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There are few descriptions of what teachers do to facilitate discussions that support students’ development of mathematical agency. Likewise, little is known about how elementary students conceptualize their own agency. This study explored how teachers’ facilitation of mathematical discussions potentially fostered students’ mathematical agency. Additionally, this study investigated ways in which students conceptualized their own mathematical agency within these classrooms. This study was situated in an urban school with a linguistically, academically, and ethnically diverse student population. The sample consisted of two upper elementary school teachers and their pupils (n = 40). Data, collected during the 2018–19 school year, included 12 observations of mathematics lessons, 4 interviews with the teacher participants, and teacher questionnaires. Student data were collected using the Student Agency Questionnaire (SAQ) and group interviews. Mathematics lessons were videotaped, transcribed, and coded to discern ways in which teacher participants facilitated mathematical discussions. Two case studies focused on participants' classroom discussion practices were created. Themes that emerged from the case studies were that teacher participants fostered students’ mathematical agency through their facilitation of discussions by 1) creating a positive learning community; 2) supporting students’ willingness to publicly engage in mathematical discussions; and 3) sharing the power of teaching and learning. Analysis of the Student Agency Questionnaire (SAQ) data indicated that students in both teacher participant classrooms reported behaviors associated with mathematical agency. Observations and group interview data supported the SAQ results that students in both classrooms displayed mathematical agency. Student group interview data analysis showed that students who considered themselves doers of mathematics exhibited the following characteristics: habits of perseverance, a confident attitude about doing mathematics, and a willingness to actively engage with mathematics. This study provides evidence that teachers’ facilitation moves have the power to maintain and extend students’ mathematical agency. This study will contribute to the little empirical research available on supporting students’ mathematical agency in elementary classrooms. Further research should continue to investigate in a larger array of classrooms at varying levels (elementary, middle and high school).

This phenomenological study explored how college students’ perceptions of experiences with their secondary mathematics teachers affected their mathematical identities. The study was rooted in Wenger’s notion that learning is an experience of identity and Dewey’s theory that all experiences are inextricably linked to past and future experiences. Constructed narratives of eight college developmental mathematics students with high and low levels of mathematics anxiety were created from autobiographical essays and semistructured interviews. Analysis of the constructed narratives employed a deductive coding process using a priori themes related to experiences with secondary teachers and dimensions of mathematical identity. The study answered three research questions: What kind of experiences did students recall having with their secondary mathematics teachers? How did students perceive that those experiences influenced their mathematical identities? What common student experiences positively or negatively affecting mathematical identity emerged from the data? Two general factors that affect student mathematical identity emerged from the research: student-teacher interactions and student-mathematics interactions. Interconnectivity existed between positive student-teacher relationships, meaningful student-mathematics interactions, and strong mathematical identities. Positive student-teacher relationships were foundational to the overall connection.

Learner performance in South Africa is poor in comparison with other countries as a result of poor teaching. At the core of the concern about learners' performance in mathematics in South Africa lies a controversy regarding how mathematics should be taught. The purpose of this study was to explore Grade 8 mathematics teachers' creation and utilisation of opportunities for learners to develop mathematical understanding in their classrooms. To accomplish this, an explorative case study was conducted to explore three mathematics teachers' instructional practices by using Schoenfeld et al.'s (2014) five dimensions of Teaching for the Robust Understanding of Mathematics (TRU Math) scheme, namely, the mathematics, cognitive demand, access to mathematical content, mathematical agency, authority and identity and uses of assessment. The three participants were conveniently selected from three private schools in Mpumalanga. The data collected consist of a document analysis, two lessons observations and a post-observation interview per teacher. This study revealed that only one of the three teachers applied all Schoenfeld et al.'s (2014) TRU Math dimensions. The dimension identified which the teachers applied most in their classrooms was the mathematics. The dimensions identified where teachers still lack skills were cognitive demand, access to mathematical content, agency, authority and identity, and uses of assessment. This study revealed that the content of most tasks and lessons was focused and coherent, and built meaningful connections. However, the content did not engage learners in important mathematical content or provided opportunities for learners to apply the content to solve real-life problems. Due to the small sample used, the results from this study cannot be generalised. However, I hope that the findings will contribute to student-teacher training and in-service teacher training in both government and private schools. Future research could possibly build on this study by examining the learners and how they learn with understanding by using the TRU Math dimensions. / Dissertation (MEd)--University of Pretoria, 2016. / Science, Mathematics and Technology Education / MEd / Unrestricted

We, as a culture, tend to lump students into broad categories to describe their relationships with mathematics, such as ‘good at math’ or ‘hates math.’ This study focuses on five students each of whom could be considered ‘good at math,’ and shows how the beliefs that make up their mathematical identities are actually significantly different. The study examined eight beliefs that affect a student's motivation to do mathematics: confidence, anxiety, enjoyment of mathematics, skill level, usefulness of mathematics, what mathematics is, what it means to be good at mathematics, and how one learns mathematics. These five students' identities, which seemed to be very similar, were so intrinsically different that they could not be readily ranked or compared on a one-dimensional scale. Each student had a unique array of beliefs. For example, the students had strikingly different ideas about the definition of mathematics and how useful it is to the world and to the individual, they had varying amounts of confidence, different aspects that cause anxiety, particular facets that they enjoy and different ways of showing enjoyment. Their commonly held beliefs also varied in specificity, conspicuousness, and importance. Recognizing that there are such differences among seemingly similar students may help teachers understand students better, and it is the first step in knowing how teachers can improve student's relationships with mathematics.

This study was designed to investigate the mathematical identity and achievement of one cohort of underrepresented male youth who participated in a pilot school intervention program in an urban middle school. Using counternarratives and a case study method, the experiences of four traditionally underserved high school students were investigated to explore their emerging mathematical identities. Results revealed the intervention program had very limited effect on the participants' mathematical identity. As engagement is prerequisite to student achievement, this study sought to understand what environmental factors (family, peers, teachers, self) affect student engagement and their developing mathematical identities. To explore the environmental factors, the Research Assessment Package for Schools (Institute for Research Reform in Education, 1998) was used to establish levels of engagement among family, peers, teachers, and self. Results indicated among the four environmental factors, family was most influential in their mathematical identity. Peers ranked second in terms of influence, self-engagement ranked third and teacher engagement ranked in the fourth position. To understand the impacts of race and culture on mathematical identity, the Multidimensional Inventory of Black Identity was administered to explore levels of race (cultural) centrality, and regard (public and private) as well as explore their identities as being members of their respective groups. A cross case analysis was conducted on the four participants to determine the impacts of race (cultural) centrality and regard (public and private) on their mathematical identity. Results revealed each member had a high race (cultural) centrality score and a high private regard score and a moderate public iii regard score. Participants were aware of stereotype and stereotype threat; however, it did not appear to affect mathematical identity. This model integrates racial and/or cultural identity and the engagement of family, peers, teachers and self to better understand the conditions that contribute to the mathematical identity of traditionally underserved young men. / Math & Science Education

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A study of students’ mathematical identity was carried out in February 2009 involving participants from two colleges of education, one in Dublin (Republic of Ireland) and one in Belfast (Northern Ireland). All participants were pre-service primary school teachers in the third year of their B.Ed. programme, having chosen to specialize in mathematics. Data was gathered using a questionnaire (with, mainly, open-ended questions) followed by focus groups, involving the same participants, on each campus. This paper considers how students’ exploration of their mathematical identity led them to deepen their insight into learning and teaching mathematics. Recommendations are made for how the methods used in this research might be beneficial on a larger scale, in different environments.

Abstract This study explored mathematical identity work by drawing on the cases of Finnish and Slovenian pre-service elementary teachers. All cases reported having had negative experiences with mathematics during their school years. These experiences were shown to have a central meaning for pre-service teachers’ mathematical identities. However, identity also extends to the future. For this reason, pre-service teachers’ anticipations of the future were also explored. The concepts of narrative identity (Ricoeur, 1992) and possible selves (Markus & Nurius, 1989) were applied in the context of mathematics education. The overall narrative perspective of the study enabled a psycho-social understanding of identity. The special interest of the study was confined to an understanding of the role that educational contexts play in pre-service teachers’ mathematical identity work. Narrative inquiry was applied as a research methodology. In-depth interviews invited pre-service teachers to construct narratives of their mathematics-related experiences. These narratives were analysed holistically and categorically, as well as in terms of content and form. The findings showed striking similarities in pre-service teachers’ school-time memories. The cases in question felt like victims of their own mathematical experiences. The anticipations of mathematics teaching were also underlined by the challenges rooted in their school-time experiences. However, a surprising finding was that the identity work in which the Finnish and Slovenian cases engaged during their teacher education differed substantially. The main reasons for the differences in identity work seemed to stem from different emphases and pedagogical practices in mathematics education courses within the Finnish and Slovenian teacher education settings. The study argued that identity work can be facilitated during teacher education. To begin such a process, it would be central to focus on pre-service teachers’ biographical context through narrative pedagogical tools. The findings also showed that neglecting issues from school-time experiences might engender further challenges for pre-service teachers’ future mathematics teaching. Finally, the study argued for the need to openly address identity during teacher education. The significant theoretical contribution of the study is the conceptualisation of ‘mathematical identity work’. / Tiivistelmä Tutkimuksessa tarkasteltiin matemaattista identiteettityötä suomalaisten ja slovenialaisten luokanopettajaopiskelijoiden kokemusten kautta. Opiskelijoiden mukaan heillä oli ollut omana kouluaikanaan kielteisiä matematiikan opintoihin liittyviä kokemuksia, joilla osoitettiin olevan negatiivisia vaikutuksia opiskelijoiden matemaattisiin identiteetteihin. Koska tutkimuksessa korostuu identiteetin tulevaisuusaspekti, tarkastelun kohteina olivat opiskelijoiden tulevaisuuteen liittyvät toiveet ja odotukset. Tutkimuksessa sovellettiin narratiivisen identiteetin (Ricoeur, 1992) ja mahdollisten minuuksien (Markus & Nurius, 1989) käsitteitä matematiikan opetuksen kontekstissa. Identiteetin ymmärtämisen psyko-sosiaalisena ilmiönä mahdollisti narratiivinen näkökulma. Erityinen huomio kohdistettiin siihen, millainen merkitys kasvatuksellisilla konteksteilla on luokanopettajaopiskelijoiden matemaattisessa identiteettityössä. Tutkimusmetodologiana käytettiin narratiivista tutkimusta. Opiskelijat kertoivat syvähaastatteluissa matematiikkaan liittyvistä kokemuksistaan. Nämä narratiivit analysoitiin holistisesti ja kategorisesti ottaen huomioon myös niiden sisältö ja muoto. Tuloksista ilmenee merkittävää samankaltaisuutta luokanopettajaopiskelijoiden omaan kouluaikaan liittyvissä muistoissa. Monet esimerkiksi kuvailivat itsensä uhreiksi. Myös tulevaan matematiikan opetukseen liittyvät ennakko-odotukset olivat värittyneet opettajaopiskelijoiden omaan kouluaikaan liittyvien haasteellisten kokemusten kautta. Yllättävä tulos oli se, että suomalaisten ja slovenialaisten opiskelijoiden luokanopettajakoulutuksen aikainen identiteettityö erosi huomattavasti toisistaan. Erojen pääsyynä ovat nähtävästi erilaiset painotukset ja käytänteet opettajankoulutuksen matematiikan pedagogisissa opinnoissa. Tutkimus osoittaa, että identiteettityötä voidaan pyrkiä edistämään opettajankoulutuksen aikana. Prosessin aloittamiseksi olisi tärkeää kohdentaa huomio opettajaopiskelijoiden elämäkerrallisiin konteksteihin soveltamalla narratiivisia pedagogisia työkaluja. Sillä että omaan kouluaikaan liittyviä kokemuksia ei oteta huomioon, voi olla kielteisiä heijastuksia opettajaopiskelijoiden tulevaan matematiikan opetukseen. Tutkimuksen mukaan identiteetti on syytä ottaa avoimesti tarkasteluun opettajankoulutuksen aikana. Tutkimuksen teorian kannalta merkittävä anti on termin matemaattinen identiteettityö käsitteellistäminen.

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