Toward inclusive mathematics education: a metatheoretical reflection about countering ableism in mathematics standards and curriculum

This article documents efforts to advance inclusive mathematics education practices involving the introduction of equity-oriented resources in state-level mathematics standards guidance documents in a Midwestern United States jurisdiction. We adopt a critical stance by looking at ways to interrogate available metatheories for these kinds of change-making processes. The guiding resources documented in the present article center on issues of difference. These issues are related to dis/ability in mathematics education standards and curriculum to not only raise teachers' awareness of constructions of difference in order to foster inclusive education, but also to promote critical self-reflections around ableism. Guiding resources are a means to support recognition of dis/ability difference as a source of multiple mathematical knowledge bases from which to learn and advance mathematics thinking. Yet, we also recognize the need to be vigilant about the complex interpretative contours and the relational dynamics at work throughout their various layers of implementation, assessment, and anti-ableist realignment. Accordingly, we reflect metatheoretically about three questions: How might concepts of access, achievement, identity, and power support teachers of mathematics in advancing inclusive practices? How do word choices in mathematics standards, curriculum, and practices dis/able students in classroom practices? What may we learn from the mathematics education experiences of individuals with dis/abilities and their families in the broad configuration of change-making dynamics of educational policies and teaching practices?     

Epistemic quality for equitable access to quality education in school mathematics

This paper reports on a study that aims to address the challenges of UN Sustainable Development Goal 4 to ensure inclusive and equitable quality education for all. The study focuses on school mathematics in particular. With regard to ensuring equitable access to quality education, it is argued that there is a need to consider the epistemic quality of what students come to know, make sense of and be able to do in school mathematics. Accordingly, the aim is to maximize the chances that all pupils will have epistemic access to school mathematics of high epistemic quality. The study is based on the theoretical framework of Joint Action Theory in Didactics (JATD). Associated research questions focus on the quality of teacher-student(s) joint action and on the epistemic quality of the content. The paper draws on empirical research findings of the Developing Mathematical Thinking in the Primary Classroom (DMTPC) project (2010–12) and also on the findings of a parallel study of mathematics teachers’ assessment practices in Ghana. One teacher’s action research project is used as an exemplar to illustrate how mathematics can become more accessible and inclusive thus leading to an evolution in mathematical thinking and high-quality epistemic access for all.     

Developing theories of mathematics education research: the ESM story

In this paper we present ananalysis of the articles in EducationalStudies in Mathematics since 1990. It ispart of a larger project looking at theproduction and use of theories of teachingand learning mathematics. We outline thetheoretical framework of our tool ofanalysis and discuss briefly some of themethodological difficulties we face. Wethen present our findings from the analysisof the journal and we also give one exampleof how we `read' an article, illustratingthe rules whereby criteria are applied. This revised version was published online in July 2006 with corrections to the Cover Date.     

高师数学教育如何适应基础教育新课程改革的要求

基础教育新数学课程的实施对中小学数学教师的教育教学工作提出了许多新的要求。从而也为培养中小学数学教师的高师数学教育提出了更高的要求．为了适应基础教育新课程的改革．高师数学教育应加强对师范生的情感态度及价值观的教育，调整高师的课程体系与内容，倡导新的学习方式，转变传统的教学方式。改革传统的评价方式.     

Unfulfilled hopes in education for equity: redesigning the mathematics curriculum in a US high school

Mathematics education aimed at empowering students for economic and democratic participation must address two critical issues: the long‐standing function of mathematics as a gatekeeper, and the complicated nature of designing and implementing systematic reform at the school department level. The study reported here examines a curricular redesign implemented by teachers in one US high school department. The department was redesigning its curriculum to remedy high failure rates in targeted courses disproportionately populated by students of colour. Using a case‐study methodology, this study examines the process of curricular redesign and its influence on these students’ access to more advanced mathematics courses. It describes redesigned courses and department characteristics that aided or challenged the redesign process, and discusses the significance of the identified challenges in constructing placement policies that did little to increase students’ likelihood of taking additional, and more advanced‐ level, mathematics courses. The analysis revealed a department that, despite its intentions, implemented a curriculum design which perpetuated inequities. This study discusses the teachers’ expectations of their students and perspectives about the nature of mathematics as a partial explanation for the department’s failure. The resigned curriculum failed to promote mathematics course‐taking because it created more defined tracks with less rigorous courses for students in low‐level courses.     

Getting Real: Exploring the perceived disconnect between education theory and practice in teacher education

This article, inspired in part by the Levine report that criticizes teacher education programs in the United States for being out of touch with practices that work in real classrooms, is a self-study that explores the rift between educational theory, particularly theory that pushes for social constructionist, child-centered approaches to teaching, and teaching practices in majority African-American, inner-city schools. The authors conducted this year-long self-study to answer the question: What could the college's education program do to improve preparation for teaching in inner-city schools? Through their year-long collaboration in a middle-school writing classroom in an inner-city charter school, the authors examined what a prospective teacher learned in his education program that helped and hindered him and then explored how the successful approaches he developed as a new teacher could be incorporated into the college's preservice program.     

Aborigines of the Imaginary: applying Lacan to Aboriginal education

This paper applies the work of Jacques Lacan, a French psychoanalyst, to decipher the desire of the teacher in Aboriginal education. It argues that the images of Aboriginal people represented in Australian classrooms are effects of the teacher's Imaginary, the Imaginary being one of the three psychoanalytic domains theorised by Lacan over a period of 30 years of teaching. The author questions whether it is possible for teacher education courses to move the student teacher beyond the Imaginary, and beyond the inventions of Aboriginal people that he or she has produced in his or her own mind. A possible way out of this endless cycle of romantic idealism and deficiency is proposed outside the usual approaches to cultural awareness training and professional development.     

The role of subject-matter content in teacher preparation: an international perspective for mathematics

International comparative studies in education provide a fresh perspective on K-12 education policy by enabling countries to learn from each other’s approaches. The recently conducted Teacher Education and Development Study—Mathematics provides a worldwide lens by which to examine the role of subject-matter in the preparation of US teachers of mathematics for primary and lower secondary students. More specifically, a previous study looking at the international top-performing teacher preparation programmes identified a common set of learning experiences (topics/content) related to mathematics. This empirically derived international benchmark is used in this paper to examine the quality of the mathematics preparation of future US teachers in various university and college programmes.     

数学教育如何体现以学生的发展为本

随着数学教育改革的深入，数学教育主张“以学生的发展为本”。数学教育“以学生发展为本”可从以下几个方面体现：从育人观看要培养学生良好的个性品质；从课程观看要让学生学习有用的数学；从教学观看要使学生主动学习主动发展；从学习观看要对学生进行学习方法指导。它们相互联系、相互影响，在进行教学实践中应融会贯通，就能促进学生数学素质的全面发展。     

Educational soundscapes: tuning in to sounds and silences in the history of education

Abstract

In order to introduce the special issue on “educational soundscapes” the editors, first of all, explore the intimate link between silence, sound and the production of social meaning. An acoustic history of education, so it is argued, cannot solely focus on silence nor can it solely focus on sound. After having demonstrated the necessity of taking into account sounds and silences at the same time, the term “educational soundscapes” consecutively is defined, historically contextualized and connected to the widely used concept of educationalization. Finally, the different contributions to the special issue are briefly introduced and connected to the main theme of the special issue, namely “educational soundscapes”.     

Two negatives don't always make a positive: Exploring how limitations in teacher knowledge and the curriculum contribute to instructional quality

This paper examines the contribution of mathematical knowledge for teaching (MKT) and curriculum materials to the implementation of lessons on integer subtraction. In particular, it investigates the instruction of three teachers with differing MKT levels using two editions of the same set of curriculum materials that provided different levels of support. This variation in MKT level and curriculum support facilitated exploring the distinct and joint contribution of MKT and the curriculum materials to instructional quality. The analyses suggest that MKT relates positively to teachers' use of representations, provision of explanations, precision in language and notation, and ability to capitalize on student contributions and move the mathematics along in a goal-directed manner. Curriculum materials set the stage for attending to the meaning of integer subtraction and appeared to support teachers' use of representations, provision of explanations, and precision in language and notation. More critically, the findings suggest that less educative curriculum materials, coupled with low levels of MKT, can lead to problematic instruction. In contrast, educative materials can help low-MKT teachers provide adequate instruction, while higher MKT levels seem to enable teachers to compensate for curriculum limitations.     

The mathematics problem: the construction of a market-led education discourse in the Republic of Ireland

Educational change in the neoliberal state is permeated by the effects of forces from outside the field of education itself. The process of governmentality welcomes, indeed demands, the participation of those non-state actors valorised by neoliberalism as well as government agencies dedicated to the advancement of such groups. Inevitably, the concerns of such organisations become central to how the state sees education. This article traces the assembly of national and international agents from industry, business and special interest groups around the concept of ‘knowledge economy’. It treats this assemblage as an apparatus (dispositif), examining how the construction of an economic problem is brought to bear on the demand for educational change, and how this construction of the problem is used to shape public opinion in order to prepare the public for a radical change of direction. Confining itself to the reform of mathematics education introduced in the Republic of Ireland in 2010, this article traces the emergence of a mathematics discourse focused on market-led education. It interrogates the construction of ‘the mathematics problem’ or ‘crisis in maths’ and argues that the discourse of the present construction is economic in nature, centring as it does on human capital production and market-led reform.     

Intersections of race and sexuality in a teacher education course

This paper examines the ways that one group of US pre‐service teachers, enrolled in an alternate route teacher education class, expressed and challenged each other’s contradictory discourses about teaching for social justice. Particularly significant are the many ways that this group of students enacted subject positions around race and sexuality as various combinations of African American, White, gay, straight, lesbian, Christian, and as members of this class. Epiphanic moments about race and sexual orientation are examined to illuminate the ways that subject positions were contested, reified, or renegotiated in order to preserve a sense of community within the class. This research demonstrates the ways that social justice teacher education differentially positions people who have been historically marginalized and how it can at times reify a hierarchy of marginality.     

From the contribution to the action approach: White teachers' experiences influencing the development of multicultural science curricula

In this exploratory case study, we sought to understand teacher's integration of multicultural curricula in science curriculum units, and how personal experiences influenced the level of integration in light of Bank's typology of ethnic content integration into school curricula. Five research participants volunteered and were selected so as to be representative of the demographic of pre‐service and in‐service teachers in the southern United States. The aim was to explore teachers' personal experiences with cultural others that either facilitated or impeded their adoption of multicultural curricula strategies in science curricula units. Case narratives present and discuss interview data and assigned curricula projects. Findings suggest that participants who had transformative cultural experiences and who identified as the marginalized cultural other, transformed science curricula at higher levels of Bank's typology for curricula' multicultural approaches. © 2012 Wiley Periodicals, Inc. J Res Sci Teach 49: 1271–1295, 2012     

Exploring the global/local boundary in education in developing countries: the case of the Caribbean

This article focuses on education in developing countries in the context of globalization and with specific reference to the Caribbean. It examines the concept of globalization and related concepts and positions developing countries within this context. It explores the possibility of the creation of a third space where the local and the global can co-mingle and new understandings can emerge. The article argues that although the global/local interface constitutes a zone of tension, it can, in the realm of education, become an area of creative opportunity. It outlines some parameters that can guide the way in which the third space can be shaped when Caribbean and other developing countries are faced with the challenge of accommodating external ideas into local education.     

"教师公正"研究

教师的教育公正及其实现程度,不仅取决于教师善良的愿望、公正的态度,更取决于教师公正施教的能力。教师公正是基于教师职业道德的要求,但又超越职业道德的范畴,是对教师的教育教学艺术提出的更高要求和挑战。     

The didactical use of models in realistic mathematics education: An example from a longitudinal trajectory on percentage

The purpose of this article is to describe how, within the Dutch approach to mathematics education, called Realistic Mathematics Education (RME), models are used to elicit students' growth in understanding of mathematics. First some background information is given about the characteristics of RME related to the role of models in this approach. Then the focus is on the use of the bar model within a longitudinal trajectory on percentage that has been designed for Mathematics in Context, a curriculum for the U.S. middle school. The power of this model is that it develops alongside both the teaching and the students: from a drawing that represents a context related to percentage to a strip for estimation and reasoning to an abstract tool that supports the use of percentage as an operator. This revised version was published online in August 2006 with corrections to the Cover Date.     

Exploring the heterogeneity of class in higher education: social and cultural differentiation in Danish university programmes

This paper examines the relationship between social background, choice of university programme and academic culture among Danish university students. Statistically and sociologically, university students are often treated as a homogeneous group, but the ever-increasing number of students in higher education demands a closer examination of the hidden heterogeneity in the students’ social origin and educational strategies. Using a mixed-method approach (register data and ethnographic observations and interviews) the paper focuses on the students’ class origins and on different cultural practices in three Danish university programmes. It is shown that the Danish university field is characterized by a significant variation in social selectivity from programme to programme, and it is argued that these different social profiles correspond with distinctively different cultural practices in the programmes. Correspondingly, the students have distinctively different strategies towards education and future work life.     

Metaphors of hierarchy in mathematics education discourse: the narrow path

This paper adopts a rhetorical perspective in order to examine language about children in the discourse of mathematics education through a study of metaphor. Previous research has tended to emphasize the notion of ‘beliefs’, which locates responsibility for problematic conceptions of children within the heads of individuals, particularly practising and preservice teachers. Using the notion of metaphor, this paper examines several texts in US mathematics education, including conversations in an elementary classroom, a university mathematics methods classroom, mathematics textbooks, and standards documents. All of these texts draw on the metaphor of children’s learning as travel along a physical path, which supports talking and thinking about children in hierarchical ways. The dominance of this metaphor presents a new challenge for teacher educators concerned with equity: that of examining their own language and practices for hierarchical language.     

情境教学在小学数学教育中的应用研究

数学新课程的教学设计尤其注重充分发挥学生的主体作用,这就要求教师要在教学中设计合适的教学情境和教学条件,充分调动学生的学习热情和动力,引导学生主动参与到教学之中。本文以情境教学在小学数学教学中作用、实现情境教学的方法和应注意事项为重点,对情境教学在小学数学教育中的应用开展了较为详细的研究。