lessons were manipulatives alone (16%), compared with 10% in SSLIs. We observed less math instruction in SSHIs where the only material was a worksheet/workbook (9% compared with 28% in SSLIs).</p> <hd id="AN0184105568-36">Open-ended questions, reflection, scaffolding, and differentiation</hd> <p>As Table 9 shows, teachers in both SSLIs and SSHIs typically summarized or reviewed key ideas from math lessons in a brief or cursory way, rarely scaffolded, and did not differentiate instruction based on student knowledge or skill levels. However, while teachers in SSLIs rarely asked open-ended questions during the math lesson, teachers in SSHIs asked open-ended questions somewhat more often, though still not frequently.</p> <p>Table 9. Open-Ended Questions, Reflection, Scaffolding, and Differentiation during Math Lessons by Classroom Type</p> <p> <ephtml> <table><thead><tr><th align="center" style="border-bottom: solid thin black" rowspan="2" valign="bottom" scope="col" colspan="1" /><th align="center" style="border-bottom: solid thin black" colspan="2" valign="bottom" scope="colgroup" rowspan="1">SSLI Classrooms</th><th align="center" style="border-bottom: solid thin black" colspan="2" valign="bottom" scope="colgroup" rowspan="1">SSHI Classrooms</th></tr><tr><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1">Mean</th><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1"><italic>SD</italic></th><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1">Mean</th><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1"><italic>SD</italic></th></tr></thead><tbody><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Degree to which teacher asked open-ended questions</th><td char="." valign="bottom" rowspan="1" colspan="1">2.1</td><td char="." valign="bottom" rowspan="1" colspan="1">1.1</td><td char="." valign="bottom" rowspan="1" colspan="1">2.6</td><td char="." valign="bottom" rowspan="1" colspan="1">1.0</td></tr><tr><th style="border-bottom: solid thin black" valign="bottom" scope="row" rowspan="1" colspan="1">Degree to which teacher encouraged mathematical reflection</th><td char="." style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">2.6</td><td char="." style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">1.2</td><td char="." style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">2.8</td><td char="." style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">.9</td></tr><tr><th style="border-bottom: solid thin black" valign="bottom" scope="row" rowspan="1" colspan="1">Total number of classroom observations</th><td char="." style="border-bottom: solid thin black" colspan="2" valign="bottom" rowspan="1">149</td><td char="." style="border-bottom: solid thin black" colspan="2" valign="bottom" rowspan="1">32</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Degree to which teacher scaffolds instruction</th><td char="." valign="bottom" rowspan="1" colspan="1">1.9</td><td char="." valign="bottom" rowspan="1" colspan="1">1.1</td><td char="." valign="bottom" rowspan="1" colspan="1">1.5</td><td char="." valign="bottom" rowspan="1" colspan="1">.9</td></tr><tr><th style="border-bottom: solid thin black" valign="bottom" scope="row" rowspan="1" colspan="1">Degree to which teacher differentiated</th><td char="." style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">.4</td><td char="." style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">.5</td><td char="." style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">.3</td><td char="." style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">.5</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Total number of classroom observations</th><td char="." colspan="2" valign="bottom" rowspan="1">113</td><td char="." colspan="2" valign="bottom" rowspan="1">32</td></tr></tbody></table> </ephtml> </p> <p>Graph</p> <p>15 Note. SSLI = school serving students from households with lower income; SSHI = school serving students from households with higher income. The teacher asked open-ended questions, encouraged mathematical reflection, and scaffolds were coded on a 1–5 Likert scale with higher values indicating more of that activity. "Teacher differentiated" was coded as yes (<reflink idref="bib1" id="ref108">1</reflink>) or no (0). The study team did not ask observers to rate the degree of scaffolding or differentiation during fall of kindergarten observations. Range of missingness (% of specific math activities) for each nature of math instruction: (<reflink idref="bib1" id="ref109">1</reflink>) Teacher asked open-ended math questions (missing, 0.0–2.9%; not applicable, 8.5–10.1%); (<reflink idref="bib2" id="ref110">2</reflink>) Teacher encouraged mathematical reflection (missing, 0.0–2.5%; not applicable, 8.2–10.8%); (<reflink idref="bib3" id="ref111">3</reflink>) Teacher scaffolds instruction (missing, 0.0–3.4%; not applicable, 6.5–8.1%); (<reflink idref="bib4" id="ref112">4</reflink>) Teacher differentiated (none missing or not applicable).</p> <hd id="AN0184105568-37">Engagement, accuracy, and classroom management</hd> <p></p> <hd id="AN0184105568-38">SSLI classrooms</hd> <p>During 89% of the math lessons observed in SSLI classrooms, students were highly engaged, and math lesson instruction was delivered clearly in 85% of the math lessons, as shown in Table 10. Classroom-management issues hindered instruction in 17% of math lessons in SSLI classrooms.</p> <p>Table 10. Engagement, Accuracy, and Classroom Management during Math Lessons by Classroom Type</p> <p> <ephtml> <table><thead><tr><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1" /><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1">SSLI Classrooms (%)</th><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1">SSHI Classrooms (%)</th></tr></thead><tbody><tr><th align="left" colspan="3" valign="bottom" scope="row" rowspan="1">Engagement during math instruction:</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Teacher was actively involved in math instruction 76%–100% of the time</th><td char="." valign="bottom" rowspan="1" colspan="1">82.9</td><td char="." valign="bottom" rowspan="1" colspan="1">85.8</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Students were engaged in math for 76%–100% of the math instruction</th><td char="." valign="bottom" rowspan="1" colspan="1">89.1</td><td char="." valign="bottom" rowspan="1" colspan="1">100.0</td></tr><tr><th align="left" colspan="3" valign="bottom" scope="row" rowspan="1">Accuracy during math instruction:</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Math instruction was delivered clearly almost all of the time</th><td char="." valign="bottom" rowspan="1" colspan="1">85.4</td><td char="." valign="bottom" rowspan="1" colspan="1">91.9</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Teacher did not make math errors</th><td char="." valign="bottom" rowspan="1" colspan="1">96.5</td><td char="." valign="bottom" rowspan="1" colspan="1">98.5</td></tr><tr><th align="left" colspan="3" valign="bottom" scope="row" rowspan="1">Classroom management during math instruction:</th></tr><tr><th style="border-bottom: solid thin black" valign="bottom" scope="row" rowspan="1" colspan="1"> Classroom-management strategies hindered math instruction</th><td char="." style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">17.3</td><td char="." style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">1.4</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Total number of classroom observations</th><td char="." valign="bottom" rowspan="1" colspan="1">149</td><td char="." valign="bottom" rowspan="1" colspan="1">32</td></tr></tbody></table> </ephtml> </p> <p>Graph</p> <p>16 Note. SSLI = school serving students from households with lower income; SSHI = school serving students from households with higher income. Range of missingness for each nature of math instruction: (<reflink idref="bib1" id="ref113">1</reflink>) Active involvement of the teacher (missing, 0.7–2.3%); (<reflink idref="bib2" id="ref114">2</reflink>) Engagement of the students (missing, 2.0–3.2%); (<reflink idref="bib3" id="ref115">3</reflink>) Math instruction delivered clearly (missing, 0.7–2.2%; not applicable, 0.0–0.1%); (<reflink idref="bib4" id="ref116">4</reflink>) Teacher math errors during math lesson (missing, 0.0–2.6%; not applicable, 6.9–9.5%); (<reflink idref="bib5" id="ref117">5</reflink>) Classroom management (missing, 0.7–2.5%).</p> <hd id="AN0184105568-39">SSHI classrooms</hd> <p>In SSHIs, students were highly engaged during all math lessons we observed, compared with 89% in SSLIs, and math lesson instruction was delivered clearly somewhat more often (92% compared with 85% in SSLIs). Classroom-management issues hindered instruction for only 1% of math lessons in SSHIs, compared with 17% in SSLIs.</p> <hd id="AN0184105568-40">Discussion</hd> <p>The current study provides one of the first detailed, large-scale observational studies of kindergarten math instruction. Over 3 years, we conducted 182 classroom observations in a large urban district, including 83 full-day observations. Moreover, we conducted observations within the district across school contexts, allowing us to compare variations in kindergarten math instruction. Although the primary contextual comparison was the level of FRPL eligibility, the student populations at SSLIs and SSHIs also differed by race/ethnicity. SSLIs served a much larger proportion of students of color.</p> <p>Our results highlight several important aspects of kindergarten math instruction. First, we find that a notable amount of math instruction occurs outside the math lesson, particularly in SSHIs. Students in SSHIs spent more than double the amount of time on average per day (37 minutes vs. 16 minutes in SSLIs) on non-math-lesson math instruction. Second, we find that kindergartners in our sample are exposed to a large amount of what is considered to be basic content in prior research. Those studies find that students had already mastered much of the content that teachers reported emphasizing in kindergarten, such as basic counting (e.g., Engel et al., [<reflink idref="bib27" id="ref118">27</reflink>], [<reflink idref="bib28" id="ref119">28</reflink>]). These results were true for students of color and from households with lower incomes (Engel et al., [<reflink idref="bib27" id="ref120">27</reflink>]). However, we also find that the content kindergartners are exposed to is substantially more complex in spring than in fall, indicating that kindergarten teachers cover a range of math topics, including content that is likely new for many kindergartners (e.g., addition and subtraction). Third, across contexts, more than 70% of kindergarten math lessons involved whole-group time or seat work, and more than 35% of math lessons did not include any materials. Finally, we document that kindergartners in both SSLIs and SSHIs experienced math instruction that included little review of key ideas, lacked scaffolding or differentiation, and provided little opportunity to respond to open-ended questions. We discuss these results, connecting them to prior research and theory, below.</p> <hd id="AN0184105568-41">Math Outside of the Math Lesson</hd> <p>A strength of the current study is its large number of full-day classroom observations. This is unusual in observational studies, which often provide a "snapshot" of instruction (e.g., La Paro et al., [<reflink idref="bib44" id="ref121">44</reflink>]; Stipek, [<reflink idref="bib65" id="ref122">65</reflink>]). Full-day observations allowed us to quantify math instruction outside the math lesson, something not documented before, to our knowledge. We find that teachers in SSLIs and SSHIs engaged in math instruction outside the math lesson. This finding is encouraging because quality math instruction provides opportunities throughout the school day (Frye et al., [<reflink idref="bib32" id="ref123">32</reflink>]) for children to build upon and expand their math skills through play and exploration (NCTM & NAEYC, [<reflink idref="bib51" id="ref124">51</reflink>]; Sarama & Clements, [<reflink idref="bib61" id="ref125">61</reflink>]; Skinner, [<reflink idref="bib63" id="ref126">63</reflink>]). In prior studies, children who engaged in playful, physically active learning experiences designed to teach math content had greater improvements in math learning than the control group (Bustamante et al., [<reflink idref="bib12" id="ref127">12</reflink>]; Vetter et al., [<reflink idref="bib72" id="ref128">72</reflink>]).</p> <p>Although this finding is promising, we find a substantial difference between SSLIs and SSHIs in terms of time on math outside the math lesson. Students in SSHIs spent an average of 37 minutes per day engaged in math outside the math lesson, whereas students in SSLIs spent only 16 minutes per day. This suggests that children from households with low income (who are also more likely, in the current study, to be Black or Hispanic) have notably less exposure to math throughout the day and are less likely to experience math integrated with other activities or subjects. Kindergartners we observed in SSHIs had more opportunities to engage with math in an interdisciplinary context. They did math in morning meetings, whole-group settings, and centers. Further, they often experienced math and literacy instruction concurrently, which has been found to build math vocabulary and improve targeted math concepts (Casey et al., [<reflink idref="bib15" id="ref129">15</reflink>]; Hassinger-Das et al., [<reflink idref="bib35" id="ref130">35</reflink>]). To increase opportunities for children in SSLIs to engage with math concepts outside the math lesson, teachers could aim to engage in shared book reading that includes mathematical concepts during whole-group instruction or to play games that involve math during small-group time where children have the agency to select from a range of activities.</p> <hd id="AN0184105568-42">Math Content</hd> <p>Counting forward by ones was one of the most common primary math practices observed during math lessons in SSLIs and SSHIs. About a quarter of the math lessons we observed in SSLIs in the fall and spring were devoted to counting forward by ones, and almost half of SSHI math lessons in the fall focused on counting forward by ones. This finding is similar to prior research that finds that kindergarten teachers place major emphasis on basic counting and shapes (Engel et al., [<reflink idref="bib27" id="ref131">27</reflink>], [<reflink idref="bib28" id="ref132">28</reflink>]). Prior empirical evidence finds that devoting additional days per month to basic counting and shapes is negatively associated with end-of-kindergarten mathematics gains (Bodovski & Farkas, [<reflink idref="bib7" id="ref133">7</reflink>]; Engel et al., [<reflink idref="bib27" id="ref134">27</reflink>], [<reflink idref="bib28" id="ref135">28</reflink>]; Ribner, [<reflink idref="bib55" id="ref136">55</reflink>]), and math instruction that focuses on basic counting and shapes is misaligned to students' math skills measured at kindergarten entry (Engel et al., [<reflink idref="bib27" id="ref137">27</reflink>]). Therefore, our finding suggests that the math lessons kindergartners across both contexts are exposed to primarily focus on content that is misaligned with students' skills and may widen the gaps between what children have been taught and what they should know. However, it can also be argued that a substantial focus on basic counting might benefit children. If the purpose of kindergarten is socialization and reinforcing what children know, bolstering children's knowledge of "basic math" (as defined by Engel et al., [<reflink idref="bib27" id="ref138">27</reflink>]) could help build their confidence and set them up for success in later grades. Given how critical the kindergarten year is, we argue that although reinforcing key concepts is important and should occur in kindergarten, evidence indicates that kindergartners should also be exposed to mathematics content that is new and challenging.</p> <p>We also find that in both SSLI and SSHI classrooms, substantially more math lesson instruction in spring was devoted to "advanced math" (as defined by Engel et al., [<reflink idref="bib27" id="ref139">27</reflink>]) as compared with fall. This was most notable in SSLIs, where we saw an increase from fall to spring in math instruction dedicated to adding single/double-digit numbers (6% vs. 12%), subtracting single/double-digit numbers (1% vs. 13%), and missing addend or missing subtrahend problems (0% vs. 7%). This is a promising finding because prior research shows that additional focus on content that is more advanced, including place value, currency, and addition and subtraction, is positively associated with end-of-kindergarten mathematics gains (Bodovski and Farkas, [<reflink idref="bib7" id="ref140">7</reflink>]; Engel et al., [<reflink idref="bib27" id="ref141">27</reflink>], [<reflink idref="bib28" id="ref142">28</reflink>]; Guarino et al., [<reflink idref="bib33" id="ref143">33</reflink>]; Ribner, [<reflink idref="bib55" id="ref144">55</reflink>]). The progression toward more advanced math content in the spring of kindergarten has not been documented in prior research, though a recent study finds that widely used kindergarten math textbooks vary notably in terms of content coverage and sequencing (Robinson et al., [<reflink idref="bib57" id="ref145">57</reflink>]). Future studies should explore the extent to which repetition of math content that many students already know in the fall of kindergarten is beneficial or detrimental to student learning. The optimal balance between content redundancy and exposure to new content for young children remains unclear.</p> <hd id="AN0184105568-43">Math Pedagogy</hd> <p>Although prior research has attempted to document kindergarten math pedagogy, studies typically combine pedagogy and content, providing a limited and broad picture of kindergarten math instruction (Bodovski & Farkas, [<reflink idref="bib7" id="ref146">7</reflink>]; Guarino et al., [<reflink idref="bib33" id="ref147">33</reflink>]). The current study builds on that work, providing a detailed exploration of how math is delivered to kindergartners.</p> <hd id="AN0184105568-44">Instructional grouping</hd> <p>Over 70% of kindergarten math lessons across contexts involved whole group or seat work. This finding does not align with best practices recommended by advocacy groups (Copple & Bredekamp, [<reflink idref="bib21" id="ref148">21</reflink>]; NCTM, [<reflink idref="bib50" id="ref149">50</reflink>]). Whole group and seat work limit children's opportunities to engage in learning with their peers, reduce opportunities for hands-on learning, and require long periods of focused listening (whole group) or isolated concentration (seat work) that are likely suboptimal for kindergartners (Bodrova & Leong, [<reflink idref="bib8" id="ref150">8</reflink>]; Herrera et al., [<reflink idref="bib37" id="ref151">37</reflink>]; Stright & Supplee, [<reflink idref="bib67" id="ref152">67</reflink>]). Although small-group instruction was less common than whole group and seat work across contexts, we find that kindergartners in SSHIs had more small-group time during math lessons (30%) than their peers in SSLIs (15%). Our findings suggest that students in schools serving larger proportions of students from households with higher income and who were most often White had more opportunities to engage in collaborative math learning with their peers. This may serve to exacerbate inequities, because prior research finds that small-group instruction positively affects student achievement (Herrera et al., [<reflink idref="bib37" id="ref153">37</reflink>]; Ramani et al., [<reflink idref="bib54" id="ref154">54</reflink>]).</p> <hd id="AN0184105568-45">Materials</hd> <p>We find that during the majority of math lesson instruction, students did not use materials, meaning that students did not use a worksheet, a workbook, manipulatives, a whiteboard, a math journal, a computer, or other materials. This finding does not align with NCTM recommendations that quality math instruction involves opportunities for children to explore multiple representations and hands-on learning opportunities (NCTM, [<reflink idref="bib50" id="ref155">50</reflink>]). Hands-on experiences support children in learning abstract concepts (Ball, [<reflink idref="bib4" id="ref156">4</reflink>]; Baroody, [<reflink idref="bib5" id="ref157">5</reflink>]), and concrete counting experiences are critical for understanding one-to-one correspondence and cardinality (Carpenter et al., [<reflink idref="bib14" id="ref158">14</reflink>]). When materials were used in math lesson instruction, we observed differences between SSLIs and SSHIs. In SSLIs, 25% of math lessons incorporated manipulatives, compared with 46% in SSHIs. Early childhood contexts that provide children with hands-on experiences allow children to learn through playful experiences (Carbonneau et al., [<reflink idref="bib13" id="ref159">13</reflink>]; Skinner, [<reflink idref="bib63" id="ref160">63</reflink>]). Thus, the differences we observe across schools serving students from different backgrounds may serve to exacerbate inequities in opportunities in math learning as early as kindergarten.</p> <hd id="AN0184105568-46">Instructional quality</hd> <p>Across contexts, we observed math pedagogy that is not generally considered best practice. We observed minimal differentiation in math instruction for children with varied needs, knowledge, or skills. Teachers summarized key ideas for students in a brief or cursory way, and they rarely scaffolded. Prior research suggests that the lack of differentiation we observed did not provide opportunities for all children to access the curriculum, reducing the likelihood that all students learned the mathematics they were taught (Deunk et al., [<reflink idref="bib22" id="ref161">22</reflink>]; Smale-Jacobse et al., [<reflink idref="bib64" id="ref162">64</reflink>]). The current study should be replicated in other contexts, and associations between math pedagogy and student outcomes should be carefully explored. To increase the amount of reflection and differentiation during math lessons, teacher education programs could provide more support in terms of math pedagogy to future teachers of mathematics in the earliest grades of formal schooling, including kindergarten.</p> <p>We find differences in classroom management during the math lesson across SSLIs and SSHIs. In SSLIs, 17% of math lessons were disrupted by classroom-management strategies, compared with only 1% in SSHIs. Classroom-management strategies that engage children and mitigate behavioral issues are positively associated with children's mathematics achievement (Stronge et al., [<reflink idref="bib68" id="ref163">68</reflink>]; van Dijk et al., [<reflink idref="bib71" id="ref164">71</reflink>]). In addition, intentional classroom-management techniques, such as building positive relationships with children, reduce children's off-task behavior and reduce negative teacher talk to children (Dicke et al., [<reflink idref="bib23" id="ref165">23</reflink>]; Hutchings et al., [<reflink idref="bib39" id="ref166">39</reflink>]). Although this finding comes from a single COEMET item, the difference between SSLIs and SSHIs in the percentage of math lessons that were disrupted by classroom-management strategies is notable and could suggest that classroom-management strategies in SSLIs constrained opportunities to learn math.</p> <p>In sum, we find that although teachers in SSLIs and SSHIs engaged in math instruction outside the math lesson, students in SSHIs spent an average of 37 minutes per day engaged in math outside the math lesson, whereas students in SSLIs spent 16 minutes per day. To increase opportunities to engage in math outside the math lesson, teachers in SSLIs could engage in shared book reading that includes mathematical concepts. Regarding math content, we find that in both SSLIs and SSHIs, about a quarter of fall math lessons were devoted to counting forward by ones, yet substantially more math lesson instruction in spring was devoted to advanced math. We argue that kindergartners should be exposed to mathematics content in both fall and spring, which is new and challenging, yet the balance between redundancy and exposure to new content for young children remains unclear. Our math pedagogy results highlight that the majority of math lessons across contexts involved whole group or seat work and children did not use materials. We observed minimal differentiation in math instruction across contexts, and teachers summarized key ideas for students in a brief or cursory way. The current study should be replicated in other contexts, and associations between math pedagogy and student outcomes should be explored.</p> <hd id="AN0184105568-47">Limitations</hd> <p>While the current study addresses gaps in knowledge about kindergarten math instruction, we note several limitations. First, this study was conducted in a single large urban district. Although this allowed us to compare how aspects of kindergarten math instruction vary across school contexts, holding the district constant, it also limits the generalizability of our findings. Although instructional experiences might be similar in large urban districts, studies should be conducted to explore variation across a range of contexts, including suburban and rural districts. In addition, we completed 149 classroom observations in SSLIs and 33 in SSHIs. The suggestive evidence from our study, that children in SSHIs experience more mathematics throughout the day, have more opportunities to work in small groups, and experience less disruption due to classroom-management techniques, is compelling. However, studies that include more observations of SSHI classes are needed. If a potential path to reducing inequalities in math outcomes is through providing better support and training for kindergarten teachers in SSLIs, more evidence on how instruction varies across contexts is needed.</p> <p>Although the current study provides a detailed description of kindergarten mathematics instruction, an additional limitation is our inability to link our classroom observational data to students or student outcomes. Therefore, we cannot test whether time on math during or outside the math lesson, content, or the pedagogical approaches that teachers used predict children's mathematics learning. Future work should explore the relationship between student outcomes and these aspects of kindergarten math instruction. Finally, most teachers were observed once or twice. Future work should incorporate a teacher survey for triangulation.</p> <hd id="AN0184105568-48">Conclusion</hd> <p>Using detailed classroom observational data from 182 observations in a large urban district, the current study contributes to our understanding of kindergarten mathematics instruction and how instruction can vary across schools serving students from different demographic backgrounds within a single district. Kindergartners in schools serving students from households with lower income and who were more likely to be Black or Hispanic spent less time on math when we consider math taught throughout the school day and integrated with other subjects or activities. They had fewer opportunities to work in small groups during math lessons and engage in hands-on math learning that included materials such as manipulatives, and their math learning was more likely to be hindered by classroom-management techniques.</p> <p>Across school contexts, we observed few math lessons where scaffolding, differentiation, or the use of open-ended questions was a regular part of math instruction. Further, across contexts, kindergartners spent the majority of math lessons engaged in whole-group instruction or seat work. Whether more time on math outside the math lesson is positively associated with math outcomes should be explored in future studies. However, we know that young children benefit from opportunities to learn that are playful and collaborative (NCTM & NAEYC, [<reflink idref="bib51" id="ref167">51</reflink>]; Sarama & Clements, [<reflink idref="bib61" id="ref168">61</reflink>]) and they can learn more math when it is integrated with other subjects or activities (McGuire et al., [<reflink idref="bib47" id="ref169">47</reflink>]; Purpura et al., [<reflink idref="bib52" id="ref170">52</reflink>]). The current study suggests that children from households with low income and children of color may have systematically lower-quality experiences with math. These findings may be of use to policy makers and administrators as they consider means to make experiences for children from minoritized populations more equitable. Although prior studies using large-scale data sets have suggested differential experiences across kindergarten contexts in terms of content exposure (e.g., Bassok et al., [<reflink idref="bib6" id="ref171">6</reflink>]; Engel et al., [<reflink idref="bib27" id="ref172">27</reflink>]), in-depth observations provide a more detailed and nuanced understanding of different means through which inequitable experiences in the classroom occur in kindergarten.</p> <hd id="AN0184105568-49">Appendix A. Kindergarten Mathematics Content Outside of the Math Lesson</hd> <p></p> <hd id="AN0184105568-50">Results</hd> <p>Table A1 captures the percentage of math instruction outside the math lesson dedicated to each primary math practice. We did not find substantive differences, by which we mean differences observably large enough that we would expect them to affect children's classroom experiences, between fall and spring for outside the math lesson content findings. Therefore, we report averages across the kindergarten year.[<reflink idref="bib9" id="ref173">9</reflink>] We observed that the majority of SSLI outside the math lesson math instruction focused on counting forward by ones (23%), comparing and ordering (10%), counting forward by tens and ones (8%), subtracting single/double-digit numbers (8%), and composing numbers (7%). Similarly, students in SSHIs spent the majority of their outside the math lesson math instruction on counting forward by ones. However, students in SSHIs engaged in more instruction that focused on counting forward by ones (36% vs. 23%, respectively). Across all non-math-lesson math instruction, SSLIs covered a larger breadth of primary math practices. In SSHIs, 57% of outside the math lesson math instruction focused on counting forward by 1s (36%) and constructing shapes (21%).</p> <hd id="AN0184105568-51">Discussion</hd> <p>To our knowledge, no prior research has documented the math practices taught during outside the math lesson math instruction. We find that outside the math lesson, similarly to within the math lesson, lessons primarily focused on counting forward by ones. In addition, teachers in SSLIs covered a broader array of math practices during math instruction outside the math lesson as compared with SSHIs. Although it is encouraging to see math instruction occur throughout the day, prior research finds that devoting additional days per month to basic counting and shapes is negatively associated with end-of-kindergarten mathematics gains (Bodovski & Farkas, [<reflink idref="bib7" id="ref174">7</reflink>]; Engel et al., [<reflink idref="bib27" id="ref175">27</reflink>], [<reflink idref="bib28" id="ref176">28</reflink>]; Ribner, [<reflink idref="bib55" id="ref177">55</reflink>]). Yet teaching more advanced math content (as defined by Engel et al., [<reflink idref="bib27" id="ref178">27</reflink>]) concurrently with another content area could be difficult for teachers. To increase more advanced math lessons outside the math lesson, teachers could conduct, for example, shared book readings that incorporate addition, subtraction, or patterning.</p> <p>Table A1. Percentage of Outside the Math Lesson Math Instruction Dedicated to Each Primary Math Practice, by Classroom Type</p> <p> <ephtml> <table><thead><tr><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1" /><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1">SSLI Classrooms (%)</th><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1">SSHI Classrooms (%)</th></tr></thead><tbody><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Numeral recognition or writing</th><td char="." valign="bottom" rowspan="1" colspan="1">6.5</td><td char="." valign="bottom" rowspan="1" colspan="1">10.4</td></tr><tr><th align="left" colspan="3" valign="bottom" scope="row" rowspan="1">Counting:</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Counting forward by 1s</th><td char="." valign="bottom" rowspan="1" colspan="1">23.1</td><td char="." valign="bottom" rowspan="1" colspan="1">35.8</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Counting backward by 1s</th><td char="." valign="bottom" rowspan="1" colspan="1">.0</td><td char="." valign="bottom" rowspan="1" colspan="1">1.5</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Counting forward by 10s</th><td char="." valign="bottom" rowspan="1" colspan="1">3.7</td><td char="." valign="bottom" rowspan="1" colspan="1">3.0</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Skip count forward by a number other than 10</th><td char="." valign="bottom" rowspan="1" colspan="1">5.6</td><td char="." valign="bottom" rowspan="1" colspan="1">1.5</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Counting forward by 10s and 1s</th><td char="." valign="bottom" rowspan="1" colspan="1">8.3</td><td char="." valign="bottom" rowspan="1" colspan="1">7.5</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Comparing and ordering</th><td char="." valign="bottom" rowspan="1" colspan="1">10.2</td><td char="." valign="bottom" rowspan="1" colspan="1">1.5</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Recognizing quantity without counting (subitizing)</th><td char="." valign="bottom" rowspan="1" colspan="1">1.9</td><td char="." valign="bottom" rowspan="1" colspan="1">3.0</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Composing numbers</th><td char="." valign="bottom" rowspan="1" colspan="1">7.4</td><td char="." valign="bottom" rowspan="1" colspan="1">6.0</td></tr><tr><th align="left" colspan="3" valign="bottom" scope="row" rowspan="1">Adding and subtracting:</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Add single/double-digit numbers</th><td char="." valign="bottom" rowspan="1" colspan="1">6.5</td><td char="." valign="bottom" rowspan="1" colspan="1">3.0</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Subtract single/double-digit numbers</th><td char="." valign="bottom" rowspan="1" colspan="1">8.3</td><td char="." valign="bottom" rowspan="1" colspan="1">3.0</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Missing addend or missing subtrahend problems</th><td char="." valign="bottom" rowspan="1" colspan="1">.9</td><td char="." valign="bottom" rowspan="1" colspan="1">.0</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Writing and interpreting equations</th><td char="." valign="bottom" rowspan="1" colspan="1">.9</td><td char="." valign="bottom" rowspan="1" colspan="1">.0</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Multiplying or dividing</th><td char="." valign="bottom" rowspan="1" colspan="1">1.9</td><td char="." valign="bottom" rowspan="1" colspan="1">.0</td></tr><tr><th align="left" colspan="3" valign="bottom" scope="row" rowspan="1">Shapes:</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Identifying familiar shapes</th><td char="." valign="bottom" rowspan="1" colspan="1">3.7</td><td char="." valign="bottom" rowspan="1" colspan="1">1.5</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Describing shapes</th><td char="." valign="bottom" rowspan="1" colspan="1">.9</td><td char="." valign="bottom" rowspan="1" colspan="1">.0</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Constructing shapes</th><td char="." valign="bottom" rowspan="1" colspan="1">.0</td><td char="." valign="bottom" rowspan="1" colspan="1">20.9</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Measuring</th><td char="." valign="bottom" rowspan="1" colspan="1">1.9</td><td char="." valign="bottom" rowspan="1" colspan="1">.0</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Patterning</th><td char="." valign="bottom" rowspan="1" colspan="1">6.5</td><td char="." valign="bottom" rowspan="1" colspan="1">.0</td></tr><tr><th style="border-bottom: solid thin black" valign="bottom" scope="row" rowspan="1" colspan="1">Other<xref ref-type="table-fn" rid="tfn18">a</xref></th><td char="." style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">1.9</td><td char="." style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">1.5</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Total number of classroom observations</th><td char="." valign="bottom" rowspan="1" colspan="1">45</td><td char="." valign="bottom" rowspan="1" colspan="1">17</td></tr></tbody></table> </ephtml> </p> <p>Graph</p> <ulist> <item>17 SSLI = school serving students from households with lower income; SSHI = school serving students from households with higher income. Columns sum to 100 (taking into account rounding).</item> <item>18 "Other" includes performing simple data collection and graphing, position words, and classifying.</item> </ulist> <hd id="AN0184105568-52">Appendix B</hd> <p>Table B1. Kindergarten Primary Math Practices</p> <p> <ephtml> <table><tbody><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Numeral recognition or writing</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Count forward by 1s</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Count backward by 1s</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Count forward by 10s</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Count backward by 10s</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Skip count forward by a number other than 10</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Count forward by 10s and 1s</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">One-to-one comparing or correspondence</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Counting to compare</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Number line and ordering</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Recognizing quantity without counting (subitizing)</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Money</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Composing numbers</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Read numbers using place value</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Add or subtract using place value</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Add single-digit numbers</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Add double-digit numbers</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Subtract single-digit numbers</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Subtract double-digit numbers</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Missing addend or missing subtrahend problems</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Writing and interpreting equations</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Identifying familiar shapes</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Identifying less familiar shapes</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Describing shapes</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Constructing shapes</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Comparing/matching shapes</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Using shapes to compose other designs</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Reading graphs</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Perform simple data collection and graphing</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Position words</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Turning, flipping, sliding shapes to find matching shapes</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Ordering by length, weight, or volume</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Measuring by units</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Measuring with ruler, yardstick, etc.</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Duplicating/copying patterns</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Extending patterns</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Recognizing pattern unit</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Fractions</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Multiplying</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Dividing</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Computer</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Classifying</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Telling time</th></tr></tbody></table> </ephtml> </p> <p>Graph</p> <p>Table B2. Collapsed Kindergarten Primary Math Practices: Math Lesson Instruction</p> <p> <ephtml> <table><tbody><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Numeral recognition or writing</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Count forward by 1s</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Complex counting</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Comparing and ordering</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Composing numbers</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Adding single/double-digit numbers</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Subtracting single/double-digit numbers</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Missing addend or missing subtrahend problems</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Writing and interpreting equations</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Multiplying or dividing</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Shapes</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Measuring</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Patterning</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Other (recognizing quantity with counting [subitizing], money, place value, computer, and classifying)</th></tr></tbody></table> </ephtml> </p> <p>Graph</p> <p>Table B3. Collapsed Kindergarten Primary Math Practices: Math Instruction Outside the Math Lesson</p> <p> <ephtml> <table><tbody><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Numeral recognition or writing</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Count forward by 1s</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Count backward by 1s</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Count forward by 10s</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Skip count forward by a number other than 10</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Count forward by 10s and 1s</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Comparing and ordering</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Recognizing quantity without counting (subitizing)</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Composing numbers</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Adding single/double-digit numbers</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Subtracting single/double-digit numbers</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Missing addend or missing subtrahend problems</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Writing and interpreting equations</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Multiplying or dividing</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Identifying familiar shapes</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Describing shapes</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Constructing shapes</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Measuring</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Patterning</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Other (performing simple data collection and graphing, position words, classifying)</th></tr></tbody></table> </ephtml> </p> <p>Graph</p> <p>Table B4. Average Minutes per Classroom Observation Dedicated to Each Primary Math Practice during Math Lesson Instruction, by Classroom Type and Kindergarten Semester</p> <p> <ephtml> <table><thead><tr><th align="center" style="border-bottom: solid thin black" rowspan="2" valign="bottom" scope="col" colspan="1" /><th align="center" style="border-bottom: solid thin black" colspan="3" valign="bottom" scope="colgroup" rowspan="1">SSLI Classrooms</th><th align="center" style="border-bottom: solid thin black" colspan="3" valign="bottom" scope="colgroup" rowspan="1">SSHI Classrooms</th></tr><tr><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1">Year</th><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1">Fall</th><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1">Spring</th><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1">Year</th><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1">Fall</th><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1">Spring</th></tr></thead><tbody><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Numeral recognition or writing</th><td char="." valign="bottom" rowspan="1" colspan="1">3.2</td><td char="." valign="bottom" rowspan="1" colspan="1">4.0</td><td char="." valign="bottom" rowspan="1" colspan="1">2.5</td><td char="." valign="bottom" rowspan="1" colspan="1">6.8</td><td char="." valign="bottom" rowspan="1" colspan="1">10.5</td><td char="." valign="bottom" rowspan="1" colspan="1">1.5</td></tr><tr><th align="left" colspan="7" valign="bottom" scope="row" rowspan="1">Counting:</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Counting forward by 1s</th><td char="." valign="bottom" rowspan="1" colspan="1">14.0</td><td char="." valign="bottom" rowspan="1" colspan="1">15.2</td><td char="." valign="bottom" rowspan="1" colspan="1">13.0</td><td char="." valign="bottom" rowspan="1" colspan="1">25.1</td><td char="." valign="bottom" rowspan="1" colspan="1">38.2</td><td char="." valign="bottom" rowspan="1" colspan="1">6.0</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Complex counting</th><td char="." valign="bottom" rowspan="1" colspan="1">1.4</td><td char="." valign="bottom" rowspan="1" colspan="1">.5</td><td char="." valign="bottom" rowspan="1" colspan="1">2.2</td><td char="." valign="bottom" rowspan="1" colspan="1">.3</td><td char="." valign="bottom" rowspan="1" colspan="1">.4</td><td char="." valign="bottom" rowspan="1" colspan="1">.0</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Comparing and ordering</th><td char="." valign="bottom" rowspan="1" colspan="1">8.7</td><td char="." valign="bottom" rowspan="1" colspan="1">15.6</td><td char="." valign="bottom" rowspan="1" colspan="1">2.4</td><td char="." valign="bottom" rowspan="1" colspan="1">4.7</td><td char="." valign="bottom" rowspan="1" colspan="1">5.2</td><td char="." valign="bottom" rowspan="1" colspan="1">3.9</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Composing numbers</th><td char="." valign="bottom" rowspan="1" colspan="1">11.2</td><td char="." valign="bottom" rowspan="1" colspan="1">14.2</td><td char="." valign="bottom" rowspan="1" colspan="1">8.4</td><td char="." valign="bottom" rowspan="1" colspan="1">18.6</td><td char="." valign="bottom" rowspan="1" colspan="1">7.5</td><td char="." valign="bottom" rowspan="1" colspan="1">34.8</td></tr><tr><th align="left" colspan="7" valign="bottom" scope="row" rowspan="1">Adding and subtracting:</th></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Add single/double-digit numbers</th><td char="." valign="bottom" rowspan="1" colspan="1">6.9</td><td char="." valign="bottom" rowspan="1" colspan="1">3.3</td><td char="." valign="bottom" rowspan="1" colspan="1">10.2</td><td char="." valign="bottom" rowspan="1" colspan="1">4.0</td><td char="." valign="bottom" rowspan="1" colspan="1">2.5</td><td char="." valign="bottom" rowspan="1" colspan="1">6.2</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Subtract single/double-digit numbers</th><td char="." valign="bottom" rowspan="1" colspan="1">4.2</td><td char="." valign="bottom" rowspan="1" colspan="1">.7</td><td char="." valign="bottom" rowspan="1" colspan="1">7.5</td><td char="." valign="bottom" rowspan="1" colspan="1">1.9</td><td char="." valign="bottom" rowspan="1" colspan="1">1.6</td><td char="." valign="bottom" rowspan="1" colspan="1">2.4</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Missing addend or missing subtrahend problems</th><td char="." valign="bottom" rowspan="1" colspan="1">2.5</td><td char="." valign="bottom" rowspan="1" colspan="1">.2</td><td char="." valign="bottom" rowspan="1" colspan="1">4.6</td><td char="." valign="bottom" rowspan="1" colspan="1">.0</td><td char="." valign="bottom" rowspan="1" colspan="1">.0</td><td char="." valign="bottom" rowspan="1" colspan="1">.0</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1"> Writing and interpreting equations</th><td char="." valign="bottom" rowspan="1" colspan="1">1.2</td><td char="." valign="bottom" rowspan="1" colspan="1">.3</td><td char="." valign="bottom" rowspan="1" colspan="1">2.1</td><td char="." valign="bottom" rowspan="1" colspan="1">2.8</td><td char="." valign="bottom" rowspan="1" colspan="1">.0</td><td char="." valign="bottom" rowspan="1" colspan="1">6.9</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Multiplying or dividing</th><td char="." valign="bottom" rowspan="1" colspan="1">1.5</td><td char="." valign="bottom" rowspan="1" colspan="1">.8</td><td char="." valign="bottom" rowspan="1" colspan="1">2.1</td><td char="." valign="bottom" rowspan="1" colspan="1">.0</td><td char="." valign="bottom" rowspan="1" colspan="1">.0</td><td char="." valign="bottom" rowspan="1" colspan="1">.0</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Shapes</th><td char="." valign="bottom" rowspan="1" colspan="1">2.4</td><td char="." valign="bottom" rowspan="1" colspan="1">.5</td><td char="." valign="bottom" rowspan="1" colspan="1">4.2</td><td char="." valign="bottom" rowspan="1" colspan="1">14.9</td><td char="." valign="bottom" rowspan="1" colspan="1">6.1</td><td char="." valign="bottom" rowspan="1" colspan="1">27.9</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Measuring</th><td char="." valign="bottom" rowspan="1" colspan="1">.0</td><td char="." valign="bottom" rowspan="1" colspan="1">.0</td><td char="." valign="bottom" rowspan="1" colspan="1">.0</td><td char="." valign="bottom" rowspan="1" colspan="1">2.0</td><td char="." valign="bottom" rowspan="1" colspan="1">1.5</td><td char="." valign="bottom" rowspan="1" colspan="1">2.8</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Patterning</th><td char="." valign="bottom" rowspan="1" colspan="1">.6</td><td char="." valign="bottom" rowspan="1" colspan="1">1.0</td><td char="." valign="bottom" rowspan="1" colspan="1">.3</td><td char="." valign="bottom" rowspan="1" colspan="1">2.0</td><td char="." valign="bottom" rowspan="1" colspan="1">2.2</td><td char="." valign="bottom" rowspan="1" colspan="1">1.8</td></tr><tr><th style="border-bottom: solid thin black" valign="bottom" scope="row" rowspan="1" colspan="1">Other<xref ref-type="table-fn" rid="tfn20">a</xref></th><td char="." style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">1.5</td><td char="." style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">1.3</td><td char="." style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">1.6</td><td char="." style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">2.3</td><td char="." style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">2.6</td><td char="." style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">1.8</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Average time (in min.) on math instruction per classroom observation</th><td char="." valign="bottom" rowspan="1" colspan="1">49</td><td char="." valign="bottom" rowspan="1" colspan="1">49</td><td char="." valign="bottom" rowspan="1" colspan="1">49</td><td char="." valign="bottom" rowspan="1" colspan="1">40</td><td char="." valign="bottom" rowspan="1" colspan="1">34</td><td char="." valign="bottom" rowspan="1" colspan="1">48</td></tr></tbody></table> </ephtml> </p> <p>Graph</p> <ulist> <item>19 SSLI = school serving students from households with lower income; SSHI = school serving students from households with higher income; SMA = specific math activity. The columns do not sum to the average time on math instruction per classroom observation in each classroom type and semester because more than one SMA (each with a different primary math practice) can occur at the same time. This results in the sum of the average time per classroom observation dedicated to each primary math practice being higher than the average time spent on math instruction per classroom observation reported in this table because the average time on SMAs per classroom observation accounts for more than one SMA occurring at the same time.</item> <item>20 "Other" includes recognizing quantity without counting (subitizing), money, place value, computer, and classifying.</item> </ulist> <p>Table B5. Materials Used during Math Lesson Instruction: Across the Kindergarten Year and by Classroom Type</p> <p> <ephtml> <table><thead><tr><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1" /><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1">SSLI Classrooms (%)</th><th align="center" style="border-bottom: solid thin black" valign="bottom" scope="col" rowspan="1" colspan="1">SSHI Classrooms (%)</th></tr></thead><tbody><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">No materials</th><td char="." valign="bottom" rowspan="1" colspan="1">37.5</td><td char="." valign="bottom" rowspan="1" colspan="1">35.6</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Worksheet/workbook only</th><td char="." valign="bottom" rowspan="1" colspan="1">27.8</td><td char="." valign="bottom" rowspan="1" colspan="1">9.4</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Worksheet/workbook with manipulatives</th><td char="." valign="bottom" rowspan="1" colspan="1">15.6</td><td char="." valign="bottom" rowspan="1" colspan="1">29.5</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Manipulatives only</th><td char="." valign="bottom" rowspan="1" colspan="1">9.7</td><td char="." valign="bottom" rowspan="1" colspan="1">16.1</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Whiteboard or math journal</th><td char="." valign="bottom" rowspan="1" colspan="1">3.2</td><td char="." valign="bottom" rowspan="1" colspan="1">1.3</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Other<xref ref-type="table-fn" rid="tfn22">a</xref></th><td char="." valign="bottom" rowspan="1" colspan="1">1.7</td><td char="." valign="bottom" rowspan="1" colspan="1">1.3</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Computer only</th><td char="." valign="bottom" rowspan="1" colspan="1">1.2</td><td char="." valign="bottom" rowspan="1" colspan="1">.0</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Manipulatives with other</th><td char="." valign="bottom" rowspan="1" colspan="1">1.0</td><td char="." valign="bottom" rowspan="1" colspan="1">4.7</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Math journal with manipulatives</th><td char="." valign="bottom" rowspan="1" colspan="1">.9</td><td char="." valign="bottom" rowspan="1" colspan="1">.0</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Worksheet/workbook with whiteboard</th><td char="." valign="bottom" rowspan="1" colspan="1">.6</td><td char="." valign="bottom" rowspan="1" colspan="1">.0</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Worksheet/workbook with manipulatives and other</th><td char="." valign="bottom" rowspan="1" colspan="1">.4</td><td char="." valign="bottom" rowspan="1" colspan="1">.0</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Manipulatives with whiteboard</th><td char="." valign="bottom" rowspan="1" colspan="1">.4</td><td char="." valign="bottom" rowspan="1" colspan="1">.0</td></tr><tr><th style="border-bottom: solid thin black" valign="bottom" scope="row" rowspan="1" colspan="1">Worksheet/workbook with other</th><td char="." style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">.1</td><td char="." style="border-bottom: solid thin black" valign="bottom" rowspan="1" colspan="1">2.0</td></tr><tr><th valign="bottom" scope="row" rowspan="1" colspan="1">Total number of classroom observations</th><td char="." valign="bottom" rowspan="1" colspan="1">149</td><td char="." valign="bottom" rowspan="1" colspan="1">32</td></tr></tbody></table> </ephtml> </p> <p>Graph</p> <ulist> <item>21 SSLI = school serving students from households with lower income; SSHI = school serving students from households with higher income.</item> <item>22 "Other" was most frequently cards with numbers or images, number lines, or 10 frames.</item> </ulist> <ref id="AN0184105568-53"> <title> Notes </title> <blist> <bibl id="bib1" idref="ref1" type="bt">1</bibl> <bibtext> This work was funded through generous support from the Heising-Simons Foundation and the Robin Hood Foundation. All errors and opinions are those of the authors. Danielle Shaw Attaway is a researcher at the American Institutes for Research; Mimi Engel is an associate professor at the University of Colorado, Boulder, in the School of Education's program in Research and Evaluation Methodology; Robin Jacob is a research professor at the University of Michigan's Institute for Social Research; Anna Erickson is a senior project manager at the University of Michigan Youth Policy Lab; Amy Claessens is a professor at the University of Wisconsin, Madison, in the Department of Educational Policy Studies, School of Education. Correspondence may be sent to Danielle Shaw Attaway at dshawattaway@air.org.</bibtext> </blist> <blist> <bibl id="bib2" idref="ref2" type="bt">2</bibl> <bibtext> Details of the larger study are withheld to maintain the district's confidentiality.</bibtext> </blist> <blist> <bibl id="bib3" idref="ref32" type="bt">3</bibl> <bibtext> We use the term "Hispanic" because it is the term used in our data sources.</bibtext> </blist> <blist> <bibl id="bib4" idref="ref102" type="bt">4</bibl> <bibtext> All classroom observations were conducted when the language of instruction for the day was English. Nineteen SSLI classroom observations were conducted in classes where the language of instruction was English and Spanish. One SSLI classroom observation was conducted in a class where the language of instruction was English and Creole.</bibtext> </blist> <blist> <bibl id="bib5" idref="ref103" type="bt">5</bibl> <bibtext> Teachers who identified as Hispanic were placed into this category. This category is mutually exclusive from White, Black, and Other, although teachers in our data set reported more complex identities (e.g., Black and Hispanic).</bibtext> </blist> <blist> <bibl id="bib6" idref="ref49" type="bt">6</bibl> <bibtext> To cross-check our qualitative coding, we used the episode descriptions from an adapted version of the <emph>Narrative Record Observation for Classrooms</emph> (Farran & Bilbrey, [31]), a measure that we collected as part of a protocol used for a larger study (Engel et al., [29]). The COEMET SMA narrative descriptions were closely aligned with the Narrative Record episode descriptions.</bibtext> </blist> <blist> <bibl id="bib7" idref="ref43" type="bt">7</bibl> <bibtext> We do not use tests of statistical significance because our samples were not randomly sampled. In turn, the assumptions required for calculating inferential statistics (that data be randomly sampled and that sample sizes be large enough or that population data are normally distributed) are not met.</bibtext> </blist> <blist> <bibl id="bib8" idref="ref107" type="bt">8</bibl> <bibtext> Results separated by fall and spring are available upon request.</bibtext> </blist> <blist> <bibl id="bib9" idref="ref15" type="bt">9</bibl> <bibtext> Results separated by fall and spring are available upon request.</bibtext> </blist> </ref> <ref id="AN0184105568-54"> <title> References </title> <blist> <bibtext> Abry, T., Taylor, M., Jimenez, M., Pratt, M. E., & LoCasale-Crouch, J. (2018). Continuity and change in low-income children's early learning experiences across the school transition: A comparison of Head Start and kindergarten classrooms. In A. J. Mashburn, J. LoCasale-Crouch, & K. C. Pears (Eds.), Kindergarten transition and readiness (pp. 85–109). Springer. https://doi.org/10.1007/978-3-319-90200-5_4</bibtext> </blist> <blist> <bibtext> Bachman, H. J., Degol, J. L., Elliott, L., Scharphorn, L., El Nokali, N. E., & Palmer, K. M. (2018). Preschool math exposure in private center-based care and low-SES children's math development. Early Education and Development, 29(3), 417–434. https://doi.org/10.1080/10409289.2017.1406245</bibtext> </blist> <blist> <bibtext> Bailey, D. H., Siegler, R. S., & Geary, D. C. (2014). Early predictors of middle school fraction knowledge. Developmental Science, 17(5), 775–785. https://doi.org/10.1111/desc.12155</bibtext> </blist> <blist> <bibtext> Ball, D. (1992). Magical hopes: Manipulatives and the reform of math education. American Educator, 16(2), 14–18.</bibtext> </blist> <blist> <bibtext> Baroody, A. J. (1989). One point of view: Manipulatives don't come with guarantees. Arithmetic Teacher, 37(2), 4–5.</bibtext> </blist> <blist> <bibtext> Bassok, D., Latham, S., & Rorem, A. (2016). Is kindergarten the new first grade? AERA Open, 2(1), 1–31. https://doi.org/10.1177/2332858415616358</bibtext> </blist> <blist> <bibtext> Bodovski, K., & Farkas, G. (2007). Do instructional practices contribute to inequality in achievement? The case of mathematics instruction in kindergarten. Journal of Early Childhood Research, 5(3), 301–322. https://doi.org/10.1177/1476718X07080476</bibtext> </blist> <blist> <bibtext> Bodrova, E., & Leong, D. (2006). Self-regulation as a key to school readiness: How early childhood teachers can promote this critical competency. In M. Zaslow & I. Martinez-Beck (Eds.), Critical issues in early childhood professional development (pp. 203–224). Paul H. Brookes.</bibtext> </blist> <blist> <bibtext> Boston, M. (2012). Assessing instructional quality in mathematics. Elementary School Journal, 113(1), 76–104. https://doi.org/10.1086/666387</bibtext> </blist> <blist> <bibtext> Bronfenbrenner, U., & Morris, P. (1998). The ecology of developmental processes. In R. M. Lerner & J. Wiley (Eds.), Handbook of child psychology: Theoretical models of human development (5th ed., Vol. 1, pp. 993–1028). Wiley.</bibtext> </blist> <blist> <bibtext> Brown, M. C., McNeil, N. M., & Glenberg, A. M. (2009). Using concreteness in education: Real problems, potential solutions. Child Development Perspectives, 3(3), 160–164. https://doi.org/10.1111/j.1750-8606.2009.00098.x</bibtext> </blist> <blist> <bibtext> Bustamante, A. S., Begolli, K. N., Alvarez-Vargas, D., Bailey, D. H., & Richland, L. E. (2022). Fraction ball: Playful and physically active fraction and decimal learning. Journal of Educational Psychology, 114(6), 1307–1320. https://doi.org/10.1037/edu0000714</bibtext> </blist> <blist> <bibtext> Carbonneau, K. J., Marley, S. C., & Selig, J. P. (2013). A meta-analysis of the efficacy of teaching mathematics with concrete manipulatives. Journal of Educational Psychology, 105(2), 380–400. https://doi.org/10.1037/a0031084</bibtext> </blist> <blist> <bibtext> Carpenter, T., Franke, M., Johnson, N., Turrou, A., & Wagner, A. (2016). Young children's mathematics: Cognitively guided instruction in early childhood education. Heinemann.</bibtext> </blist> <blist> <bibtext> Casey, B., Erkut, S., Ceder, I., & Young, J. M. (2008). Use of a storytelling context to improve girls' and boys' geometry skills in kindergarten. Journal of Applied Developmental Psychology, 29(1), 29–48. https://doi.org/10.1016/j.appdev.2007.10.005</bibtext> </blist> <blist> <bibtext> Chiatovich, T., & Stipek, D. (2016). Instructional approaches in kindergarten: What works for whom? Elementary School Journal, 117(1), 1–29. https://doi.org/10.1086/687751</bibtext> </blist> <blist> <bibtext> Claessens, A., Duncan, G., & Engel, M. (2009). Kindergarten skills and fifth-grade achievement: Evidence from the ECLS-K. Economics of Education Review, 28(4), 415–427. https://doi.org/10.1016/j.econedurev.2008.09.003</bibtext> </blist> <blist> <bibtext> Claessens, A., & Engel, M. (2013). How important is where you start? Early mathematics knowledge and later school success. Teachers College Record, 115(6), 1–29. https://doi.org/10.1177/016146811311500603</bibtext> </blist> <blist> <bibtext> Clements, D. H., & Sarama, J. (2011). Early childhood mathematics intervention. Science, 333(6045), 968–970. https://doi.org/10.1126/science.1204537</bibtext> </blist> <blist> <bibtext> Cohen-Vogel, L., Little, M., Jang, W., Burchinal, M., & Bratsch-Hines, M. (2021). A missed opportunity? Instructional content redundancy in pre-K and kindergarten. AERA Open, 7(1), 1–15. https://doi.org/10.1177/23328584211006163</bibtext> </blist> <blist> <bibtext> Copple, C., & Bredekamp, S. (2009). Developmentally appropriate practice in early childhood programs serving children from birth through age 8 [Position statement]. National Association for the Education of Young Children. https://<ulink href="http://www.naeyc.org/sites/default/files/globally-shared/downloads/PDFs/resources/position-statements/PSDAP.pdf">www.naeyc.org/sites/default/files/globally-shared/downloads/PDFs/resources/position-statements/PSDAP.pdf</ulink></bibtext> </blist> <blist> <bibtext> Deunk, M. I., Smale-Jacobse, A. E., de Boer, H., Doolaard, S., & Bosker, R. J. (2018). Effective differentiation practices: A systematic review and meta-analysis of studies on the cognitive effects of differentiation practices in primary education. Educational Research Review, 24, 31–54. https://doi.org/10.1016/j.edurev.2018.02.002</bibtext> </blist> <blist> <bibtext> Dicke, T., Elling, J., Schmeck, A., & Leutner, D. (2015). Reducing reality shock: The effects of classroom management skills training on beginning teachers. Teaching and Teacher Education, 48, 1–12. https://doi.org/10.1016/j.tate.2015.01.013</bibtext> </blist> <blist> <bibtext> Doabler, C. T., Nelson, N. J., Kosty, D. B., Fien, H., Baker, S. K., Smolkowski, K., & Clarke, B. (2014). Examining teachers' use of evidence-based practices during core mathematics instruction. Assessment for Effective Intervention, 39(2), 99–111. https://doi.org/10.1177/1534508413511848</bibtext> </blist> <blist> <bibtext> Duncan, G., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P., Pagani, L. S., Feinstein, L., Engel, M., Brooks-Gunn, J., Sexton, H., & Duckworth, K. (2007). School readiness and later achievement. Developmental Psychology, 43(6), 1428–1446. https://doi.org/10.1037/0012-1649.43.6.1428</bibtext> </blist> <blist> <bibtext> Early, D. M., Iruka, I. U., Ritchie, S., Barbarin, O. A., Winn, D.-M. C., Crawford, G. M., Frome, P. M., Clifford, R. M., Burchinal, M., Howes, C., Bryant, D. M., & Pianta, R. C. (2010). How do pre-kindergartners spend their time? Gender, ethnicity, and income as predictors of experiences in pre-kindergarten classrooms. Early Childhood Research Quarterly, 25(2), 177–193. https://doi.org/10.1016/j.ecresq.2009.10.003</bibtext> </blist> <blist> <bibtext> Engel, M., Claessens, A., & Finch, M. A. (2013). Teaching students what they already know? The (mis)alignment between mathematics instructional content and student knowledge in kindergarten. Educational Evaluation and Policy Analysis, 35(2), 157–178. https://doi.org/10.3102/0162373712461850</bibtext> </blist> <blist> <bibtext> Engel, M., Claessens, A., Watts, T., & Farkas, G. (2016). Mathematics content coverage and student learning in kindergarten. Educational Researcher, 45(5), 293–300. https://doi.org/10.3102/0013189X16656841</bibtext> </blist> <blist> <bibtext> Engel, M., Jacob, R., Claessens, A., & Erickson, A. (2021). Kindergarten in a large urban district. Educational Researcher, 50(6), 401–415. https://doi.org/10.3102/0013189X211041586</bibtext> </blist> <blist> <bibtext> Engel, M., Jacob, R., Hart Erickson, A., Mattera, S., Shaw Attaway, D., & Claessens, A. (2024). The alignment of P–3 math instruction. AERA Open, 10, 23328584241281483. https://doi.org/10.1177/23328584241281483</bibtext> </blist> <blist> <bibtext> Farran, D., & Bilbrey, C. (2004). Narrative record [Unpublished instrument]. Peabody Research Institute, Vanderbilt University.</bibtext> </blist> <blist> <bibtext> Frye, D., Baroody, A. J., Burchinal, M., Carver, S., Jordan, N. C., & McDowell, J. (2013). Teaching math to young children: A practice guide. National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education.</bibtext> </blist> <blist> <bibtext> Guarino, C. M., Hamilton, L. S., Lockwood, J. R., Rathbun, A. H., & Hausken, E. (2006). Teacher qualifications, instructional practices, and reading and mathematics gains of kindergartners (NCES 2006-031). National Center for Education Statistics, U.S. Department of Education.</bibtext> </blist> <blist> <bibtext> Hall, T., Vue, G., Strangman, N., & Meyer, A. (2003). Differentiated instruction and implications for UDL implementation. National Center on Accessing the General Curriculum. https://<ulink href="http://www.cast.org/resources/tips-articles/differentiated-instruction-and-implications-for-udl-implementation/">www.cast.org/resources/tips-articles/differentiated-instruction-and-implications-for-udl-implementation/</ulink></bibtext> </blist> <blist> <bibtext> Hassinger-Das, B., Jordan, N. C., & Dyson, N. (2015). Reading stories to learn math: Mathematics vocabulary instruction for children with early numeracy difficulties. Elementary School Journal, 116(2), 242–264. https://doi.org/10.1086/683986</bibtext> </blist> <blist> <bibtext> Hattie, J. (2009). Visible learning: A synthesis of over 800 meta-analyses relating to achievement. Routledge.</bibtext> </blist> <blist> <bibtext> Herrera, S., Phillips, B. M., Newton, Y.-C., Dombek, J. L., & Hernandez, J. A. (2021). Effectiveness of early literacy instruction: Summary of 20 years of research (REL 2021–084). U.S. Department of Education, Institute of Education Sciences, National Center for Education Evaluation and Regional Assistance, Regional Educational Laboratory Southeast. https://ies.ed.gov/ncee/edlabs/regions/southeast/pdf/REL_2021084.pdf</bibtext> </blist> <blist> <bibtext> Hindman, A. H. (2013). Mathematics instruction in Head Start: Nature, extent, and contributions to children's learning. Journal of Applied Developmental Psychology, 34(5), 230–240. https://doi.org/10.1016/j.appdev.2013.04.003</bibtext> </blist> <blist> <bibtext> Hutchings, J., Martin-Forbes, P., Daley, D., & Williams, M. E. (2013). A randomized controlled trial of the impact of a teacher classroom management program on the classroom behavior of children with and without behavior problems. Journal of School Psychology, 51(5), 571–585. https://doi.org/10.1016/j.jsp.2013.08.001</bibtext> </blist> <blist> <bibtext> Jacob, R., Erickson, A., & Mattera, S. (2020). Evaluating the impact of small group supplemental math enrichment in kindergarten. Journal of Research on Educational Effectiveness, 13(3), 381–407. https://doi.org/10.1080/19345747.2020.1726539</bibtext> </blist> <blist> <bibtext> Jordan, N. C., Kaplan, D., Ramineni, C., & Locuniak, M. N. (2009). Early math matters: Kindergarten number competence and later mathematics outcomes. Developmental Psychology, 45(3), 850–867. https://doi.org/10.1037/a0014939</bibtext> </blist> <blist> <bibtext> Justice, L. M., Jiang, H., Purtell, K. M., Lin, T.-J., & Ansari, A. (2022). Academics of the early primary grades: Investigating the alignment of instructional practices from pre-K to third grade. Early Education and Development, 33, 1237–1255. https://doi.org/10.1080/10409289.2021.1946762</bibtext> </blist> <blist> <bibtext> Klingner, J. K., & Vaughn, S. (2000). The helping behaviors of fifth graders while using collaborative strategic reading during ESL content classes. TESOL Quarterly, 34(1), 69. https://doi.org/10.2307/3588097</bibtext> </blist> <blist> <bibtext> La Paro, K. M., Hamre, B. K., LoCasale-Crouch, J., Pianta, R. C., Bryant, D., Early, D., Clifford, R., Barbarin, O., Howes, C., & Burchinal, M. (2009). Quality in kindergarten classrooms: Observational evidence for the need to increase children's learning opportunities in early education classrooms. Early Education and Development, 20(4), 657–692. https://doi.org/10.1080/10409280802541965</bibtext> </blist> <blist> <bibtext> Manches, A., & O'Malley, C. (2016). The effects of physical manipulatives on children's numerical strategies. Cognition and Instruction, 34(1), 27–50. https://doi.org/10.1080/07370008.2015.1124882</bibtext> </blist> <blist> <bibtext> Mayer, D. P. (1999). Measuring instructional practice: Can policymakers trust survey data? Educational Evaluation and Policy Analysis, 21(1), 29–45.</bibtext> </blist> <blist> <bibtext> McGuire, P., Himot, B., Clayton, G., Yoo, M., & Logue, M. E. (2021). Booked on math: Developing math concepts in pre-K classrooms using interactive read-alouds. Early Childhood Education Journal, 49(2), 313–323. https://doi.org/10.1007/s10643-020-01073-1</bibtext> </blist> <blist> <bibtext> Mu, J., Bayrak, A., & Ufer, S. (2022). Conceptualizing and measuring instructional quality in mathematics education: A systematic literature review. Frontiers in Education, 7, 1–30. https://doi.org/10.3389/feduc.2022.994739</bibtext> </blist> <blist> <bibtext> Mullender-Wijnsma, M. J., Hartman, E., De Greeff, J. W., Doolaard, S., Bosker, R. J., & Visscher, C. (2019). Follow-up study investigating the effects of a physically active academic intervention. Early Childhood Education Journal, 47(6), 699–707. https://doi.org/10.1007/s10643-019-00968-y</bibtext> </blist> <blist> <bibtext> National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics (Vol. 1). National Council of Teachers of Mathematics.</bibtext> </blist> <blist> <bibtext> National Council of Teachers of Mathematics & National Association for the Education of Young Children. (2010). Early childhood mathematics: Promoting good beginnings [Position statement]. <ulink href="http://www.naeyc.org/positionstatements/mathematics">http://www.naeyc.org/positionstatements/mathematics</ulink></bibtext> </blist> <blist> <bibtext> Purpura, D. J., Napoli, A. R., Wehrspann, E. A., & Gold, Z. S. (2017). Causal connections between mathematical language and mathematical knowledge: A dialogic reading intervention. Journal of Research on Educational Effectiveness, 10(1), 116–137. https://doi.org/10.1080/19345747.2016.1204639</bibtext> </blist> <blist> <bibtext> Purpura, D. J., & Reid, E. E. (2016). Mathematics and language: Individual and group differences in mathematical language skills in young children. Early Childhood Research Quarterly, 36, 259–268. https://doi.org/10.1016/j.ecresq.2015.12.020</bibtext> </blist> <blist> <bibtext> Ramani, G. B., Siegler, R. S., & Hitti, A. (2012). Taking it to the classroom: Number board games as a small group learning activity. Journal of Educational Psychology, 104(3), 661–672. https://doi.org/10.1037/a0028995</bibtext> </blist> <blist> <bibtext> Ribner, A. D. (2020). Executive function facilitates learning from math instruction in kindergarten: Evidence from the ECLS-K. Learning and Instruction, 65, 101251. https://doi.org/10.1016/j.learninstruc.2019.101251</bibtext> </blist> <blist> <bibtext> Ritchie, S. J., & Bates, T. C. (2013). Enduring links from childhood mathematics and reading achievement to adult socioeconomic status. Psychological Science, 24(7), 1301–1308. https://doi.org/10.1177/0956797612466268</bibtext> </blist> <blist> <bibtext> Robinson, K., Hubbard, D., Jacob, R., Erickson, A., & Engel, M. (2023). Variation in mathematics content coverage, instructional grouping, and representational strategies: An analysis of three US kindergarten mathematics textbooks. Elementary School Journal, 124(2), 270–296.</bibtext> </blist> <blist> <bibtext> Rowan, B., Jacob, R., & Correnti, R. (2009). Using instructional logs to identify quality in educational settings. New Directions for Youth Development, 2009(121), 13–31. https://doi.org/10.1002/yd.294</bibtext> </blist> <blist> <bibtext> Sameroff, A., & Haith, M. (Eds.). (1996). The five to seven year shift: The age of reason and responsibility. University of Chicago Press.</bibtext> </blist> <blist> <bibtext> Sarama, J., & Clements, D. (2008). Classroom Observation of Early Mathematics—Environment and Teaching Protocol (COEMET).</bibtext> </blist> <blist> <bibtext> Sarama, J., & Clements, D. H. (2009). Building blocks and cognitive building blocks: Playing to know the world mathematically. American Journal of Play, 1(3), 313–337.</bibtext> </blist> <blist> <bibtext> Senden, B., Nilsen, T., & Blömeke, S. (2022). Instructional quality: A review of conceptualizations, measurement approaches, and research findings. In M. Blikstad-Balas, K. Klette, & M. Tengberg (Eds.), Ways of analyzing teaching quality: Potentials and pitfalls (pp. 140–172). Scandinavian University Press. https://doi.org/10.18261/9788215045054-2021-05</bibtext> </blist> <blist> <bibtext> Skinner, E. (2018). Children's developmental needs during the transition to kindergarten: What can research on social-emotional, motivational, cognitive, and self-regulatory development tell us? In A. Mashburn, J. LoCasale–Crouch, & K. Pears (Eds.), Kindergarten transition and readiness (pp. 31–57). Springer.</bibtext> </blist> <blist> <bibtext> Smale-Jacobse, A. E., Meijer, A., Helms-Lorenz, M., & Maulana, R. (2019). Differentiated instruction in secondary education: A systematic review of research evidence. Frontiers in Psychology, 10. https://doi.org/10.3389/fpsyg.2019.02366</bibtext> </blist> <blist> <bibtext> Stipek, D. (2004). Teaching practices in kindergarten and first grade: Different strokes for different folks. Early Childhood Research Quarterly, 19(4), 548–568. https://doi.org/10.1016/j.ecresq.2004.10.010</bibtext> </blist> <blist> <bibtext> Stipek, D., & Chiatovich, T. (2017). The effect of instructional quality on low- and high-performing students. Psychology in the Schools, 54(8), 773–791. https://doi.org/10.1002/pits.22034</bibtext> </blist> <blist> <bibtext> Stright, A. D., & Supplee, L. H. (2002). Children's self-regulatory behaviors during teacher-directed, seat-work, and small-group instructional contexts. Journal of Educational Research, 95(4), 235–244. https://doi.org/10.1080/00220670209596596</bibtext> </blist> <blist> <bibtext> Stronge, J. H., Ward, T. J., & Grant, L. W. (2011). What makes good teachers good? A cross-case analysis of the connection between teacher effectiveness and student achievement. Journal of Teacher Education, 62(4), 339–355. https://doi.org/10.1177/0022487111404241</bibtext> </blist> <blist> <bibtext> Tonyan, H. A., & Howes, C. (2003). Exploring patterns in time children spend in a variety of child care activities: Associations with environmental quality, ethnicity, and gender. Early Childhood Research Quarterly, 18(1), 121–142. https://doi.org/10.1016/S0885-2006(03)00006-1</bibtext> </blist> <blist> <bibtext> van Den Heuvel-Panhuizen, M., Elia, I., & Robitzsch, A. (2016). Effects of reading picture books on kindergartners' mathematics performance. Educational Psychology, 36(2), 323–346. https://doi.org/10.1080/01443410.2014.963029</bibtext> </blist> <blist> <bibtext> van Dijk, W., Gage, N. A., & Grasley-Boy, N. (2019). The relation between classroom management and mathematics achievement: A multilevel structural equation model. Psychology in the Schools, 56(7), 1173–1186. https://doi.org/10.1002/pits.22254</bibtext> </blist> <blist> <bibtext> Vetter, M., O'Connor, H., O'Dwyer, N., & Orr, R. (2018). Learning "math on the move": Effectiveness of a combined numeracy and physical activity program for primary school children. Journal of Physical Activity and Health, 15(7), 492–498. https://doi.org/10.1123/jpah.2017-0234</bibtext> </blist> <blist> <bibtext> Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes (M. Cole, Ed.). Harvard University Press.</bibtext> </blist> <blist> <bibtext> Watts, T. W., Duncan, G. J., Clements, D. H., & Sarama, J. (2018). What is the long-run impact of learning mathematics during preschool? Child Development, 89(2), 539–555. https://doi.org/10.1111/cdev.12713</bibtext> </blist> <blist> <bibtext> Watts, T. W., Duncan, G. J., Siegler, R. S., & Davis-Kean, P. E. (2014). What's past is prologue: Relations between early mathematics knowledge and high school achievement. Educational Researcher, 43(7), 352–360. https://doi.org/10.3102/0013189X14553660</bibtext> </blist> </ref> <aug> <p>By Danielle Shaw Attaway; Mimi Engel; Robin Jacob; Anna Erickson and Amy Claessens</p> <p>Reported by Author; Author; Author; Author; Author</p> </aug> <nolink nlid="nl1" bibid="bib59" firstref="ref3"></nolink> <nolink nlid="nl2" bibid="bib63" firstref="ref4"></nolink> <nolink nlid="nl3" bibid="bib30" firstref="ref6"></nolink> <nolink nlid="nl4" bibid="bib42" firstref="ref7"></nolink> <nolink nlid="nl5" bibid="bib25" firstref="ref8"></nolink> <nolink nlid="nl6" bibid="bib56" firstref="ref9"></nolink> <nolink nlid="nl7" bibid="bib74" firstref="ref10"></nolink> <nolink nlid="nl8" bibid="bib38" firstref="ref12"></nolink> <nolink nlid="nl9" bibid="bib58" firstref="ref13"></nolink> <nolink nlid="nl10" bibid="bib46" firstref="ref14"></nolink> <nolink nlid="nl11" bibid="bib48" firstref="ref16"></nolink> <nolink nlid="nl12" bibid="bib62" firstref="ref17"></nolink> <nolink nlid="nl13" bibid="bib66" firstref="ref18"></nolink> <nolink nlid="nl14" bibid="bib61" firstref="ref19"></nolink> <nolink nlid="nl15" bibid="bib35" firstref="ref20"></nolink> <nolink nlid="nl16" bibid="bib47" firstref="ref21"></nolink> <nolink nlid="nl17" bibid="bib72" firstref="ref22"></nolink> <nolink nlid="nl18" bibid="bib37" firstref="ref23"></nolink> <nolink nlid="nl19" bibid="bib67" firstref="ref24"></nolink> <nolink nlid="nl20" bibid="bib13" firstref="ref25"></nolink> <nolink nlid="nl21" bibid="bib22" firstref="ref26"></nolink> <nolink nlid="nl22" bibid="bib64" firstref="ref27"></nolink> <nolink nlid="nl23" bibid="bib51" firstref="ref28"></nolink> <nolink nlid="nl24" bibid="bib18" firstref="ref29"></nolink> <nolink nlid="nl25" bibid="bib19" firstref="ref30"></nolink> <nolink nlid="nl26" bibid="bib28" firstref="ref31"></nolink> <nolink nlid="nl27" bibid="bib17" firstref="ref34"></nolink> <nolink nlid="nl28" bibid="bib41" firstref="ref36"></nolink> <nolink nlid="nl29" bibid="bib75" firstref="ref39"></nolink> <nolink nlid="nl30" bibid="bib27" firstref="ref40"></nolink> <nolink nlid="nl31" bibid="bib33" firstref="ref42"></nolink> <nolink nlid="nl32" bibid="bib55" firstref="ref44"></nolink> <nolink nlid="nl33" bibid="bib16" firstref="ref48"></nolink> <nolink nlid="nl34" bibid="bib20" firstref="ref51"></nolink> <nolink nlid="nl35" bibid="bib15" firstref="ref53"></nolink> <nolink nlid="nl36" bibid="bib32" firstref="ref54"></nolink> <nolink nlid="nl37" bibid="bib73" firstref="ref56"></nolink> <nolink nlid="nl38" bibid="bib12" firstref="ref59"></nolink> <nolink nlid="nl39" bibid="bib49" firstref="ref61"></nolink> <nolink nlid="nl40" bibid="bib53" firstref="ref62"></nolink> <nolink nlid="nl41" bibid="bib52" firstref="ref64"></nolink> <nolink nlid="nl42" bibid="bib70" firstref="ref67"></nolink> <nolink nlid="nl43" bibid="bib10" firstref="ref72"></nolink> <nolink nlid="nl44" bibid="bib21" firstref="ref74"></nolink> <nolink nlid="nl45" bibid="bib50" firstref="ref75"></nolink> <nolink nlid="nl46" bibid="bib40" firstref="ref77"></nolink> <nolink nlid="nl47" bibid="bib43" firstref="ref78"></nolink> <nolink nlid="nl48" bibid="bib54" firstref="ref79"></nolink> <nolink nlid="nl49" bibid="bib45" firstref="ref81"></nolink> <nolink nlid="nl50" bibid="bib11" firstref="ref83"></nolink> <nolink nlid="nl51" bibid="bib34" firstref="ref84"></nolink> <nolink nlid="nl52" bibid="bib36" firstref="ref86"></nolink> <nolink nlid="nl53" bibid="bib71" firstref="ref88"></nolink> <nolink nlid="nl54" bibid="bib68" firstref="ref89"></nolink> <nolink nlid="nl55" bibid="bib24" firstref="ref92"></nolink> <nolink nlid="nl56" bibid="bib26" firstref="ref94"></nolink> <nolink nlid="nl57" bibid="bib65" firstref="ref95"></nolink> <nolink nlid="nl58" bibid="bib69" firstref="ref98"></nolink> <nolink nlid="nl59" bibid="bib60" firstref="ref104"></nolink> <nolink nlid="nl60" bibid="bib44" firstref="ref121"></nolink> <nolink nlid="nl61" bibid="bib57" firstref="ref145"></nolink> <nolink nlid="nl62" bibid="bib14" firstref="ref158"></nolink> <nolink nlid="nl63" bibid="bib23" firstref="ref165"></nolink> <nolink nlid="nl64" bibid="bib39" firstref="ref166"></nolink>
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  Data: Understanding Mathematics Instruction in Kindergarten
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  Group: Lang
  Data: English
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Danielle+Shaw+Attaway%22">Danielle Shaw Attaway</searchLink><br /><searchLink fieldCode="AR" term="%22Mimi+Engel%22">Mimi Engel</searchLink><br /><searchLink fieldCode="AR" term="%22Robin+Jacob%22">Robin Jacob</searchLink><br /><searchLink fieldCode="AR" term="%22Anna+Erickson%22">Anna Erickson</searchLink><br /><searchLink fieldCode="AR" term="%22Amy+Claessens%22">Amy Claessens</searchLink>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="SO" term="%22Elementary+School+Journal%22"><i>Elementary School Journal</i></searchLink>. 2025 125(3):518-547.
– Name: Avail
  Label: Availability
  Group: Avail
  Data: University of Chicago Press. Journals Division, P.O. Box 37005, Chicago, IL 60637. Tel: 877-705-1878; Tel: 773-753-3347; Fax: 877-705-1879; Fax: 773-753-0811; e-mail: subscriptions@press.uchicago.edu; Web site: http://www.press.uchicago.edu
– Name: PeerReviewed
  Label: Peer Reviewed
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  Data: Y
– Name: Pages
  Label: Page Count
  Group: Src
  Data: 30
– Name: DatePubCY
  Label: Publication Date
  Group: Date
  Data: 2025
– Name: TypeDocument
  Label: Document Type
  Group: TypDoc
  Data: Journal Articles<br />Reports - Research
– Name: Audience
  Label: Education Level
  Group: Audnce
  Data: <searchLink fieldCode="EL" term="%22Early+Childhood+Education%22">Early Childhood Education</searchLink><br /><searchLink fieldCode="EL" term="%22Elementary+Education%22">Elementary Education</searchLink><br /><searchLink fieldCode="EL" term="%22Kindergarten%22">Kindergarten</searchLink><br /><searchLink fieldCode="EL" term="%22Primary+Education%22">Primary Education</searchLink>
– Name: Subject
  Label: Descriptors
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Kindergarten%22">Kindergarten</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Instruction%22">Mathematics Instruction</searchLink><br /><searchLink fieldCode="DE" term="%22Low+Income+Students%22">Low Income Students</searchLink><br /><searchLink fieldCode="DE" term="%22Socioeconomic+Status%22">Socioeconomic Status</searchLink><br /><searchLink fieldCode="DE" term="%22Large+Group+Instruction%22">Large Group Instruction</searchLink><br /><searchLink fieldCode="DE" term="%22Teaching+Methods%22">Teaching Methods</searchLink><br /><searchLink fieldCode="DE" term="%22Manipulative+Materials%22">Manipulative Materials</searchLink><br /><searchLink fieldCode="DE" term="%22Scaffolding+%28Teaching+Technique%29%22">Scaffolding (Teaching Technique)</searchLink><br /><searchLink fieldCode="DE" term="%22Individualized+Instruction%22">Individualized Instruction</searchLink><br /><searchLink fieldCode="DE" term="%22Urban+Schools%22">Urban Schools</searchLink><br /><searchLink fieldCode="DE" term="%22Interdisciplinary+Approach%22">Interdisciplinary Approach</searchLink>
– Name: DOI
  Label: DOI
  Group: ID
  Data: 10.1086/734379
– Name: ISSN
  Label: ISSN
  Group: ISSN
  Data: 0013-5984<br />1554-8279
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Kindergartners' math skills predict later academic outcomes. However, we know little about kindergarten mathematics instruction. Using data from 182 classroom observations in a large urban district, we explore time spent on mathematics and math content coverage. We also examine two underinvestigated aspects of kindergarten math instruction: (1) whether math is incorporated into other subjects and (2) math pedagogy. We focus on schools serving students from households with lower income and include a small higher-income comparison sample. We find that kindergartners in schools serving students from households with lower income experience more whole-group math instruction and have fewer opportunities to use manipulatives in math. Kindergartners in schools serving students from households with higher incomes are exposed to more math during other subjects. In math, kindergartners across contexts experience cursory reviews of key ideas, rarely have scaffolded instruction, and instruction is not differentiated for students based on their performance or skills.
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  Group: Date
  Data: 2025
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  Label: Accession Number
  Group: ID
  Data: EJ1464634
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=eric&AN=EJ1464634
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1086/734379
    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 30
        StartPage: 518
    Subjects:
      – SubjectFull: Kindergarten
        Type: general
      – SubjectFull: Mathematics Instruction
        Type: general
      – SubjectFull: Low Income Students
        Type: general
      – SubjectFull: Socioeconomic Status
        Type: general
      – SubjectFull: Large Group Instruction
        Type: general
      – SubjectFull: Teaching Methods
        Type: general
      – SubjectFull: Manipulative Materials
        Type: general
      – SubjectFull: Scaffolding (Teaching Technique)
        Type: general
      – SubjectFull: Individualized Instruction
        Type: general
      – SubjectFull: Urban Schools
        Type: general
      – SubjectFull: Interdisciplinary Approach
        Type: general
    Titles:
      – TitleFull: Understanding Mathematics Instruction in Kindergarten
        Type: main
  BibRelationships:
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      – PersonEntity:
          Name:
            NameFull: Danielle Shaw Attaway
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            NameFull: Mimi Engel
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            NameFull: Robin Jacob
      – PersonEntity:
          Name:
            NameFull: Anna Erickson
      – PersonEntity:
          Name:
            NameFull: Amy Claessens
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2025
          Identifiers:
            – Type: issn-print
              Value: 0013-5984
            – Type: issn-electronic
              Value: 1554-8279
          Numbering:
            – Type: volume
              Value: 125
            – Type: issue
              Value: 3
          Titles:
            – TitleFull: Elementary School Journal
              Type: main
ResultId 1