'Sage on the Stage' or 'Meddler in the Middle': Shifting Mathematics Teachers' Identities to Support Student Engagement
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| Title: | 'Sage on the Stage' or 'Meddler in the Middle': Shifting Mathematics Teachers' Identities to Support Student Engagement |
|---|---|
| Language: | English |
| Authors: | Bobis, Janette (ORCID |
| Source: | Journal of Mathematics Teacher Education. Dec 2020 23(6):615-632. |
| Availability: | Springer. Available from: Springer Nature. One New York Plaza, Suite 4600, New York, NY 10004. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-460-1700; e-mail: customerservice@springernature.com; Web site: https://link.springer.com/ |
| Peer Reviewed: | Y |
| Page Count: | 18 |
| Publication Date: | 2020 |
| Document Type: | Journal Articles Reports - Research |
| Education Level: | Elementary Education Grade 5 Intermediate Grades Middle Schools Grade 6 Grade 7 Junior High Schools Secondary Education |
| Descriptors: | Mathematics Teachers, Professional Identity, Learning Processes, Teacher Attitudes, Concept Mapping, Intervention, Personal Autonomy, Learner Engagement, Grade 5, Grade 6, Grade 7, Mathematical Concepts, Teacher Student Relationship |
| DOI: | 10.1007/s10857-019-09444-1 |
| ISSN: | 1386-4416 |
| Abstract: | Mathematics teachers' identities profoundly influence how they interact with and position their students to learn mathematics. In this paper, we examine how a year-long teacher learning intervention supportive of student engagement in mathematics helped shift teachers' mathematics-related identities. We use an implied identity perspective as a theoretical lens to explore changes in what teachers perceive as legitimate ways of being as a result of their participation in the intervention. Data from pre- and post-intervention concept maps and focus groups with 15 grade 5-7 teachers of mathematics were integrated for this purpose. Teachers reported shifts in their identities, describing themselves as "facilitators," "learners" and "co-creators" of knowledge. We argue that such shifts in the mathematics-related identities of teachers can have practical consequences in terms of improving students' engagement, and in particular, their autonomy for learning mathematics. |
| Abstractor: | As Provided |
| Entry Date: | 2020 |
| Accession Number: | EJ1273933 |
| Database: | ERIC |
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| FullText | Links: – Type: pdflink Url: https://content.ebscohost.com/cds/retrieve?content=AQICAHj0k_4E0hTGH8RJwT4gCJyBsGNe_WN95AvKlDbXJGqwxwEQWdlHe2ENN-qWp6uQVbiNAAAA4zCB4AYJKoZIhvcNAQcGoIHSMIHPAgEAMIHJBgkqhkiG9w0BBwEwHgYJYIZIAWUDBAEuMBEEDHrNL0JiGgS23yOFIQIBEICBm25hmYSvWEj5HGHFUfIbQdJ4yOd_cHn1es_Slr7YG4ghcvAVAMfrt1zMmTH93wbCFKe0dYZn9NP99PUC76IlMpM8EzsCqrSuwXauDYH7c6WIRtSMSeLSvQh9mwbsLuN6rpyBQdBwZYtsw27viXBifZ62Tcge2jgKpl7tE8I09ZMAuTfLhKvK0sh3wvQcxn923rHbNt5RBdPVPjQa Text: Availability: 1 Value: <anid>AN0146533722;oih01dec.20;2020Oct22.05:14;v2.2.500</anid> <title id="AN0146533722-1">"Sage on the stage" or "meddler in the middle": shifting mathematics teachers' identities to support student engagement </title> <p>Mathematics teachers' identities profoundly influence how they interact with and position their students to learn mathematics. In this paper, we examine how a year-long teacher learning intervention supportive of student engagement in mathematics helped shift teachers' mathematics-related identities. We use an implied identity perspective as a theoretical lens to explore changes in what teachers perceive as legitimate ways of being as a result of their participation in the intervention. Data from pre- and post-intervention concept maps and focus groups with 15 grade 5–7 teachers of mathematics were integrated for this purpose. Teachers reported shifts in their identities, describing themselves as "facilitators," "learners" and "co-creators" of knowledge. We argue that such shifts in the mathematics-related identities of teachers can have practical consequences in terms of improving students' engagement, and in particular, their autonomy for learning mathematics.</p> <p>Keywords: Student engagement; Implied identity; Mathematics-related teacher identity; Professional learning</p> <p>Janette Bobis and Maryam Khosronejad have contributed equally to the preparation of this paper.</p> <hd id="AN0146533722-2">Introduction</hd> <p>Positive identities are considered critical to mathematics learning because of their "tendency to act as self-fulfilling prophecies" (Sfard and Prusak [<reflink idref="bib31" id="ref1">31</reflink>], p. 19) and their potential to influence career and higher education aspirations (Black et al. [<reflink idref="bib4" id="ref2">4</reflink>]). Research indicates that the mathematics-related identity of teachers can influence how they interact with their students (Clark et al. [<reflink idref="bib9" id="ref3">9</reflink>]; Reay and Wiliam [<reflink idref="bib29" id="ref4">29</reflink>]), how they position themselves as teachers of mathematics and their students as learners of mathematics (Tait-McCutcheon and Loveridge [<reflink idref="bib34" id="ref5">34</reflink>]), thus directly impacting their engagement levels and, over time, shaping their students' identities with mathematics (Grootenboer and Zevenbergen [<reflink idref="bib15" id="ref6">15</reflink>]). For example, students not only learn about mathematical concepts and skills, but also learn about themselves as capable and autonomous learners when they succeed in solving challenging problems (Assor [<reflink idref="bib2" id="ref7">2</reflink>]). Students' sense of belonging, autonomy and the mathematical identities they develop arise from direct experiences of mathematics and interactions with their peers and teachers—a process that is facilitated by teachers of mathematics.</p> <p>The establishment of an engagement-supportive learning environment is very much shaped by teachers' mathematics-related identities (Lutovac and Kaasila [<reflink idref="bib23" id="ref8">23</reflink>]), their perceptions of how mathematics should be taught and how students become engaged in it (Bobis et al. [<reflink idref="bib6" id="ref9">6</reflink>]). Therefore, how their identities as teachers of mathematics develop, shift or might be reshaped to those that are more supportive of student engagement is an important aspect of teacher development to explore. Such explorations are suggested by Skott ([<reflink idref="bib32" id="ref10">32</reflink>]) to provide new understandings that may improve future teacher learning and development initiatives. The study reported here addresses this intention by investigating shifts in teachers' mathematics-related identifies facilitated by a professional learning program that aimed to establish enhanced engagement-supportive learning environments. We use Lutovac and Kaasila's ([<reflink idref="bib24" id="ref11">24</reflink>], p. 506) term "mathematics-related teacher identity" because it refers to the identity of <emph>all</emph> teachers of mathematics and our study involved both specialist (i.e., secondary) and non-specialist (i.e., primary) teachers of mathematics. While recognizing the differences that generally exist between the two groups of teachers in terms of their personal relationships with the subject, our focus was on the shifts in their professional identities as teachers of mathematics in response to a shared professional learning experience and therefore consider the term "mathematics-related teacher identity" to be the most appropriate term for our study.</p> <hd id="AN0146533722-3">Identity: a lens to explore teacher professional learning and development</hd> <p>We see teacher learning as a process of becoming and mathematics-related teacher identity formation as situated within cultural, social and physical communities of practice (Lave and Wenger [<reflink idref="bib21" id="ref12">21</reflink>]). Sociocultural approaches to identity bring our attention to contextual factors in the development of teacher identities and help us explore its context-dependent nature through interaction and across various contexts (Lutovac and Kaasila [<reflink idref="bib23" id="ref13">23</reflink>]). Research shows contextual issues hinder or facilitate processes of identity change (Andersson [<reflink idref="bib1" id="ref14">1</reflink>]) and that teacher educators need to take into account that "it is the teacher who controls his or her destiny" (Chapman and Heater [<reflink idref="bib8" id="ref15">8</reflink>], p. 457). In this paper, we extend previous research by exploring teacher responses to the contextual aspects of the learning environment (a teacher professional learning program) through an implied identity theoretical lens, suggesting that programs of professional learning can become resources for mathematics-related teacher identity formation.</p> <hd id="AN0146533722-4">Identity and implied identity</hd> <p>There is little consensus about the construct of identity or how it can be studied (Darragh [<reflink idref="bib11" id="ref16">11</reflink>]), but "with more clarity, the concept of identity can continue to provide helpful insights into our experiences of learning mathematics" (p. 29). Our use of the term identity draws on the concept of position from positioning theory (Davies and Harré [<reflink idref="bib12" id="ref17">12</reflink>]). We use position, as opposed to the classical notion of "role" (which is perceived as a fixed set of responsibilities), to illustrate the dynamicity of identity through which teachers position themselves as teachers, in relation to other teachers, their students and to the discipline of mathematics. Therefore, identity practices are characterized as constantly shifting positions emerging through social interaction. Participation in professional learning programs involves both practices of self-identification (or self-positioning) and identification by others (other-identification or other-positioning) through acts such as "telling stories, joining groups, and acting in a particular way at a particular time" (Darragh [<reflink idref="bib11" id="ref18">11</reflink>], p. 29). As Darragh ([<reflink idref="bib11" id="ref19">11</reflink>]) suggests, perceiving identity as an act that may or may not be recognized as desired is a useful future direction for identity research. Our investigation is based on the premise that teachers' acts of identity in positioning themselves and their students is the result of what they recognize as <emph>legitimate ways of being</emph>, in different contexts, including professional development programs. We use <emph>implied identity</emph> (Khosronejad et al. [<reflink idref="bib19" id="ref20">19</reflink>]) as a theoretical lens to examine if and how a teacher professional learning program might facilitate shifts in teachers' identities as teachers of mathematics to ones that are more supportive of student engagement in mathematics.</p> <p>Guided by a situative approach, the process of identity formation is the result of engagement in professional learning activities and therefore the interaction between learners and their learning experience contexts. This interaction is not unidirectional. While teachers' professional identities predominantly emerge from their experiences, their identities can also influence the way they perceive these experiences (Noonan [<reflink idref="bib27" id="ref21">27</reflink>]). A number of terminologies have emerged to explore the complexity of this interaction. Cobb and Hodge ([<reflink idref="bib10" id="ref22">10</reflink>]), for instance, look at the interplay between <emph>normative identity</emph> (who you should become to be recognized as a competent professional in a particular context); and <emph>core identity</emph> (who you think you are and who you would like to be) in emerging personal identities. In contrast, Sfard and Prusak ([<reflink idref="bib31" id="ref23">31</reflink>]) use the terms <emph>actual</emph> and <emph>designated</emph> identities and recognize learning as closing the gap between the two as learners move from who they think they are, to their designated identity, of who they think they can or should become.</p> <p> <emph>Normative identity</emph> and <emph>designated identity</emph> are expressions of a positioning mechanism in the sense that they provide teacher–learners with suggestions of legitimate <emph>ways of being</emph> a teacher of mathematics. However, in order to understand the process of identity formation, we need to look into the process of meaning making by teachers. The concept of <emph>implied identity</emph> (Khosronejad et al. [<reflink idref="bib19" id="ref24">19</reflink>]) refers to what teachers, as learners, perceive as suggested <emph>ways of being</emph> in relation to the context of their experience.</p> <p>Applying the implied identity approach helps explain the complexities involved in the dialogic interaction between the teacher–learner and their learning environment (Khosronejad et al. [<reflink idref="bib19" id="ref25">19</reflink>]). It places emphasis on the interactions between what educational designers intend for learners and the learner interpretation of it (see Fig. 1). In the current investigation, the professional learning program was conceptualized as a resource for identity formation to provide teachers with new knowledge, skills and competencies related to student engagement in mathematics as initially intended by the researchers. It was anticipated that teachers would perceive <emph>implied identities</emph> of being a teacher through their participation in the professional learning activities, including group discussions and their access to new materials and tasks. Individual or collective responses to different aspects of the learning program were expected in the form of both practice and reflection, potentially leading to changes in perceptions of the ideal teacher and perceptions of self. The interaction between the learner and the learning environment is considered a dialogic process, informing both the teacher–learners' future perceptions or practices and the context of experience in shaping normative identities.</p> <p>Graph: Fig. 1 Implied identity framework (Khosronejad et al. [<reflink idref="bib19" id="ref26">19</reflink>])</p> <p>The components of teachers' reflective responses to the learning experiences depicted in Fig. 1 help unpack the relations between teacher perceptions and their practices. To elaborate, a teacher's actions within a particular context of experience is mediated by implied identities—her perceptions of what it means to be a teacher of mathematics within that particular context—and her reflection on what she already thinks about the profession (ideal teacher of mathematics) as well as what she thinks about herself (perception of self). Furthermore, any changes in the teacher's perceptions of self and the ideal teacher of mathematics are facilitated by her perceived implied identities across different contexts of her experience over time.</p> <p>The implied identity approach reconceptualizes our inferences about collected teacher data—when examining mathematics-related teacher identity formation relating to specific contexts such as professional learning programs—and directs our attention to <emph>implied identities</emph> as the subject of inquiry rather than focusing on identities per se. In this paper, we address the research question: How did the implied identities of being a teacher of mathematics perceived by teachers change during a professional learning program that focused on supporting student engagement in mathematics?</p> <hd id="AN0146533722-5">Methodology</hd> <p>A teacher intervention was conducted as part of a large two-year project that aimed to enhance the mathematical motivation and engagement of students in grades 5 through 7 (approximately 10–14 years of age). The intervention involved two different cohorts of teachers and their students drawn from the same school system. The two cohorts experienced the same program of activities, data collection methods and processes. Each cohort was followed throughout an academic school year from February to December. This paper reports on findings related only to the teachers who participated in the project. We report on two data sources, including pre- and post-intervention focus group interviews and teacher-produced concept maps, to elicit teacher perceptions of legitimate ways of teaching concerning student motivation and engagement in mathematics. We explore shifts in teachers' perceptions as indicators of <emph>implied identities</emph> perceived during their participation in the program and as facilitators of teachers' repositioning practices.</p> <hd id="AN0146533722-6">Intervention</hd> <p>The intervention was a teacher professional learning program conducted over 11 months of the school year. The program incorporated seven full-day workshops that were held at a centrally located school to allow easy access for teachers traveling from neighboring schools. The workshops focused on challenging teachers' perceptions of student engagement in mathematics, building their knowledge of motivation and engagement theoretical frameworks and of evidence-based instructional strategies for promoting student engagement in mathematics. Hence, the intervention aimed to provide teachers with suggestions (knowledge and resources) for becoming teachers of mathematics who were supportive of student engagement.</p> <p>The researchers adopted the role of workshop facilitators. They introduced teachers to the theoretical frameworks of Fredricks et al. ([<reflink idref="bib14" id="ref27">14</reflink>]) and Martin ([<reflink idref="bib26" id="ref28">26</reflink>]) as vehicles to build their knowledge about the nature of engagement. Neither of these frameworks specifically relate to mathematical engagement. To address this, the facilitators drew upon mathematical contexts to help explain and highlight the classroom implications of various aspects referred to in the frameworks. For instance, self-belief, an aspect in Martin's Motivation and Engagement Wheel was explained in the context of students' beliefs and confidence in their ability to perform well in mathematics. Mathematical self-belief was discussed and explored through activities adapted from Leatham and Hill ([<reflink idref="bib22" id="ref29">22</reflink>]). It was also discussed in the workshop as to how the activities could be modified for use with their students. In one such activity, teachers were presented with descriptive words such as interested/bored and confident/not confident at either end of a series of continua. Teachers were asked to indicate where they would place themselves according to their perceived relationship with mathematics. They then discussed the implications of mathematical self-belief for themselves and their students.</p> <p>Teachers completed between-meeting tasks involving the collection of information about their students' identities and engagement in mathematics. This information was used as a stimulus for discussion and formed the basis of progress reports on school-based action research projects at subsequent workshops.</p> <p>The role of the researchers was to build teacher knowledge and stimulate reflection upon their existing perceptions of student engagement and achievement in mathematics through activities requiring collaboration and discussion. Researchers sought to facilitate discussion around evidence-based teaching practices linked to the enhancement of student engagement in mathematics for teachers to trial in their classrooms as part of their school-based action research projects. For example, the researchers provided teachers with published research-based readings (e.g., Bobis et al. [<reflink idref="bib5" id="ref30">5</reflink>]; Hattie and Timperley [<reflink idref="bib17" id="ref31">17</reflink>]), which helped stimulate whole-group discussions and challenge their thinking about existing pedagogy and how it might change to promote greater student engagement in mathematics.</p> <hd id="AN0146533722-7">Participants</hd> <p>Participating teachers were from 4 secondary and 10 primary schools that were part of a Catholic Education school system located in the suburbs of a capital city on the east coast of Australia. In this school system, primary school comprises Kindergarten to grade 6 and secondary school comprises grades 7 to 12. Primary schools were invited to participate in the project on the basis that they represented the largest "feeder" schools to the invited secondary schools. It was envisaged that such a "connection" between schools and teachers would assist in developing a shared purpose of strengthening students' mathematical engagement. Of the 39 grade 5 to 7 teachers who participated in the study, data from 15 teachers (5 secondary and 10 primary) are reported in this paper. Data from these teachers were selected because they included a broad representation of teachers who participated in the project in terms of teaching experience (ranging from 2 years to more than 15 years), comprised male and female, primary and secondary teachers, comprised all members from three different focus groups, were present for both pre- and post-intervention data gathering sessions and gave their consent to participate in the study. The inclusion of data from the remaining focus groups was considered unnecessary when analysis of transcripts reached saturation point with no new codes emerging (Saunders et al. [<reflink idref="bib30" id="ref32">30</reflink>]).</p> <hd id="AN0146533722-8">Data collection methods and procedures</hd> <p>A multistage data collection process involving concept mapping followed by focus groups occurred pre- and post-intervention. Concept maps are intended to reveal how individuals organize and change their perceptions and knowledge (Novak and Caña [<reflink idref="bib28" id="ref33">28</reflink>]). They traditionally consist of hierarchically arranged pieces of information or concepts (nodes) with the relationship between particular nodes represented by a uni- or bidirectional arrow called a link or a cross-link if connections are made between different map segments. Prior to the first concept mapping activity, teachers were provided with an example of a concept map on an unrelated topic. They were then asked to create a concept map with the prompt: How is student motivation and engagement in mathematics promoted? The concept maps were returned to teachers just prior to the second focus group interview session at the conclusion of the intervention, where they were asked to study their initial map and make modifications using a different colored pen. The concept maps provided a graphical snapshot of each teacher's unique experiences, understandings and perceptions of student motivation and engagement in mathematics and how they perceived it was promoted in their classrooms at two crucial points in time, thus revealing shifts in teachers' perceptions over the course of the intervention. The maps also provided an opportunity for teachers to "collect their thoughts" in preparation for the focus group that immediately followed each concept mapping session.</p> <p>Focus groups are a type "of group interview that capitalizes on communication between the research participants in order to generate data" (Kitzinger [<reflink idref="bib20" id="ref34">20</reflink>], p. 299). They are particularly suitable for sociocultural research approaches that aim to encourage participants to explore and clarify their own understandings, perceptions and views of concepts and issues that are of importance to the whole group (Marshall and Rossman [<reflink idref="bib25" id="ref35">25</reflink>]). The purpose of the focus groups in this study was twofold: first, they provided a collective view of teachers' pre- and post-intervention knowledge and practices perceived to be supportive of student engagement in mathematics. Second, they were used to help elaborate on and begin to extend individual teacher's initial perceptions of student engagement and how it is promoted in their classrooms represented in their concept maps.</p> <p>After individually completing the concept map, focus groups consisting of 5 or 6 teachers representing a mix of schools and grades taught, were formed, and ensuring that no more than two secondary (specialist) mathematics teachers were in each group. The same group of teachers met again after the post-intervention concept mapping exercise was completed. Each focus group was facilitated by one of the researchers, who asked a series of open–ended questions that required teachers to reflect on their own students and teaching contexts, safeguarding that each member had sufficient opportunity to contribute to the group discussion. For instance, one question asked teachers if (and how) they could recognize if a student in their class was engaged in mathematics. Another asked about the instructional strategies they specifically employed to promote student engagement as per the prompt used by teachers to construct their concept maps. Focus groups were approximately 45 min in duration, were audio-recorded and transcribed to assist with analysis.</p> <hd id="AN0146533722-9">Analysis</hd> <p>Concept maps were analyzed inductively, using a content analysis approach similar to that described by Hough et al. ([<reflink idref="bib18" id="ref36">18</reflink>]). This process focused on the identification of concepts (nodes) and the links and crosslinks to reveal relationships between concepts (content) and teachers' perceptions. Individual concepts and content linked via arrows drawn by teachers or their written elaborations adjacent major nodes formed the initial themes by which data were categorized. Two researchers independently identified concepts and the related themes emerging from time 1 data collection that reappeared, evolved or were absent in time 2 data. The two sets of themes were then compared until a single set of initial themes was agreed upon. For instance, the promotion of confidence in mathematics was mentioned in four teachers' time 1 and seven teachers' time 2 concept maps. Confidence was mentioned in connection with teachers' own levels of confidence and students' feelings of success and prior experiences of mathematics. Analysis focused on how the maps revealed shifts in teachers' perceptions of what it meant to be a teacher of mathematics who is capable of promoting student engagement and how they repositioned themselves and their students in the mathematics classroom. Three examples of concept maps (constructed by one teacher from each of the three focus groups) are provided in Figs. 2, 3 and 4. These three concept maps were selected based on the representativeness of the final set of themes used to report the data and because of their clarity when electronically reproduced. As is evident from the three example concept maps, many maps did not conform to a strict traditional definition of concept map. Nevertheless, they all represented individual teacher-generated constructions of their experiences, and perceptions of student engagement in mathematics at two points in time and therefore provided valuable data. In this paper, we report on the themes that emerged from a cross-case analysis that were reflective of key components of the theoretical framework guiding the investigation and draw upon aspects of the three example teachers' maps to provide evidence of change at the individual teacher level.</p> <p>Graph: Fig. 2 Example of concept map generated by Abigail, a grade 6 teacher from focus group 1 (time 2 text is bolded)</p> <p>Graph: Fig. 3 Example of concept map generated by Barb, a grade 5 teacher from focus group 2 (time 2 text is bolded)</p> <p>Analysis of the focus group transcripts was mostly deductive involving an adaption of Braun and Clarke's ([<reflink idref="bib7" id="ref37">7</reflink>]) process of thematic analysis. We started with the key ideas (such as "the promotion of student confidence") identified in the content analysis of the concept maps and conducted multiple readings across three main phases of analysis. During the first phase, the transcripts were read to gain an overview of the discussion, to develop familiarity with content and check relevance and consistency of themes between the concept maps and focus group data. NVivo was then used to assist coding of transcripts starting with the initial themes emerging from analysis of the concept maps. Finally, an inductive approach was once again employed to identify significant themes emerging from the focus groups that were not highlighted from the initial set of themes but were considered relevant for addressing the research question. The researchers returned to the concept maps to deductively search for corroborating evidence to support the inclusion of any new themes. The theme "teacher as a co-creator of knowledge and co-learner" was added using this iterative approach.</p> <hd id="AN0146533722-10">Results</hd> <p>Findings from concept maps and focus groups are reported for both time 1 (<emph>T</emph>1) and time 2 (<emph>T</emph>2) data collection, whereby data from one method is used to support and confirm those identified in the other. In this way, ideas expressed by individuals via their concept maps could be directly linked to the same or similar ideas collectively discussed and elaborated upon during the focus group interviews. While the implied identity framework draws attention to individual teacher's perceptions of what it means to be a teacher capable of supporting student engagement in mathematics, it also emphasizes the significance of interactions between individual teacher–learners and the broader community of teachers in the future shaping of normative identities. In the current study, the voicing of teachers implied identities and the shaping of normative identities was considered an important outcome by teachers, all of whom were accustomed to collaboratively planning their mathematics teaching programs.</p> <p>In the following section, results are presented according to the five main themes identified during the analysis process, including: teacher as a co-creator of knowledge and co-learner; teacher as a facilitator of student interaction; teacher as a promoter of student confidence; teaching mathematics as a process-oriented practice; and teaching as a practice of linking mathematics to real-life.</p> <hd id="AN0146533722-11">Teacher as a co-creator of knowledge and co-learner</hd> <p>Time 1 concept maps revealed twelve of the fifteen teachers linking the use of technology, physical resources and games to student engagement in mathematics. For example, the concept maps of Abigail (Fig. 2), Barb (Fig. 3) and Colleen (Fig. 4) at time 1, each referred to these resources. During focus group interviews, teachers explained their views of how students learn mathematics while using these resources and described how they used games and movement to "keep them physically engaged" (FG2, <emph>T</emph>1) as part of their teaching practices. They generally described themselves as transferring knowledge to students whereby they "give it (knowledge) to them ... we spoon-feed them by giving step by step by step instructions" (FG1, <emph>T</emph>1). Teachers remarked that it was often difficult to get students to "realize that they've actually got to do something" and that "it's not just us (teachers)" doing the thinking (FG1, <emph>T</emph>1). A grade 6 teacher summarized her teaching approach as follows:I explain it and then encourage questions. But if I don't get questions then I'll be moving around the class and helping them and if I find that there are quite a few children that I've seen haven't understood a concept then I'll go back to the board and maybe go through something again. (FG2, T1)</p> <p>Graph: Fig. 4 Example of concept map generated by Colleen, a grade 7 teacher from focus group 3 (time 2 text is bolded)</p> <p>Teachers in each focus group talked about the importance of building relationships with their students and "getting to know" their mathematical needs. They described a wide range of strategies they perceived helped them achieve these things, including "pretesting" (FG2, <emph>T</emph>1), monitoring students by "walking around making sure students are on track" (FG1, <emph>T</emph>1), "putting kids in alphabetical order so there is no way they can hide at the back" (FG2, <emph>T</emph>1), giving "stickers and sweets" to encourage participation (FG3, <emph>T</emph>1) and randomly asking questions so that "the kids don't know who's going to get asked."</p> <p>In the second round of data collection, eight teachers included nodes on their concept map referring to allowing students to take greater responsibility for their own learning. For example, Abigail (Fig. 2) linked students "making decisions" to their willingness to take "risks" in their learning of mathematics while Colleen (Fig. 4) included new nodes concerning students "aiming for personal bests." Nodes referring to teacher "questioning" rather than "telling" them the answer appeared in ten teachers' time 2 concept maps (e.g., see Fig. 3). In focus groups, Barb (grade 5 teacher) elaborated upon how she tried to shift responsibility for learning mathematics back to the students:... rather than being the 'sage on the stage' - being the teacher that stands up and saying, 'yes, that's it'. More of the 'meddler in the middle' and helping them and questioning them. And saying, "so do you think that really is the right answer? How do you know it?"... So, in fact they're still being responsible for providing their own answer.</p> <p>A grade 7 teacher from Focus Group 2 reported that he now considered it better if students "see the connections" for themselves, rather than starting "straight with the formula." While acknowledging that it was "more challenging for students to figure out the connection," the group agreed that "resilience is important too, ... it can't all be fun and bells and whistles, sometimes things are hard, and you just have to apply yourself" (FG2, <emph>T</emph>2).</p> <p>Rather than viewing themselves as merely the transmitters of knowledge, teachers acknowledged themselves as co-learners of mathematics whereby they and their students "will learn from each other" (FG1, <emph>T</emph>2). A grade 7 teacher expressed her agreement with the view that "it's okay for them (teachers) to make mistakes" too, considering "the whole process to be a learning experience" (FG3, <emph>T</emph>2) for them as it was for their students. A particular shift in practices that teachers from all focus groups emphasized was their reliance on student feedback and how this now informed their teaching. In focus groups, a grade 5 teacher described how she had "actually been asking the students what motivates them, how they learn maths or how they perceive maths and why they enjoy it ... having their input on what works for them" (FG2, <emph>T</emph>2). Additionally, teachers across all three focus groups acknowledged that the nature of the tasks they now provided their students had changed quite dramatically to "things that I'd never tried before" (FG1, <emph>T</emph>2). For instance, Barb referred to tasks requiring students to reflect on their learning or provide feedback on the teaching in her time 2 concept map and explained her thinking to her focus group: "I've learnt the value of the kids reflecting at the end of lessons ... I like that [exit] ticket idea. I use that a lot at the end of a lesson, to see what the children have learnt. ... I've learnt that they don't have to be at their desk with pen and paper all the time."</p> <hd id="AN0146533722-12">Teacher as a facilitator of student interaction</hd> <p>Teachers expressed quite diverse views about the merits of student–student interactions in the mathematics classroom prior to the intervention. Nearly all primary teachers supported the use of collaborative learning in their mathematics lessons, but two grade 7 teachers from two different focus groups and three grade 6 teachers were initially skeptical of its merits. A grade 7 teacher explained that it "was a tricky area" (FG3, <emph>T</emph>1) and "depends on how the group works ... if you have it <emph>collaboratively</emph> where everyone is involved in it, so each person actually has a task in the group," it "could be an asset" to learning mathematics (FG1, <emph>T</emph>1).</p> <p>At time 2 data collection, ten out of 15 concept maps included new nodes linked to the concept of collaborative learning. Colleen, a grade 7 teacher (see Fig. 4) referred to "working together" and drew links to "sharing problem solving strategies" and "helping each other." Similarly, Abigail's time 2 concept map (see Fig. 2) shows new links among student engagement, "collaborative" learning and students "taking risks." Teachers provided detailed examples of how they incorporated student–student interactions into their teaching. In addition to the peer design task described earlier, a grade 7 teacher remarked how she encouraged "peer conversations" and "peer tutoring" so students can "learn from each other" (FG2, <emph>T</emph>2). Abigail elaborated upon her concept map explaining how an emphasis on collaborative learning had had a positive impact on the learning environment in her classroom; her students were now more willing to "take risks" and viewed their achievements as a reflection of "a group learning" process that encouraged greater student "autonomy for their learning."</p> <hd id="AN0146533722-13">Teacher as a promoter of student confidence</hd> <p>Only two teachers at time 1 referred to their own confidence with either mathematics or the teaching it as having an impact on their students' mathematical confidence levels in their concept maps. Barb (Fig. 3) linked her own confidence in mathematics with her "approach to maths" teaching and a grade 7 teacher in his first year of teaching indicated that greater experience would help build his confidence. In focus groups, teachers initially considered a lack of student confidence in mathematics as a major reason for their poor motivation and engagement in the subject area. A grade 5 teacher expressed the view that "If they don't feel good about themselves, obviously they're not going to be motivated ... the biggest problem is that they lack motivation because they feel they can't do it" (FG1, <emph>T</emph>1). Teachers agreed that they could easily identify students who "believe in themselves" because they are the ones who "will look at the page and sit up nice and straight" (FG2, <emph>T</emph>1). Meanwhile, students who lacked confidence in mathematics were identified by an experienced grade 7 teacher by the "diversionary tactics" they employed, such as the "need to go to the toilet, get up and look for tissues, can't find their books, can't find their pencils ..." (FG3, <emph>T</emph>1). Teachers also affirmed comments by a grade 5 teacher that some students with very low confidence levels "might be actually very anxious and ... almost paralysed with fear" (FG2, <emph>T</emph>1).</p> <p>Teachers varied in their approaches for addressing poor student confidence, with a grade 6 teacher believing that confidence would improve if students would "practice it [mathematics]" because "... the more you practice it, the easier it becomes" (FG1, <emph>T</emph>1). A year 7 teacher required her "less confident" students to "sit up the front row" (FG2, <emph>T</emph>1), while another recounted how he gave students more "thinking time ... It takes that anxiety and that pressure off" (FG2, <emph>T</emph>1).</p> <p>Teachers emphasized the importance of student self-belief and student confidence in their time 2 concept maps and interview responses with many referring to "noticing how much of a difference confidence can play with results and how they (students) perform. So just targeting students' confidence—and building that up; that's probably the biggest thing I have learned" (FG1, <emph>T</emph>2). Teachers recognized that it was their "responsibility" to "lead them [students] towards success" (FG3, <emph>T</emph>2) by building a stronger "belief in themselves" (FG2, <emph>T</emph>2). In tandem with this goal, teachers referred to their own feelings of confidence in mathematics; an aspect they felt had been strengthened by "having more strategies and more understanding" to address student confidence levels in mathematics (FG1, <emph>T</emph>2).</p> <hd id="AN0146533722-14">Teaching mathematics as a process-oriented practice</hd> <p>Prior to the intervention, teachers likened the process of learning mathematics to learning a language, one word at a time. Barb emphasized students using the "correct mathematical language" in her time 1 concept map (Fig. 3), and when she raised this point in the focus group, another group member agreed and then added that in mathematics "you have to learn the basics ... and you build on that ... It's a skill that you need to practice and build on ..." (FG2, <emph>T</emph>1). However, unlike words that could vary their meaning according to their context, "the answer in maths is always ... precise" (FG1, <emph>T</emph>1). Mathematics, as depicted in Abigail's time 1 concept map (Fig. 2), was more about students mastering "skills" than the development of understanding.</p> <p>The increased attention teachers paid to mathematical processes—rather than the "precise answer" (FG3, <emph>T</emph>1)—was evident in their responses at the end of the intervention. In her time 2 concept map, Barb (Fig. 3) linked the "idea of process" to her questioning of students to elicit their reasoning, indicating that the process "can be more important than the answer." Another node in her concept map referred to positioning herself as "a meddler in the middle through questioning" students to stimulate greater reasoning and justification of their answers. During the follow-up focus group, other teachers affirmed that the process was "just as important, if not more so important, than the actual answer" (FG2, <emph>T</emph>2).</p> <p>Teachers' choices of assessment tasks also reflected a greater focus on teaching mathematics as a process. In her time 2 map, Barb linked "assessment" to consideration of "where can I take that student?" rather than just giving "a mark." Similar sentiments were expressed regarding tasks they selected for assessment by focus group members. Focus Group 2 teachers expressed their agreement of one teacher's statement that she tries to select assessment tasks that not only show students can find the correct answer but will reveal the "process that students have taken to get to it" (FG2, <emph>T</emph>2).</p> <hd id="AN0146533722-15">Teaching as a practice of linking mathematics to real-life</hd> <p>The practice of teaching mathematics according to "topics"-dominated conversations in two of the three focus groups, as teachers referred to "topic tests" (FG3, <emph>T</emph>1) and the fact that individual student's levels of engagement differed because "some topics are drier than others" (FG1, <emph>T</emph>1). Despite this, making connections between mathematics and students' lives or between one mathematical concept and another was agreed upon as an extremely important aspect of teaching mathematics by members of all three focus groups. Only four teachers included a node linking student engagement and making students "own experiences/everyday life" in their time 1 concept maps (e.g., see Fig. 3). Barb explained her position: "if you're truly going to understand something you actually have to be able to ... connect it to your understanding of a whole lot of different things." However, she considered that the connections she made during mathematics lessons were mostly "serendipitous to the situation" and not deliberately planned. A year 6 teacher from the same focus group gave an example of how she deliberately used "authentic problems ... like when we had this building actually built, we've got to carpet this building..., how much carpet are we going to need to get?" to help make connections between mathematics and students' lives.</p> <p>At time 2, 9 teachers included new nodes on their concept maps that referred to "real world examples" (see Fig. 2), "investigations that stem from students' interests" or experiences (see Fig. 4) and "open–ended tasks" that were considered to be more authentic reflecting students' interests and lives, but that would also maintain their engagement and reveal their understandings. Colleen (Fig. 4) explained how she now used tasks that were open–ended and encouraged autonomous learning strategies to help her assess student understanding, such as a peer design task, whereby "I ask them to design a task ... and develop the questions ... Then pass it on [to another student]. That really shows...the sophistication of their understanding through the questions that they've developed" and was perceived to be "more interesting" for students.</p> <hd id="AN0146533722-16">Discussion</hd> <p>Understanding identity development is an essential part of studying teacher professional learning because it is identity that "mediates what makes its way into the classroom" (Battey and Franke [<reflink idref="bib3" id="ref38">3</reflink>]). In the current research, we applied the notion of implied identity to understand shifts in how teachers positioned themselves and their students. An analysis of changes in teachers' self-reported perceptions of improving student engagement in mathematics was presented as implied identities perceived during teachers' participation in the program. In this section, we discuss how the main perceived implied identities are linked to shifts in teachers' positioning of themselves and their students. Additionally, we explain what these repositioning practices mean in terms of students' learning.</p> <hd id="AN0146533722-17">"Sage on the stage" to "meddler in the middle"</hd> <p>The most significant implied identity to emerge from the intervention was that of teacher as co-creator of knowledge and teacher as facilitator or in other words, teacher as the "meddler in the middle"—one who actively scaffolds student learning rather than simply "telling." Teacher responses prior to the intervention indicate that teachers positioned themselves as "sages on the stage," transmitting mathematics content to students via controlling practices involving "step-by-step" instructions with few opportunities for students to independently interact with each other or to explore mathematical connections for themselves. Teachers initially positioned their students as mostly unreceptive learners, dependent upon them to deliver content. Their goals of engaging students were translated into practices whereby teachers felt that they needed to <emph>do</emph> most of the higher order thinking. While teachers expressed their views identified with engagement-supportive teaching practices, such as the importance of making connections between mathematics concepts and real-life contexts and highlighting the crucial role of student confidence in developing engaged learners of mathematics, they felt constrained by their own lack of strategies for enacting these views in the classroom.</p> <p>As teachers' identities shifted to being facilitators of student learning, they positioned their students as autonomous learners who were afforded greater responsibility for their own learning. The increased significance placed upon autonomous learning was evidenced by changes in the nature of the tasks teachers provided their students; there was increased use of open–ended and collaborative tasks, and tasks that required students to reflect on their own learning. While changes in teachers' perceptions do not necessarily lead to changes in practice, a body of research suggests such a relation exists (Fang [<reflink idref="bib13" id="ref39">13</reflink>]; Thompson [<reflink idref="bib35" id="ref40">35</reflink>]). For instance, views about mathematics teaching that position teachers in control of students' learning were shown by Stipek et al. ([<reflink idref="bib33" id="ref41">33</reflink>]) to be linked to classroom contexts that value extrinsic motivational strategies. In contrast, autonomy-supportive contexts place greater value on intrinsic motivation derived from task relevance, student confidence and students' perceived satisfaction of their need for autonomy (Assor [<reflink idref="bib2" id="ref42">2</reflink>]). Perceived autonomy is important for engagement; students reporting greater autonomy in the classroom were shown by Hafen et al. ([<reflink idref="bib16" id="ref43">16</reflink>]) to have increasing levels of engagement in mathematics, whereas students with low autonomy showed declines in their engagement as the academic year progressed.</p> <hd id="AN0146533722-18">"Teacher as knower" to "teacher as learner"</hd> <p>The second main implied identity to emerge as a result of the intervention was "teacher as learner" which occurred at two levels. First, "teacher as learner" is implied merely by teachers' preparedness to participate in the intervention and second, by teachers repositioning themselves and their students in the mathematics classroom. While the intervention was not purposefully designed to achieve the first outcome, it inherently positioned teachers as learners and co-creators of knowledge through their interaction with the researchers of the study and with other teacher participants when sharing ideas about, and strategies to enhance student engagement in mathematics. The "teacher as learner" implied identity, therefore, acted as a mediator for other repositioning practices such as those associated with teacher as "co-creator of knowledge."</p> <p>In terms of the classroom, teachers initially positioned themselves as the "knowers" of mathematics, which translated into practices that emphasized mathematics as a solitary activity where individuals obtained precise answers and students who lacked mathematical confidence were positioned as procrastinators who employed "diversionary tactics" to avoid learning it. Later, teachers repositioned themselves as "learners," as evidenced by their increased attention to student feedback as a mechanism for improving their teaching. Much of their learning focused on how to strengthen students' own mathematical identities and stemmed from their increased knowledge and awareness of strategies for addressing students' mathematical engagement. Similarly, a study by Bobis et al. ([<reflink idref="bib6" id="ref44">6</reflink>]) indicates that professional learning can positively affect teachers' capacities for improving student engagement. In the current study, increased knowledge of student engagement gained from the intervention resulted in teachers paying greater attention to emotional and cognitive aspects of engagement. Intentions to increase these aspects of engagement were translated into teaching and assessment practices that placed greater emphasis on student autonomy, open–ended tasks, student feedback and building student confidence in mathematics.</p> <hd id="AN0146533722-19">Limitations and suggestions for future research</hd> <p>It is important to consider the limitations of this study. First, we did not consider teachers' actual classroom practices or explore students' responses to the implementation of such practices in this paper. In other words, little is known for certain about how manifestation of teachers' views in practice will impact on students. Studies of teacher identity that include longitudinal classroom observations are needed to determine if self-reported changes in teachers' views and practices (implied identities) have already been accepted by teachers as their ideal being and/or perceptions of self. It is also important to explore the mechanisms that lead to students' repositioning through classroom interactions and activities.</p> <p>Furthermore, teachers' narratives delivered in a group interview, may have been influenced by the presence of researchers' and or the views expressed by other teachers in the focus group. For instance, during the group interviews, teachers regularly expressed agreement or disagreement with the views voiced by others. On occasions, teachers openly admitted that they had not previously considered the perspectives expressed by others and that such exposure caused them to think differently. As explained by Kitzinger ([<reflink idref="bib20" id="ref45">20</reflink>]), a deliberate intention of focus group methodology is to use group interactions to generate data. In this case, individual teachers were encouraged to talk, comment on or question the experiences, practices and perspectives of others and exchange narratives—the stories that illustrated their views, practices and student responses to such practices—so as to clearly explain how and why they think and act in certain ways. Such level of detail may not have been so easily obtained if individual interviews were employed. Indeed, it was through these interactions, that teachers began to reflect upon their views and the views of others that gradually impacted upon their mathematical identities. While future research should explore changes to individual teachers' mathematical identities via one-to-one interviews and individual case studies, investigations that involve groups of teachers interacting with each other in complex ways will better inform educators about effective strategies for teacher professional learning.</p> <hd id="AN0146533722-20">Conclusion</hd> <p>Teachers' identities are difficult to investigate, partly due to the complexity of the identity construct. Nevertheless, such investigations are important—effective teaching is dependent upon teachers possessing well-developed identities (Grootenboer and Zevenbergen [<reflink idref="bib15" id="ref46">15</reflink>]). In the current study, we addressed this complexity by drawing on an implied identity framework to help structure and guide our inferences. Teachers' experiences of the intervention, as an identity resource, provided them with suggestions of teacher identity, or what it means to be a teacher who is capable of supporting student engagement in mathematics. Self-reported changes in teachers' perceptions were conceptualized as perceived implied identities that mediate teachers' repositioning of themselves in terms of their mathematics-related teacher identity and therefore have potential implications for new teacher practices. For example, teachers' adaptations of an autonomy-supportive learning perspective, led to their repositioning as facilitators of students' learning and as co-creators of knowledge. The use of strategies to foster student–student interactions is also indicative of teachers repositioning their students as responsible agents for their own learning. Further repositioning practices are evident in other categories of change including the adaptation of new teaching resources and student assessment approaches, which in turn, positions teachers as learners who are more likely to welcome and adapt new practices in the future.</p> <p>An increased understanding of the mechanisms that support the development of healthy identities in teachers is important because of the direct benefits to student learning. The data showed how teachers' experiences of the professional learning program, as an identity resource, provided them with suggestions of what it means to be a teacher who is capable of supporting student engagement in the mathematics classroom. The findings indicate that teachers' repositioning of themselves as "facilitators," "learners" and "co-creators of knowledge" can have practical benefits such as improving students' confidence, engagement and level of autonomy for learning mathematics. The framework was also useful in deepening our understanding of teachers' learning—information that can be applied to support their future development. In particular, the framework directed our attention to the often-hidden experiences or resources (such as feedback from students and interactions with other teachers) that enabled teachers to begin reshaping their identities to ones that could more positively support student engagement in mathematics.</p> <hd id="AN0146533722-21">Acknowledgement</hd> <p>This research was funded by the Australian Research Council, in partnership with the Catholic Schools Office, Broken Bay Diocese, Project ID LP110200596.</p> <hd id="AN0146533722-22">Publisher's Note</hd> <p>Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p> <ref id="AN0146533722-23"> <title> References </title> <blist> <bibl id="bib1" idref="ref14" type="bt">1</bibl> <bibtext> Andersson A. 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| Items | – Name: Title Label: Title Group: Ti Data: 'Sage on the Stage' or 'Meddler in the Middle': Shifting Mathematics Teachers' Identities to Support Student Engagement – Name: Language Label: Language Group: Lang Data: English – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Bobis%2C+Janette%22">Bobis, Janette</searchLink> (ORCID <externalLink term="http://orcid.org/0000-0001-7733-287X">0000-0001-7733-287X</externalLink>)<br /><searchLink fieldCode="AR" term="%22Khosronejad%2C+Maryam%22">Khosronejad, Maryam</searchLink> (ORCID <externalLink term="http://orcid.org/0000-0001-9749-5000">0000-0001-9749-5000</externalLink>)<br /><searchLink fieldCode="AR" term="%22Way%2C+Jennifer%22">Way, Jennifer</searchLink> (ORCID <externalLink term="http://orcid.org/0000-0002-8731-0612">0000-0002-8731-0612</externalLink>)<br /><searchLink fieldCode="AR" term="%22Anderson%2C+Judy%22">Anderson, Judy</searchLink> (ORCID <externalLink term="http://orcid.org/0000-0002-8040-8430">0000-0002-8040-8430</externalLink>) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="SO" term="%22Journal+of+Mathematics+Teacher+Education%22"><i>Journal of Mathematics Teacher Education</i></searchLink>. Dec 2020 23(6):615-632. – Name: Avail Label: Availability Group: Avail Data: Springer. Available from: Springer Nature. One New York Plaza, Suite 4600, New York, NY 10004. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-460-1700; e-mail: customerservice@springernature.com; Web site: https://link.springer.com/ – Name: PeerReviewed Label: Peer Reviewed Group: SrcInfo Data: Y – Name: Pages Label: Page Count Group: Src Data: 18 – Name: DatePubCY Label: Publication Date Group: Date Data: 2020 – 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="%22Elementary+Education%22">Elementary Education</searchLink><br /><searchLink fieldCode="EL" term="%22Grade+5%22">Grade 5</searchLink><br /><searchLink fieldCode="EL" term="%22Intermediate+Grades%22">Intermediate Grades</searchLink><br /><searchLink fieldCode="EL" term="%22Middle+Schools%22">Middle Schools</searchLink><br /><searchLink fieldCode="EL" term="%22Grade+6%22">Grade 6</searchLink><br /><searchLink fieldCode="EL" term="%22Grade+7%22">Grade 7</searchLink><br /><searchLink fieldCode="EL" term="%22Junior+High+Schools%22">Junior High Schools</searchLink><br /><searchLink fieldCode="EL" term="%22Secondary+Education%22">Secondary Education</searchLink> – Name: Subject Label: Descriptors Group: Su Data: <searchLink fieldCode="DE" term="%22Mathematics+Teachers%22">Mathematics Teachers</searchLink><br /><searchLink fieldCode="DE" term="%22Professional+Identity%22">Professional Identity</searchLink><br /><searchLink fieldCode="DE" term="%22Learning+Processes%22">Learning Processes</searchLink><br /><searchLink fieldCode="DE" term="%22Teacher+Attitudes%22">Teacher Attitudes</searchLink><br /><searchLink fieldCode="DE" term="%22Concept+Mapping%22">Concept Mapping</searchLink><br /><searchLink fieldCode="DE" term="%22Intervention%22">Intervention</searchLink><br /><searchLink fieldCode="DE" term="%22Personal+Autonomy%22">Personal Autonomy</searchLink><br /><searchLink fieldCode="DE" term="%22Learner+Engagement%22">Learner Engagement</searchLink><br /><searchLink fieldCode="DE" term="%22Grade+5%22">Grade 5</searchLink><br /><searchLink fieldCode="DE" term="%22Grade+6%22">Grade 6</searchLink><br /><searchLink fieldCode="DE" term="%22Grade+7%22">Grade 7</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+Concepts%22">Mathematical Concepts</searchLink><br /><searchLink fieldCode="DE" term="%22Teacher+Student+Relationship%22">Teacher Student Relationship</searchLink> – Name: DOI Label: DOI Group: ID Data: 10.1007/s10857-019-09444-1 – Name: ISSN Label: ISSN Group: ISSN Data: 1386-4416 – Name: Abstract Label: Abstract Group: Ab Data: Mathematics teachers' identities profoundly influence how they interact with and position their students to learn mathematics. In this paper, we examine how a year-long teacher learning intervention supportive of student engagement in mathematics helped shift teachers' mathematics-related identities. We use an implied identity perspective as a theoretical lens to explore changes in what teachers perceive as legitimate ways of being as a result of their participation in the intervention. Data from pre- and post-intervention concept maps and focus groups with 15 grade 5-7 teachers of mathematics were integrated for this purpose. Teachers reported shifts in their identities, describing themselves as "facilitators," "learners" and "co-creators" of knowledge. We argue that such shifts in the mathematics-related identities of teachers can have practical consequences in terms of improving students' engagement, and in particular, their autonomy for learning mathematics. – Name: AbstractInfo Label: Abstractor Group: Ab Data: As Provided – Name: DateEntry Label: Entry Date Group: Date Data: 2020 – Name: AN Label: Accession Number Group: ID Data: EJ1273933 |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s10857-019-09444-1 Languages: – Text: English PhysicalDescription: Pagination: PageCount: 18 StartPage: 615 Subjects: – SubjectFull: Mathematics Teachers Type: general – SubjectFull: Professional Identity Type: general – SubjectFull: Learning Processes Type: general – SubjectFull: Teacher Attitudes Type: general – SubjectFull: Concept Mapping Type: general – SubjectFull: Intervention Type: general – SubjectFull: Personal Autonomy Type: general – SubjectFull: Learner Engagement Type: general – SubjectFull: Grade 5 Type: general – SubjectFull: Grade 6 Type: general – SubjectFull: Grade 7 Type: general – SubjectFull: Mathematical Concepts Type: general – SubjectFull: Teacher Student Relationship Type: general Titles: – TitleFull: 'Sage on the Stage' or 'Meddler in the Middle': Shifting Mathematics Teachers' Identities to Support Student Engagement Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Bobis, Janette – PersonEntity: Name: NameFull: Khosronejad, Maryam – PersonEntity: Name: NameFull: Way, Jennifer – PersonEntity: Name: NameFull: Anderson, Judy IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 12 Type: published Y: 2020 Identifiers: – Type: issn-print Value: 1386-4416 Numbering: – Type: volume Value: 23 – Type: issue Value: 6 Titles: – TitleFull: Journal of Mathematics Teacher Education Type: main |
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