View in EDS HTML Full Text PDF Full Text

An Investigation into whether Student Use of Graphics Calculators Matches Their Teacher's Expectations

Saved in:
Bibliographic Details
Title: An Investigation into whether Student Use of Graphics Calculators Matches Their Teacher's Expectations
Language: English
Authors: Graham, E., Headlam, C., Sharp, J., Watson, B.
Source: International Journal of Mathematical Education in Science and Technology. Mar 2008 39(2):179-196.
Availability: Taylor & Francis, Ltd. 325 Chestnut Street Suite 800, Philadelphia, PA 19106. Tel: 800-354-1420; Fax: 215-625-2940; Web site: http://www.tandf.co.uk/journals/default.html
Peer Reviewed: Y
Page Count: 18
Publication Date: 2008
Document Type: Journal Articles
Reports - Research
Education Level: Grade 8
Secondary Education
Descriptors: Graphing Calculators, Mathematics Education, Technology Uses in Education, Interviews, Classroom Communication, Grade 8, Educational Research, Algebra, Foreign Countries, Teacher Expectations of Students, Feedback (Response), Secondary School Mathematics
Geographic Terms: United Kingdom (England), United Kingdom (Wales)
DOI: 10.1080/00207390701607307
ISSN: 0020-739X
Abstract: This research examines students' use of graphics calculators and investigates the extent to which the students' use meets their teachers aim when using graphics calculators in the classroom. The teacher's use of her graphics calculator was analysed over a week using Key Record software. The teacher was questioned about her aims and expectations for the students when using a graphics calculator. As a result an interview schedule for students was constructed in order to determine whether the teacher's aims had been met. It was found that in general all of the teachers' aims were met to some extent by most of the students. (Contains 8 figures and 1 table.)
Abstractor: Author
Number of References: 24
Entry Date: 2008
Accession Number: EJ788446
Database: ERIC
Full text is not displayed to guests.
FullText Links:
  – Type: pdflink
    Url: https://content.ebscohost.com/cds/retrieve?content=AQICAHj0k_4E0hTGH8RJwT4gCJyBsGNe_WN95AvKlDbXJGqwxwHjWmHqvVkRvFzdNXIezrwnAAAA4jCB3wYJKoZIhvcNAQcGoIHRMIHOAgEAMIHIBgkqhkiG9w0BBwEwHgYJYIZIAWUDBAEuMBEEDGY_auBpgTqS3Ps8QwIBEICBmpRCPgzlzUNbI0FFYdzOkqGP2HN80K2q2N41wEZb0cBRLYGHJ1lxe1uArzJcdrenzpzLtZ6UooZCQga2VRgC7IyrYTLkYPsmpT9xzzI-DOcbHSEuXQuvsDsgZmvA6zUSkXB2IqqzA6Eu3VTlKJBjGvcYGXYzwou-iwYf7c0FN6HCKIh0lmszIp7ik6rAzx_BzM94L7qFsn2Ob5g=
Text:
  Availability: 1
  Value: <anid>AN0031271248;imt01mar.08;2019Feb27.14:40;v2.2.500</anid> <title id="AN0031271248-1">An investigation into whether student use of graphics calculators matches their teacher's expectations. </title> <sbt id="AN0031271248-2">1. Introduction</sbt> <p>This research examines students' use of graphics calculators and investigates the extent to which the students' use meets their teachers aim when using graphics calculators in the classroom. The teacher's use of her graphics calculator was analysed over a week using Key Record software. The teacher was questioned about her aims and expectations for the students when using a graphics calculator. As a result an interview schedule for students was constructed in order to determine whether the teacher's aims had been met. It was found that in general all of the teachers' aims were met to some extent by most of the students.</p> <p>Since graphics calculators were first produced in 1985 they have been utilized by some teachers within the field of mathematics education. Their relatively low cost and portability mean that they can provide a valuable resource within the mathematics classroom.</p> <p>It was not until the1990s that research papers first appeared relating to the use of graphics calculators in the mathematics classroom and the need for ongoing research into aspects of their use is still acknowledged. Dunham and Dick [<reflink idref="bib1" id="ref1">1</reflink>] carried out a substantial review of research available at that time, and observed that 'Most studies mentioned in this article have been descriptive; they tell us <emph>what</emph> happens in the classroom equipped with graphing calculators. For research effectively to guide curriculum development and instruction we need to find out <emph>why</emph>.'</p> <p>Two years after Dunham and Dick posed these questions, Penglase and Arnold [<reflink idref="bib2" id="ref2">2</reflink>] conducted another major review of research over a decade of use of graphics calculators in the mathematics classroom. They investigated the ways in which graphics calculators can be used to maximize learning and achievement, and also the teaching practices and learning environments that best complement their use in order to bring about maximum benefit for students. They concluded that the current state of research into the use and effects of graphics calculators remains inconclusive. Few studies distinguish carefully between the use of the tool and the context of that use.</p> <p>In a comprehensive review of research findings and implications for classroom practice with handheld graphing technology, Burrill <emph>et al</emph>. [<reflink idref="bib3" id="ref3">3</reflink>] concluded that future research should be focused and coordinated, and that 'by conducting rigorous studies of important questions and relating the results to classroom practice, we can ensure that handheld graphing technology contributes in positive ways to improved mathematics education.'</p> <p>Various researchers point to the advantages of portability and price of graphics calculators for use as effective classroom resources. Many schools consider them to offer good value since a class set, together with a teacher's model with OHP display pad currently costs no more than one or two desktop computers. Hennessey [<reflink idref="bib4" id="ref4">4</reflink>] stressed the advantages of the individual use that could be made of graphics calculators by students, concluding that 'Although GC screens are more limited in size, the calculators are even more portable and easily affordable by individual students, making them even more controllable by students.'</p> <p>In order to investigate the effectiveness of graphics calculators as a teaching and learning resource in the mathematics classroom, it is important to consider why teachers use handheld graphing technology and to investigate how this use is related to their knowledge and beliefs about technology, mathematics and teaching mathematics. Doerr and Zangor [<reflink idref="bib5" id="ref5">5</reflink>] found that rule-based teachers were less likely to have positive views of the use of handheld technology. If a teacher believes that mathematical procedures should be mastered by hand before using calculators then their focus is likely to be on controlling the use that the students make of the technology. Teachers who are less rigid in this belief are likely to give students more freedom in their choices of how to use the technology.</p> <p>Tharp <emph>et al</emph>. [<reflink idref="bib6" id="ref6">6</reflink>] found that 'the use of the graphing calculator was associated with higher levels of discourse in the classroom, including higher-level questioning by the instructor and more active learning behaviours by the students'</p> <p>There are some fundamental questions that need to be asked when considering the effects of the use of graphics calculators on student learning, understanding and achievement:</p> <p>Does the use of graphics calculators enhance the learning of mathematics?</p> <p>In what areas of mathematics can learning be enhanced?</p> <p>Under what circumstances and conditions is learning enhanced?</p> <p>How do students view the use of graphics calculators in their learning of mathematics?</p> <p>Harskamp <emph>et al</emph>. [<reflink idref="bib7" id="ref7">7</reflink>] found that 'the graphics calculator seems to be a useful instrument for the improvement of mathematics education' but found that for this improvement to take place it was important for students to use the calculator for a prolonged period of time and that 'short-term use is not sufficient to establish a firm knowledge and understanding' This is consistent with the findings of Merriweather and Tharp [<reflink idref="bib8" id="ref8">8</reflink>] who conducted a comparative study of eighth grade students (age 14) and concluded that 'Graphing calculators need to be used more consistently and over a prolonged period of time. Students want to learn and use the graphing calculators. However, if they are not comfortable with the technology they will not use it and will turn to those methods they are most comfortable and familiar with.' Another significant finding of this study was the fact that students found that they could solve problems with the graphics calculator that they could not solve before, for example the solution of quadratic equations which would not normally be taught until the following year. This excited the students and encouraged them to become more involved in their learning.</p> <p>When graphics calculators first began to be used in the mathematics classroom the most significant difference between the graphic and the scientific calculator was the facility to draw graphs of functions. Although the graphics calculator has many other facilities that can be utilized within the mathematics classroom it is the impact upon student learning of graphical representations that has come under closest scrutiny in research studies.</p> <p>Adams [<reflink idref="bib9" id="ref9">9</reflink>] carried out a comparative study which focused on the concept of function. Her theoretical framework was based on the work of Yerushalmy [<reflink idref="bib10" id="ref10">10</reflink>] who asserted that investigating functions is the only topic in a traditional algebra course that utilizes visual-graphic representation, and Clement [<reflink idref="bib11" id="ref11">11</reflink>] who suggested that the graph has the potential of enhancing the concept of function and that the graphing calculator is a medium by which this can be done. The key findings of Adams' research were that students' conception of function was significantly affected by the interaction of using graphing calculators and concluded that 'They must have a basic understanding of the concept in order to understand the reasoning behind the operation of the graphing calculator. Otherwise, the student will see the graphing calculator as a machine for doing mathematics instead of a tool for learning'</p> <p>Other studies such as those by Graham and Thomas [<reflink idref="bib12" id="ref12">12</reflink>] and Gage [<reflink idref="bib13" id="ref13">13</reflink>] have investigated the use of the graphics calculator as a tool. Gage's findings led her to conclude that within this model the graphics calculator can be used as a mediating tool and that the students' peers and the graphics calculator together enable the student to reach a higher level of understanding of a variable than would have been the case without such a tool. However the study by Doerr and Zangor [<reflink idref="bib14" id="ref14">14</reflink>] also identified constraints and limitations caused by the students' use of the calculator, including the students' tendency to view the calculator as a 'black box' and the use of the calculator as a tool to pursue individual solutions which caused problems in group thinking and communication. This view that individual use of the calculator can undermine group communication needs to be balanced with the view of the graphics calculator as a shared tool. This is supported by Drijvers and Doorman [<reflink idref="bib15" id="ref15">15</reflink>] who concluded that the graphics calculator could support the use of realistic data and that it seemed to stimulate many students towards exploratory activity. The role of the teacher is clearly vital in directing the students towards the most effective ways of utilizing the calculator so that it can enhance aspects of their learning such as collaborative problem solving and so that it does not cause problems in communication through excessive individual use.</p> <p>One particularly important aspect of individual calculator use is the use of the graphics calculator in examination conditions. Current regulations in England and Wales permit students to take graphics calculators into their KS3 SAT examinations and their GCSE Mathematics examinations in any papers where a calculator is permitted. Until 2004 the AS and A-Level regulations restricted students to using only a scientific calculator in certain module examinations, but since 2004 the arrangements have been revised so that one module is examined without any type of calculator being permitted, with all other modules allowing any type of calculator. Some syllabuses now actively encourage the use of graphics calculators and certain Further Mathematics modules expect students to use a graphics calculator in investigations of curves. Since graphics calculators are utilized as a teaching resource it is of great importance to consider their use and effect in examination conditions. Studies by Graham <emph>et al</emph>. [<reflink idref="bib16" id="ref16">16</reflink>], Monaghan [<reflink idref="bib17" id="ref17">17</reflink>], Forster and Mueller [<reflink idref="bib18" id="ref18">18</reflink>] and Taylor [<reflink idref="bib19" id="ref19">19</reflink>] discovered that students significantly underutilize the available technology in examination conditions. Graham <emph>et al</emph>. [<reflink idref="bib16" id="ref20">16</reflink>] set out to investigate how a small group of students actually used their graphics calculators under examination conditions. Their study utilized key-recording software to capture the students' keystrokes while they used their graphics calculators in an externally set mock A-Level examination and also involved interviews with the students. The most striking thing to have come out of the investigation was how limited the students' use of the graphics calculator was in the examination. This research also categorized students use in three ways: quasi-scientific, semi-proficient and proficient. In their conclusion the authors noted that 'if students are to make effective use of graphics calculators in examinations, the students need to be encouraged to make more extensive use of graphics calculators throughout their mathematics studies, so that they become more familiar with them and confident to use them.'</p> <p>In relation to students' use of graphics calculators in examination conditions, Forster [<reflink idref="bib20" id="ref21">20</reflink>] observed that many students had failed to check their answers, and noted that Lagrange [<reflink idref="bib21" id="ref22">21</reflink>] also reported underutilization of checking with technology, whilst regarding checking as a higher-order skill.</p> <p>The use of graphics calculators by teachers was investigated by Honey and Graham [<reflink idref="bib22" id="ref23">22</reflink>] in a study which followed three student teachers and investigated their initial beliefs and attitudes towards the use of graphics calculators and their subsequent classroom practice. The key-recording software used by Graham <emph>et al</emph>. [<reflink idref="bib16" id="ref24">16</reflink>] had been developed by Berry <emph>et al</emph>. [<reflink idref="bib23" id="ref25">23</reflink>] in a study which observed student working styles when using graphics calculators to solve mathematics problems. This work utilizes the same software in order to follow on from the work of Graham <emph>et al</emph>. [<reflink idref="bib16" id="ref26">16</reflink>] and seeks to investigate the aims of the teacher in her use of the graphics calculator as a teaching resource, and to what extent her aims were met.</p> <hd id="AN0031271248-3">2. Methodology</hd> <p></p> <hd id="AN0031271248-4">2.1. The purpose of the study</hd> <p>This study investigated the reasons why graphics calculators were used in the way that they were used, and whether or not benefit accrued from their use. The reasons why a teacher used the graphics calculator in her teaching were considered and compared to the usage of the graphics calculator by a selected group of students. This involved establishing the specific aims of the teacher and investigating to what extent these aims had been met.</p> <hd id="AN0031271248-5">2.2. The teacher's purpose in making use of a graphics calculator</hd> <p>The teacher who took part in the study was a proficient user of the graphics calculator and an advocate of its use. We wanted to evaluate an existing situation rather than create an intervention. The key-recording software used by Graham <emph>et al</emph>. [<reflink idref="bib16" id="ref27">16</reflink>], allowed us to monitor the teacher's routine use of the calculator with minimal intrusion. The teacher was not asked to make specific use of the calculator or to prepare specific lessons or activities. No one observed the teacher in the classroom. Over a two-week period the key-recording software in the teacher's calculator logged every keystroke that was made. The use of the calculator was then replayed and analysed by the research team with the assistance of the teacher.</p> <p>The key-recording software facilitates the transfer of keystroke information and images of the calculator screen onto videotape. The calculator itself was also used with software, TI Connect, to produce paper transcripts of the calculator usage.</p> <p>The research team sought to establish the aims of the teacher in using the graphics calculator. The video material and transcripts were made available to members of the research team who then met with the teacher. It was necessary to involve the teacher in the analysis in order to establish which topics had been taught to which classes and the aims of the teacher in each instance where the graphics calculator had been used.</p> <p>After analysing the teacher's data, a group with the greatest exposure to the graphics calculator was identified and selected for the next stage of the study. This group consisted of five year-12 students studying A-level Mathematics.</p> <hd id="AN0031271248-6">2.3. Students' use of graphics calculators</hd> <p>The students were interviewed to try to determine the extent to which the teacher's aims were being met. While we had identified specific aims of the teacher, we did not think that closed questions on the success of these aims would provide insight into the students' use and relationships with the graphics calculator. Consequently we adopted a semi-structured interview as our method of data collection. Students were interviewed individually and the same opening questions were put to each student. Depending on the responses, the interviewer then probed for further detail. The structure of the interviews was similar to the sequential structure with simple feedback loops as described by Keats [<reflink idref="bib24" id="ref28">24</reflink>]. The interviewer was known to the students but was not their teacher and the questions posed to the students were not specifically related to the sessions analysed for the identification of the teacher's aims. We believe that this allowed the students to respond with minimal inhibition and minimal bias. All interviews were tape recorded with the students' permission.</p> <p>The interviewer started each interview by asking how confident the student was in using a graphics calculator. From their response to this question the interviewer then probed their inclination to and/or aversion for different uses and aspects of the graphics calculator. The students were shown example mathematics questions and asked whether they would use a graphics calculator to answer them. Depending on the responses the interviewer then probed how the student would use the calculator or why they would not use it.</p> <p>After the interviews the recordings were transcribed and their response to each question was summarized in a table. This enabled the researchers to investigate the extent to which the teacher's aims had been met.</p> <hd id="AN0031271248-7">3. Data collection and findings</hd> <p></p> <hd id="AN0031271248-8">3.1. The teacher interview</hd> <p>The first stage of the data gathering was to record the use by the teacher of the graphics calculator over a two week period. This recording was then used to create a video file that could be played back to the teacher and an interview panel. As the calculator use was replayed, the playback was paused so that the panel could ask the teacher what she had been doing with the calculator and what she had hoped to achieve by her actions.</p> <p>The recording had included a number of classes at different levels. Not all of the use by the teacher will be described here, but a number of examples that cover the main aspects of the use raised during the interview with the teacher will be included. For each lesson, a summary of the ways in which the calculator was being used are presented, along with the aims and motivation of the teacher, as revealed through the discussions with the interview panel.</p> <p>Several of the lessons where the graphics calculator was used were with the same group of year-12 students. Each of the lessons with them is described, as this group was later selected by the interview panel as the best group to move forward to the next stage of the research.</p> <hd id="AN0031271248-9">Lesson 1</hd> <p>The teacher was using the binomial distribution function with a year-12 statistics class. A screen shot from the calculator is shown in figure 1.</p> <p>Graph: Figure 1. Screen shot for the work on the binomial distribution.</p> <p>The interview discussion explored the reasons behind the use of the graphics calculators in this context. The teacher had three very specific aims. The first was to make sure that the students were aware that the binomial distribution functions existed on their calculator. The second was to develop their confidence in the use of these functions and become familiar with the syntax that was required to use them. The third aim was to relate the use of the graphics calculator in this way to past examination questions, so that students could see the value of using the calculators in an examination situation.</p> <p>Further discussion with the teacher revealed a number of issues that were behind her more specific aims. When the recording was carried out, the graphics calculators were still relatively new to the students and there was still an element of reluctance among some of the students to use the calculators, with several of the students appearing to need more time to become comfortable with the calculators. There were still a number of students in the class who needed to be reminded of the syntax that is required for various operations. The other issue related to the textbook for the module that was being studied, which used an approach that was based on using books of tables rather than calculator methods. This background illustrates how the teacher had arrived at her three main aims described above.</p> <p>At the interview the teacher said that she felt that after that lesson the students did seem more confident with the graphics calculators and were having less difficulty with the syntax.</p> <p>A further lesson on this topic made use of the graphics calculators again in a similar way.</p> <hd id="AN0031271248-10">Lesson 2</hd> <p>In this lesson, with a year-9 class, the teacher was simply using the calculator to obtain the results of various calculations. The emphasis of the lesson was to look at issues of rounding and the use of brackets in calculations. Figure 2 shows a screen shot from this lesson.</p> <p>Graph: Figure 2. Screen shot for the year-9 lesson.</p> <p>The focus of the lesson was on rounding numbers that result from calculations and in using brackets correctly when carrying out calculations with a calculator. The teacher had therefore made the decision not to work on her whiteboard, but to use the calculator to display the results of her calculations, rather than writing them on the board. The teacher felt that it was more valuable for the students to see the actual calculator display.</p> <hd id="AN0031271248-11">Lesson 3</hd> <p>In this lesson, a year-12 group were being taught how to calculate the median and inter-quartile range using their calculators. This group included some of the same students who had earlier used the graphics calculators for the binomial distribution. Figure 3 shows a screen shot from this lesson.</p> <p>Graph: Figure 3. Screen shot from the lesson on the median and inter-quartile range.</p> <p>The teacher's aim here was primarily to show the students how they could use the graphics calculator to answer question related to these topics. She did also have a secondary aim of building the confidence of these students with their graphics calculators. This is similar to her description of her aims for lesson 1 above.</p> <hd id="AN0031271248-12">Lesson 4</hd> <p>In this lesson, again with year-12, the students were exploring the topic of logarithms with their graphics calculators. The teacher said that this was an introductory lesson on the topic of logarithms, where she was working with base 10 logarithms. It is worth noting that due to the way that the mathematical content for years 12 and 13 is split, logarithms are covered in year 12, but that logarithms to the base <emph>e</emph> are not included. This explains the emphasis in the lesson on logarithms to base 10. Figure 4 shows a screen shot from this lesson.</p> <p>Graph: Figure 4. Screen shot from the logarithms lesson.</p> <p>The aim of this lesson was for the students to gain an understanding of the basic properties of logarithms by exploring the values of different logarithms on their calculators. The teacher described at interview, how she had intended the students to first discover for themselves the relation log<subs>10</subs>(10<sups><emph>n</emph></sups>) = <emph>n</emph>. She had hoped that as a consequence of this exploration, the students would have a better understanding of the properties of logarithms.</p> <hd id="AN0031271248-13">3.2. After the teacher interview</hd> <p>After the teacher interview the panel discussed the aims of the teacher in using the graphics calculators in her lessons. There were a number of different ways in which the graphics calculator had been used and different types of aims that the teacher had for different lessons. The panel discussed these and negotiated the following list that they feel covers all of the examples seen in the video recording that was discussed with the teacher at interview.</p> <hd id="AN0031271248-14">The teacher's aims</hd> <p></p> <ulist> <item> 1. To make her students confident users of the graphics calculators.</item> <p></p> <item> 2. To make her students aware of the functions and tools in the calculator that are related to the mathematical topics encountered in the course that they are studying.</item> <p></p> <item> 3. To enable her students to see how the graphics calculator can be used to help answer examination questions.</item> <p></p> <item> 4. To use the graphics calculator as a display tool, particularly when considering calculator use.</item> <p></p> <item> 5. To use the graphics calculator as an investigative tool, when introducing new mathematical topics.</item> <p></p> <item> 6. To encourage students to use the graphics calculator as a tool for checking their working.</item> </ulist> <p>After the panel had agreed on the summary presented above it was shown to the teacher, who was asked to confirm whether or not she felt that this was an accurate expression of teaching aims when working with the graphics calculator.</p> <p>Having identified the teacher's aims in this way the next stage of the investigation was to see whether these aims were being met. The research team decided that they would use interviews with the year-12 students to conduct this aspect of the investigation. The year-12 group were selected as they were the group that had the greatest exposure to the graphics calculators during the first data gathering phase of the research. Interviews were selected as the number of students in the group was fairly small and it was anticipated that the interviews would provide the richest source of data for further analysis.</p> <p>A set of interview questions were developed by the interview panel. These were designed to assess how well the teacher's aims had been met, through the use of direct questions but also through questions based on asking the student how they might or might not use a graphics calculator to solve a particular problem. A copy of the interview questions is included in the appendix.</p> <hd id="AN0031271248-15">3.3. The student interviews</hd> <p>The second stage of the data gathering was to interview the five students in order to see if the teacher's aims were being met. The student's responses are summarized in Table 1. The responses were analysed with the teacher's aims in mind.</p> <p>Table 1. Summary of student responses to interview questions</p> <p> <ephtml> <table><thead valign="middle"><tr><td /><td>How confident do you feel when you are using your gc?</td><td>How aware are you of the different functions and commands that exist on your gc?</td><td>How would you use your gc in question A? In an exam?</td><td>How would you use your gc in question B? In an exam?</td><td>How would you use your gc in question C? In an exam?</td><td>Do you find it helpful to see gc screens projected onto a screen by a teacher in a lesson? Why?</td><td>Describe something you have learned by experimenting or exploring with your gc</td><td>There are 2 answers to question D. How could you decide which is correct?</td></tr></thead><tbody valign="top"><tr><td>Student 1</td><td>Quite confident, but not so confident with stats. Forgets the functions.</td><td>Fairly well aware.</td><td>To check things.</td><td>Put it into the calculator and look through the table. The sameiIn an exam.</td><td>Not sure – forgetful of the stats.</td><td>Yes, definitely</td><td>Polar graphs</td><td>Calculate the definite integral on the calculator.</td></tr><tr><td>Student 2</td><td>Reasonably confident.</td><td>Well aware of those taught in school.</td><td>For sketching the curve and using the trace function.</td><td>To substitute the values into the formula.</td><td>Use the Binomial distribution function.</td><td>Yes.</td><td>Exploration of graphs</td><td>Start by hand then use the calculator at the end.</td></tr><tr><td>Student 3</td><td>Very confident, especially with drawing graphs.</td><td>Aware of those used regularly in class.</td><td>Sketch the curve and check.</td><td>Use the table function.</td><td>Use the distribution menu.</td><td>Yes, as you can "match up" your screen with the teacher's.</td><td>No</td><td>Do the integration myself.</td></tr><tr><td>Student 4</td><td>Fairly.</td><td>Familiar with those taught.</td><td>Sketch the graph.</td><td>Calculate values using the function facility.</td><td>Confused about the question?</td><td>Yes, to see what the teacher is doing.</td><td>Not sure. No.</td><td>Use the calculator to do a numerical integration.</td></tr><tr><td>Student 5</td><td>Very confident. Uses it in all lessons and tests.</td><td>Good general awareness.</td><td>Drawing the graph. Checking the work done by differentiation.</td><td>Efficient use of table function and numerical integration.</td><td>Use the distribution menu to find the binomial probabilities.</td><td>Yes, to check that the screen matches the teacher's.</td><td>Using matrices for chi-squared test.</td><td>Use the calculator to do a numerical integration.</td></tr></tbody></table> </ephtml> </p> <hd id="AN0031271248-16">Aim 1: To make the students confident users of the graphics calculator.</hd> <p>Two of the students (students 3 and 5) said that they were very confident in their use of the graphics calculator, Student 5 stating "<emph>I have been using it for almost two years on and off and recently got one of my own about a year ago and have got really confident using it. I use it in all my lessons and tests</emph>." Student 3 was still very confident despite having a different calculator than everyone else. The other three students ranged from quite confident to reasonably or fairly confident. The reason that all three gave for their lack of confidence was that they tended to forget how to do certain things:</p> <p>"<emph>Not so confident with stats, I forget it has these things</emph>" – student 1</p> <p>"<emph>Sometimes I forget what I'm doing if it involves several menus</emph>" – student 2</p> <p>"<emph>Sometimes I forget what I'm meant to be doing</emph>" – student 4</p> <p>In general students were confident with the techniques that they had used regularly as was found in Harskamp <emph>et al</emph>. [<reflink idref="bib7" id="ref29">7</reflink>]. The students were less confident in techniques and procedures that were used less frequently.</p> <hd id="AN0031271248-17">Aim 2: To make the students aware of the functions and commands that exist on the graphics ca...</hd> <p>All of the students felt that they had a good awareness of the different commands and functions on the calculator that had been introduced to them by the teacher. The teacher had obviously made a point of showing how the graphics calculator can be used in different situations, one student commenting "<emph>Whenever there is something we need to do we get taught how to do it</emph>" – student 4, " <emph>I</emph>'<emph>m aware of the ones we use regularly in class like graphing functions</emph>" – student 3. Student 2 was a bit more proactive in finding out about the functionality: "<emph>I keep finding out there are more and more things you can do on it</emph>."</p> <p>All five students had a good awareness of the functions and commands that the teacher had used in the class or had told them about.</p> <hd id="AN0031271248-18">Aim 3: To enable the students to see how the graphics calculator can be used to help answer e...</hd> <p>The students were shown three different examination questions A, B and C as shown in the appendix. The teacher had chosen the three questions in order to give a range of opportunities that the calculator could be used for, graphing, numerical and statistical use. The interviewer first asked "How would you use your graphics calculator in this question?" This was then followed up by asking if the student would use the graphics calculator differently if it was an exam question.</p> <hd id="AN0031271248-19">Question A</hd> <p>The teacher expected that the students would use the graphics calculator to sketch the curve and then use the trace facility or calculate facility to find the minimum point as a way of checking their working in finding the minimum.</p> <p>All five students would use the graphics calculator in tackling the question, Student 1 would check the maximum and roots, the other four students would sketch the curve as well as checking the minimum and roots. When asked if they would do anything different in an exam all five students said that they would use the graphics calculator to check their answers. Student 5 saw no difference between the use of her graphics calculator in a classroom situation and an exam situation:</p> <p>"<emph>I would probably just use it the same way as I use it in class because you get used to doing it in a certain way and it is really good for checking in the exam</emph>."</p> <p>For two of the students the time constraints in an examination pushed the graphics calculator use to the end:</p> <p>"<emph>I wouldn't do my checking until the end. Only if I have time</emph>." – Student 1</p> <p>"<emph>I like to do things myself then check them on the calculator because I have a habit of pressing the wrong buttons, especially in an exam because I do things quickly.</emph>" – Student 2</p> <p>In conclusion, all five students would do what the teacher had expected if the question was set in a non-exam environment. However in an exam situation, the students would not be quite so happy in using the calculator.</p> <hd id="AN0031271248-20">Question B</hd> <p>In this question the teacher would expect the students to set up the table and obtain the missing values. It was also expected that some students would use the graphics calculator to obtain the value of the integral thus checking that their numerical answer was a good approximation.</p> <p>All five students would use the graphics calculator for this question. For part (i) four out of the five would use the Y = and TABL E functions while Student 2 would calculate the function for each value as shown in figure 5.</p> <p>Graph: Figure 5. The students' two different approaches to question B (i).</p> <p>For part (ii) Student 5 would make effective use of the integration function on the graphics calculator and said that she would do the integral on the calculator to "<emph>check the similarity</emph>" with her solution as shown in Figure 6.</p> <p>Graph: Figure 6. Student 5's approach to checking her solution to question B (ii).</p> <p>When asked if they would do things different in an examination all five were adamant that they would use the calculator in the same way to calculate the numerical values. Two students said that they would write more things down in an examination than they would in a classroom situation.</p> <p>Once again all five students used the graphics calculator in the way expected by the teacher both in a classroom and an examination situation, with one student fully meeting the teacher's expectation.</p> <hd id="AN0031271248-21">Question C</hd> <p>In this question the teacher expected the students to use the graphics calculator to obtain the Binomial CDF and PDF as shown in figure 7.</p> <p>Graph: Figure 7. Teacher's expected use of the graphics calculator in question C.</p> <p>All five students again could see that they could use their graphics calculator in this question. Although a couple could not remember how, they were all aware of the statistical functions available on the calculator and said they would use them. "<emph>Yes most definitely. All the different distributions are already programmed into it so it makes it quick and easy rather than looking through programs or tables</emph>." – Student 3. In an exam situation three students said that they would probably do the same as in the classroom situation however Student 2 said she would not use the inbuilt functions but would "<emph>like to check through by using the actual formula by inputting that into the calculator.</emph>"</p> <p>While all students felt that they would use their graphics calculator in an examination question the way they used them was slightly different. They became more of a checking facility (if there was time) and also some students were aware of the need to 'write things down' in an examination which would prevent them using the calculator efficiently in question C for example.</p> <hd id="AN0031271248-22">Aim 4: To use the graphics calculator as a display tool.</hd> <p>The teacher makes use of a Viewscreen in the classroom which displays her calculator screen via an overhead projector. All five students felt that it was a beneficial experience especially when they were meant to be following the procedure on their own calculator:</p> <p>"<emph>You can see what the teacher is seeing and you can find things on your own</emph>" – Student 4.</p> <p>"<emph>sometimes it is easier, rather than being told what to do, to see it happening on the screen and check on your own screen whether you have got the same on it</emph>" – Student 5.</p> <p>The students' comments showed that the teachers aim to use the graphics calculator as an effective display tool has been met.</p> <hd id="AN0031271248-23">Aim 5: To use the graphics calculator as an investigative tool.</hd> <p>The students were asked "Describe one thing that you have learned by experimenting or exploring the graphics calculator. Is there something you have found out for yourself?" The teacher envizaged that this aim would be achieved by the students recalling lessons such as 'lesson 4' described earlier where the teacher introduces a new topic through an exploration or investigation on the graphics calculator. The student interviews did not really get to the hub of this question, the students responded in two different ways – learning new calculator techniques or learning new mathematics.</p> <p>Student 1 felt that she had learnt some new mathematics when she discovered the polar mode on the calculator. She asked the teacher what it was and then spent some time exploring polar functions. She felt that "<emph>I wouldn</emph>'<emph>t have come across that if it wasn</emph>'<emph>t for the graphics calculator</emph>".</p> <p>Student 2, although she did not think it useful, used the graphics calculator to explore graphs: "<emph>I have spent a lot of time working out how I can do different patterns with the graphs but that is possibly not very practical</emph>". When the teacher requires an item from a menu she would usually scroll down to the desired item. However Student 2 discovered a different technique: "<emph>It is quite useful finding shortcuts for the menus rather than having to scroll down. I can usually remember which letter I use</emph>."</p> <p>Student 3 felt she had learnt a great deal just by trying things out on the graphics calculator: "<emph>I think it is just generally the amazingness of graphs. Just to be able to picture a graph rather than draw things out. Things like the sin graphs; to see the periodicy of them it is really useful</emph>".</p> <p>Student 4 could not think of anything she had learnt where as Student 5 learnt how to use the calculator to do something her teacher did not know how to do: "<emph>The chi squared thing, it was actually something the teacher didn</emph>'<emph>t know how to do at first. I had been doing it in biology as well and had seen it done and been using it and we figured how to use it in matrices</emph>."</p> <p>So although the teacher's aim had not been fully explored by the question posed to the students it can be seen that for four out of the five students discovered some new aspect of mathematics as a consequence of having a graphics calculator. For example Student 1 discovered the polar graphing function on the graphics calculator and with help from the teacher went on to explore their properties. Polar Graphs is not on the syllabus and she commented "<emph>I wouldn</emph>'<emph>t have come across that if it wasn</emph>'<emph>t for the graphics calculator</emph>". Having met Aim 1 (being confident users) allowed some students to explore the different functions and buttons on the calculator thus enabling them to meet new mathematics.</p> <hd id="AN0031271248-24">Aim 6: To encourage the students to use the graphics calculator as a checking tool.</hd> <p>To test this aim the students were shown the following statement:</p> <p></p> <p> <ephtml> <table><tbody valign="top"><tr><td>Here are two statements. How would you decide which, if any of them, is correct?</td><td><p><graphic href="tmes_a_260583_o_um0001.gif" content-type="Graph" /></p></td></tr></tbody></table> </ephtml> </p> <p>For this question the teacher expected the student to use the integration function of the calculator as shown in figure 8.</p> <p>Graph: Figure 8. Teacher's expectation of graphics calculator use as a checking tool.</p> <p>All the students had seen this technique and three of the students said that they would use it to check which answer was correct. Two of the students said that they would do the integration by hand and just use the calculator for doing the final calculation (i.e. putting in the values). Student 3 expressed a concern about doing too much on the calculator: "<emph>I always try and do it first using my head, pen and paper because that way I know I haven</emph>'<emph>t pressed the wrong button because that is quite easy to do. You can muddle up a negative sign. It also means I am getting more proficient at maths rather than just using a calculator</emph>."</p> <p>From the students comments it is felt that this aim is the one which has not been fully met with only three students using the calculator effectively as a checking tool. However checking is regarded as a higher order skill by Lagrange [<reflink idref="bib21" id="ref30">21</reflink>].</p> <p>In general it can be said that with this sample of students all six of the teacher's aims were met to some extent or another. The fact that the first aim of confidence was achieved by all five students had a bearing on the other aims especially to use the graphics calculator as an investigative tool.</p> <hd id="AN0031271248-25">4. Conclusions</hd> <p>In investigating the specific aims of the teacher, as set out in section 3.2, it was found that in general all of the teachers' aims were met to some extent by most of the students. The first aim was to make the students confident users of the graphics calculator. This aim was fully met with all students describing themselves as 'fairly' or very 'confident' users. The second aim was to make the students aware of the functions and commands and all students reported a good awareness particularly of those functions that they met regularly in lessons. The aim of students using the graphics calculator in an examination was met partially by all students. They all said they would use it in an examination but when probed it appeared that this use was not always a proficient use but more a tool for checking. All students were positive about the teacher's use of the viewscreen. The teacher's aim that the students would use their graphics calculator as an investigative tool was partially met in that some investigation took place with considerable guidance from the teacher. The final aim to use the graphics calculator as a checking tool was met by three out of the five students using the calculator in proficient way. Overall it can be concluded that with this small group of students the teacher's aims were generally all met to some extent.</p> <hd id="AN0031271248-26">Appendix</hd> <p></p> <hd id="AN0031271248-27">Year 12 Graphics Calculator Interview Questions</hd> <p></p> <hd id="AN0031271248-28">Question 1</hd> <p>How confident do you feel when you are using your graphics calculator?</p> <p> <emph>Please describe some things that you are confident to do on the graphics calculator.</emph> </p> <p> <emph>Describe some things that you are not confident to do on the graphics calculator.</emph> </p> <hd id="AN0031271248-29">Question 2</hd> <p>How aware are you of the different function and commands that exist on your graphics calculator?</p> <p> <emph>Are you able to find commands or functions that will do the things that you need in your mathematics lessons?</emph> </p> <p> <emph>Are there things that you feel that the graphics calculator can do, but that you don't know how to make it do them?</emph> </p> <hd id="AN0031271248-30">Question 3</hd> <p>Please look at question A.</p> <p>Would you use a graphics calculator to help you answer this question?</p> <p></p> <p> <ephtml> <table><tbody valign="top"><tr><td>Question A</td></tr><tr><td>The equation of a curve is given by <italic>y</italic> − (<italic>x</italic> − l)<sup>2</sup>(<italic>x</italic> + 2).</td></tr><tr><td>(i)</td><td>Write (<italic>x</italic> − 1)2(<italic>x</italic> + 2) in the form <italic>x</italic><sup>3</sup> + <italic>px</italic><sup>2</sup> + <italic>qx</italic> + <italic>r</italic> where <italic>p</italic>, <italic>q</italic> and <italic>r</italic> are to be determined.</td><td><xref ref-type="bibr" rid="bibr2">2</xref></td></tr><tr><td>(ii)</td><td>Show that the curve <italic>y</italic> = (<italic>x</italic> − l)<sup>2</sup>(<italic>x</italic> + 2) has a maximum point when <italic>x</italic> = −1 and find the coordinates of the minimum point.</td><td><xref ref-type="bibr" rid="bibr7">7</xref></td></tr><tr><td>(iii)</td><td>Sketch the curve <italic>y</italic> = (<italic>x</italic> − l)<sup>2</sup>(<italic>x</italic> + 2).</td><td><xref ref-type="bibr" rid="bibr1">1</xref></td></tr><tr><td>(iv)</td><td>For what values of <italic>k</italic> does (<italic>x</italic> − 1)<sup>2</sup>(<italic>x</italic> + 2) = <italic>k</italic> have exactly one root.</td><td><xref ref-type="bibr" rid="bibr3">3</xref></td></tr></tbody></table> </ephtml> </p> <p>If so how?</p> <p>Would you use your graphics calculator in the same way in an exam?</p> <hd id="AN0031271248-31">Question 4</hd> <p>Please look at question B.</p> <p>Would you use a graphics calculator to help you answer this question?</p> <p></p> <p> <ephtml> <table><tbody valign="top"><tr><td>Question B</td></tr><tr><td> Some values of the function f(<italic>x</italic>) = 1/1 + <italic>x</italic><sup>2</sup> are given in the table below.</td></tr><tr><td> The figures are rounded to 5 decimal places.</td></tr><tr><td><italic>x</italic></td><td char=".">0.0</td><td char=".">0.2</td><td char=".">0.4</td><td char=".">0.6</td><td char=".">0.8</td><td char=".">1.0</td></tr><tr><td>f(<italic>x</italic>)</td><td /><td char=".">0.96154</td><td char=".">0.86207</td><td /><td char=".">0.60976</td><td /></tr><tr><td>(i)</td><td>Find the values of f(<italic>x</italic>) missing from the table.</td><td><xref ref-type="bibr" rid="bibr1">1</xref></td></tr><tr><td>(ii)</td><td>Use the trapezium rub with 5 strips to estimate the value of: <p><inline-graphic href="tmes_a_260583_o_ilm0001.gif" /></p>.</td><td><xref ref-type="bibr" rid="bibr4">4</xref></td></tr></tbody></table> </ephtml> </p> <p>If so how?</p> <p>Would you use your graphics calculator in the same way in an exam?</p> <hd id="AN0031271248-32">Question 5</hd> <p>Please look at question C.</p> <p>Would you expect to use your graphics calculator in a statistics question like this one?</p> <p></p> <p> <ephtml> <table><tbody valign="top"><tr><td>Question C</td><td /></tr><tr><td>At a doctor's surgery, records show that 20% of patients who make an appointment fail to turn up. During afternoon surgery the doctor has time to see 16 patients.</td></tr><tr><td>There are 16 appointments to see the doctor one afternoon.</td></tr><tr><td>(i) Find me probability that all 16 patients turn up.</td><td><xref ref-type="bibr" rid="bibr2">2</xref></td></tr><tr><td>(ii) Find the probability that more than 3 patients do not turn up.</td><td><xref ref-type="bibr" rid="bibr3">3</xref></td></tr><tr><td>To improve efficiency, the doctor decides to make more than 16 appointments for afternoon surgery, although there will still only be enough time to see 16 patients. There must be a probability of at least 0.9 that the doctor will have enough time to see all the patients who turn up.</td></tr><tr><td>(iii) The doctor makes 17 appointments for afternoon surgery. Find the probability that at least one patient does not turn up. Hence show that making 17 appointments is satisfactory.</td><td><xref ref-type="bibr" rid="bibr3">3</xref></td></tr><tr><td>(iv) Now find the greatest number of appointments the doctor can make for afternoon surgery and still have a probability of at least 0.9 of having time to see all patients who turn up.</td><td><xref ref-type="bibr" rid="bibr4">4</xref></td></tr><tr><td>A computerised appointment system is introduced at the surgery. It is decided to test, at the 5% level, whether the proportion of patients failing to turn up for their appointments has changed. There we always 20 appointments to sec the doctor at morning surgery. On a randomly chosen morning, I patient does not turn up.</td></tr><tr><td>(v) Write down suitable hypotheses and carry out the tesl.</td><td><xref ref-type="bibr" rid="bibr7">7</xref></td></tr></tbody></table> </ephtml> </p> <hd id="AN0031271248-33">Question 6</hd> <p>Do you find it helpful to see graphics calculator screens projected onto a screen by a teacher during lessons?</p> <p> <emph>Please explain why</emph>.</p> <hd id="AN0031271248-34">Question 7</hd> <p>Describe one thing, if any, that you have learned by experimenting or exploring with your graphics calculator.</p> <hd id="AN0031271248-35">Question 8</hd> <p>Please look at question D.</p> <p></p> <p> <ephtml> <table><tbody valign="top"><tr><td>Here are two statements. How would you decide which, if any of them, is correct?</td><td><p><graphic href="tmes_a_260583_o_um0002.gif" content-type="Graph" /></p></td></tr></tbody></table> </ephtml> </p> <ref id="AN0031271248-36"> <title> References </title> <blist> <bibl id="bib1" idref="ref1" type="bt">1</bibl> <bibtext> Dunham, P and Dick, T. 1994. Research on graphing calculators. The Mathematics Teacher, 87: 440–445.</bibtext> </blist> <blist> <bibl id="bib2" idref="ref2" type="bt">2</bibl> <bibtext> Penglase, M and Arnold, S. 1996. The graphics calculator in mathematics education: A critical review of recent research. Mathematics Education Research Journal, 8(1): 58–90.</bibtext> </blist> <blist> <bibl id="bib3" idref="ref3" type="bt">3</bibl> <bibtext> Burrill, G, Allison, J, Breaux, G, Kastberg, S, Leatham, K and Sanchez, W. 2002. Handheld Graphing Technology in Secondary Mathematics: Research Findings and Implications for Classroom Practice, Texas Instruments.</bibtext> </blist> <blist> <bibl id="bib4" idref="ref4" type="bt">4</bibl> <bibtext> Hennessey, S. 1998. The Potential of Portable Technologies for Supporting Graphing Investigations, Milton Keynes: Institute of Educational Technology, Open University.</bibtext> </blist> <blist> <bibl id="bib5" idref="ref5" type="bt">5</bibl> <bibtext> Doerr, HM and Zangor, R. 2000. Creating meaning for and with the graphing calculator. Educational Studies in Mathematics, 41: 143–163.</bibtext> </blist> <blist> <bibl id="bib6" idref="ref6" type="bt">6</bibl> <bibtext> Tharp, M, Fitzsimmons, J and Ayers, R. 1997. Negotiating a technological shift: teacher perception of the implementing of graphing calculators. Journal of Computers in Mathematics and Science Teaching, 16: 551–575.</bibtext> </blist> <blist> <bibl id="bib7" idref="ref7" type="bt">7</bibl> <bibtext> Harskamp, EG, Suhre, CJM and Streun, A. 1998. The graphics calculator in mathematics education: an experiment in the Netherlands. Hiroshima Journal of Mathematics Education, 6: 13–31.</bibtext> </blist> <blist> <bibl id="bib8" idref="ref8" type="bt">8</bibl> <bibtext> Merriweather, M and Tharp, M. 1999. The effect of instruction with graphing calculators on how general mathematics students naturalistically solve algebraic problems. Journal of Computers in Mathematics and Science Teaching, 18(1): 7–22.</bibtext> </blist> <blist> <bibl id="bib9" idref="ref9" type="bt">9</bibl> <bibtext> Adams, TL. 1997. Addressing students' difficulties with the concept of function: applying graphing calculators and a model of conceptual change. Focus on Learning Problems in Mathematics, 19: 43–51.</bibtext> </blist> <blist> <bibtext> Yerushalmy, M. 1991. Student perceptions of aspects of algebraic functions using multiple representation software. Journal of Computer Assisted Learning, 7(1): 42–57.</bibtext> </blist> <blist> <bibtext> Clement, J. 1989. The concept of variation and misconception in Cartesian graphing. Focus on Learning Problems in Mathematics, 11(1): 77–87.</bibtext> </blist> <blist> <bibtext> Graham, A and Thomas, M. 2000. Building a versatile understanding of algebraic variables with a graphic calculator. Educational Studies in Mathematics, 41: 265–282.</bibtext> </blist> <blist> <bibtext> Gage, J. 2002. Using the graphic calculator to form a learning environment for the early teaching of algebra. The International Journal of Computer Algebra in Mathematics Education, 9(1): 1–24.</bibtext> </blist> <blist> <bibtext> Doerr, HM and Zangor, R. 1999. The teacher, the task, the tool: the emergence of classroom norms. The International Journal of Computer Algebra in Mathematics Education, 6(4): 267–280.</bibtext> </blist> <blist> <bibtext> Drijvers, P and Doorman, M. 1996. The graphics calculator in mathematics education. Journal of Mathematical Behaviour, 15: 425–440.</bibtext> </blist> <blist> <bibtext> Graham, T, Headlam, C, Honey, S, Sharp, J and Smith, A. 2003. The use of graphics calculators by students in an examination: what do they really do?. International Journal of Mathematical Education in Science and Technology, 34: 319–334.</bibtext> </blist> <blist> <bibtext> Monaghan, J. 2000. Some issues surrounding the use of algebraic calculators in traditional examinations. International Journal of Mathematical Education in Science and Technology, 31(3): 381–392.</bibtext> </blist> <blist> <bibtext> Forster, PA and Mueller, U. 2001. Outcomes and implications of students' use of graphics calculators in the public examination of calculus. International Journal of Mathematics Education in Science and Technology, 32: 37–52.</bibtext> </blist> <blist> <bibtext> Taylor, M. 1995. Calculators and computer algebra systems: their use in mathematics examinations. The Mathematical Gazette, 79: 68–83.</bibtext> </blist> <blist> <bibtext> Forster, PA. 2004. Assessing technology-based approaches for teaching and learning mathematics. International Journal of Mathematical Education in Science and Technology, 37: 145–164.</bibtext> </blist> <blist> <bibtext> Lagrange, J-B. 1999. Complex calculators in the classroom: theoretical and practical reflections on teaching precalculus. International Journal of Computers for Mathematical Learning, 4: 51–81.</bibtext> </blist> <blist> <bibtext> Honey, S and Graham, T. 2003. To use or not to use graphic calculators on teaching practice: a case study of three trainee-teachers' beliefs and attitudes. The International Journal of Computer Algebra in Mathematics Education, 10(2): 81–99.</bibtext> </blist> <blist> <bibtext> Berry, J, Graham, E and Smith, A. 2006. Observing student working styles when using graphic calculators to solve mathematics problems. International Journal of Mathematical Education in Science and Technology, 37: 291–308.</bibtext> </blist> <blist> <bibtext> Keats, DM. 2000. Interviewing – A Practical Guide for Students and Professionals, Milton Keynes: Open University Press.</bibtext> </blist> </ref> <aug> <p>By E. Graham; C. Headlam; J. Sharp and B. Watson</p> <p>Reported by Author; Author; Author; Author</p> </aug> <nolink nlid="nl1" bibid="bib10" firstref="ref10"></nolink> <nolink nlid="nl2" bibid="bib11" firstref="ref11"></nolink> <nolink nlid="nl3" bibid="bib12" firstref="ref12"></nolink> <nolink nlid="nl4" bibid="bib13" firstref="ref13"></nolink> <nolink nlid="nl5" bibid="bib14" firstref="ref14"></nolink> <nolink nlid="nl6" bibid="bib15" firstref="ref15"></nolink> <nolink nlid="nl7" bibid="bib16" firstref="ref16"></nolink> <nolink nlid="nl8" bibid="bib17" firstref="ref17"></nolink> <nolink nlid="nl9" bibid="bib18" firstref="ref18"></nolink> <nolink nlid="nl10" bibid="bib19" firstref="ref19"></nolink> <nolink nlid="nl11" bibid="bib20" firstref="ref21"></nolink> <nolink nlid="nl12" bibid="bib21" firstref="ref22"></nolink> <nolink nlid="nl13" bibid="bib22" firstref="ref23"></nolink> <nolink nlid="nl14" bibid="bib23" firstref="ref25"></nolink> <nolink nlid="nl15" bibid="bib24" firstref="ref28"></nolink>
Header DbId: eric
DbLabel: ERIC
An: EJ788446
AccessLevel: 3
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: An Investigation into whether Student Use of Graphics Calculators Matches Their Teacher's Expectations
– Name: Language
  Label: Language
  Group: Lang
  Data: English
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Graham%2C+E%2E%22">Graham, E.</searchLink><br /><searchLink fieldCode="AR" term="%22Headlam%2C+C%2E%22">Headlam, C.</searchLink><br /><searchLink fieldCode="AR" term="%22Sharp%2C+J%2E%22">Sharp, J.</searchLink><br /><searchLink fieldCode="AR" term="%22Watson%2C+B%2E%22">Watson, B.</searchLink>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="SO" term="%22International+Journal+of+Mathematical+Education+in+Science+and+Technology%22"><i>International Journal of Mathematical Education in Science and Technology</i></searchLink>. Mar 2008 39(2):179-196.
– Name: Avail
  Label: Availability
  Group: Avail
  Data: Taylor & Francis, Ltd. 325 Chestnut Street Suite 800, Philadelphia, PA 19106. Tel: 800-354-1420; Fax: 215-625-2940; Web site: http://www.tandf.co.uk/journals/default.html
– Name: PeerReviewed
  Label: Peer Reviewed
  Group: SrcInfo
  Data: Y
– Name: Pages
  Label: Page Count
  Group: Src
  Data: 18
– Name: DatePubCY
  Label: Publication Date
  Group: Date
  Data: 2008
– 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="%22Grade+8%22">Grade 8</searchLink><br /><searchLink fieldCode="EL" term="%22Secondary+Education%22">Secondary Education</searchLink>
– Name: Subject
  Label: Descriptors
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Graphing+Calculators%22">Graphing Calculators</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Education%22">Mathematics Education</searchLink><br /><searchLink fieldCode="DE" term="%22Technology+Uses+in+Education%22">Technology Uses in Education</searchLink><br /><searchLink fieldCode="DE" term="%22Interviews%22">Interviews</searchLink><br /><searchLink fieldCode="DE" term="%22Classroom+Communication%22">Classroom Communication</searchLink><br /><searchLink fieldCode="DE" term="%22Grade+8%22">Grade 8</searchLink><br /><searchLink fieldCode="DE" term="%22Educational+Research%22">Educational Research</searchLink><br /><searchLink fieldCode="DE" term="%22Algebra%22">Algebra</searchLink><br /><searchLink fieldCode="DE" term="%22Foreign+Countries%22">Foreign Countries</searchLink><br /><searchLink fieldCode="DE" term="%22Teacher+Expectations+of+Students%22">Teacher Expectations of Students</searchLink><br /><searchLink fieldCode="DE" term="%22Feedback+%28Response%29%22">Feedback (Response)</searchLink><br /><searchLink fieldCode="DE" term="%22Secondary+School+Mathematics%22">Secondary School Mathematics</searchLink>
– Name: Subject
  Label: Geographic Terms
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22United+Kingdom+%28England%29%22">United Kingdom (England)</searchLink><br /><searchLink fieldCode="DE" term="%22United+Kingdom+%28Wales%29%22">United Kingdom (Wales)</searchLink>
– Name: DOI
  Label: DOI
  Group: ID
  Data: 10.1080/00207390701607307
– Name: ISSN
  Label: ISSN
  Group: ISSN
  Data: 0020-739X
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This research examines students' use of graphics calculators and investigates the extent to which the students' use meets their teachers aim when using graphics calculators in the classroom. The teacher's use of her graphics calculator was analysed over a week using Key Record software. The teacher was questioned about her aims and expectations for the students when using a graphics calculator. As a result an interview schedule for students was constructed in order to determine whether the teacher's aims had been met. It was found that in general all of the teachers' aims were met to some extent by most of the students. (Contains 8 figures and 1 table.)
– Name: AbstractInfo
  Label: Abstractor
  Group: Ab
  Data: Author
– Name: Ref
  Label: Number of References
  Group: RefInfo
  Data: 24
– Name: DateEntry
  Label: Entry Date
  Group: Date
  Data: 2008
– Name: AN
  Label: Accession Number
  Group: ID
  Data: EJ788446
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=eric&AN=EJ788446
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1080/00207390701607307
    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 18
        StartPage: 179
    Subjects:
      – SubjectFull: Graphing Calculators
        Type: general
      – SubjectFull: Mathematics Education
        Type: general
      – SubjectFull: Technology Uses in Education
        Type: general
      – SubjectFull: Interviews
        Type: general
      – SubjectFull: Classroom Communication
        Type: general
      – SubjectFull: Grade 8
        Type: general
      – SubjectFull: Educational Research
        Type: general
      – SubjectFull: Algebra
        Type: general
      – SubjectFull: Foreign Countries
        Type: general
      – SubjectFull: Teacher Expectations of Students
        Type: general
      – SubjectFull: Feedback (Response)
        Type: general
      – SubjectFull: Secondary School Mathematics
        Type: general
      – SubjectFull: United Kingdom (England)
        Type: general
      – SubjectFull: United Kingdom (Wales)
        Type: general
    Titles:
      – TitleFull: An Investigation into whether Student Use of Graphics Calculators Matches Their Teacher's Expectations
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Graham, E.
      – PersonEntity:
          Name:
            NameFull: Headlam, C.
      – PersonEntity:
          Name:
            NameFull: Sharp, J.
      – PersonEntity:
          Name:
            NameFull: Watson, B.
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 03
              Type: published
              Y: 2008
          Identifiers:
            – Type: issn-print
              Value: 0020-739X
          Numbering:
            – Type: volume
              Value: 39
            – Type: issue
              Value: 2
          Titles:
            – TitleFull: International Journal of Mathematical Education in Science and Technology
              Type: main
ResultId 1