Professional Development in Statistics, Technology, and Cognitively Demanding Tasks: Classroom Implementation and Obstacles
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| Title: | Professional Development in Statistics, Technology, and Cognitively Demanding Tasks: Classroom Implementation and Obstacles |
|---|---|
| Language: | English |
| Authors: | Foley, Gregory D., Khoshaim, Heba Bakr, Alsaeed, Maha, Er, S. Nihan |
| Source: | International Journal of Mathematical Education in Science and Technology. 2012 43(2):177-196. |
| 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 |
| Peer Reviewed: | Y |
| Page Count: | 20 |
| Publication Date: | 2012 |
| Document Type: | Journal Articles Reports - Evaluative |
| Education Level: | High Schools |
| Descriptors: | Professional Development, Statistics, Mathematics Instruction, Technology, Computer Literacy, Teacher Improvement, Program Effectiveness, Communities of Practice, Pedagogical Content Knowledge, Secondary School Teachers, High Schools, Secondary School Mathematics |
| DOI: | 10.1080/0020739X.2011.592616 |
| ISSN: | 0020-739X |
| Abstract: | Attending professional development programmes can support teachers in applying new strategies for teaching mathematics and statistics. This study investigated (a) the extent to which the participants in a professional development programme subsequently used the techniques they had learned when teaching mathematics and statistics and (b) the obstacles they encountered in enacting cognitively demanding instructional tasks in their classrooms. The programme created an intellectual learning community among the participants and helped them gain confidence as teachers of statistics, and the students of participating teachers became actively engaged in deep mathematical thinking. The participants indicated, however, that time, availability of resources and students' prior achievement critically affected the implementation of cognitively demanding instructional activities. (Contains 1 figure.) |
| Abstractor: | As Provided |
| Number of References: | 52 |
| Entry Date: | 2012 |
| Accession Number: | EJ986039 |
| Database: | ERIC |
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| FullText | Links: – Type: pdflink Url: https://content.ebscohost.com/cds/retrieve?content=AQICAHj0k_4E0hTGH8RJwT4gCJyBsGNe_WN95AvKlDbXJGqwxwH3MyzZT-JXyzZTeTPEBkmIAAAA4jCB3wYJKoZIhvcNAQcGoIHRMIHOAgEAMIHIBgkqhkiG9w0BBwEwHgYJYIZIAWUDBAEuMBEEDCwJCw8TaEvRkpUYtAIBEICBmqcrWVtf_VrowCtgsvbkXZFMXYmK-ARpcjU3kUUVpQ9VLEmAUe43hWRKNuwtl92aBYjfhn12XmokwFNy-v7R2M61xXTB8f1LajOj0potlox0jlxTlOBipnk2DAzAGCeAYOKSeim7d5DFuW4TO8cxCgQBmXarlqG_bhk_O1AIzK5VxstAXJWCr9CVuUFe5dcF8--j9K09JS0xbaQ= Text: Availability: 1 Value: <anid>AN0071924346;imt01mar.12;2019Mar01.13:20;v2.2.500</anid> <title id="AN0071924346-1">Professional development in statistics, technology, and cognitively demanding tasks: classroom implementation and obstacles. </title> <p>Attending professional development programmes can support teachers in applying new strategies for teaching mathematics and statistics. This study investigated (a) the extent to which the participants in a professional development programme subsequently used the techniques they had learned when teaching mathematics and statistics and (b) the obstacles they encountered in enacting cognitively demanding instructional tasks in their classrooms. The programme created an intellectual learning community among the participants and helped them gain confidence as teachers of statistics, and the students of participating teachers became actively engaged in deep mathematical thinking. The participants indicated, however, that time, availability of resources and students' prior achievement critically affected the implementation of cognitively demanding instructional activities.</p> <p>Keywords: professional development; statistics; technology; cognitively demanding tasks; mathematical tasks framework; task analysis guide; technological pedagogical content knowledge</p> <hd id="AN0071924346-2">1. Introduction</hd> <p>Eight high school mathematics teachers from a Midwestern US state participated in a yearlong professional development (PD) programme to advance their content knowledge, pedagogical expertise and facility with technology for teaching statistics using cognitively demanding instructional tasks. The study reported herein is an exploratory investigation of the application of the ideas and methods taught in the PD programme as well as the obstacles faced by programme participants, with special attention to the implementation of cognitively demanding instructional tasks. The results were used in the iterative research and development process described below.</p> <p>The common use of data-based decision making in many careers and in everyday life has led several key organizations and national initiatives in the US to advocate for increased statistics education in Grades 9–12 [[<reflink idref="bib1" id="ref1">1</reflink>]]. Unfortunately, many US mathematics teachers have only a limited academic background in statistics, and teaching statistics calls for problem-solving and pedagogical processes different from those used in other areas of the mathematical sciences [[<reflink idref="bib7" id="ref2">7</reflink>]]. In particular, statistics instruction should engage students in the use of technologies to collect and process data and should develop their capacity to formulate and answer questions that anticipate the variability of resulting responses [<reflink idref="bib4" id="ref3">4</reflink>],[<reflink idref="bib10" id="ref4">10</reflink>]. Moreover, the level of cognitive demand of instructional tasks has been identified as a key predictor of student learning in mathematics classrooms. Yet, most US students do not experience such tasks [[<reflink idref="bib11" id="ref5">11</reflink>]]. Stigler and Hiebert [<reflink idref="bib11" id="ref6">11</reflink>] found that US students spend most of their mathematics instructional time memorizing facts and practicing procedures.</p> <hd id="AN0071924346-3">2. Context of the study</hd> <p></p> <hd id="AN0071924346-4">2.1. Iterative design</hd> <p>The PD programme that was investigated is Quantifying Uncertainty and Analyzing Numerical Trends (QUANT). QUANT is a yearlong programme that begins with a 2-week summer institute and continues with follow-up workshops and ongoing support during the ensuing school year. The QUANT project uses an iterative research and development design to address the question, How can teacher PD improve instruction in data analysis, probability and statistical reasoning at the high school level?</p> <p>Beginning in autumn 2007, the project has approached the development of the PD curriculum as a <emph>design science</emph>, that is, as a combination of instructional engineering and education research [<reflink idref="bib14" id="ref7">14</reflink>]. The project team has used feedback from the prior enactments of the PD curriculum to revise the materials and methods. The QUANT programme has been enacted five times and has gone through three yearlong iterative cycles. For the first enactment, the curriculum was developed using a <emph>backward design</emph>[<reflink idref="bib15" id="ref8">15</reflink>], beginning with project goals, PD goals and progressing to objectives for participant learning. The PD activities and data collection instruments were then developed based on these objectives. The initial development team included two university mathematics educators, one mathematician, two school practitioners and one doctoral student. After this initial design and development, the project team enacted the programme via an institute in June 2008 and follow-up during 2008–2009 and, using feedback from the June 2008 institute, enacted the programme a second time via an institute in August 2008 and follow-up concurrent with the first enactment. This article reports on the research concerning the classroom implementation of the third enactment of the programme, which took place during June 2009 with follow-up during the school year 2009–2010. The fourth and fifth enactments occurred during 2010–2011, and a sixth enactment (fourth yearlong iteration) is planned for 2011–2012.</p> <p>Figure 1 shows a model of the interactions among the objects of research in the QUANT project. The left-to-right arrows show a chain of events from developer planning to student outcomes. The arrows looping back to the left represent ongoing development based on feedback from teacher practice and student attainment. This feedback is being used to refine the PD materials and at times, as indicated by the dotted line in Figure 1, even the premises of the design itself to achieve the desired outcomes.</p> <p>Graph: Figure 1. The iterative research and development design of the PD programme.</p> <hd id="AN0071924346-5">2.2. Description of the PD intervention</hd> <p>The yearlong QUANT PD programme is designed to improve teachers' technological pedagogical content knowledge (TPACK) in the areas of data analysis, probability and statistics. (Extensive details of the QUANT programme are provided in [<reflink idref="bib10" id="ref9">10</reflink>],[<reflink idref="bib16" id="ref10">16</reflink>].)</p> <p>The first two QUANT institutes took place in summer 2008. The 15 practicing teachers and other attendees in these institutes participated in follow-up activities during the school year 2008–2009. The data from these programmes were used to develop the third QUANT programme, which is the focus of the research reported here.</p> <p>This third QUANT programme began with a 2-week institute in June 2009 at the Ohio Resource Center. The participants in this programme were eight practicing high school mathematics teachers. The institute consisted of ten 6-h days of integrated instruction on technology, pedagogy and content in data analysis, probability and statistics. The key aims of the programme were as follows:</p> <p></p> <ulist> <item> 1. To deepen participants' understanding of content and pedagogy for teaching data analysis, probability, and statistics.</item> <p></p> <item> 2. To develop participants' knowledge of the mathematical tasks framework (MTF) and task analysis guide (TAG) [<reflink idref="bib17" id="ref11">17</reflink>],[<reflink idref="bib18" id="ref12">18</reflink>].</item> <p></p> <item> 3. To advance participants' working knowledge of selected instructional technology and their facility in integrating handheld technology into their instruction.</item> <p></p> <item> 4. To encourage participants' use of cognitively demanding tasks during instruction in data analysis, probability, and statistics in their classrooms.</item> </ulist> <p>The third QUANT programme explored inquiry-based activities in mathematics and statistics using manipulatives, data collection devices and Texas Instruments' TI-<emph>n</emph>spire™ CAS software, which includes a graphing utility, spreadsheet and statistical package and runs on handheld, laptop and desktop computers. Pedagogically, the participants used the MTF and the TAG presented by Stein et al. [<reflink idref="bib18" id="ref13">18</reflink>]. The purpose of introducing the participants to the MTF was to focus on the relationship between the nature of the instructional tasks that a teacher employs and the student learning results. The purpose of introducing the participants to the TAG was to enhance their ability to identify the two categories of mathematical tasks associated with high cognitive demands – <emph>doing mathematics</emph> and <emph>procedures with connections –</emph> as well as two categories of mathematical tasks associated with low cognitive demands – <emph>memorization</emph> and <emph>procedures without connections.</emph> To address the importance of the TAG and to set expectations for classroom implementation, participants in the summer institute prepared and presented sample lessons that reflected their capacity to teach statistical concepts using high-level (i.e. cognitively demanding) tasks. These lessons gave the participants the opportunity to practice the new ideas and methods they had learned and served as an authentic summative assessment for the institute. During the follow-up workshops, which were held at the Ohio Resource Center on 3 October 2009 and 13 March 2010, participants discussed their implementation of these and other lessons that involved high-level classroom activities.</p> <p>The QUANT programme uses TPACK as a means to develop statistical proficiency for teaching among its participants. The QUANT development team defines <emph>statistical proficiency for teaching</emph> as 'teachers' knowledge that is useful in promoting the statistical proficiency of their students' [<reflink idref="bib10" id="ref14">10</reflink>, p. 5]. Statistical proficiency is based on the same five major components as mathematical proficiency: conceptual understanding, procedural fluency, strategic competence, adaptive reasoning and productive disposition [<reflink idref="bib19" id="ref15">19</reflink>].</p> <p>The June 2009 QUANT summer institute consisted of a series of participant activities designed to model strategic use of technology, cognitively demanding tasks and purposeful classroom discourse. Most of the QUANT activities were technology-rich, such as An Arm and a Leg and One Thing 21 Times, both of which are detailed on-line [<reflink idref="bib10" id="ref16">10</reflink>]. The Double Stuf activity asked participants to design, carry out and report on a statistical study to investigate the question, Are Oreo® Double Stuf cookies really double stuffed? Other activities – such as Words of Statistics, What is Random? and Analyzing Some Misconceptions in Probabilistic and Statistical Reasoning – were intended to develop conceptual understanding and promote opportunities for meaningful discourse.</p> <p>The institute had three primary instructors. The lead instructor for both weeks was an associate professor of mathematics, PhD in mathematics education, and experienced statistics instructor who had participated in the second enactment of QUANT. Coinstructing the first week was an experienced high school teacher who was a certified Texas Instruments instructor. Coinstructing the second week was another experienced high school teacher who had participated in the second enactment of QUANT. Foley, the first author of this article and QUANT project director, provided limited instruction as well.</p> <hd id="AN0071924346-6">2.3. Research purpose and research questions</hd> <p>This article reports the findings of an exploratory qualitative study that investigated the perspectives of the participants in the third QUANT programme and the effects that the programme had on them and their teaching. The main goal of the study was to investigate how the programme influenced the participants' knowledge for teaching and their implementation of high-level tasks. In the follow-up phase, the research team investigated the degree to which participants actually applied or adapted – or were willing to apply or adapt – the content, pedagogy and technology they had experienced in the QUANT programme. The study examined whether the QUANT programme's activities aligned with the participants' teaching goals and specifically the extent to which the participants used high-level tasks when teaching mathematics. The main research questions for the study were as follows:</p> <p></p> <ulist> <item> • Did the QUANT participants implement or intend to implement high-level tasks in teaching mathematics?</item> <p></p> <item> • What, if any, changes did the QUANT participants make to their teaching methods as a result of using the TAG and TI-<emph>n</emph>spire™ CAS software or handhelds?</item> <p></p> <item> • What did the QUANT participants identify as supporting or inhibiting their implementation of high-level tasks and other aspects of the programme?</item> </ulist> <p>All of these questions were designed to provide iterative feedback concerning how future QUANT programmes could support the participants in applying the content, pedagogy and technology experienced in the programme.</p> <hd id="AN0071924346-7">3. Literature review</hd> <p></p> <hd id="AN0071924346-8">3.1. The MTF and the TAG</hd> <p>In the QUASAR project, a national educational reform effort in the US, researchers sought to improve mathematical instruction by focusing on reasoning and problem-solving skills [<reflink idref="bib20" id="ref17">20</reflink>]. One of the main findings of this project was that mathematical tasks are not all the same. They differ in the type of cognitive demands and the level of thinking required from students to solve them. A second important conclusion was that the cognitive demands associated with a task may change when it is implemented in the classroom. As a result, the design of the MTF reflects the different phases a task passes through during instruction [<reflink idref="bib17" id="ref18">17</reflink>]. Researchers have used the MTF as a lens to reflect on the tasks in mathematical instruction [<reflink idref="bib18" id="ref19">18</reflink>],[<reflink idref="bib21" id="ref20">21</reflink>],[<reflink idref="bib22" id="ref21">22</reflink>]. In addition, Stein et al. [<reflink idref="bib18" id="ref22">18</reflink>] have used the TAG to classify the tasks presented in instructional materials as high-level, including doing mathematics and procedures with connections, or low-level, including memorization and procedures without connections. They concluded that applying cognitively demanding tasks in mathematics classrooms is not straightforward.</p> <hd id="AN0071924346-9">3.2. Cognitively demanding tasks</hd> <p>Even though engaging students in cognitively demanding tasks has been proved to be beneficial to learning, it is not, most of the time, what students experience in the classroom. Swan [<reflink idref="bib12" id="ref23">12</reflink>] claims that implementing high-level tasks encourages the in-class discussion of concepts, representations and misconceptions and that these discussions lead students to construct new concepts and knowledge. Swan's study found that use of cognitively demanding tasks was associated with a student-centred, collaborative learning environment.</p> <p>Stylianides and Stylianides [<reflink idref="bib23" id="ref24">23</reflink>] examined the implementation of high-level tasks in mathematics classrooms and the factors associated with teachers' willingness to apply them. They concluded that teachers' beliefs, knowledge and experiences are key elements that influence the implementation of high-level tasks in classrooms. In addition, teachers' enthusiasm [<reflink idref="bib24" id="ref25">24</reflink>] and well-chosen tasks [<reflink idref="bib18" id="ref26">18</reflink>],[<reflink idref="bib25" id="ref27">25</reflink>],[<reflink idref="bib26" id="ref28">26</reflink>] may motivate students to stay engaged.</p> <p>Teacher preparation and PD programmes provide the mathematical, pedagogical and technological knowledge necessary to understand, appreciate and apply cognitively demanding tasks in the classroom [<reflink idref="bib18" id="ref29">18</reflink>],[<reflink idref="bib21" id="ref30">21</reflink>],[<reflink idref="bib23" id="ref31">23</reflink>],[<reflink idref="bib26" id="ref32">26</reflink>]. Teachers translate and absorb the knowledge and techniques introduced during PD programmes into their unique pedagogies [<reflink idref="bib27" id="ref33">27</reflink>]. Pierson [<reflink idref="bib28" id="ref34">28</reflink>] found a positive relationship between teachers who engaged their students in cognitively demanding tasks and discourse and the mathematics achievement of the students within the context of an integrated system of teacher PD, representational mathematics software and associated curriculum materials.</p> <p>Several studies have investigated the relationship between mathematical tasks and students' learning. Boston and Smith [<reflink idref="bib21" id="ref35">21</reflink>], Silver and Stein [<reflink idref="bib20" id="ref36">20</reflink>] and Stein et al. [<reflink idref="bib17" id="ref37">17</reflink>] examined the extent to which teachers set up and implemented high-level tasks as a result of participating in a PD programme and found a positive correlation between the two. In addition, students improved their ability to communicate mathematically and to solve problems as they became increasingly competent in providing multiple representations of tasks. The benefit of applying high-level tasks in classrooms is not limited to students. Two studies have shown that the cognitive level of classroom tasks influence how teachers think about instructional planning and implementation [<reflink idref="bib29" id="ref38">29</reflink>],[<reflink idref="bib30" id="ref39">30</reflink>]. Arbaugh and Brown [<reflink idref="bib29" id="ref40">29</reflink>] found that, as teachers became aware of the effect of high-level tasks on students' learning, they became increasingly reflective on their teaching and incorporated more such tasks into their practice.</p> <hd id="AN0071924346-10">3.3. Critical features of PD programmes</hd> <p></p> <hd id="AN0071924346-11">3.3.1. Blending content with pedagogy</hd> <p>A key aim of PD is to improve teacher knowledge in ways that will support student learning. So it is natural to focus on the development of 'pedagogical content knowledge' (PCK), which Shulman [<reflink idref="bib31" id="ref41">31</reflink>] refers to as the knowledge that supports teachers in presenting specific content while using pedagogical strategies to develop student understanding. Embedding pedagogy into content knowledge for teaching has been a growing trend since Shulman introduced the construct of PCK. Evidence suggests that teachers embrace PD that blends content with pedagogy. Using a US national sample of 1027 mathematics and science teachers, Garet et al. [<reflink idref="bib32" id="ref42">32</reflink>] identified the characteristics that make PD programmes effective and found that programmes that emphasize PCK and actively engage participants in cognitively demanding activities tend to influence teaching practice.</p> <hd id="AN0071924346-12">3.3.2. Progressing from PCK to TPACK</hd> <p>The tremendous growth in the number of technological innovations that address mathematical teaching and learning [<reflink idref="bib33" id="ref43">33</reflink>],[<reflink idref="bib34" id="ref44">34</reflink>] indicates that students can learn more by using appropriate technological tools effectively. The key is how teachers integrate technology in instruction. TPACK is an extension of PCK that integrates a teacher's content knowledge, pedagogical expertise and facility with technology [<reflink idref="bib35" id="ref45">35</reflink>]. TPACK is not a teacher's technological knowledge in isolation, but in combination with PCK.</p> <p>In mathematics education, the responsibility for developing teachers' TPACK lies partially with PD programmes. Niess et al. [<reflink idref="bib36" id="ref46">36</reflink>] suggested that teachers should learn to use updated technological tools to support their mathematics instruction. They considered in-service PD experiences to be the only way to improve the TPACK of current teachers who are limited in their technological experiences.</p> <hd id="AN0071924346-13">3.3.3. Community of learners</hd> <p>Besides improving TPACK, effective PD programmes build an intellectual community among the participants. Lachance and Confrey [<reflink idref="bib37" id="ref47">37</reflink>] concluded that developing teacher knowledge via PD should involve active participant engagement and should create a community of learners. Teachers who participated in PD programmes reported that they felt professional and respected because they had heard from someone who fully understood instruction and was able to give them effective advice, especially in an era of curriculum reform that requires extra attention and planning from the teachers [<reflink idref="bib38" id="ref48">38</reflink>]. Working within a community in which members can exchange knowledge and experience is critical for teachers, especially when implementing new technologies and approaches in their classrooms [<reflink idref="bib39" id="ref49">39</reflink>]. In Japan, for instance, mathematics teachers meet several times to discuss pedagogical strategies before agreeing on a lesson plan for a specific topic [<reflink idref="bib11" id="ref50">11</reflink>].</p> <p>As a learning community, PD participants can share expertise, plan lessons together, enact and reflect on implemented lessons and exchange student work samples. Schmoker [<reflink idref="bib40" id="ref51">40</reflink>] explained how such professional learning communities can quickly lead to positive instructional change. McLaughlin and Talbert [<reflink idref="bib41" id="ref52">41</reflink>] detailed the process of developing learning communities for improved student outcomes. A shared language, a common vision for instruction and aligned goals provide a basis for such a community. The QUANT programme purposely included these elements with the idea of building an intellectual community of teacher–scholars.</p> <p>In the article <emph>Unfinished Business: Challenges for Mathematics Educators in the Next Decades</emph>, Kilpatrick and Silver [<reflink idref="bib42" id="ref53">42</reflink>] discussed the main challenges for school mathematics in the new century: to guarantee mathematics for all; to promote students' understanding; to maintain balance in the curriculum; to use evaluation as an opportunity for learning and to develop professional practice. With respect to PD programmes, Kilpatrick and Silver [<reflink idref="bib42" id="ref54">42</reflink>] argued that one of the important characteristics is working with colleagues to improve teaching practice for the whole community:</p> <p>Most mathematics teachers work in relative isolation, with little support for innovation and few incentives to improve their practice. The possibility of collaborating with other teachers in developing instructional materials and assessment tools is typically absent. Many realize that they need to keep abreast of the field and to improve their preparation for teaching mathematics, but nothing in their workplace provides them with the requisite opportunities and resources (p. 230).</p> <hd id="AN0071924346-14">3.3.4. Other critical characteristics of PD</hd> <p>In addition to focusing on the development of teacher knowledge – pedagogy, content and technology – and collaboration within a learning community, Sowder [<reflink idref="bib43" id="ref55">43</reflink>] detailed other elements of effective PD, including the theoretical basis and the length and intensity of the programme. The QUANT programme uses TPACK as a means to develop statistical proficiency for teaching. The 2-week institute provides an intensive start, and the follow-up programme gives it a sustained character. According to Sowder, when a PD programme is appropriate in length and provides support for classroom implementation, it tends to be effective. In addition, continued contact with the participants and helping them overcome the difficulties they face during implementation can be catalysts for changing their teaching practice. Garet et al. [<reflink idref="bib32" id="ref56">32</reflink>] reported that the duration of a PD programme is linked to its effectiveness. The results from California mathematics teacher institutes indicate that the length of a PD programme and the number of follow-up meetings are positively correlated with the programme's impact [<reflink idref="bib44" id="ref57">44</reflink>].</p> <hd id="AN0071924346-15">3.3.5. Obstacles that prevent change</hd> <p>PD programmes can be effective in transforming teacher behaviours and improving student achievement [<reflink idref="bib22" id="ref58">22</reflink>],[<reflink idref="bib28" id="ref59">28</reflink>],[<reflink idref="bib32" id="ref60">32</reflink>], and many factors can influence the effectiveness of such programmes [<reflink idref="bib32" id="ref61">32</reflink>],[<reflink idref="bib37" id="ref62">37</reflink>],[<reflink idref="bib38" id="ref63">38</reflink>],[[<reflink idref="bib43" id="ref64">43</reflink>]]. PD organizers should consider and address the challenges and obstacles that teachers face when trying to implement new content, pedagogy and technology in their classroom instruction. Lack of time is one of the main factors that may impede the implementation of new content, pedagogy and technology. Heid et al. [<reflink idref="bib46" id="ref65">46</reflink>] investigated how teachers' responsibilities and roles change as they implement new technologies. Heid et al. identified three new teaching roles – technical assistant, catalyst and facilitator – and they found that the time needed to complete a lesson may increase when the teacher is using new technologies.</p> <p>Time management, however, is not an issue exclusive to teaching while using new technological tools. Limited instructional time affects teachers' ability to implement other innovative or reform-based methods as well as the nature and quality of their implementation [<reflink idref="bib22" id="ref66">22</reflink>]. In the case of the Core-Plus mathematics curriculum, for instance, teachers reported that time limitations affected their ability to enact the curriculum as they would have hoped. Instead of introducing the topics as facts and procedures in small units as they traditionally had, teachers were required to organize lessons around major conceptual themes, which conflicted with the limited time block for mathematics provided by schools [<reflink idref="bib39" id="ref67">39</reflink>].</p> <p>Due to the increasing focus on using technological tools when teaching mathematics, many PD programmes incorporate the use of technology. If these resources are not available to teachers in their classrooms, however, the PD programme's impact will be greatly diminished. Teachers will not be able to apply the new instructional innovation in their teaching. The unavailability of resources is another major obstacle to applying educational innovation in classrooms [<reflink idref="bib47" id="ref68">47</reflink>].</p> <p>Not all PD programmes are considered to be transformative of students' learning. The problem is not always the lack of PD programmes, resources or tools; sometimes the issue lies with the teachers themselves. Classroom instruction that supports students' active engagement comes from teachers who hold positive beliefs about students' mathematical practices and mathematical thinking [<reflink idref="bib48" id="ref69">48</reflink>]. Furthermore, teachers' beliefs about mathematics, teaching and learning may conflict with reform-based mathematics instruction and the implementation of cognitively demanding tasks that some PD programmes advocate [<reflink idref="bib22" id="ref70">22</reflink>]. Kagan [<reflink idref="bib27" id="ref71">27</reflink>] stated that teachers' beliefs and practices show strong resistance to change in spite of a PD programme's promising recommended practices. Regardless of whether teachers attend PD workshops, if they are not convinced that the new pedagogy works, they may never attempt to enact it.</p> <p>Teachers' beliefs and perspectives about the nature of learning mathematics are another potential obstacle to implementing the types of pedagogical shifts encouraged by PD programmes. Specifically, concerns about student success tend to make teachers unwilling to allow their students to struggle through cognitively demanding tasks. Such teachers provide unnecessary scaffolding for their students [<reflink idref="bib22" id="ref72">22</reflink>]. When working with cognitively demanding tasks, this practice negatively affects the teachers' attempt to change their traditional teaching methods. Smith [<reflink idref="bib38" id="ref73">38</reflink>] called this action on the teachers' part a dilemma that they strove to resolve in their PD. On the one hand, teachers wanted to have high cognitive expectations for their students, but on the other hand, they wanted to relieve the students' struggle by giving them support that ultimately reduced the complexity of the tasks and the associated learning.</p> <hd id="AN0071924346-16">4. Methodology</hd> <p></p> <hd id="AN0071924346-17">4.1. Subjects</hd> <p>All eight of the participants in the third QUANT programme were practicing teachers at public high schools in Ohio. All of these participants were invited to be subjects in the study; five agreed to do so. Ohio is a Midwestern US state of some 106,000 km<sups>2</sups> with a population of roughly 11.5 million. According to 2009 US Census Bureau estimates, 84.7% are white; 12.1% are black; 6.1% speak languages other than English at home; and 13.3% are below the poverty level. Ohio has several large urban centres, numerous small towns and extensive rural areas that include both large farming tracts and rugged Appalachian foothills. The more than 500 local school district boards possess a good deal of autonomy, so the 802 public high schools in Ohio have substantial curricular diversity. The subjects of the study hailed from various regions in the state, and none were from the same high school or school district. To maintain the anonymity of the participants in the study, their schools and districts are not identified here. As a further guard on participant anonymity, below we refer to them by letter as Participant A, Participant B, etc.</p> <hd id="AN0071924346-18">4.2. Data collection and transcription</hd> <p>From 10 October 2009 through 1 November 2009, the authors Khoshaim, Alsaeed, and Er conducted face-to-face interviews, using a semistructured protocol based on 11 specific open-ended questions. Each interview lasted approximately 60 min. The interviews provided participants an opportunity to express their thoughts and provide feedback regarding the QUANT programme. The researchers used follow-up questions when appropriate. Each interviewee responded to approximately 20–30 questions. Meetings with two of the interviewees took place in their classrooms, which provided insight into their teaching environment. All of the interviews were audiorecorded in their entirety and each was transcribed by the researcher who conducted the interview. All of the quotations used in this article were double-checked for accuracy using the original recordings.</p> <p>The participants were asked to reflect on negative or positive experiences in implementing what they had learned in the QUANT programme and on how this affected their daily practice. The interviewers invited the teachers to reflect on the type of classroom environment that would support such implementation. Other questions addressed the usefulness of the QUANT materials and resources given to participants to help them use innovative teaching strategies.</p> <hd id="AN0071924346-19">4.3. Data analysis</hd> <p>After the interviews and transcriptions, the data analysis phase began. The interview team read through the transcribed data several times, and they organized and categorized the data. Next, they identified themes and perspectives to organize their interpretations of the data [<reflink idref="bib49" id="ref74">49</reflink>]. The entire research team agreed on providing direct quotations to support the results and interpretations.</p> <hd id="AN0071924346-20">4.4. Possible limitations</hd> <p>This is an exploratory study with a small sample size. Participation in the study was voluntary, and the participants self-reported their opinions. The participants may have tried to say what they thought the researchers wanted to hear. To address this concern, the researchers assured the interviewees that the purpose of this study was to understand the effectiveness of the QUANT programme, not to evaluate their teaching ability or mathematical knowledge. Moreover, the three interviewers were not involved in developing the QUANT materials and were not instructors in the programme. The participants could express their views freely without concern that the interviewers would feel as if they were being evaluated.</p> <p>Three of the QUANT programme participants chose not to take part in the study and were not interviewed. The results and conclusions were based on the data collected from the remaining five participants, thus representing a sample of 62.5% of the 2009–2010 QUANT programme participants.</p> <hd id="AN0071924346-21">5. Findings</hd> <p></p> <hd id="AN0071924346-22">5.1. Participants' perspectives regarding the implementation of high-level tasks</hd> <p>Some participants indicated that their level of comfort and confidence had improved as a result of realizing how implementing high-level tasks enriched students' learning of mathematics. In varying degrees, when asked about the relative proportion of their implementation of high-level tasks, all five interviewees reported using cognitively demanding instructional tasks. Their self-reported use of such tasks varied from 5–10% to 20–30% of instruction:</p> <p></p> <ulist> <item> • Participant B stated 'maybe five to ten percent [5–10%] of the questions'.</item> <p></p> <item> • Participant E reported using high-level tasks 'maybe once a week' but went on to suggest that it was really less than 10% of the time.</item> <p></p> <item> • Participant D said, 'ten percent [10%], but this is better than what I was doing. ... probably in the exams, twenty percent [20%]'.</item> <p></p> <item> • Participant A, said, 'it is probably about a quarter [25%] high level ... unfortunately'.</item> <p></p> <item> • Participant C reported, 'over the course of a week I would hope at least twenty or thirty percent [20 or 30%] of my time is the higher level stuff'.</item> </ulist> <p>In addition, all interviewees indicated that the QUANT programme had helped them to use innovative pedagogy for teaching mathematics. Participant A, for example, reordered the sequence of tasks in a typical lesson: instead of teaching all of the techniques and procedures at the beginning, Participant A now opens with a high-level task, which leads to the main point of the lesson. If necessary, the teacher re-teaches or applies scaffolding. Participant D, on the other hand, now spends more time thinking about and developing the assessment questions used on tests. Participant D rewrote test questions used in the past and asked challenging questions during class discussions so as to encourage students' thinking.</p> <p>Participant B discussed how the implementation of high-level tasks had led students to become more actively engaged in meaningful whole-class discussions: 'Some of the questions [the students] come up with are deeper, and they come up with special cases on their own and say, "What about this?" ' In addition, Participant A stated that students were progressively improving in their ways of solving mathematical problems. Participant D noted, 'They [students] see the application of what they are doing. Once I had an activity with them, and one student was absent, so the next day her friend looked at her and said, "You missed it"'. Some participants discussed the nature of the activities in which they had engaged their students, for example:</p> <p>We gave [the students] a list of numbers ... half of the kids had music playing the first time they memorized the numbers and the other half had silence, and then they switched. ... And then we compared their scores. So the analytic skills are a little more complicated. ... They could put everyone who had music together and compare those scores compared to the ones who had silence. (Participant B)</p> <hd id="AN0071924346-23">5.2. Participants' perspectives regarding being part of a learning community</hd> <p>The participants appreciated working among high school teachers and mathematics education experts, sharing and exchanging teaching experiences and ideas. For some participants, this experience was the first step in building a network with colleagues.</p> <p>The best thing was meeting the other statistics teachers because this is only my second year of teaching statistics, and this is only the second year when we even had statistics here in this school. So I kind of felt isolated, you know, ... , I felt that I was the only statistics teacher I knew until QUANT. So that's why I really liked QUANT because now I know other statistics teachers around Ohio. (Participant C)</p> <p>The QUANT programme community gave the participants a chance to see mathematics teaching through the lens of other practitioners. 'I really enjoyed meeting other teachers who are teaching the same subject and are interested in the same topics' (Participant E).</p> <hd id="AN0071924346-24">5.3. Participants' perspectives regarding the use of technology</hd> <p>Analysis of the transcripts indicated that participants regarded their experience with the TI-<emph>n</emph>spire™ as valuable and that the programme helped them become aware of when and how to use the technology to achieve the goals of the lesson. Some participants stated that technology is a key component in their teaching strategies. 'I use technology all the time ... I can hardly imagine teaching without technology' (Participant C).</p> <p>Especially when implementing high-level tasks, the TI-<emph>n</emph>spire™ became a useful technological tool. One participant pointed out that the key benefit of the TI-<emph>n</emph>spire™ was to help the students visualize problems and understand them – a key component to solving cognitively demanding tasks. Another participant saw this technological tool as a way to capture students' attention and imagination.</p> <p>The technology is a key component. We have to use technology properly, but it is also key as far as getting the students to understand [the content]. That is just a tool to get us to a point where you are looking at the graph, you are looking at some numbers. How do you interpret that graph? How do you interpret those numbers? This is the big part. If you cannot interpret what you are seeing, ... it has been a waste of time. (Participant A)</p> <hd id="AN0071924346-25">5.4. Perspectives regarding the obstacles to implementing high-level tasks</hd> <p>A goal of this study was to understand the level of difficulty in implementing new teaching techniques, such as applying high-level tasks or rich activities, in the classroom. The interviewees said that time was the main constraint. The participants expressed their concern that they sometimes had to sacrifice quality teaching in order to address specific content in a limited time frame. Four of the interviewees commented that time alone influenced their decision whether to apply high-level tasks in the classroom.</p> <p>Time, I would say, is by far, always the biggest obstacle to anything that we try to do in education! ... I do not mind doing them, it is just, does our time fit them in? By far time is the biggest constraint. ... Most algebra teachers, geometry teachers are told [you have to cover this book]. And you might have a great high-level activity you would like to do, but it's when do you squeeze that in? So that's always the dilemma. (Participant C)</p> <p>Another participant indicated, 'To do a good, deep, rich activity takes time, and to cover a lot of material takes time, and sometimes you have to choose' (Participant E).</p> <p>Time limitation was not the only factor that discouraged shifting from traditional teaching to applying rich activities. The level of the cognitive abilities of students can determine a teacher's approach. According to Participant E, students with high cognitive abilities and a high level of motivation were not in need of high-level tasks:</p> <p>The upper-level students have lots of material to cover, so they have to go wide, but I think with lower-level student, deeper approaches are better for them. They are not expected to know much material and a lot of time if you go wide with them and not very deep, then they do not understand. I think it is just different approaches depending on the ability of the students ... ... Some [concepts] students can just pick up by being told ... Everything to me comes back to the wide versus deep debate ... My top students find depth on their own. If they are interested, they will ask more appropriate questions, and they will talk about how they apply something they learned in everyday life.</p> <hd id="AN0071924346-26">5.5. Perspectives regarding the obstacles to implementing technology</hd> <p>The QUANT programme emphasized the development of mathematics teachers' TPACK. Nevertheless, some participants indicated that the unavailability of TI-<emph>n</emph>spire™ handhelds in their schools inhibited their ability to apply what they had experienced in the QUANT programme. 'They [students] are not using the TI-<emph>n</emph>spire, but a few of my students have the TI-<emph>n</emph>spire. But it is too expensive to require everyone to purchase, and the school district is not in a position to purchase them for us' (Participant E). The interviewees indicated that such technology requires continued and extended practice. So teachers who cannot reinforce their working knowledge of the TI-<emph>n</emph>spire™ in their classrooms may not be able to use it effectively in the future even if it should become available.</p> <hd id="AN0071924346-27">5.6. Perspectives regarding the lack of motivation among fellow teachers to attend PD</hd> <p>A finding not sought but widely mentioned was that attendance at PD workshops was entirely self-motivated. Several participants reported that PD is simply unimportant to many of their fellow teachers: these individuals feel they have achieved job security and do not see the value in PD workshops:</p> <p>You know the way the education system works here, .... there is no real incentive other than self-motivation ... to be a good teacher. ... As long as you stay out of trouble, you cannot lose your job. The evaluations we get from the principals are virtually meaningless. They come in and watch us maybe one class a year and poke their head in the door for five minutes every two weeks. There is not enough oversight and not enough accountability for teachers, and there is no effort to separate or recognize good teaching versus bad teaching. We got a lot of great teachers in my school, but the only reason that they are great teachers is because they want to be. We also have a lot of bad teachers too, who do not do much. (Participant E)</p> <hd id="AN0071924346-28">6. Discussion</hd> <p>One of the most important results was participants' overwhelmingly positive feeling about their teaching as a result of the QUANT programme. Participating teachers felt that they were doing a better job than they had done previously and seemed to have tried to change their teaching methods after attending the QUANT institute. The QUANT programme helped them gain confidence in their teaching. During the interviews, participants provided evidence concerning their level of implementation of high-level tasks in their classrooms. For example, they reported using sports or business data to capture students' interest and to help them connect their mathematical knowledge to everyday situations. Specifically, four of the five participants referred to particular tasks from the QUANT materials that they had implemented to enrich students' experiences and to increase their mathematical thinking. This result is consistent with the finding that PD programmes influence teachers' practice and that teachers can learn how to implement high-level tasks for student learning [<reflink idref="bib21" id="ref75">21</reflink>],[<reflink idref="bib29" id="ref76">29</reflink>].</p> <p>The overall goal of any PD programme is to improve the learning of the participants' students. The QUANT participants indicated that their students engaged more actively in class and that they asked deeper questions that reflected their interests and understanding. The teachers incorporated genuine data into lessons to support students' engagement in the tasks and to help students connect the mathematics to real-life situations. This result is consistent with prior research on the relationship between mathematical tasks and students' learning, which showed that students improved in problem solving as they became competent in providing multiple representations of tasks and in their ability to communicate mathematically [<reflink idref="bib17" id="ref77">17</reflink>],[<reflink idref="bib20" id="ref78">20</reflink>],[<reflink idref="bib21" id="ref79">21</reflink>].</p> <p>The interviews suggested that the participants regarded the QUANT programme as a valuable opportunity for exchanging ideas and experiences with other high school teachers, especially those who taught statistics. Much of the transformative power of the experience may have been due to the participants' engagement in a community of discourse that supported a shift in pedagogy from the traditional US instructional focus on memorization and procedures without connections to the use of cognitively demanding tasks. The literature indicates that maintaining a rich environment of collaboration and communication among students in the classroom is essential to the successful implementation of high-level tasks. However, teachers need to experience rich collaborative discourse in their own education if they are to create and maintain such an environment. Whether in undergraduate classes or in-service PD programmes, teachers need to have direct experience with a rich collaborative environment to support the transfer of such a learning environment to their own classrooms [<reflink idref="bib50" id="ref80">50</reflink>].</p> <p>One of the most important features of the third QUANT programme was the support given to the participants with regard to the use of the TI-<emph>n</emph>spire™ handheld computer. The data indicated that participants were comfortable using such a device and that they appreciated the training they received. The literature shows that teachers' level of confidence regarding the use of technological tools in their classrooms can increase as a result of the support given by PD programmes [<reflink idref="bib51" id="ref81">51</reflink>]. The QUANT development and instructional team gave participants ample opportunities to experience the TI-<emph>n</emph>spire™ in PD activities that they were encouraged to adapt for their classrooms. Moreover, the participants stated that using the technology in their classrooms had supported students' understanding of the concepts being taught.</p> <p>Identifying the obstacles that may prevent the implementation of high-level tasks was a key goal of this study. The participants stated that time was a critical factor in their decisions regarding whether and how to implement high-level tasks in their classrooms. Participants in this study were teaching in various school districts, had varying lengths of teaching experience, and were teaching students with a wide range of academic proficiency. There was no direct question that investigated the effect of time on applying high-level tasks in the classrooms. However, four of the interviewees spontaneously commented that time alone influenced their decisions regarding whether and how often to apply high-level tasks in the classroom. The only teacher who did not count time as the main obstacle when enacting cognitively rich activities was the one who taught in 90-min class periods. The results indicated that class-period duration could support or inhibit implementing high-level activities when teaching mathematics. In addition to time per class period, total instructional time was one of the factors that concerned teachers. Teachers' desire to cover certain topics during the school year may conflict with their regularly employing rich activities. Although the QUANT programme seemed to convince all of the interviewees of the importance of engaging students in cognitively demanding tasks, most of them were still concerned that they would not be able to do so because of the time constraints. Class duration and the syllabus to be covered appear to be two key factors that pressure teachers when making instructional decisions.</p> <p>Time is not the only constraint, however. One participant indicated that students' prior achievement should influence the teacher's decision whether to set up and maintain cognitively demanding tasks. For this particular participant, applying high-level tasks on a regular basis is not only infeasible but also unnecessary for all students. This participant said that students with high-cognitive abilities and high motivation to learn do not need to experience high-level tasks but that students with less ability or motivation could benefit from such tasks. This finding differs from prior results concerning teachers' reluctance to maintain the cognitive demand of a task out of concern for students' struggles [<reflink idref="bib22" id="ref82">22</reflink>].</p> <p>QUANT is a technology-rich PD programme. To enable effective use of the TI-<emph>n</emph>spire™, the QUANT programme engaged the participants in activities that required the use of various features and tools on this handheld computer. The participants indicated their appreciation for such learning opportunities but expressed concerns regarding the unavailability of this technological tool in their classrooms. Several participants indicated that they would have been more likely to change their teaching procedures if the TI-<emph>n</emph>spire™ had been available to their students. They stated that to use such technology effectively requires continual practice and that, even if this tool were to become available to their students in the future, they would have forgotten how to teach using many of its features.</p> <p>Participants in this study considered themselves highly self-motivated. According to them, mathematics teachers in Ohio who believe they have secure jobs do not see the value and the benefits of participating at PD workshops; self-motivation is the only factor that may lead teachers to attend lectures, participate in PD workshops or read professional articles. One of the participants, who values PD, stated that 'for some teachers it would be hard to give up two solid weeks in [their] summer' (Participant C).</p> <hd id="AN0071924346-29">7. Conclusion</hd> <p>According to the Third International Mathematics and Science Study, students in the US do not experience cognitively demanding tasks to the same degree as students in other top-performing countries [<reflink idref="bib52" id="ref83">52</reflink>]: US students spend 96% of their classroom practicing procedural activities that require them to recall previously memorized formulae while Japanese students spend most of their time engaged in complex tasks that require inventing mathematical procedures and analysing associated mathematical concepts [<reflink idref="bib52" id="ref84">52</reflink>]. This study reported on the perspectives of participants who attended a PD programme that attempted to assist teachers in critically choosing, analysing and implementing cognitively demanding statistical tasks that go beyond the current US tradition of drill and practice in mathematics classrooms.</p> <p>To support the improvement of teaching of mathematics, it is essential to report the voices and perspectives of teachers who consider themselves highly motivated and who face the challenge to improve their instructional practice by attending PD programmes. The QUANT programme provides a professional learning experience that integrates pedagogy, content and technology to support a community of practice and to facilitate reform of classroom instruction. It is the combination and integration of these elements that engaged the participating teachers in rich statistical problem solving. The teachers' involvement in the cognitively demanding tasks of the programme was catalysed by the applications of the TI-<emph>n</emph>spire™ that allowed them to collect, explore and analyse statistical data.</p> <p>Participants of the QUANT programme indicated how they had tried to change their instruction by introducing high-level tasks into their teaching. They had become more confident in teaching statistical concepts and were staying in communication with others who were teaching the same subject. The students of the participants also benefited from the experience and had begun to ask deeper questions that demonstrated their engagement in creative thinking. Students of the participants exhibited enjoyment as they collected and analysed genuine data that developed their sense of understanding of statistics in context.</p> <p>The second major aspect of the study was to gain an understanding of the teachers' perspectives about the obstacles to changing their traditional teaching practice. The participating teachers indicated that cognitively demanding task-based instruction required a great amount of implementation time. In addition, one revealed a lack of perceived need to implement cognitively rich tasks for their highly motivated students who have already exhibited extensive ability to engage in complex thinking. Even if teachers show a high willingness to transform their instruction, limited materials inhibited their implementation. Identifying such obstacles is important for planning future QUANT enactments and other PD programmes.</p> <p>This exploratory study investigated the classroom implementation of the ideas and skills taught in the third QUANT programme and the obstacles that participants faced when implementing cognitively demanding instructional tasks. The results have been used to refine the QUANT programme materials and instruction in keeping with the iterative design of the programme. Moreover, during 2010–2011, in a related PD programme, the research team has been conducting classroom observations and analysing student work samples to delve deeper into the nature of classroom implementation and student learning. In addition, during summer 2010, an ethnographer videotaped this entire PD institute and took notes regarding the formation of the learning community among the participants. This research will inform future QUANT programmes and related PD efforts using the model illustrated in Figure 1. The intent is to strengthen the PD materials and PD workshop instruction and to support teachers' implementation in ways that improve student learning.</p> <p>The influence of PD programmes on participants' practice should not be taken for granted. The results of our exploratory investigation offer promise for improving our future PD programmes, and we encourage other PD organizers to use similar methods to revise and refine their programmes. Organizers of any PD programme should conduct research to assess the extent to which participants implement the concepts and techniques that they were taught in the programme.</p> <hd id="AN0071924346-30">Acknowledgements</hd> <p>The QUANT programme has been supported by grants from the Improving Teacher Quality Programme of the Ohio Board of Regents, the Mathematics PD Programme of the Ohio Department of Education, the US Department of Education, the South East Ohio Center for Excellence in Mathematics and Science and the Martha Holden Jennings Foundation. We acknowledge this generous private, state and federal support as well as the assistance of the following additional colleagues and research associates who have assisted with the materials development, workshop instruction or the associated research and evaluation: Thomas R. Butts, Laura J. Moss, Jeremy F. Strayer, Sigrid Wagner, Michelle Reed, George A. Johanson, Jeffery Connor, Jerry L. Moreno, Ralph Martin, A. 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| Items | – Name: Title Label: Title Group: Ti Data: Professional Development in Statistics, Technology, and Cognitively Demanding Tasks: Classroom Implementation and Obstacles – Name: Language Label: Language Group: Lang Data: English – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Foley%2C+Gregory+D%2E%22">Foley, Gregory D.</searchLink><br /><searchLink fieldCode="AR" term="%22Khoshaim%2C+Heba+Bakr%22">Khoshaim, Heba Bakr</searchLink><br /><searchLink fieldCode="AR" term="%22Alsaeed%2C+Maha%22">Alsaeed, Maha</searchLink><br /><searchLink fieldCode="AR" term="%22Er%2C+S%2E+Nihan%22">Er, S. Nihan</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>. 2012 43(2):177-196. – 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 – Name: PeerReviewed Label: Peer Reviewed Group: SrcInfo Data: Y – Name: Pages Label: Page Count Group: Src Data: 20 – Name: DatePubCY Label: Publication Date Group: Date Data: 2012 – Name: TypeDocument Label: Document Type Group: TypDoc Data: Journal Articles<br />Reports - Evaluative – Name: Audience Label: Education Level Group: Audnce Data: <searchLink fieldCode="EL" term="%22High+Schools%22">High Schools</searchLink> – Name: Subject Label: Descriptors Group: Su Data: <searchLink fieldCode="DE" term="%22Professional+Development%22">Professional Development</searchLink><br /><searchLink fieldCode="DE" term="%22Statistics%22">Statistics</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Instruction%22">Mathematics Instruction</searchLink><br /><searchLink fieldCode="DE" term="%22Technology%22">Technology</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+Literacy%22">Computer Literacy</searchLink><br /><searchLink fieldCode="DE" term="%22Teacher+Improvement%22">Teacher Improvement</searchLink><br /><searchLink fieldCode="DE" term="%22Program+Effectiveness%22">Program Effectiveness</searchLink><br /><searchLink fieldCode="DE" term="%22Communities+of+Practice%22">Communities of Practice</searchLink><br /><searchLink fieldCode="DE" term="%22Pedagogical+Content+Knowledge%22">Pedagogical Content Knowledge</searchLink><br /><searchLink fieldCode="DE" term="%22Secondary+School+Teachers%22">Secondary School Teachers</searchLink><br /><searchLink fieldCode="DE" term="%22High+Schools%22">High Schools</searchLink><br /><searchLink fieldCode="DE" term="%22Secondary+School+Mathematics%22">Secondary School Mathematics</searchLink> – Name: DOI Label: DOI Group: ID Data: 10.1080/0020739X.2011.592616 – Name: ISSN Label: ISSN Group: ISSN Data: 0020-739X – Name: Abstract Label: Abstract Group: Ab Data: Attending professional development programmes can support teachers in applying new strategies for teaching mathematics and statistics. This study investigated (a) the extent to which the participants in a professional development programme subsequently used the techniques they had learned when teaching mathematics and statistics and (b) the obstacles they encountered in enacting cognitively demanding instructional tasks in their classrooms. The programme created an intellectual learning community among the participants and helped them gain confidence as teachers of statistics, and the students of participating teachers became actively engaged in deep mathematical thinking. The participants indicated, however, that time, availability of resources and students' prior achievement critically affected the implementation of cognitively demanding instructional activities. (Contains 1 figure.) – Name: AbstractInfo Label: Abstractor Group: Ab Data: As Provided – Name: Ref Label: Number of References Group: RefInfo Data: 52 – Name: DateEntry Label: Entry Date Group: Date Data: 2012 – Name: AN Label: Accession Number Group: ID Data: EJ986039 |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1080/0020739X.2011.592616 Languages: – Text: English PhysicalDescription: Pagination: PageCount: 20 StartPage: 177 Subjects: – SubjectFull: Professional Development Type: general – SubjectFull: Statistics Type: general – SubjectFull: Mathematics Instruction Type: general – SubjectFull: Technology Type: general – SubjectFull: Computer Literacy Type: general – SubjectFull: Teacher Improvement Type: general – SubjectFull: Program Effectiveness Type: general – SubjectFull: Communities of Practice Type: general – SubjectFull: Pedagogical Content Knowledge Type: general – SubjectFull: Secondary School Teachers Type: general – SubjectFull: High Schools Type: general – SubjectFull: Secondary School Mathematics Type: general Titles: – TitleFull: Professional Development in Statistics, Technology, and Cognitively Demanding Tasks: Classroom Implementation and Obstacles Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Foley, Gregory D. – PersonEntity: Name: NameFull: Khoshaim, Heba Bakr – PersonEntity: Name: NameFull: Alsaeed, Maha – PersonEntity: Name: NameFull: Er, S. Nihan IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Type: published Y: 2012 Identifiers: – Type: issn-print Value: 0020-739X Numbering: – Type: volume Value: 43 – Type: issue Value: 2 Titles: – TitleFull: International Journal of Mathematical Education in Science and Technology Type: main |
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