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This paper reports from a case study which explores kindergarten children's mathematical abstraction in a teaching–learning activity about reflection symmetry. From a dialectical perspective, abstraction is here conceived as a process, as a genuine part of human activity, where the learner establishes "a point of view from which the concrete can be seen as meaningfully related" (van Oers & Poland Mathematics Education Research Journal, 19(2), 10–22, 2007, p. 13–14). A cultural-historical semiotic perspective to embodiment is used to explore the characteristics of kindergarten children's mathematical abstraction. In the selected segment, two 5-year-old boys explore the concept of reflection symmetry using a doll pram. In the activity, the two boys first point to concrete features of the sensory manifold, then one of the boys' awareness gradually moves to the imagined and finally to grasping a general and establishing a new point of view. The findings illustrate the essential role of gestures, bodily actions, and rhythm, in conjunction with spoken words, in the two boys' gradual process of grasping a general. The study advances our knowledge about the nature of mathematical abstraction and challenges the traditional view on abstraction as a sort of decontextualised higher order thinking. This study argues that abstraction is not a matter of going from the concrete to the abstract, rather it is an emergent and context-bound process, as a genuine part of children's concrete embodied activities. [ABSTRACT FROM AUTHOR]

This paper reports on concept images of 38 secondary school mathematics prospective teachers, regarding the evenness of numbers. Written assignments, individual interviews, and lesson transcripts uncover salient, erroneous concept images of even numbers as numbers that are two times "something" (i.e., 2i is an even number), or to reject the evenness of zero. The notion of concept image serves in the analysis of the findings, and the findings serve in offering two refinement notions: mis-in concept images that mistakenly grant non-examples the status of examples (e.g., 2i is an even number), and mis-out concept images that mistakenly regard examples as non-examples (e.g., zero is not an even number). We discuss possible benefits in distinguishing between these two refinement notions in mathematics education. [ABSTRACT FROM AUTHOR]

The work that mathematics teachers do is frequently mathematical in nature and different from other professions. Understanding and describing common ways that teachers draw upon their content knowledge in the practice of teaching is important. Building on the descriptions by McCrory et al. (Journal for Research in Mathematics Education 43(5) 584-615, ) of two primary ways teachers use their content knowledge-decompressing and trimming-this paper differentiates between micro- and macro-levels of mathematical complexity as a way to extend and further conceptualize the moves that teachers make at a more nuanced grain size. This paper explains and portrays their counterparts, micro-level trimming and macro-level decompressing, which we discuss as concealing and foreshadowing complexity, respectively. Support for their use in teachers' work is provided through specific examples. Implications for the mathematical preparation and professional development of teachers are discussed. [ABSTRACT FROM AUTHOR]

Girls' underrepresentation in high-level post-compulsory mathematics is a longstanding issue of concern in many Western nations, with innumerable efforts to increase their participation producing little impact. In this paper, we shed new light on girls' underrepresentation through a post-structural feminist investigation of mathematics teachers' discursive constructions of high-level senior secondary mathematics students. Our analysis of semi-structured interviews with 22 Australian mathematics teachers revealed gendered views that serve to exclude many students from the high-level mathematics student category. Most concerning was their recurring naturalised construction of successful high-level mathematics students as endowed with the right, invariably male, brain. In so doing, teachers repeatedly closed off the possibility of success to those lacking such a 'mathematics gift', effectively 'counting girls out'. We argue that increasing girls' participation in mathematics requires moving beyond current efforts to raise female interest and confidence to, more profoundly, disrupt enduring discourses of male superiority in mathematics. [ABSTRACT FROM AUTHOR]

This paper reports the activity of three secondary school mathematics departments in England in self-initiated states of change that led to overall improvements in students' achievements when compared to previous cohorts. This took place without intervention and without their participation in external projects. They provide examples of departments that can work effectively on their own development, and hence, their work adds to our knowledge of the potential for development through collaboration. The departments were monitored over 3 years, and data were analysed using the lens of activity theory. In contrast to departments in many studies, these departments worked overtly on mathematics pedagogy through the shared production and discussion of resources, shared planning and task design. Also in contrast to several other studies, they developed distinct ways to handle differences of subject knowledge among the teachers in the department. Their focus changed during the study from developing resource banks to supporting students' learning through hybrid teaching. [ABSTRACT FROM AUTHOR]

When language is defined narrowly in mathematics classrooms, racially and linguistically minoritized students in classrooms could be systematically positioned as "learners of deficiency." Recent scholarship calls for expanding the notion of language to emphasize embodied expression of mathematical ideas. Taking a critical perspective to understand racialized experiences of using languages in disciplinary learning spaces, this article proposes the reconceptualization of embodiment as a language for racialized multilingual learners. This study was conducted in a Grade 1 classroom in a linguistically and racially diverse school in Canada. Through a series of professional development sessions, we worked with an experienced teacher to redesign the normalized and institutionalized pedagogy toward greater mobility of racialized multilingual learners' bodies, which was intertwined with their intellectual liberation. Focusing on the spatiality of pedagogy, the previously restrictive areas in the school were transformed into a place that augments embodied expression of mathematical ideas and agentive participation of minoritized learners. The analysis focused on the embodied discourse that participating racialized multilingual students used to actively engage in mathematical discussion. Our findings show that the designed pedagogy, characterized by the spatial and temporal expansion of the learning environment, offered more spaces for uncertainty and spontaneity with the decreased control of the teacher as an explicator. Our article furthers anti-colonial approaches to understand the intersection of racialized bodies and language in mathematics education. [ABSTRACT FROM AUTHOR]

In this study, the authors examined a group of related literatures that used the same large-scale nationally representative dataset with algebra achievement as the outcome to explore why results from the same dataset may differ across studies. More specially, the authors synthesized the extant research literature that utilized data from the High School Longitudinal Study of 2009 (HSLS:09) to investigate the student-, teacher-, school-, and parent-level characteristics associated with algebra achievement and whether these relationships were consistent across students' backgrounds (i.e., race/ethnicity, gender, socio-economic status, and prior achievement). The authors have summarized the results of 21 studies across 2 outcome variables (ninth- and eleventh-grade algebra achievement) using optimal resource theory as a framework to summarize evidence-based practices for improving student outcomes. [ABSTRACT FROM AUTHOR]

Feedback provided by mathematics teachers usually addresses procedural skills and, to a much lesser extent, other competencies such as conceptual understanding or engagement in mathematical practices. As most previous literature has studied feedback provided on homework or video prompts, how teachers provide such feedback in the classroom is poorly understood. Here, sixteen lessons taught by five teachers were purposefully sampled from a larger video study (172 lessons) as lessons with high-quality feedback according to a standardized observation instrument. The analysis focused on the instructional situations in which teachers provided feedback. When teachers provided procedural feedback, the situations were orderly and effective. Feedback on conceptual understanding and mathematical practices was provided in situations when students were especially challenged, and entailed a series of complex decisions, thereby placing demands on the teachers to manage both the students' understanding and behavior. We argue that researchers should focus on how teachers and students negotiate the instructional situation to allow for feedback on conceptual understanding or mathematical practices. [ABSTRACT FROM AUTHOR]

A broad categorisation of different reading styles for mathematics text is generated in this research. The styles derive from those found in literature around academic reading skills. These styles are inductively refined using video transcripts of five specially chosen students studying out loud from a prescribed mathematics textbook. The context is a self-study mathematics course directed at high school mathematics teachers with weak content knowledge. Reading is understood as a transaction (enacted curriculum) between text (written curriculum) and reader. Reading styles are characterised in terms of depth of reading, focus on different components of text or not, connections within text or to prior knowledge, and performance on exercises. Five different styles of reading mathematics text are identified: close reading with strong connections, close reading with some connections, scanning, skimming, and avoiding. The different reading styles are also interpreted in terms of structure, voice, and genre of the textbook. [ABSTRACT FROM AUTHOR]

Reform-based discourses in mathematics education have fabricated different subjectivities for teachers such as the "traditional" and the "new" teacher. Professional development programs are proposed as effective mechanisms to fabricate the "new" teacher. However, this teacher has proved hard to produce. Thus, the "resistor" teacher has emerged into the field as a way to explain failure within school mathematics reform. In this article, I assume that resistance is a consequential response against particular forms of subjectivation imposed on mathematics teachers. Using conceptual tools from Hall and Foucault, I explore the ways wherein a high school mathematics teacher reinvents meanings of being a mathematics teacher in the context of a professional development program aimed to implement problem-solving instruction. Against the myth of the resistor teacher unwilling to change, what emerges is a process of struggle over meaning. School mathematics reform, considered as an ideological event, becomes a site in which competing meanings about being a mathematics teacher are negotiated, contested, and resisted. [ABSTRACT FROM AUTHOR]

In order to develop a deeper understanding of mathematics teaching expertise, in this study we use the Documentational Approach to Didactics to explore the resource systems of three Chinese mathematics 'expert' teachers. Exploiting the Western and Eastern literature we examine the notion of 'mathematics teaching expertise', as it is perceived in the East and the West. The data consist of two rounds of in-depth interviews, observations and teachers' representations of their resource systems, where teachers describe their resources connected to their practice, their perceptions of mathematics teaching expertise, and how to develop it. Subsequently, the data are analyzed with respect to the different facets of the notion of teaching expertise and related to the teachers' views and practices, in order to deepen our understandings of what proficiency in mathematics teaching might mean and how to develop it, seen through the lens of 'resources'. The significance of the study relates to the enhancement of mathematics teachers' expertise and capacity building when working in collectives (e.g., in teacher professional development), in order to develop a strong workforce for supporting and helping to improve pupil learning. [ABSTRACT FROM AUTHOR]

For decades, educators have advocated using history of mathematics in mathematics classrooms. Empirical research on the efficacy of this practice, however, is scarce. A quasi-experiment was used to investigate the effects of using history as a tool to teach mathematics on grade 11 students' mathematics achievement. Effects in three affective domains (attitudes, anxiety, and motivation) were also measured. Four classes from a school in Singapore participated in this quasi-experiment. The experimental group ( n = 51) and control group ( n = 52) were each made up of two classes. Results indicated that using history as a tool to teach mathematics had a significant positive effect on students' mathematics achievement, in an initial posttest and in two retention tests taken 4 months and 1 year, respectively, after the last intervention session. Significant positive effects were also found on two subscales within the affective domain variables (perceived value of mathematics and introjection, a type of extrinsic motivation), but only at a posttest administered midway through the study. These results suggest that using history in mathematics classrooms have both immediate short- and long-term effects on students' achievement, but only short-term positive effects in the affective domains. These results were discussed using qualitative feedback obtained from the participants of this study. [ABSTRACT FROM AUTHOR]