Learning mathematics and learning to teach: Learning cycles in mathematics teacher education

The reconceptualization of mathematics teacher education based on current mathematics education reform efforts necessitates the elaboration of theoretical frameworks to guide both the practice of and research on teacher education. The author presents a framework which has been useful in shaping two major mathematics teacher education research and development projects. This framework for mathematics teacher learning builds recursively on a framework for mathematics learning which derives from a social constructivist view of learning and incorporates aspects of French didactical theory using the organizing structure of the Karplus Learning Cycle. The framework can be used to think about the content and organization of a particular lesson or of an entire course or program for teachers. Further, it describes the interconnection between different domains of teacher knowledge.     

关于数学与数学教育——科学家关于数学的论述及其对我们的启示

在学习、理解科学家关于数学论述的基础上 ,进一步阐述了对数学与数学教育等问题的新认识     

Structural adjustment and education: Adapting to a growing global market

Structural adjustment effects on education have largely been viewed as policies imposed by the International Monetary Fund and the World Bank. This view overlooks the larger process of structural adjustment in a rapidly growing global economy. This article seeks to locate the structural adjustment implication for education within a global framework. Education's systemic dependence and system influence are identified. Specific educational effects of structural adjustment are discussed, addressing both short-term implications and long-term responses. Educational policy implications and research trends are addressed in the light of the evolving world system of education.     

Incorporating out-of-school mathematics: from cultural context to embedded practice

Connecting students’ cultural and community mathematical practices to school mathematics is a critical issue in mathematics education. The goal of the study was to identify how teachers incorporate children’s cultural and out-of-school mathematics in instruction. Four related practices were identified, and three drew on children’s cultural or out-of-school experiences: (a) using these experiences as contexts for problems, (b) linking these experiences to school mathematics, and (c) identifying embedded mathematical practices prominent in these experiences. A fourth category, teacher initiated situated settings, focused on shared experiences using the classroom as a site of culture. Findings suggest that these practices represent varying levels of complexity and that use of this framework might support teachers in better relating students’ cultural and out-of-school experiences to mathematics.     

Constructivism,mathematics and mathematics education

Learning theories such as behaviourism, Piagetian theories and cognitive psychology, have been dominant influences in education this century. This article discusses and supports the recent claim that Constructivism is an alternative paradigm, that has rich and significant consequences for mathematics education. In the United States there is a growing body of published research that claims to demonstrate the distinct nature of the implications of this view. There are, however, many critics who maintain that this is not the case, and that the research is within the current paradigm of cognitive psychology. The nature and tone of the dispute certainly at times appears to describe a paradigm shift in the Kuhnian model. In an attempt to analyse the meaning of Constructivism as a learning theory, and its implications for mathematics education, the use of the term by the intuitionist philosophers of mathematics is compared and contrasted. In particular, it is proposed that Constructivism in learning theory does not bring with it the same ontological commitment as the Intuitionists' use of the term, and that it is in fact a relativist thesis. Some of the potential consequences for the teaching of mathematics of a relativist view of mathematical knowledge are discussed here.     

Capitalizing on advances in mathematics and k-12 mathematics education in undergraduate mathematics: An inquiry-oriented approach to differential equations

This paper provides an overview of the Inquiry-Oriented Differential Equations (IO-DE) project and reports on the main results of a study that compared students’ beliefs, skills, and understandings in IO-DE classes to more conventional approaches. The IO-DE project capitalizes on advances within mathematics and mathematics education, including the instructional design theory of Realistic Mathematics Education and the social negotiation of meaning. The main results of the comparison study found no significant difference between project students and comparison students on an assessment of routine skills and a significant difference in favor of project students on an assessment of conceptual understanding. Given these encouraging results, the theoretical underpinnings of the innovative approach may be useful more broadly for undergraduate mathematics education reform.     

Physical discipline and children's adjustment: cultural normativeness as a moderator

Interviews were conducted with 336 mother-child dyads (children's ages ranged from 6 to 17 years; mothers' ages ranged from 20 to 59 years) in China, India, Italy, Kenya, the Philippines, and Thailand to examine whether normativeness of physical discipline moderates the link between mothers' use of physical discipline and children's adjustment. Multilevel regression analyses revealed that physical discipline was less strongly associated with adverse child outcomes in conditions of greater perceived normativeness, but physical discipline was also associated with more adverse outcomes regardless of its perceived normativeness. Countries with the lowest use of physical discipline showed the strongest association between mothers' use and children's behavior problems, but in all countries higher use of physical discipline was associated with more aggression and anxiety.     

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?     

Developing complex understandings: On the relation of mathematics education research to mathematics

This article explores some of the intellectual bases of the apparent cultural divide between the fields of mathematics and mathematics education research. The chasm is in part attributable to epistemologies or theoretical `paradigms', fashionable in education, that dismiss or deny the integrity of fundamental aspects of mathematical and scientific knowledge. The solution offered is for the next generation of mathematics education researchers to knowledgeably and thoughtfully abandon such `isms' in favor of a unifying scientific and eclectic approach to research.     

略论现代远程教育文化的内涵

现代远程教育文化是现代远程教育研究的重要课题之一.开展现代远程教育文化研究,既是远程教育实践发展的需要,也是远程教育学科建设的需要,更是我国建设学习型社会的需要.在对文化研究理论的简单归纳基础上,本文就其主要内容展开了讨论,包括物质文化、精神文化、教学文化和制度文化四个维度的十个方面.并指出了现代远程教育文化研究的价值和意义有利于培养积极向上的学习方式和生活方式,有利于营造健康和谐的远程教育文化生态,有利于形成具有中国特色的现代远程教育文化.     

Girls and basic education in Ghana: a cultural enquiry

This paper attempts to do three things: first to provide an argument for acknowledging and using the cultural dimension in educational development; second to put the case for a culturally more appropriate research methodology; and third to address the issue of access and gender in schooling within a cultural framework.Using predominantly life history interviews with women teachers and girls in and out of school, the research identifies three domains of enquiry: the home, economy and school, where problems and solutions of girls' access to schooling are to be found. It concludes with implications for policy makers at national and local level.     

Training leaders in mathematics education a contrast with science education

Some additional thoughts in JRST's continuing attention to the evolution of doctoral programs in education.     

Hierarchies in mathematics education

In mathematics education literature the term hierarchy is used in a number of ways. It is important that the mathematics educator consider the usefulness of the hierarchies presented by various researchers and theorists, in the light of their application to teaching. Current works on mathematical learning hierarchies are illustrated and in particular the work of the mathematics team of the research project Concepts in Secondary Mathematics and Science is examined.     

Book Review: A common ground of mathematics and mathematics education for the classroom and for researchers. Erich Christian Wittmann (2021) Connecting mathematics and mathematics education. Collected papers on mathematics education as a design science

Educational Studies in Mathematics -     

Women and girls in mathematics—Equity in mathematics education

Conclusions What then can be said that is known about sex-related differences in mathematics and factors related to such differences? Certainly, when both females and males study the same amount of mathematics, differences in learning mathematics are minimal and perhaps decreasing. Many fewer females elect to study mathematics and therein lies the problem. Variables which appear to contribute to this non-election are females' lesser confidence in their ability to learn mathematics and their belief that mathematics is not useful to them. In addition, differential teacher treatment of males and females is important. All variables appear to be directly related to the stereotyping of mathematics as a male domain.There is nothing inherent (Sherman [30]) which keeps females from learning mathematics at the same level as do males. Intervention programs can and must be designed and implemented within schools which will increase females' participation in mathematics. Such programs should include male students, female students and their teachers. Only when such intervention programs become effective can true equity in mathematics education be accomplished.