Educational Studies in Mathematics最新文献

As increasing numbers of Black immigrant students attend schools in Chile, we examine classroom practices to consider the limits of the mathematics education equity promise for this student population. We focus on the practices of a third-grade teacher who participated in professional development for enhancing reform-based mathematics teaching in a racially diverse classroom. Drawing on Stuart Hall’s approach to race, our analysis shows how two technologies of race-power fabricate the Black immigrant child as an uneducable and impossible mathematics learner. We contend that rather than enhancing the inclusion of Black immigrant students, reform-based mathematics teaching might maintain and reinforce racial hierarchies of mathematics ability.

In university mathematics education, students do not simply learn mathematics but are shaped and shape themselves into someone new—mathematicians. In this study, we focus on the becoming of disabled mathematical subjects. We explore the importance of abilities in the processes of being and becoming in university mathematics. Our interest lies in how teaching and assessment practices provide students with ways to understand themselves as both able and disabled, as disabilities are only understood with respect to the norm. We analyse narratives of nine university students diagnosed with learning disabilities or mental health issues to investigate how their subjectivity is constituted in discourse. Our analysis shows how the students are shaped and shape themselves as disabled mathematicians in relation to speed in mathematical activities, disaffection in mathematics, individualism in performing mathematics, and measurability of performance. These findings cast light on the ableist underpinnings of the teaching and assessment practices in university mathematics education. We contend that mathematical ableism forms a watershed for belonging in mathematics learning practices, constituting rather narrow, “normal” ways of being “mathematically able”. We also discuss how our participants challenge and widen the idea of an “able” mathematics student. We pave the way for more inclusive futures of mathematics education by suggesting that rather than understanding the “dis” in disability negatively, the university mathematics education communities may use dis by disrupting order. Perhaps, we ask, if university mathematics fails to enable accessible learning experiences for students who care about mathematics, these practices should indeed be disrupted.

This article proposes an in-depth mathematics analysis of simple and compound interest through an exploration of the mathematical structures underlying these concepts. Financial numeracy concepts (simple and compound interest, interest rates, interest period, present and future value, etc.) have been added to the mathematics curriculum of the Canadian province of Quebec in 2016. Yet, little is known with regards to mathematics teachers’ knowledge of financial concepts. We mobilized the relational paradigm framework in the context of simple and compound interest to construct an assessment instrument of teacher knowledge. Based on 36 teachers’ responses to the questionnaire, we observed that the majority of teachers did not use mathematical structures in problem solving; they were not able to make sense of simple and compound interest in ways that do not involve standard formulas. Such results indicate opportunities for professional development in regard to secondary mathematics teachers’ knowledge of mathematics in the context of simple and compound interest situations.

The notion of multilingual students’ first language has been advocated as a resource in mathematics learning for some time. However, few studies have investigated how implementing students’ L1 in the teaching practice impacts multilingual students’ mathematics learning opportunities. Based on a 9-month-long ethnographic study conducted in Iran, we investigate what a long-term shift from mathematics teaching in the language of instruction (Persian) to mathematics teaching that includes students’ first language (Turkish) may mean in terms of learning opportunities. In language positive classrooms, students’ socialization into mathematics and language includes using students’ first languages and paying explicit attention to different aspects of language use in mathematics. Among other things, socialization events provide possibilities to share explanations of mathematical thinking. The results of this study suggest that using students’ first languages may reinforce other language positive socialization events and provide mathematics learning opportunities during individual assignment activities. Furthermore, the results suggest that the conceived value of mathematics education in the local communities changed with the introduction of students’ L1 in the teaching practice. Consequently, this study indicates that using students’ first languages in mathematics classrooms may be a key issue in multilingual contexts.

In this essay, I examine coloniality as a racializing force within international education curricula. I focus on the British-developed Cambridge Assessment International Education (CAIE) curriculum, previously known as the Cambridge International Education (CIE) curriculum. Using the CAIE as a specific case, I discuss how international curricula serve as vehicles of coloniality and simultaneously reproduce racialized narratives about Sub-Saharan Africans. The persistence of CAIE is implicated in the ongoing project of coloniality, sustaining and reproducing racial hierarchies and the marginalization of Sub-Saharan African communities. I contend that CAIE privileges a singular way of thinking and being in mathematics and uses assessment practices to perpetuate coloniality. By recognizing the ways in which coloniality and racialization are interconnected, we can better understand the complex systems of power and privilege that shape international mathematics curricula.

This study introduces a framework for analyzing opportunities for mathematical reasoning (MR) in school mathematics, using MR-relevant claims and their derivation as the unit of analysis. We contend that this approach can effectively capture a broad range of opportunities for MR across various teaching situations. The framework, rooted in commognition, entails identifying necessary object-level narratives (NOLs) and the processes involved in their construction and substantiation. After theoretical development, the framework was refined through analyses of mathematics lessons in Norwegian primary school classrooms. Examples from the data illustrate how to utilize the framework in analysis and what such analyses can reveal in four typical teaching situations: the introduction of new mathematical objects, the introduction of procedures, work on exercise tasks, and work on problem-solving tasks. Drawing from the analysis of these examples, we discuss the value of the framework for analyzing MR in school mathematics and how such analysis can benefit teachers and researchers.

Abstract

An important approach for developing children’s algebraic thinking involves introducing them to generalized arithmetic at the time they are learning arithmetic. Our aim in this study was to investigate children’s attention to and expression of generality with the subtraction-compensation property, as evidence of a type of algebraic thinking known as relational thinking. The tasks involved subtraction modelled as difference and comparing the heights of towers of blocks. In an exploratory qualitative study, 22 middle primary (9–11-year-old) students from two schools participated in individual videoed interviews. The tasks were designed using theoretical perspectives on embodied visualization and concreteness fading to provide multiple opportunities for the students to make sense of subtraction as difference and to advance their relational thinking. Twelve out of 22 students evidenced conceptual understanding of the comparison model of subtraction (subtraction as difference) and expression of the compensation property of equality. Four of these students repeatedly evidenced relational thinking for true/false tasks and open equivalence tasks. A proposed framework for levels of attention to/expression of generality with the subtraction-compensation property is shared and suggestions for further research are presented.

Using Balacheff’s (2013) model of conceptions, we inferred potential conceptions in three examples presented in the spanning sets section of an interactive linear algebra textbook. An analysis of student responses to two similar reading questions revealed additional strategies that students used to decide whether a vector was in the spanning set of a given set of vectors. An analysis of the correctness of the application of these strategies provides a more nuanced understanding of student responses that might be more useful for instructors than simply classifying the responses as right or wrong. These findings add to our knowledge of the textbook’s presentation of span and student understanding of span. We discuss implications for research and practice.