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Professional Development for Teaching Mathematics with Technology: A Comparative Study of Facilitators' Beliefs and Practices in China and Germany

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Title: Professional Development for Teaching Mathematics with Technology: A Comparative Study of Facilitators' Beliefs and Practices in China and Germany
Language: English
Authors: Daniel Thurm (ORCID 0000-0001-6531-5271), Shuhui Li (ORCID 0000-0002-5231-7785), Bärbel Barzel (ORCID 0000-0001-6249-0891), Lianghuo Fan (ORCID 0000-0002-4680-6937), Na Li (ORCID 0000-0001-7718-4184)
Source: Educational Studies in Mathematics. 2024 115(2):247-269.
Availability: Springer. Available from: Springer Nature. One New York Plaza, Suite 4600, New York, NY 10004. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-460-1700; e-mail: customerservice@springernature.com; Web site: https://link.springer.com/
Peer Reviewed: Y
Page Count: 23
Publication Date: 2024
Document Type: Journal Articles
Reports - Research
Descriptors: Facilitators (Individuals), Faculty Development, Cultural Differences, Beliefs, Educational Practices, Mathematics Instruction, Educational Technology, Cooperation, Instructional Materials, Professional Identity, Technological Literacy, Pedagogical Content Knowledge, Self Efficacy, Foreign Countries
Geographic Terms: China, Germany
DOI: 10.1007/s10649-023-10284-3
ISSN: 0013-1954
1573-0816
Abstract: Facilitators, i.e., individuals who lead professional development (PD) programs, play a crucial role in providing high-quality PD to teachers, which is particularly relevant in the context of teaching mathematics with technology given the ubiquitous calls to exploit the potential of digital mathematical tools (DMT). However, quantitative research investigating facilitators' beliefs and practices remains scarce, particularly research comparing countries. In this cross-national study conducted in China and Germany, we developed an online questionnaire and surveyed n = 340 facilitators to provide a comprehensive quantitative picture of facilitators' beliefs and practices concerning PD for teaching mathematics with DMT. The results highlight various commonalities and differences between facilitators in China and Germany. We reveal significant differences concerning cooperation among facilitators, adaptation of PD materials, how facilitators professionalise themselves, and beliefs about when and how to use DMT. Furthermore, Chinese facilitators emphasise technical competence more strongly, while German facilitators focus more on developing teachers' pedagogical content knowledge. A critical commonality was that facilitators' self-efficacy concerning teaching with DMT and their self-efficacy for conducting PD for teaching mathematics with DMT was low. We discuss how the results can be linked to differences in the educational and cultural context and outline possible complements and enrichments for both countries' educational systems.
Abstractor: As Provided
Entry Date: 2024
Accession Number: EJ1411615
Database: ERIC
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  Value: <anid>AN0175360864;esm01feb.24;2024Feb13.05:08;v2.2.500</anid> <title id="AN0175360864-1">Professional development for teaching mathematics with technology: a comparative study of facilitators' beliefs and practices in China and Germany </title> <p>Facilitators, i.e., individuals who lead professional development (PD) programs, play a crucial role in providing high-quality PD to teachers, which is particularly relevant in the context of teaching mathematics with technology given the ubiquitous calls to exploit the potential of digital mathematical tools (DMT). However, quantitative research investigating facilitators' beliefs and practices remains scarce, particularly research comparing countries. In this cross-national study conducted in China and Germany, we developed an online questionnaire and surveyed n = 340 facilitators to provide a comprehensive quantitative picture of facilitators' beliefs and practices concerning PD for teaching mathematics with DMT. The results highlight various commonalities and differences between facilitators in China and Germany. We reveal significant differences concerning cooperation among facilitators, adaptation of PD materials, how facilitators professionalise themselves, and beliefs about when and how to use DMT. Furthermore, Chinese facilitators emphasise technical competence more strongly, while German facilitators focus more on developing teachers' pedagogical content knowledge. A critical commonality was that facilitators' self-efficacy concerning teaching with DMT and their self-efficacy for conducting PD for teaching mathematics with DMT was low. We discuss how the results can be linked to differences in the educational and cultural context and outline possible complements and enrichments for both countries' educational systems.</p> <p>Keywords: Facilitators; Professional development; International comparison; Beliefs; Digital mathematical tools; Technology</p> <p>Supplementary Information The online version contains supplementary material available at https://doi.org/10.1007/s10649-023-10284-3.</p> <hd id="AN0175360864-2">Introduction</hd> <p>Facilitators of professional development (PD), i.e., individuals who lead PD programs for practising mathematics teachers, have received increasing attention in recent years since their practices are crucial "for the success of spreading mathematics educational ideas and innovations into schools and strengthening the professional expertise of teachers" (Karsenty et al., [<reflink idref="bib20" id="ref1">20</reflink>], p. 27). This is particularly true regarding teaching with technology. Given the continual emergence of new technologies and the often reported quantitative and qualitative gap between teachers' use of technology and the opportunities suggested by research and policy, PD for teaching with technology and the role of the facilitator in this context are regarded as crucial (Thurm et al., [<reflink idref="bib46" id="ref2">46</reflink>]; Thurm et al., [<reflink idref="bib47" id="ref3">47</reflink>]). However, research on mathematics facilitators remains at an early stage, and both quantitative studies on facilitators in general and such studies that consider digital mathematical tools remain scarce (e.g., Thurm et al., [<reflink idref="bib47" id="ref4">47</reflink>]).</p> <p>Partly due to the consistently outstanding mathematics performance of East Asian students compared with their Western counterparts in several large-scale international assessments, such as PISA (e.g., Schleicher, [<reflink idref="bib40" id="ref5">40</reflink>]) and TIMSS (e.g., Mullies et al., [<reflink idref="bib33" id="ref6">33</reflink>]), cross-national comparative studies delving into social and cultural influences on mathematics education, have received a great deal of attention in recent decades, and it has been argued that there are differences in mathematics education between East Asian countries (such as China) and Western countries (such as Germany) (e.g., Gasteiger et al., [<reflink idref="bib11" id="ref7">11</reflink>]; Kaiser & Bloemeke, [<reflink idref="bib18" id="ref8">18</reflink>]). In particular, many researchers compared the mathematics teacher education systems of China and Germany, examining commonalities and differences in mathematics teacher knowledge, teacher noticing, and teacher modelling competencies (e.g., Schmidt et al., [<reflink idref="bib41" id="ref9">41</reflink>]; Yang et al., [<reflink idref="bib53" id="ref10">53</reflink>]).</p> <p>However, none of these studies have addressed mathematics <emph>facilitators'</emph> practices and beliefs. Our study addresses this research gap by investigating facilitators' beliefs and practices in a cross-national comparison between China and Germany. We chose China and Germany since they not only represent different cultural backgrounds (see Section 3.3), but also are representatives of two different overarching approaches to mathematics PD (see Sections 3.1 and 3.2): China has a well-organised and nationally coordinated hierarchical approach to teacher PD, with facilitators working full-time in their profession. In contrast, Germany has a decentralised, non-hierarchical approach where facilitators work mostly part-time in addition to their job as a teacher. Overall, the goal of this cross-national comparative study is not only "to describe another system or set of practices" but also "to identify commonalities and differences between countries and infer from these" to "learn about others", "from others", and "about ourselves" (Baistow, [<reflink idref="bib1" id="ref11">1</reflink>], pp. 8–9). In particular, we expect to get valuable insights that allow us to reflect on how educational and cultural traditions play roles in issues related to PD in the context of teaching mathematics with DMT.</p> <hd id="AN0175360864-3">Theoretical background</hd> <p></p> <hd id="AN0175360864-4">Teaching mathematics with technology</hd> <p>Due to the rapid development of technology, the types and capabilities of digital technologies that are available for teaching mathematics have expanded considerably. Some such technologies are general technologies for communication, documentation, and presentation (e.g., presentation software), while others are used specifically in mathematics education. In this paper, we focus on the latter, specifically on <emph>digital mathematical tools</emph> (DMT; Günster & Weigand, [<reflink idref="bib13" id="ref12">13</reflink>]), which include, for example, dynamic geometry software, function plotters, statistical tools, computer algebra systems, and graphing calculators. A factor that these tools have in common is that they can be used not only to address a limited set of problems or situations, but also in flexible ways across different tasks or content areas. It is well established that DMT can support students' ability to discover concepts, access and link multiple representations, and support individualised learning (e.g., Thurm & Barzel, [<reflink idref="bib45" id="ref13">45</reflink>]).</p> <p>To exploit the potential of teaching with DMT, several researchers have consistently highlighted the fact that mathematics teachers' competencies are an important factor. In particular, research has identified several competence facets of teachers that are important for teaching with DMT (e.g., Barzel & Biehler, [<reflink idref="bib3" id="ref14">3</reflink>]; Clark-Wilson et al., [<reflink idref="bib6" id="ref15">6</reflink>]; Thurm & Barzel, [<reflink idref="bib45" id="ref16">45</reflink>]; Thurm et al., [<reflink idref="bib47" id="ref17">47</reflink>]). These include[<reflink idref="bib1" id="ref18">1</reflink>]:</p> <p></p> <ulist> <item> Mathematical content knowledge</item> <p></p> <item> Pedagogical content knowledge (PCK, e.g., the knowledge necessary to adapt/create tasks using DMT, the knowledge necessary to design and implement lessons with DMT)</item> <p></p> <item> Noticing skills (e.g., noticing, perceiving, and interpreting the learning process when teaching with DMT)</item> <p></p> <item> Self-efficacy beliefs[<reflink idref="bib2" id="ref19">2</reflink>] for teaching with DMT (e.g., the self-efficacy necessary to adapt/create tasks using DMT, the self-efficacy necessary to design and implement lessons with DMT)</item> <p></p> <item> Beliefs about teaching with DMT (e.g., positive beliefs about the potential of DMT)</item> <p></p> <item> Technical knowledge necessary to operate DMT</item> </ulist> <p>Given the aforementioned importance of teacher competencies for teaching with DMT, high-quality PD programs that address these competencies directly are regarded as important (Thurm & Barzel, [<reflink idref="bib44" id="ref20">44</reflink>]). However, what constitutes high-quality PD? In the past two decades, researchers have provided principles for effective PD pertaining to context, content, and activities (e.g., Lipowsky & Rzejak, [<reflink idref="bib27" id="ref21">27</reflink>]; Timperley et al., [<reflink idref="bib48" id="ref22">48</reflink>]). While different publications may use different terms for these principles, they essentially refer to similar aspects. In this study, we refer to the following six research-based design principles for teacher PD identified by the DZLM (German Centre for Mathematics Teacher Education) based on a comprehensive literature review (Barzel & Biehler, [<reflink idref="bib3" id="ref23">3</reflink>]; Kuzle & Biehler, [<reflink idref="bib21" id="ref24">21</reflink>]):</p> <p></p> <ulist> <item> Competence orientation: Orientation towards professional competencies, such as the beliefs and knowledge of the PD participants.</item> <p></p> <item> Participant orientation: Orientation towards the individual needs and individual situation of the PD participants. This means, for example, that the PD considers the individual knowledge and beliefs of the teachers in order to develop them further. Moreover, participants get actively involved in the PD.</item> <p></p> <item> Stimulation of cooperation: PD should encourage teachers to work cooperatively, to develop lessons cooperatively, and engage into discourses with other teachers. Ideally, professional learning communities are initiated.</item> <p></p> <item> Case-relatedness: PD should be linked as closely as possible to the teaching practice of the teachers. Thus, examples from teachers' own practice should serve both as a starting point and as a field for extending competencies within the learning processes. This means, for example, using video cases or representations of students work.</item> <p></p> <item> Use of diverse instruction formats: PD should use different methodological approaches to actively involve teachers in the PD and to ensure a fit between methods and the objectives of the different PD phases (e.g., alternation of theory/input-, practice-, and reflection-phases).</item> <p></p> <item> Fostering reflection: PD should actively promote the reflection processes of PD participants. This includes, for example, reflecting on one's own beliefs and classroom practices.</item> </ulist> <hd id="AN0175360864-5">Facilitators</hd> <p>To design and implement high-quality PD in line with the aforementioned design principles, the role of "facilitators" has been highlighted (Beswick & Chapman, [<reflink idref="bib4" id="ref25">4</reflink>]; Prediger et al., [<reflink idref="bib37" id="ref26">37</reflink>]; Roesken-Winter et al., [<reflink idref="bib39" id="ref27">39</reflink>])[<reflink idref="bib3" id="ref28">3</reflink>]. In particular, facilitators are especially relevant actors for scaling PD, for example, in implementing innovations such as teaching with technology (Maass et al., [<reflink idref="bib30" id="ref29">30</reflink>]). The term <emph>facilitator</emph> indicates an individual who leads teacher PD:A facilitator is a professional who manages the PD activities, sets norms for interactions, supports teachers' exchange of experiences and insights, monitors the discussion, and works with teachers toward the goals set for the PD. This is a highly demanding job, which requires preparation and support (Karsenty et al., [<reflink idref="bib20" id="ref30">20</reflink>], p. 28).</p> <p>Research related to PD facilitators is an emerging field (Beswick & Chapman, [<reflink idref="bib4" id="ref31">4</reflink>]; Prediger et al., [<reflink idref="bib37" id="ref32">37</reflink>]) and is advancing in several directions, such as investigations of facilitators' preparation, needed competencies, and evolving practices (Karsenty et al., [<reflink idref="bib20" id="ref33">20</reflink>]). However, despite the growing literature on facilitators in general, research on mathematics facilitators remains at an early stage (Karsenty et al., [<reflink idref="bib20" id="ref34">20</reflink>]; Thurm et al., [<reflink idref="bib46" id="ref35">46</reflink>]). Furthermore, most research on mathematics facilitators is qualitative (e.g., Kuzle & Biehler, [<reflink idref="bib21" id="ref36">21</reflink>]; Schwarts et al., [<reflink idref="bib42" id="ref37">42</reflink>]), and quantitative studies on mathematics facilitators are extremely rare (Thurm et al., [<reflink idref="bib46" id="ref38">46</reflink>]). The scarcity of quantitative studies is also due to the fact that there are fewer facilitators than pupils or teachers; hence, it is more challenging to collect larger sample sizes in this context.</p> <p>Concerning those limited quantitative studies on mathematics facilitators, Roesken-Winter et al. ([<reflink idref="bib39" id="ref39">39</reflink>]) reported that German facilitators (<emph>n</emph> = 12) valued competence orientation and participant orientation as the most important design principles. The study conducted by Weißenrieder et al. ([<reflink idref="bib51" id="ref40">51</reflink>]) found only limited effects of a facilitator PD course in Germany on self-efficacy concerning promoting teacher cooperation. In China, Huang et al. ([<reflink idref="bib17" id="ref41">17</reflink>]) surveyed 547 facilitators and revealed that learning through reading, attending specific training programs, etc., jointly contribute to developing facilitators' professional knowledge and competence. Mao et al. ([<reflink idref="bib31" id="ref42">31</reflink>]) found that Chinese facilitators highlight the importance of teachers' ability to grasp digital technologies specifically for mathematics education, primarily concerning dynamic geometry software.</p> <hd id="AN0175360864-6">Theoretical framework</hd> <p>A challenge faced by researchers in the emerging field of research on facilitators pertains to the task of developing frameworks to conceptualise the profession of the facilitator (Karsenty et al., [<reflink idref="bib20" id="ref43">20</reflink>]). One reason for this challenge is that "analyzing facilitation practices requires references to two levels, the classroom level and the PD level, with the former being nested within the latter" (Schwarts et al., [<reflink idref="bib43" id="ref44">43</reflink>], p. 4). The recently developed ROGI model (Karsenty et al., [<reflink idref="bib20" id="ref45">20</reflink>]) accounts for this nested structure by conceptualising the factors underlying facilitators' practices at different levels (where practices are considered as the observable behaviour (e.g., utterances, actions); Karsenty et al., [<reflink idref="bib20" id="ref46">20</reflink>]). According to the ROGI model, the factors underlying facilitators' practices are teachers' classroom practices and "resources" (the intellectual, material, contextual, social resources, etc., on which the person draws), "orientations" (overarching and domain-specific beliefs, attitudes, values, and preferences), "goals", and "identity". For our study, we combine the ROGI model with the typical situational demands that teachers/facilitators must face according to the framework for content-related facilitator expertise proposed by Prediger et al. ([<reflink idref="bib38" id="ref47">38</reflink>]). These demands include the tasks of professionalising themselves as facilitators, cooperating with other facilitators, and preparing, conducting, and reflecting on PD. The final theoretical model is shown in Fig. 1.</p> <p>Graph: Fig. 1Theoretical framework for conceptualising facilitators' practices and their underlying aspects. Yellow boxes are related to the ROGI model (Karsenty et al., [<reflink idref="bib20" id="ref48">20</reflink>]) while green and grey boxes are related to the typical situational demands (Prediger et al., [<reflink idref="bib38" id="ref49">38</reflink>]).</p> <p>In our study, we focus on facilitator practices and orientations-more precisely, on beliefs. According to the broadly accepted definition proposed by Philipp ([<reflink idref="bib35" id="ref50">35</reflink>]), teacher beliefs can be defined as "psychologically held understandings, premises, or propositions about the world that are thought to be true" (p. 259). Beliefs are important because they are especially proximal to practice, as they shape the ways in which we see the world and offer us direction regarding how to act in a given situation (Levin, [<reflink idref="bib24" id="ref51">24</reflink>]; Thurm & Barzel, [<reflink idref="bib45" id="ref52">45</reflink>]). For example, facilitators' self-efficacy beliefs at the <emph>classroom level</emph> may impact their PD practice: If a facilitator has low self-efficacy beliefs about designing tasks for teaching with DMT, this situation is likely also to impact whether and how task design for DMT is addressed when conducting PD for teaching mathematics with DMT (DMT-PD). Also, facilitators' classroom practices (if they continue to teach at school) underlie the facilitators' practices at the PD level. For example, if a facilitator uses (or has used) DMT only for practising known content but not for exploring new content in his or her classroom teaching, the facilitator may privilege the use of DMT for practising known content in his or her DMT-PD.</p> <hd id="AN0175360864-7">Research context</hd> <p></p> <hd id="AN0175360864-8">Educational context in China</hd> <p>China has established a hierarchical and institutionalised five-level system (e.g., Fan et al., [<reflink idref="bib9" id="ref53">9</reflink>]; Yang et al., [<reflink idref="bib52" id="ref54">52</reflink>]), with the national-level <emph>Department of Teacher Education, Ministry of Education</emph> developing national curriculum standards and <emph>Teaching Research Offices</emph> belonging to <emph>Departments of Education or Education Bureaus</emph> at the provincial, prefectural, and county levels; finally, at the school level, teachers are engaged in <emph>Teaching Research Groups</emph> and <emph>Lesson Planning Groups</emph> (Fan et al., [<reflink idref="bib9" id="ref55">9</reflink>]).</p> <p>In our study, we focus on <emph>Teaching Research Fellows (TRFs)</emph>, a special and representative group of facilitators (who educate practising teachers) working at the three levels of teaching research offices (namely, provincial (highest level), prefectural, and county (lowest level)), which have received worldwide research interest over the past decade (e.g., Yin et al., [<reflink idref="bib54" id="ref56">54</reflink>]). Generally, teaching research offices organise or liaise with other educational institutions to organise PD for in-service teachers. TRFs are usually responsible for facilitating consultation and teacher PD programs, guiding teaching research activities, organising various competitions about teaching skills, overseeing teaching quality in schools on behalf of educational bureaus, and promoting high-quality classroom teaching (Fan et al., [<reflink idref="bib9" id="ref57">9</reflink>]; Huang et al., [<reflink idref="bib17" id="ref58">17</reflink>], [<reflink idref="bib16" id="ref59">16</reflink>]). Although official documents (e.g., Ministry of Education, [<reflink idref="bib32" id="ref60">32</reflink>]) provide guidelines to TRFs regarding goals, regular tasks, essential duties and responsibilities, and qualifications, no official qualification or certification for TRFs has been implemented.</p> <hd id="AN0175360864-9">Educational context in Germany</hd> <p>In Germany, school education is mainly the responsibility of the 16 federal states. The Federal Ministry of Education and Research is an important player in this context, particularly by supporting and framing research in education. In addition, Germany features a "Standing Conference of the Ministers of Education and Culture (KMK)" that consists of representatives from each state, which aims to promote nationwide coherence and cooperation, for example, by developing national teaching standards that can serve as guidelines for state curricula. However, at the national level, a systematic approach to educating facilitators is missing, and no guidelines or standards for the qualification of facilitators are available.</p> <p>At present, facilitators in Germany are usually experienced in-service teachers working at the district level, who receive a reduction in their school teaching duties to work part-time as facilitators. These facilitators offer PD programs attended by teachers from different schools in the district or provide school-based PD to teachers. However, various scientific evaluations (e.g., Lipowsky & Rzejak, [<reflink idref="bib28" id="ref61">28</reflink>]) have repeatedly criticised severe problems regarding the current teacher PD situation in Germany. These include a lack of funding for PD, a lack of systematic qualifications for facilitators, low-quality PD programs, a focus on short-term instead of long-term PD, a low level of cooperation with the scientific community, and a lack of innovative in-service PD formats that focus on teacher cooperation. However, the DZLM and the KMK are currently making joint efforts to address these issues.</p> <hd id="AN0175360864-10">Cultural context of China and Germany</hd> <p>China and Germany are located within different cultural[<reflink idref="bib4" id="ref62">4</reflink>] contexts. Grounded in the Confucian philosophy, Chinese culture emphasises collectivism, hierarchy/authority, and social harmony. In contrast, Western cultures like Germany have been characterised as individualistic, valuing uniqueness, democracy, and equality. Cultural differences are also reflected in education. Leung ([<reflink idref="bib22" id="ref63">22</reflink>]) describes these differences in terms of six dichotomies: product versus process, rote learning versus meaningful learning, studying hard versus pleasurable learning, extrinsic versus intrinsic motivations, whole class teaching versus individualised learning, and competence of teachers: subject matter versus pedagogy. Leung ([<reflink idref="bib22" id="ref64">22</reflink>]) highlights that this does not mean that all Eastern countries are on one side of the dichotomy and all Western countries on the opposite side: "[...] it is a matter of the relative positions of the two cultures on a continuum between two extremes rather than two incompatible standpoints" (p. 38).</p> <p>Furthermore, the conceptions of teacher expertise also differ based on cultural differences of collectivism and individualism (Kaiser & Blömeke, [<reflink idref="bib18" id="ref65">18</reflink>]). For example, Kaiser and Li ([<reflink idref="bib19" id="ref66">19</reflink>]) describe the Eastern perspective as content-oriented with content-oriented lesson planning "aiming for a systemic change of the teaching-and-learning processes in school by strengthening teachers as researchers and developing expertise in scientific work" (p. 349). This entails that expert teachers are expected to act as a researcher, which entails writing books and scientific papers in teacher journals. In contrast, "Characteristic for the Western approach to expertise is the focus on the individual student, who is put into the centre of reflections and actions [...]" (p. 349). This means that expertise is related to being passionate about mathematics and creating learning environments that support the idea that students can develop an understanding of mathematics on their own.</p> <hd id="AN0175360864-11">Research question</hd> <p>As noted, research on facilitators is limited, a claim that holds particularly true for quantitative studies on facilitators in the context of professional development for teaching with digital mathematical tools (DMT-PD). Accordingly, international comparisons regarding this issue are even rarer. In our study, we aim to address this research gap by investigating the following research question:</p> <p> <emph> What are the commonalities and differences between the beliefs and practices of facilitators in China (TRFs) and Germany in the context of PD for teaching mathematics with digital mathematical tools? </emph> </p> <hd id="AN0175360864-12">Methods</hd> <p>To answer the research question, we pursue a quantitative approach with questionnaires, as our aim is not to elucidate the particular/the specific—as in qualitative research—but to survey and profile a situation to develop an overall pattern. In addition, questionnaires allow us to capture many different aspects of practices and beliefs economically.</p> <hd id="AN0175360864-13">Questionnaire development</hd> <p>The questionnaire design was guided by the theoretical framework described in Section 2.3, distinguishing between facilitators' practices and beliefs at the PD and classroom levels. As a quantitative questionnaire for facilitators did not exist, we designed a questionnaire by drawing on the literature referenced in the theoretical background section.</p> <p>Most items/scales focused specifically on DMT/DMT-PD. However, we also included some items/scales that target general aspects (i.e., aspects that are not specifically related to DMT-PD) as these may influence facilitators' practice or beliefs related to DMT (for an overview, see Table 1). The questionnaire was developed over the course of multiple cycles. These cycles included discussion about wording, adapting items/scales to the Chinese and German context, and discussing questions of validity, equivalence of terms, and comparability of measures. In addition, the questionnaire was pilot-tested among some facilitators in China and Germany, and the resulting feedback led to clarifications in the final version. A professional translation agency checked the equivalence of the two versions, which led to minor changes in wording. Table 1 gives an overview of the items/scales. The complete questionnaire can be found in the Online Resource.</p> <p>Table 1 Overview of the items/scales included in the questionnaire</p> <p> <ephtml> <table frame="hsides" rules="groups"><tbody><tr><td align="left"><p>Contextual variables</p></td><td align="left"><p>Gender, age, federal state/province of working as a facilitator, number of years of experience as a facilitator, scope of employment as a facilitator (full-/part-time), number of years of experience as a mathematics teacher, currently teaching at school (yes/no)</p></td></tr><tr><td align="left" colspan="2"><p>Classroom level</p></td></tr><tr><td align="left"><p> Beliefs</p></td><td align="left"><p><italic>DMT-PD specific</italic></p><p>CL_B1<sup>s</sup>: Beliefs about advantages of DMT (3)</p><p>CL_B2<sup>s</sup>: Beliefs about disadvantages of DMT (3)</p><p>CL_B3<sup>s</sup>: Beliefs about prior mastery by hand (4)</p><p>CL_B4: Beliefs about the suitability of DMT for introducing or practising content</p><p>CL_B5_1<sup>s</sup>: Self-efficacy for task design using DMT (4)</p><p>CL_B5_2<sup>s</sup>: Self-efficacy for lesson design and implementation using DMT (4)</p></td></tr><tr><td align="left"><p> Practices</p></td><td align="left"><p><italic>DMT-PD specific</italic></p><p>CL_P1: Type of DMT used regularly</p><p>CL_P2: Use of DMT in teaching (introducing or practising content)</p></td></tr><tr><td align="left" colspan="2"><p>PD level</p></td></tr><tr><td align="left"><p> Beliefs</p></td><td align="left"><p><italic>General</italic></p><p>PD_B1<sup>s</sup>: Beliefs about cooperation with other facilitators (3)</p><p>PD_B2: Beliefs about the importance of facilitators' teaching experience</p><p><italic>DMT-PD specific</italic></p><p>PD_B3<sup>s</sup>: Self-efficacy about supporting teachers in task design for teaching with DMT (4)</p><p>PD_B4<sup>s</sup>: Self-efficacy about supporting teachers lesson design and implementation for teaching with DMT (5)</p><p>PD_B5<sup>s</sup>: Self-efficacy about fostering teachers' situation-specific skills for teaching with DMT (4)</p><p>PD_B6<sup>s</sup>: Self-efficacy about fostering teachers' self-efficacy beliefs for teaching with DMT (5)</p><p>PD_B7<sup>s</sup>: Self-efficacy about fostering teachers' beliefs about teaching with DMT (4)</p><p>PD_B8<sup>s</sup>: Self-efficacy about fostering teachers' cooperation (3)</p><p>PD_B9<sup>s</sup>: Self-efficacy about fostering teachers' pedagogical content knowledge (4)</p></td></tr><tr><td align="left" rowspan="9"><p> Practices</p></td><td align="left"><p><italic>General</italic></p><p>PD_P1: Ways of professionalising oneself as a facilitator</p><p>PD_P2: Literature read by the facilitators</p></td></tr><tr><td align="left"><p>PD_P3: Cooperation with other facilitators</p></td></tr><tr><td align="left"><p>PD_P4: Belonging to a professional learning community of facilitators</p><p><italic>DMT-PD specific</italic></p></td></tr><tr><td align="left"><p>PD_P5: Types of DMT addressed</p></td></tr><tr><td align="left"><p>PD_P6: Mathematical content addressed</p></td></tr><tr><td align="left"><p>PD_P7: Source of DMT-PD material</p></td></tr><tr><td align="left"><p>PD_P8: Determinants of DMT-PD content</p></td></tr><tr><td align="left"><p>PD_P9: Important facets of DMT-PD</p></td></tr><tr><td align="left"><p>PD_P10: Design principles of DMT-PD</p></td></tr></tbody></table> </ephtml> </p> <p>The number in brackets indicates the total number of items included in the scale <sups>s</sups>Scales consisting of multiple items</p> <hd id="AN0175360864-14">Data collection and sample description</hd> <p>Data were collected in Germany between November 2021 and May 2022 and in China in January 2022 using online questionnaires. Overall, 138 German and 202 Chinese facilitators (129 from the East China region, including Shanghai, Jiangsu, and Zhejiang, and 73 from other regions, mostly West China) submitted the questionnaire.[<reflink idref="bib5" id="ref67">5</reflink>] The mean ages of Chinese and German facilitators were quite similar at approximately 48 years. Chinese and German facilitators had similar amounts of teaching experience (approximately 20 years) and similar amounts of experience as a facilitator (CN, 9.48; DE, 7.73 years). However, Chinese and German facilitators differed concerning gender, as 61.4% of the Chinese facilitators were male, while 70.0% of the German facilitators were female. Another difference was that most Chinese facilitators did not teach at school (83.7%), while most German facilitators were teaching at school (89.3%). In addition, most Chinese facilitators (89.1%) worked as full-time facilitators, while in Germany, only 11.1% of the participants worked as full-time facilitators.</p> <hd id="AN0175360864-15">Data analysis</hd> <p>For all scales, we calculated reliability using Cronbach's alpha. Reliability was good for all scales (exact values can be found in the Online Resource). Data were analysed using descriptive statistics, such as means, standard deviations, and frequencies. We used inferential statistics such as <emph>t</emph> tests, chi-square tests, and Mann–Whitney <emph>U</emph> tests (in accordance with the type of data in question) to investigate differences between facilitators in Germany and China. Since the eastern regions of China (Shanghai, Jiangsu, Zhejiang) are significantly more economically powerful than other regions of China, which may impact local educational practices, we conducted statistical significance tests for all items/scales between these eastern regions and the other regions. We report the aggregated results for all regions of China and do not distinguish between eastern regions and other regions, as we found only small differences for two items and two scales in this regard (as shown in Sections 6.3 and 6.4).</p> <hd id="AN0175360864-16">Results</hd> <p></p> <hd id="AN0175360864-17">Classroom-level beliefs</hd> <p>This subsection refers to the results displayed in Table 2. Both Chinese and German facilitators are convinced of the advantages of DMT for teaching mathematics (DE, 4.83; CN, 4.98) and concerned about the possible disadvantages of DMT (DE, 3.02; CN, 2.99). Also, Chinese and German facilitators believe that DMTs are suitable for supporting mathematical learning when introducing new content (DE, 4.47; CN, 4.63). Furthermore, self-efficacy is only moderately pronounced, ranging between 12.12 and 13.48 (on a scale ranging from 0 to 20). A major difference is that Chinese facilitators are much more convinced that students should master mathematics using pen and paper before they are allowed to use DMT (DE, 2.76; CN, 3.82).</p> <p>Table 2 Results regarding beliefs at the classroom level</p> <p> <ephtml> <table frame="hsides" rules="groups"><thead><tr><th /><th colspan="2"><p>China</p></th><th colspan="2"><p>Germany</p></th><th><p><italic>p</italic> value</p></th></tr><tr><th /><th><p>Mean (SD)</p></th><th><p><italic>n</italic></p></th><th><p>Mean (SD)</p></th><th><p><italic>n</italic></p></th><th /></tr></thead><tbody><tr><td colspan="6"><p>CL_B1-CL_B3: Beliefs about DMT<sup>a</sup></p></td></tr><tr><td><p> CL_B1<sup>s</sup>: Advantages</p></td><td><p>4.98 (1.02)</p></td><td><p>202</p></td><td><p>4.83 (1.01)</p></td><td><p>126</p></td><td><p>0.223</p></td></tr><tr><td><p> CL_B2<sup>s</sup>: Disadvantages</p></td><td><p>2.99 (1.31)</p></td><td><p>202</p></td><td><p>3.02 (1.22)</p></td><td><p>124</p></td><td><p>0.817</p></td></tr><tr><td><p> CL_B3<sup>s</sup>: Prior mastery by hand</p></td><td><p>3.82 (1.18)</p></td><td><p>202</p></td><td><p>2.76 (1.37)</p></td><td><p>125</p></td><td><p>0.000***</p></td></tr><tr><td colspan="6"><p>CL_B4: Beliefs about the suitability of DMT for<sup>b</sup></p></td></tr><tr><td><p> Introducing new content</p></td><td><p>4.63 (1.10)</p></td><td><p>202</p></td><td><p>4.47 (1.34)</p></td><td><p>129</p></td><td><p>0.248</p></td></tr><tr><td><p> Practising content</p></td><td><p>4.30 (1.29)</p></td><td><p>202</p></td><td><p>4.79 (1.09)</p></td><td><p>129</p></td><td><p>0.000***</p></td></tr><tr><td colspan="6"><p>CL_B5: Self-efficacy beliefs about using DMT in teaching<sup>c</sup></p></td></tr><tr><td><p> CL_B5_1<sup>s</sup>: Task design</p></td><td><p>12.83 (4.24)</p></td><td><p>202</p></td><td><p>12.04 (5.51)</p></td><td><p>111</p></td><td><p>0.194</p></td></tr><tr><td><p> CL_B5_2<sup>s</sup>: Lesson design and implementation</p></td><td><p>12.12 (4.64)</p></td><td><p>202</p></td><td><p>13.48 (5.13)</p></td><td><p>110</p></td><td><p>0.017*</p></td></tr></tbody></table> </ephtml> </p> <p>Test type: <emph>t</emph> tests *<emph>p</emph> < 0.05 ***<emph>p</emph> < 0.001 <sups>s</sups>Scale consisting of multiple items. <sups>a</sups>Six-point Likert scale ranging from 1 = strongly disagree to 6 = strongly agree <sups>b</sups>Six-point Likert scale ranging from 1 = not suitable to 6 = highly suitable <sups>c</sups>Each scale was rated from 0, 1, 2,... to 20</p> <hd id="AN0175360864-18">Classroom-level practices</hd> <p>The results are shown in Table 3. The limited number of respondents from China is due to the fact that most facilitators in China do not teach at schools (see Section 3.1). In both countries, dynamic geometry software is the most used DMT (DE, 69.6%; CN, 90.9%), followed by spreadsheets (DE, 46.4%; CN, 75.8%). Larger differences between China and Germany can be found with respect to using spreadsheets (DE, 46.4%; CN, 75.8%) and using DMT when introducing new content (DE, 4.02; CN, 5.00).</p> <p>Table 3 Results regarding practices at the classroom level</p> <p> <ephtml> <table frame="hsides" rules="groups"><thead><tr><th /><th colspan="2"><p>China</p></th><th colspan="2"><p>Germany</p></th><th><p><italic>p</italic> value</p></th></tr></thead><tbody><tr><td><p>CL_P1: Type of DMT used<sup>a</sup></p></td><td><p>Fre. (%)</p></td><td><p><italic>n</italic> = 33</p></td><td><p>Fre. (%)</p></td><td><p><italic>n</italic> = 56</p></td><td /></tr><tr><td><p> Dynamic Geometry Software</p></td><td><p>30 (90.9%)</p></td><td rowspan="6" /><td><p>39 (69.6%)</p></td><td rowspan="6" /><td><p>0.020*</p></td></tr><tr><td><p> Function plotter</p></td><td><p>12 (36.4%)</p></td><td><p>18 (32.1%)</p></td><td><p>0.684</p></td></tr><tr><td><p> Spreadsheet</p></td><td><p>25 (75.8%)</p></td><td><p>26 (46.4%)</p></td><td><p>0.007**</p></td></tr><tr><td><p> Statistical tools</p></td><td><p>10 (30.3%)</p></td><td><p>6 (10.7%)</p></td><td><p>0.020*</p></td></tr><tr><td><p> Computer Algebra System</p></td><td><p>5 (15.2%)</p></td><td><p>23 (41.1%)</p></td><td><p>0.011*</p></td></tr><tr><td><p> Graphing calculator</p></td><td><p>6 (18.2%)</p></td><td><p>15 (26.8%)</p></td><td><p>0.356</p></td></tr><tr><td><p>CL_P2: Use of DMT in teaching<sup>b</sup></p></td><td><p>Mean (SD)</p></td><td><p><italic>n</italic> = 33</p></td><td><p>Mean (SD)</p></td><td><p><italic>n</italic> = 58</p></td><td /></tr><tr><td><p> Introducing new content</p></td><td><p>5.00 (1.12)</p></td><td rowspan="2" /><td><p>4.02 (1.79)</p></td><td rowspan="2" /><td><p>0.002**</p></td></tr><tr><td><p> Practising content</p></td><td><p>4.45 (1.77)</p></td><td><p>4.43 (1.52)</p></td><td><p>0.947</p></td></tr></tbody></table> </ephtml> </p> <p>Test type: chi-square tests for CL_P1 and <emph>t</emph> tests for CL_P2 *<emph>p</emph> < 0.05 **<emph>p</emph> < 0.01 <sups>a</sups>Multiple choice item <sups>b</sups>Six-point Likert scale ranging from 1 = never to 6 = several times a week</p> <hd id="AN0175360864-19">PD-level beliefs</hd> <p>This subsection refers to the results displayed in Table 4.</p> <p>Table 4 Results regarding beliefs at the PD level</p> <p> <ephtml> <table frame="hsides" rules="groups"><thead><tr><th /><th colspan="2"><p>China</p></th><th colspan="2"><p>Germany</p></th><th><p><italic>p</italic> value</p></th></tr><tr><th /><th><p>Mean (SD)</p></th><th><p><italic>n</italic></p></th><th><p>Mean (SD)</p></th><th><p><italic>n</italic></p></th><th /></tr></thead><tbody><tr><td><p>PD_B1<sup>s</sup>: Beliefs about cooperation with other facilitators<sup>a</sup></p></td><td><p>4.85 (1.18)</p></td><td><p>202</p></td><td><p>5.56 (0.57)</p></td><td><p>70</p></td><td><p>0.000***</p></td></tr><tr><td colspan="6"><p>PD_B2: Beliefs about the importance of facilitators' teaching experience<sup>b</sup></p></td></tr><tr><td><p> Importance of that facilitators have their own teaching experience at school</p></td><td><p>5.68 (0.75)</p></td><td><p>202</p></td><td><p>5.71 (0.80)</p></td><td><p>70</p></td><td><p>0.768</p></td></tr><tr><td><p> Importance of that facilitators teach at school while working as facilitators</p></td><td><p>3.98 (1.45)</p></td><td><p>202</p></td><td><p>5.14 (1.12)</p></td><td><p>70</p></td><td><p>0.000***</p></td></tr><tr><td colspan="6"><p>PD_B3-PD_B9: Self-efficacy beliefs about...<sup>c</sup></p></td></tr><tr><td><p> PD_B3<sup>s</sup>: supporting teachers in task design for teaching with DMT</p></td><td><p>11.38 (4.90)</p></td><td><p>202</p></td><td><p>11.63 (4.91)</p></td><td><p>67</p></td><td><p>0.718</p></td></tr><tr><td><p> PD_B4<sup>s</sup>: supporting teachers in lesson design/implementation for teaching with DMT</p></td><td><p>11.34 (5.07)</p></td><td><p>202</p></td><td><p>12.50 (4.60)</p></td><td><p>65</p></td><td><p>0.102</p></td></tr><tr><td><p> PD_B5<sup>s</sup>: fostering teachers' situation-specific skills for teaching with DMT</p></td><td><p>11.86 (5.07)</p></td><td><p>202</p></td><td><p>10.30 (4.96)</p></td><td><p>64</p></td><td><p>0.032</p></td></tr><tr><td><p> PD_B6<sup>s</sup>: fostering teachers' self-efficacy beliefs for teaching with DMT</p></td><td><p>11.50 (4.75)</p></td><td><p>202</p></td><td><p>10.84 (4.43)</p></td><td><p>58</p></td><td><p>0.340</p></td></tr><tr><td><p> PD_B7<sup>s</sup>: fostering teachers' beliefs about teaching with DMT</p></td><td><p>12.40 (4.73)</p></td><td><p>202</p></td><td><p>11.34 (4.54)</p></td><td><p>58</p></td><td><p>0.128</p></td></tr><tr><td><p> PD_B8<sup>s</sup>: fostering teachers' cooperation</p></td><td><p>12.13 (5.05)</p></td><td><p>202</p></td><td><p>9.48 (5.08)</p></td><td><p>62</p></td><td><p>0.000***</p></td></tr><tr><td><p> PD_B9<sup>s</sup>: fostering teachers' PCK</p></td><td><p>12.45 (4.88)</p></td><td><p>202</p></td><td><p>10.67 (4.61)</p></td><td><p>60</p></td><td><p>0.013*</p></td></tr></tbody></table> </ephtml> </p> <p>Test type: <emph>t</emph> tests <emph>PCK</emph> pedagogical content knowledge *<emph>p</emph> < 0.05 ***<emph>p</emph> < 0.001 <sups>s</sups>Scale consisting of multiple items <sups>a</sups>Six-point Likert scale ranging from 1 = strongly disagree to 6 = strongly agree <sups>b</sups>Six-point Likert scale ranging from 1 = not important at all to 6 = very important <sups>c</sups>Each scale was rated from 0, 1,... to 20</p> <hd id="AN0175360864-20">General beliefs</hd> <p>German and Chinese facilitators strongly believe that cooperation with other facilitators is important (DE, 5.56; CN, 4.85). Furthermore, facilitators in both countries believe it is important for facilitators to have teaching experience at school (DE, 5.71; CN, 5.68). Additionally, facilitators in Germany strongly believe facilitators should still be teaching, a belief shared by the Chinese facilitators, albeit to a lower extent (DE, 5.14; CN, 3.98).</p> <hd id="AN0175360864-21">DMT-PD-related beliefs</hd> <p>Concerning facilitators' self-efficacy, it can be seen that the mean values vary between 9.48 and 12.50 (on a 0–20 scale), indicating that the facilitators have only moderately pronounced self-efficacy beliefs.[<reflink idref="bib6" id="ref68">6</reflink>] A difference between China and Germany was found with respect to facilitators' self-efficacy about fostering teacher cooperation in DMT-PD, with German facilitators being less confident in this aspect (DE, 9.48; CN, 12.13).</p> <hd id="AN0175360864-22">PD-level practices</hd> <p>This subsection refers to the results displayed in Tables 5, 6, and 7.</p> <p>Table 5 Results regarding general practices at the PD level</p> <p> <ephtml> <table frame="hsides" rules="groups"><thead><tr><th /><th colspan="2"><p>China</p></th><th colspan="2"><p>Germany</p></th><th><p><italic>p</italic> value</p></th></tr></thead><tbody><tr><td><p>PD_P1: Ways of professionalising oneself as a facilitator<sup>a</sup></p></td><td><p>Mean (SD)</p></td><td><p><italic>n</italic></p></td><td><p>Mean (SD)</p></td><td><p><italic>n</italic></p></td><td /></tr><tr><td><p> Training programs for facilitators</p></td><td><p>4.48 (1.35)</p></td><td><p>202</p></td><td><p>2.66 (1.36)</p></td><td><p>130</p></td><td><p>0.000***</p></td></tr><tr><td><p> Conference visits</p></td><td><p>5.36 (1.17)</p></td><td><p>202</p></td><td><p>2.73 (1.17)</p></td><td><p>129</p></td><td><p>0.000***</p></td></tr><tr><td><p> Self-study</p></td><td><p>3.23 (1.39)</p></td><td><p>202</p></td><td><p>4.79 (1.42)</p></td><td><p>129</p></td><td><p>0.000***</p></td></tr><tr><td><p>PD_P2: Literature read by facilitators</p></td><td><p>Fre. (%)</p></td><td><p><italic>n</italic> = 202</p></td><td><p>Fre. (%)</p></td><td><p><italic>n</italic> = 136</p></td><td /></tr><tr><td><p> None</p></td><td><p>0 (0.0%)</p></td><td rowspan="4" /><td><p>47 (34.6%)</p></td><td rowspan="4" /><td rowspan="4"><p>0.000***</p></td></tr><tr><td><p> Only research-oriented journals</p></td><td><p>0 (0.0%)</p></td><td><p>0 (0.0%)</p></td></tr><tr><td><p> Only practice-oriented journals</p></td><td><p>153 (75.7%)</p></td><td><p>82 (60.3%)</p></td></tr><tr><td><p> Both</p></td><td><p>49 (24.3%)</p></td><td><p>7 (5.1%)</p></td></tr><tr><td><p>PD_P3: Cooperation with other facilitators<sup>b</sup></p></td><td><p>Mean (SD)</p></td><td><p><italic>n</italic> = 202</p></td><td><p>Mean (SD)</p></td><td><p><italic>n</italic> = 69</p></td><td /></tr><tr><td><p> Conducting PD in a team</p></td><td><p>2.13 (0.79)</p></td><td /><td><p>2.51 (1.22)</p></td><td /><td><p>0.019*</p></td></tr><tr><td><p> Developing PD cooperatively</p></td><td><p>1.97 (0.80)</p></td><td /><td><p>2.64 (1.12)</p></td><td /><td><p>0.000***</p></td></tr><tr><td><p> Exchanging experiences/information</p></td><td><p>2.31 (0.78)</p></td><td /><td><p>2.90 (0.97)</p></td><td /><td><p>0.000***</p></td></tr><tr><td><p>PD_P4: Belonging to a Professional Learning Community of facilitators</p></td><td><p>Fre. (%)</p></td><td><p><italic>n</italic> = 202</p></td><td><p>Fre. (%)</p></td><td><p><italic>n</italic> = 72</p></td><td /></tr><tr><td><p> Yes</p></td><td><p>110 (54.5%)</p></td><td rowspan="2" /><td><p>46 (63.9%)</p></td><td rowspan="2" /><td rowspan="2"><p>0.165</p></td></tr><tr><td><p> No</p></td><td><p>92 (45.5%)</p></td><td><p>26 (36.1%)</p></td></tr><tr><td><p> If yes: How often does the Professional Learning Community meet?<sup>c</sup></p></td><td><p>Mean (SD) 2.72 (1.31)</p></td><td><p><italic>n</italic> = 110</p></td><td><p>Mean (SD) 2.42 (1.32)</p></td><td><p><italic>n</italic> = 45</p></td><td><p>0.204</p></td></tr></tbody></table> </ephtml> </p> <p>Test type: <emph>t</emph> tests for PD_P1 and PD_P4 (if yes, how often?), chi-square tests for PD_P2 and PD_P4 (yes or no), and Mann–Whitney <emph>U</emph> tests for PD_P3 *<emph>p</emph> < 0.05 ***<emph>p</emph> < 0.001 <sups>a</sups>Six-point Likert scale ranging from 1 = never to 6 = multiple times per month <sups>b</sups>Four-point Likert scale ranging from 1 = rarely (less than approx. 25% of my PD courses) to 4 = very often (more than 75% of my PD courses) <sups>c</sups>Five-point Likert-scale ranging from 1 = approx. 1–2 times per year to 5 = more than 2 times per month</p> <p>Table 6 Results regarding DMT practices at the PD level</p> <p> <ephtml> <table frame="hsides" rules="groups"><thead><tr><th /><th colspan="2"><p>China</p></th><th colspan="2"><p>Germany</p></th><th><p><italic>p</italic> value</p></th></tr></thead><tbody><tr><td><p>PD_P5: Types of DMT addressed<sup>a</sup></p></td><td><p>Fre. (%)</p></td><td><p><italic>n</italic> = 202</p></td><td><p>Fre. (%)</p></td><td><p><italic>n</italic> = 105</p></td><td /></tr><tr><td><p> Dynamic geometry software</p></td><td><p>187 (92.6%)</p></td><td rowspan="6" /><td><p>67 (63.8%)</p></td><td rowspan="6" /><td><p>0.000***</p></td></tr><tr><td><p> Function plotter</p></td><td><p>48 (23.8%)</p></td><td><p>26 (24.8%)</p></td><td><p>0.846</p></td></tr><tr><td><p> Spreadsheet</p></td><td><p>181 (89.6%)</p></td><td><p>49 (46.7%)</p></td><td><p>0.000***</p></td></tr><tr><td><p> Statistical tools</p></td><td><p>72 (35.6%)</p></td><td><p>5 (4.8%)</p></td><td><p>0.000***</p></td></tr><tr><td><p> Computer algebra system</p></td><td><p>19 (9.4%)</p></td><td><p>40 (38.1%)</p></td><td><p>0.000***</p></td></tr><tr><td><p> Graphing calculator</p></td><td><p>72 (35.6%)</p></td><td><p>27 (25.7%)</p></td><td><p>0.077</p></td></tr><tr><td><p>PD_P6: Mathematical content addressed<sup>a</sup></p></td><td><p>Fre. (%)</p></td><td><p><italic>n</italic> = 202</p></td><td><p>Fre. (%)</p></td><td><p><italic>n</italic> = 111</p></td><td /></tr><tr><td><p> Arithmetic</p></td><td><p>64 (31.7%)</p></td><td rowspan="7" /><td><p>38 (34.2%)</p></td><td rowspan="7" /><td><p>0.645</p></td></tr><tr><td><p> Functions</p></td><td><p>137 (67.8%)</p></td><td><p>77 (69.4%)</p></td><td><p>0.778</p></td></tr><tr><td><p> Algebra</p></td><td><p>71 (35.1%)</p></td><td><p>28 (25.2%)</p></td><td><p>0.071</p></td></tr><tr><td><p> Geometry</p></td><td><p>180 (89.1%)</p></td><td><p>82 (73.9%)</p></td><td><p>0.000***</p></td></tr><tr><td><p> Probability and Statistics</p></td><td><p>119 (58.9%)</p></td><td><p>55 (49.5%)</p></td><td><p>0.111</p></td></tr><tr><td><p> Calculus</p></td><td><p>19 (9.4%)</p></td><td><p>52 (46.8%)</p></td><td><p>0.000***</p></td></tr><tr><td><p> Analytic geometry/linear algebra</p></td><td><p>42 (20.8%)</p></td><td><p>34 (30.6%)</p></td><td><p>0.052</p></td></tr><tr><td><p>PD_P7: Sources of DMT-PD material<sup>b</sup></p></td><td><p>Mean (SD)</p></td><td><p><italic>n</italic></p></td><td><p>Mean (SD)</p></td><td><p><italic>n</italic></p></td><td /></tr><tr><td><p> Using ready-made PD materials with no/minor adaptations</p></td><td><p>2.27 (0.71)</p></td><td><p>202</p></td><td><p>1.61 (0.78)</p></td><td><p>87</p></td><td><p>0.000***</p></td></tr><tr><td><p> Heavily adapting ready-made PD materials</p></td><td><p>2.59 (0.77)</p></td><td><p>202</p></td><td><p>2.28 (0.77)</p></td><td><p>87</p></td><td><p>0.003**</p></td></tr><tr><td><p> Self-development of PD-materials</p></td><td><p>2.30 (0.86)</p></td><td><p>202</p></td><td><p>2.77 (0.99)</p></td><td><p>90</p></td><td><p>0.000***</p></td></tr><tr><td><p>PD_P8: Determinants of DMT-PD content<sup>b</sup></p></td><td><p>Mean (SD)</p></td><td><p><italic>n</italic></p></td><td><p>Mean (SD)</p></td><td><p><italic>n</italic></p></td><td /></tr><tr><td><p> Specific requirements from [DE: school administration] [CN: TRO]</p></td><td><p>2.41 (0.83)</p></td><td><p>202</p></td><td><p>1.79 (1.05)</p></td><td><p>94</p></td><td><p>0.000***</p></td></tr><tr><td><p> Specific requests from schools</p></td><td><p>2.30 (0.77)</p></td><td><p>202</p></td><td><p>2.01 (0.94)</p></td><td><p>91</p></td><td><p>0.006**</p></td></tr><tr><td><p> Content that interests me the most</p></td><td><p>2.84 (0.84)</p></td><td><p>202</p></td><td><p>2.29 (0.94)</p></td><td><p>87</p></td><td><p>0.000***</p></td></tr><tr><td><p> Content most relevant for teachers</p></td><td><p>2.84 (0.78)</p></td><td><p>202</p></td><td><p>3.04 (0.96)</p></td><td><p>89</p></td><td><p>0.007**</p></td></tr></tbody></table> </ephtml> </p> <p>Test type: chi-square tests for PD_P5 and PD_P6 and Mann–Whitney <emph>U</emph> tests for PD_P7 and PD_P8 **<emph>p</emph> < 0.01 ***<emph>p</emph> < 0.001 <sups>a</sups>Multiple choice item <sups>b</sups>Four-point Likert scale ranging from 1 = rarely (less than approx. 25% of my PD courses) to 4 = very often (more than 75% of my PD courses)</p> <p>Table 7 Results regarding DMT practices at the PD level</p> <p> <ephtml> <table frame="hsides" rules="groups"><thead><tr><th /><th colspan="2"><p>China</p></th><th colspan="2"><p>Germany</p></th><th><p><italic>p</italic> value</p></th></tr></thead><tbody><tr><td><p>PD_P9: Important facets of DMT-PD<sup>a</sup></p></td><td><p>Mean (SD)</p></td><td rowspan="10"><p><italic>n</italic> = 202</p></td><td><p>Mean (SD)</p></td><td rowspan="10"><p><italic>n</italic> = 89</p></td><td /></tr><tr><td><p> Technical competence for DMT</p></td><td><p>1.56 (0.73)</p></td><td><p>0.93 (0.70)</p></td><td><p>0.000***</p></td></tr><tr><td><p> Mathematical content knowledge</p></td><td><p>0.87 (0.93)</p></td><td><p>0.73 (0.90)</p></td><td><p>0.228</p></td></tr><tr><td><p> Establishing teacher cooperation</p></td><td><p>1.08 (0.87)</p></td><td><p>0.83 (0.87)</p></td><td><p>0.026*</p></td></tr><tr><td><p> PCK for task design with DMT</p></td><td><p>1.06 (0.76)</p></td><td><p>1.26 (0.81)</p></td><td><p>0.034*</p></td></tr><tr><td><p> PCK to design and implement lessons with DMT</p></td><td><p>1.06 (0.69)</p></td><td><p>1.31 (0.79)</p></td><td><p>0.004**</p></td></tr><tr><td><p> Fostering self-efficacy for teaching with DMT</p></td><td><p>0.95 (0.78)</p></td><td><p>1.01 (0.82)</p></td><td><p>0.523</p></td></tr><tr><td><p> Fostering positive beliefs about teaching with DMT</p></td><td><p>0.78 (0.79)</p></td><td><p>0.87 (0.77)</p></td><td><p>0.340</p></td></tr><tr><td><p> Supporting teachers to perceive and interpret learning processes when teaching with DMT</p></td><td><p>0.82 (0.74)</p></td><td><p>0.87 (0.80)</p></td><td><p>0.686</p></td></tr><tr><td><p> Providing good materials for teaching with DMT</p></td><td><p>0.80 (0.77)</p></td><td><p>0.94 (0.80)</p></td><td><p>0.162</p></td></tr><tr><td><p>PD_P10: Design principles of DMT-PD<sup>b</sup></p></td><td><p>Mean (SD)</p></td><td rowspan="7"><p><italic>n</italic> = 202</p></td><td><p>Mean (SD)</p></td><td rowspan="7"><p><italic>n</italic> = 76</p></td><td /></tr><tr><td><p> Competence orientation</p></td><td><p>2.00 (1.26)</p></td><td><p>1.78 (1.27)</p></td><td><p>0.163</p></td></tr><tr><td><p> Participant orientation</p></td><td><p>1.33 (1.26)</p></td><td><p>1.51 (1.18)</p></td><td><p>0.279</p></td></tr><tr><td><p> Case-relatedness</p></td><td><p>1.21 (1.03)</p></td><td><p>0.58 (0.97)</p></td><td><p>0.000***</p></td></tr><tr><td><p> Using various instruction formats</p></td><td><p>0.57 (0.83)</p></td><td><p>0.89 (1.09)</p></td><td><p>0.035*</p></td></tr><tr><td><p> Stimulating cooperation</p></td><td><p>0.46 (0.78)</p></td><td><p>0.58 (0.88)</p></td><td><p>0.385</p></td></tr><tr><td><p> Fostering self-reflection</p></td><td><p>0.40 (0.66)</p></td><td><p>0.55 (0.85)</p></td><td><p>0.300</p></td></tr></tbody></table> </ephtml> </p> <p>Test type: Mann–Whitney <emph>U</emph> tests <emph>PCK</emph> pedagogical content knowledge *<emph>p</emph> < 0.05 **<emph>p</emph> < 0.01 ***<emph>p</emph> < 0.001 <sups>a</sups>2 = particularly relevant, 1 = relevant, and 0 = not picked <sups>b</sups>3 = first place, 2 = second place, 1 = third place, and 0 = not picked</p> <hd id="AN0175360864-23">General practices</hd> <p>Chinese facilitators frequently attend conferences (DE, 2.73; CN, 5.36) and participate in training programs (DE, 2.66; CN, 4.48), while German facilitators professionalise themselves more through self-study (DE, 4.79; CN, 3.23). Furthermore, all Chinese facilitators report that they read journals related to mathematics education while 34.6% of the German facilitators do not read any such journals. In contrast to facilitators in Germany, a substantial portion of the Chinese facilitators also read research-oriented journals (DE, 5.1%; CN, 24.3%). Concerning cooperation, we found that Chinese and German facilitators engaged in various forms of cooperation in approximately 50% of the PD courses. However, German facilitators cooperate more intensively than Chinese facilitators (DE, >2.51; CN, <2.31).</p> <hd id="AN0175360864-24">DMT-PD-related practices</hd> <p>A main difference was that Chinese facilitators prefer to use ready-made PD materials and either use them unchanged or adapt these materials. In contrast, German facilitators develop PD materials on their own more often than Chinese facilitators (DE, 2.77; CN, 2.30) and report that they rarely use ready-made materials unchanged. Both Chinese and German facilitators most often choose the content for the DMT-PD based on what interests them most (DE, 2.29; CN, 2.84) or what they think is most relevant for teachers (DE, 3.04; CN, 2.84). Another difference is that Chinese facilitators prioritise conveying technical competence to operate DMT, establishing teacher cooperation, and conveying PCK. In contrast, German facilitators prioritise PCK while fostering teachers' technical competence is considered much less important. Finally, by a large margin, competence orientation is the most important aspect for both facilitators in China and Germany (DE, 1.78; CN, 2.00), followed by participant orientation (DE, 1.51; CN, 1.33).[<reflink idref="bib7" id="ref69">7</reflink>]</p> <hd id="AN0175360864-25">Discussion and conclusion</hd> <p></p> <hd id="AN0175360864-26">Commonalities</hd> <p>Despite the differences in the educational and cultural context (see Section 3), we found some major commonalities between Chinese and German facilitators. <emph>Facilitators' positive beliefs about DMT</emph> in both countries are an encouraging finding since it seems reasonable to assume that positive facilitator beliefs are a prerequisite for the development of positive beliefs by teachers in DMT-PD. The positive beliefs might be an international phenomenon since many countries nowadays value technological progress in education and emphasise the integration of ICT into mathematics classrooms.</p> <p>A critical finding pertains to the <emph>limited self-efficacy of facilitators</emph>, which is particularly worrying in light of the significant experiences of the facilitators in this study. It might be grounded in facilitators' moderate levels of knowledge and competence in using technology for mathematics teaching (Huang et al., [<reflink idref="bib17" id="ref70">17</reflink>]). Hence, the results clearly support the hypothesis that not only teachers but also facilitators require PD to enhance their self-efficacy (Weißenrieder et al., [<reflink idref="bib51" id="ref71">51</reflink>]). In particular, policymakers and researchers need to put more attention on fostering facilitators' self-efficacy and recruiting/identifying facilitators that are proficient in teaching with DMT which in turn supports conducting PD in this area. Additionally, the fact that most Chinese facilitators no longer teach at school may hinder the development of their self-efficacy, as building confidence in facilitators is likely to be supported by incorporating "the past experiences of teaching mathematics to students into the new and evolving experiences of facilitating", which is why facilitators' PD "should not be limited to experiencing the PD core practices, but should also include enacting reform based instruction in actual classrooms" (Valoyes-Chávez & Felmer, [<reflink idref="bib49" id="ref72">49</reflink>], p. 1107).</p> <p>Furthermore, Chinese and German facilitators agree about important <emph>design principles for DMT-PD</emph>, and both value competence orientation the most, followed by participant orientation. Concerning Germany, this finding quantitatively substantiates similar findings reported in the smaller-scale study by Roesken-Winter et al. ([<reflink idref="bib39" id="ref73">39</reflink>]).</p> <p>Another major commonality is that the <emph>determination of PD topics</emph> is based on the perceived relevance of topics for teachers' and on facilitators' interests. This shows, on one hand, that facilitators are willing to address the important design principle of participant orientation but that, on the other hand, affective components are relevant. This might pose a barrier to integrating emerging DMT for facilitators who no longer teach (as in China) as it may be challenging to develop interest in and enthusiasm for teaching with an emerging DMT if they are no longer teaching.</p> <hd id="AN0175360864-27">Differences</hd> <p>First, we found that Chinese facilitators used highly diverse <emph>methods of professionalisation</emph> (consistent with the finding of Huang et al. ([<reflink idref="bib17" id="ref74">17</reflink>])) which contrasts German facilitators. This is likely related to the fact that facilitators in China work full-time and thus have more time to engage in professionalisation activities than German facilitators (who work only part-time). Moreover, the hierarchical system in the Chinese education system gives facilitators the possibility to be promoted, for which professionalisation activities can be helpful. From a cultural point of view, the high value of education and lifelong learning in China and the aspect of hierarchy may also contribute to Chinese facilitators pursuing further professionalisation. In contrast, in Germany, there is no systematic ongoing PD for teachers, let alone facilitators, and only a marginal opportunity to be promoted.</p> <p>Another difference that seems to be linked to differences in the educational and cultural context comprises the <emph>adaptation of ready-made PD-materials</emph>: Chinese facilitators use more ready-made materials and adapt them less frequently than their German counterparts. One reason may be that Chinese facilitators more frequently attend PD programs (see above) and, therefore, have better access and training to use ready-made PD materials. However, values of hierarchy and authority may also support that ready-made PD materials are used with little adaptation since these materials are often developed by a higher—and hence more expert—authority. Also, low self-efficacy beliefs (see Section 7.1) might play a role for facilitators using ready-made PD materials. In contrast, the values of individualization, creativity, and autonomy of Western cultures may support that German facilitators are more prone to adaptation of materials (despite their similarly low self-efficacy). In a certain way, our observation also seems to parallel and carry forward previous findings on the classroom level where Chinese teachers were found, for example, to more closely follow the textbook while Western teachers base their teaching decisions less on pre-structured materials (Leung, [<reflink idref="bib23" id="ref75">23</reflink>]).</p> <p>Concerning <emph>cooperation</emph>, the differences were more nuanced. Substantial cooperation among facilitators was realised in both countries, and Chinese and German facilitators regarded cooperation as an important aspect. This highlights the need to focus on this aspect more strongly, as research has hitherto focused mainly on <emph>teacher</emph> cooperation and how facilitators can foster it (e.g., Griese et al., [<reflink idref="bib12" id="ref76">12</reflink>]; Pöhler, [<reflink idref="bib36" id="ref77">36</reflink>]). The low cooperation between Chinese facilitators found in this study may be grounded in the lack of proper coordination and collaboration among teaching research offices at different levels in China, as reported by Wang and Hu ([<reflink idref="bib50" id="ref78">50</reflink>]) and Fan et al. ([<reflink idref="bib10" id="ref79">10</reflink>]). In addition, it might be related to the hierarchical system as it leads to competition and conflicts of interest among teachers or facilitators, "which negates the development advantages brought about by cooperation" (Liu & Xiu, [<reflink idref="bib29" id="ref80">29</reflink>]). The reason that Chinese facilitators feel more confident in establishing teacher cooperation in PD may be that cooperation among teachers is already institutionalised at the school level in China, and teacher PD in China is usually conducted at schools. In contrast, similar structures are missing in Germany, and PD is often conducted across schools where participating teachers come from different schools.</p> <p>Another major difference pertains to <emph>when and how to use DMT</emph> in classroom teaching. Facilitators in China held much stronger beliefs that DMT should only be used by <emph>students</emph> after the mathematics has been understood without DMT ("whitebox/blackbox principle"; Buchberger, [<reflink idref="bib5" id="ref81">5</reflink>]), and thus they do not fully exploit the potential of DMT. This might reflect the stronger emphasis of Chinese education on basic skills and may also be a consequence of DMT not being allowed in high-stake exams in China (besides Shanghai and Hong Kong) (Li et al., [<reflink idref="bib25" id="ref82">25</reflink>]). At first, this finding seems contradictory to the finding that Chinese facilitators agree that DMTs are suitable for introducing new topics. But this can be explained by the fact that facilitators oppose <emph>students'</emph> use of technology before mastering the mathematics by hand—which does not mean that <emph>teachers</emph> cannot use technology. Hence, the results indicate that Chinese facilitators value DMT when introducing new content in a <emph>teacher-centred</emph> way, for example, to show how the graph of a function changes if one varies the parameters. Such teacher-centred use of DMT—which was also revealed in Fan et al. ([<reflink idref="bib8" id="ref83">8</reflink>], [<reflink idref="bib7" id="ref84">7</reflink>])—may also be a reflection of the Chinese heritage culture in which the role model of the teacher is highlighted and which often "results in the typical 'direct teaching to the whole-class'" (Leung, [<reflink idref="bib22" id="ref85">22</reflink>], p. 44).</p> <p>Moreover, concerning design principles for DMT-PD, Chinese facilitators appreciate <emph>case</emph><bold>-</bold><emph>relatedness</emph> much more than German facilitators. The low importance of case-relatedness for German facilitators has also been reported by Roesken-Winter et al. ([<reflink idref="bib39" id="ref86">39</reflink>]) and might be linked to the low level of professionalisation activities, which may support that German facilitators orient themselves less on state-of-the-art scientific evidence, which highlights case-relatedness as a central design principle (Barzel & Biehler, [<reflink idref="bib3" id="ref87">3</reflink>]). In contrast, China has established <emph>systematic</emph> exemplary lesson development as a model of in-service teacher education (Huang & Bao, [<reflink idref="bib15" id="ref88">15</reflink>]) and organised teaching contests at different levels (Li & Li, [<reflink idref="bib26" id="ref89">26</reflink>]), in which abundant teaching cases were generated as materials that can be used by facilitators in designing PD.</p> <p>Finally, one of the most interesting findings was a different <emph>priority of competence facets in DMT-PD</emph>. Chinese facilitators regard technical competence as the most important aspect that must be addressed in DMT-PD, followed by establishing teacher cooperation and conveying PCK. In contrast, German facilitators focus more on developing teachers' PCK and fostering teacher self-efficacy. One possible explanation could be related to the product-process dichotomy (see Section 3.3): Chinese education emphasises the product, i.e., the mathematics content and the <emph>procedures or skills</emph> in dealing with the content. Similarly, facilitators seem to emphasise the <emph>procedures or skills</emph> in dealing with the DMT.</p> <hd id="AN0175360864-28">Limitations</hd> <p>This study is not based on a representative sample. However, considering the fact that there are far fewer facilitators than students or teachers, our sample size (<emph>n</emph> = 340) is larger than that of most previous studies on mathematics facilitators. Furthermore, our findings may not be generalizable to other regions and countries. Another limitation is that, due to the large sample size, the data collection in this study relied on quantitative questionnaires, and the questionnaire data were not triangulated. Furthermore, we did not capture all aspects of facilitators' practices and beliefs included in the theoretical framework (see Fig. 1), and we encourage future complementary research to address this issue. Finally, cross-cultural comparative studies always carry the risk that misunderstandings may arise from translations and different cultural contexts. However, the questionnaires underwent a translation, adaptation, and validation process to ensure the equivalence of terms and comparability of measures used.</p> <hd id="AN0175360864-29">Conclusion</hd> <p>Overall, our study provides some pioneering insights into facilitators' practices and beliefs, with a particular focus on DMT. We found four major commonalities and six differences that can (partly) be explained by referring to differences in the educational and cultural context. Hence, our study indicates that educational and cultural contexts have a profound impact on practices and beliefs of facilitators. In addition, the question arises: which consequences may be drawn based on this national comparison to improve facilitators' PD? Kaiser and Blömeke ([<reflink idref="bib18" id="ref90">18</reflink>]) caution that because of cultural dependency, it is not appropriate simply to take isolated measures from another educational system; however, it is possible to complement and enrich practices and views on education.</p> <p>Of course, we can only briefly indicate some possible complements and enrichments. Apparently, we face a similar challenge concerning facilitators' low self-efficacy, and focusing more on supporting facilitators' self-efficacy, therefore, seems important in both countries. This may, in turn, promote more effective teacher PD concerning digital mathematical tools, which often fail to achieve the desired outcomes (Thurm & Barzel, [<reflink idref="bib44" id="ref91">44</reflink>]). Yet the question arises of how we can approach this challenge—with attention to the cultural differences—especially since culture may affect sources of self-efficacy (Oettingen, [<reflink idref="bib34" id="ref92">34</reflink>]). Furthermore, China (or countries with a similar educational and cultural context) may want to support more critical thinking and autonomy for adapting ready-made PD materials, as ready-made PD materials may need to be tailored to a specific target group (participant orientation). Germany (or countries with a similar educational and cultural context) may want to learn from the teacher and facilitator promotion system and think about how to make professionalisation more an integral part of facilitators' practices. Furthermore, both countries may need to reflect on the question and consequences of how much a facilitator should teach at school. The results of our study indicate arguments against and in favour of it. Yet, besides the different arguments discussed in this paper (see Sections 7.1 and 7.2), aspects of facilitators' "identity" (Karsenty et al., [<reflink idref="bib20" id="ref93">20</reflink>]) may also need to be considered concerning this question.</p> <p>Finally, on a theoretical level, our study contributes by adapting the ROGI model (Karsenty et al., [<reflink idref="bib20" id="ref94">20</reflink>]) and applying it to the design of a quantitative questionnaire, which may help frame future research on facilitators' practices and beliefs.</p> <hd id="AN0175360864-30">Author contributions</hd> <p>DT initiated the project. All authors participated in designing the study. Data analysis was conducted by NL, SL, and DT. All authors participated in writing and revising the manuscript and approved the final manuscript. LF led the data collection and SL coordinated the data analysis in China.</p> <hd id="AN0175360864-31">Funding</hd> <p>The research conducted in China was supported by three research grants: Science and Technology Commission of Shanghai Municipality (award no: 22DZ2229014), East China Normal University (award no: 2019ECNU-XF2H004), Asian Centre for Mathematics Education (award no: 92900-120215-10514).</p> <hd id="AN0175360864-32">Data Availability</hd> <p>Upon request.</p> <hd id="AN0175360864-33">Declarations</hd> <p></p> <hd id="AN0175360864-34">Competing interests</hd> <p>The authors declare no competing interests.</p> <hd id="AN0175360864-35">Supplementary information</hd> <p>Graph: (DOCX 38 kb)</p> <hd id="AN0175360864-36">Publisher's note</hd> <p>Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p> <ref id="AN0175360864-37"> <title> References </title> <blist> <bibl id="bib1" idref="ref11" type="bt">1</bibl> <bibtext> Baistow K. 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Asia Pacific Education Review. 2020; 21; 2: 311-323. 10.1007/s12564-020-09626-0</bibtext> </blist> </ref> <ref id="AN0175360864-38"> <title> Footnotes </title> <blist> <bibtext> We note that these aspects of competence are not exhaustive; however, they cover important facets that have consistently been identified and described in the literature.</bibtext> </blist> <blist> <bibtext> Self-efficacy beliefs are "beliefs in one's capabilities to organize and execute the courses of action required to produce given attainments" (Bandura, [2], p. 3).</bibtext> </blist> <blist> <bibtext> Facilitators are referred to in the literature as leaders, PD providers, multipliers, and other terms. Facilitators are a specific and important subgroup of "Mathematics Teacher Educators", a term that commonly refers to both individuals who educate prospective teachers and those who educate practising teachers (Karsenty et al., [20]).</bibtext> </blist> <blist> <bibtext> Culture can be defined as the "shared motives, values, beliefs, identities, and interpretations or meanings of significant events that result from common experiences of members of collectives that are transmitted across generations" (House et al.[14], p. 15).</bibtext> </blist> <blist> <bibtext> More detailed information regarding the characteristics of facilitators can be found in the Online Resource. For the Chinese questionnaire, almost all items (except for age) were compulsory, and the questionnaire could only be submitted after answering all the questions. For the German questionnaire, facilitators could drop out at any point.</bibtext> </blist> <blist> <bibtext> For fostering teachers' self-efficacy beliefs for teaching with DMT (PD_B6), we found a small significant difference (<emph>p</emph> = 0.034) between the East China region (12.03) and other regions of China (10.56), which was also the case for fostering teachers' PCK (PD_B9, <emph>p</emph> = 0.050; CN-East, 12.99; CN-other, 11.50).</bibtext> </blist> <blist> <bibtext> For competence orientation (in PD_P10), we found a small significant difference (<emph>p</emph> = 0.031) between the East China region (1.84) and other regions of China (2.29), which was also the case for case relatedness (in PD_P10, <emph>p</emph> = 0.050; CN-East, 1.32; CN-other, 1.03).</bibtext> </blist> </ref> <aug> <p>By Daniel Thurm; Shuhui Li; Bärbel Barzel; Lianghuo Fan and Na Li</p> <p>Reported by Author; Author; Author; Author; Author</p> </aug> <nolink nlid="nl1" bibid="bib20" firstref="ref1"></nolink> <nolink nlid="nl2" bibid="bib46" firstref="ref2"></nolink> <nolink nlid="nl3" bibid="bib47" firstref="ref3"></nolink> <nolink nlid="nl4" bibid="bib40" firstref="ref5"></nolink> <nolink nlid="nl5" bibid="bib33" firstref="ref6"></nolink> <nolink nlid="nl6" bibid="bib11" firstref="ref7"></nolink> <nolink nlid="nl7" bibid="bib18" firstref="ref8"></nolink> <nolink nlid="nl8" bibid="bib41" firstref="ref9"></nolink> <nolink nlid="nl9" bibid="bib53" firstref="ref10"></nolink> <nolink nlid="nl10" bibid="bib13" firstref="ref12"></nolink> <nolink nlid="nl11" bibid="bib45" firstref="ref13"></nolink> <nolink nlid="nl12" bibid="bib44" firstref="ref20"></nolink> <nolink nlid="nl13" bibid="bib27" firstref="ref21"></nolink> <nolink nlid="nl14" bibid="bib48" firstref="ref22"></nolink> <nolink nlid="nl15" bibid="bib21" firstref="ref24"></nolink> <nolink nlid="nl16" bibid="bib37" firstref="ref26"></nolink> <nolink nlid="nl17" bibid="bib39" firstref="ref27"></nolink> <nolink nlid="nl18" bibid="bib30" firstref="ref29"></nolink> <nolink nlid="nl19" bibid="bib42" firstref="ref37"></nolink> <nolink nlid="nl20" bibid="bib51" firstref="ref40"></nolink> <nolink nlid="nl21" bibid="bib17" firstref="ref41"></nolink> <nolink nlid="nl22" bibid="bib31" firstref="ref42"></nolink> <nolink nlid="nl23" bibid="bib43" firstref="ref44"></nolink> <nolink nlid="nl24" bibid="bib38" firstref="ref47"></nolink> <nolink nlid="nl25" bibid="bib35" firstref="ref50"></nolink> <nolink nlid="nl26" bibid="bib24" firstref="ref51"></nolink> <nolink nlid="nl27" bibid="bib52" firstref="ref54"></nolink> <nolink nlid="nl28" bibid="bib54" firstref="ref56"></nolink> <nolink nlid="nl29" bibid="bib16" firstref="ref59"></nolink> <nolink nlid="nl30" bibid="bib32" firstref="ref60"></nolink> <nolink nlid="nl31" bibid="bib28" firstref="ref61"></nolink> <nolink nlid="nl32" bibid="bib22" firstref="ref63"></nolink> <nolink nlid="nl33" bibid="bib19" firstref="ref66"></nolink> <nolink nlid="nl34" bibid="bib49" firstref="ref72"></nolink> <nolink nlid="nl35" bibid="bib23" firstref="ref75"></nolink> <nolink nlid="nl36" bibid="bib12" firstref="ref76"></nolink> <nolink nlid="nl37" bibid="bib36" firstref="ref77"></nolink> <nolink nlid="nl38" bibid="bib50" firstref="ref78"></nolink> <nolink nlid="nl39" bibid="bib10" firstref="ref79"></nolink> <nolink nlid="nl40" bibid="bib29" firstref="ref80"></nolink> <nolink nlid="nl41" bibid="bib25" firstref="ref82"></nolink> <nolink nlid="nl42" bibid="bib15" firstref="ref88"></nolink> <nolink nlid="nl43" bibid="bib26" firstref="ref89"></nolink> <nolink nlid="nl44" bibid="bib34" firstref="ref92"></nolink>
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Items – Name: Title
  Label: Title
  Group: Ti
  Data: Professional Development for Teaching Mathematics with Technology: A Comparative Study of Facilitators' Beliefs and Practices in China and Germany
– Name: Language
  Label: Language
  Group: Lang
  Data: English
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Daniel+Thurm%22">Daniel Thurm</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0001-6531-5271">0000-0001-6531-5271</externalLink>)<br /><searchLink fieldCode="AR" term="%22Shuhui+Li%22">Shuhui Li</searchLink> (ORCID <externalLink term="http://orcid.org/0000-0002-5231-7785">0000-0002-5231-7785</externalLink>)<br /><searchLink fieldCode="AR" term="%22Bärbel+Barzel%22">Bärbel Barzel</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0001-6249-0891">0000-0001-6249-0891</externalLink>)<br /><searchLink fieldCode="AR" term="%22Lianghuo+Fan%22">Lianghuo Fan</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0002-4680-6937">0000-0002-4680-6937</externalLink>)<br /><searchLink fieldCode="AR" term="%22Na+Li%22">Na Li</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0001-7718-4184">0000-0001-7718-4184</externalLink>)
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  Label: Source
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  Data: <searchLink fieldCode="SO" term="%22Educational+Studies+in+Mathematics%22"><i>Educational Studies in Mathematics</i></searchLink>. 2024 115(2):247-269.
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  Data: Springer. Available from: Springer Nature. One New York Plaza, Suite 4600, New York, NY 10004. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-460-1700; e-mail: customerservice@springernature.com; Web site: https://link.springer.com/
– Name: PeerReviewed
  Label: Peer Reviewed
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  Data: Y
– Name: Pages
  Label: Page Count
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  Data: 23
– Name: DatePubCY
  Label: Publication Date
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  Data: 2024
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  Data: Journal Articles<br />Reports - Research
– Name: Subject
  Label: Descriptors
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Facilitators+%28Individuals%29%22">Facilitators (Individuals)</searchLink><br /><searchLink fieldCode="DE" term="%22Faculty+Development%22">Faculty Development</searchLink><br /><searchLink fieldCode="DE" term="%22Cultural+Differences%22">Cultural Differences</searchLink><br /><searchLink fieldCode="DE" term="%22Beliefs%22">Beliefs</searchLink><br /><searchLink fieldCode="DE" term="%22Educational+Practices%22">Educational Practices</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Instruction%22">Mathematics Instruction</searchLink><br /><searchLink fieldCode="DE" term="%22Educational+Technology%22">Educational Technology</searchLink><br /><searchLink fieldCode="DE" term="%22Cooperation%22">Cooperation</searchLink><br /><searchLink fieldCode="DE" term="%22Instructional+Materials%22">Instructional Materials</searchLink><br /><searchLink fieldCode="DE" term="%22Professional+Identity%22">Professional Identity</searchLink><br /><searchLink fieldCode="DE" term="%22Technological+Literacy%22">Technological Literacy</searchLink><br /><searchLink fieldCode="DE" term="%22Pedagogical+Content+Knowledge%22">Pedagogical Content Knowledge</searchLink><br /><searchLink fieldCode="DE" term="%22Self+Efficacy%22">Self Efficacy</searchLink><br /><searchLink fieldCode="DE" term="%22Foreign+Countries%22">Foreign Countries</searchLink>
– Name: Subject
  Label: Geographic Terms
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22China%22">China</searchLink><br /><searchLink fieldCode="DE" term="%22Germany%22">Germany</searchLink>
– Name: DOI
  Label: DOI
  Group: ID
  Data: 10.1007/s10649-023-10284-3
– Name: ISSN
  Label: ISSN
  Group: ISSN
  Data: 0013-1954<br />1573-0816
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Facilitators, i.e., individuals who lead professional development (PD) programs, play a crucial role in providing high-quality PD to teachers, which is particularly relevant in the context of teaching mathematics with technology given the ubiquitous calls to exploit the potential of digital mathematical tools (DMT). However, quantitative research investigating facilitators' beliefs and practices remains scarce, particularly research comparing countries. In this cross-national study conducted in China and Germany, we developed an online questionnaire and surveyed n = 340 facilitators to provide a comprehensive quantitative picture of facilitators' beliefs and practices concerning PD for teaching mathematics with DMT. The results highlight various commonalities and differences between facilitators in China and Germany. We reveal significant differences concerning cooperation among facilitators, adaptation of PD materials, how facilitators professionalise themselves, and beliefs about when and how to use DMT. Furthermore, Chinese facilitators emphasise technical competence more strongly, while German facilitators focus more on developing teachers' pedagogical content knowledge. A critical commonality was that facilitators' self-efficacy concerning teaching with DMT and their self-efficacy for conducting PD for teaching mathematics with DMT was low. We discuss how the results can be linked to differences in the educational and cultural context and outline possible complements and enrichments for both countries' educational systems.
– Name: AbstractInfo
  Label: Abstractor
  Group: Ab
  Data: As Provided
– Name: DateEntry
  Label: Entry Date
  Group: Date
  Data: 2024
– Name: AN
  Label: Accession Number
  Group: ID
  Data: EJ1411615
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1007/s10649-023-10284-3
    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 23
        StartPage: 247
    Subjects:
      – SubjectFull: Facilitators (Individuals)
        Type: general
      – SubjectFull: Faculty Development
        Type: general
      – SubjectFull: Cultural Differences
        Type: general
      – SubjectFull: Beliefs
        Type: general
      – SubjectFull: Educational Practices
        Type: general
      – SubjectFull: Mathematics Instruction
        Type: general
      – SubjectFull: Educational Technology
        Type: general
      – SubjectFull: Cooperation
        Type: general
      – SubjectFull: Instructional Materials
        Type: general
      – SubjectFull: Professional Identity
        Type: general
      – SubjectFull: Technological Literacy
        Type: general
      – SubjectFull: Pedagogical Content Knowledge
        Type: general
      – SubjectFull: Self Efficacy
        Type: general
      – SubjectFull: Foreign Countries
        Type: general
      – SubjectFull: China
        Type: general
      – SubjectFull: Germany
        Type: general
    Titles:
      – TitleFull: Professional Development for Teaching Mathematics with Technology: A Comparative Study of Facilitators' Beliefs and Practices in China and Germany
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Daniel Thurm
      – PersonEntity:
          Name:
            NameFull: Shuhui Li
      – PersonEntity:
          Name:
            NameFull: Bärbel Barzel
      – PersonEntity:
          Name:
            NameFull: Lianghuo Fan
      – PersonEntity:
          Name:
            NameFull: Na Li
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      – BibEntity:
          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2024
          Identifiers:
            – Type: issn-print
              Value: 0013-1954
            – Type: issn-electronic
              Value: 1573-0816
          Numbering:
            – Type: volume
              Value: 115
            – Type: issue
              Value: 2
          Titles:
            – TitleFull: Educational Studies in Mathematics
              Type: main
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