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     

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?     

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.     

The language of mathematics teaching: a text mining approach to explore the zeitgeist of US mathematics education

Educational Studies in Mathematics - Exploring language provides us with one approach to better understanding the practices and beliefs of a community. With advances in...     

Re/writing the subject: a contribution to post-structuralist theory in mathematics education

This text, occasioned by a critical reading of Mathematics Education and Subjectivity (Brown, 2011) and constituting a response to the book, aims at contributing to the building of (post-structuralist) theory in mathematics education. Its purpose was to re/write two major positions that Mathematics Education and Subjectivity articulates: that which it takes with respect to (a) L. S. Vygotsky and the activity theory he gave rise to, which are subject and subjected to critique, and (b) Lacan and his theory of the subject, which radically change signification in and through their adoption in the book. Moving between languages becomes a major issue of theory building captured in the diction “traduttore, traditore” (translating is committing treason). The present text should be read as a contribution to an ongoing dialogue on theory, incomplete and partial, as (perfectly) imperfect as Mathematics Education and Subjectivity itself.     

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 -     

研究性数学、教育数学与数学教育

数学可分为研究性数学和教育性数学。研究性数学主要注重科学逻辑的序,而教育性数学则注重科学逻辑的序与认知心理的序之间的完美结合,后者即“教育数学”。教育数学是在研究性数学基础上的再创造、再提高,教育数学对数学教育改革具有深远的意义。     

数学教师专业化与高师数学教育专业课改

数学教师专业化是世界数学教师教育的发展潮流,其内涵包括:数学教师数学专业化、数学教师教育专业化和数学教师专业情意.当前高师数学教育在课程设置上不适应数学教师专业化要求,改革重点是构建合理的课程体系.     

Understanding practices in mathematics education: structure and text

The practices of mathematics education can be investigated at a wide variety of levels: from the actions of individual students or teachers through classroom interactions, school structures, curriculum specifications and materials, teacher development programmes and local, national or international systems of instruction and assessment. These levels are, however, inter-related. The study of a national curriculum gains significance as we see how it impacts upon and is interpreted by teachers and students. The study of an individual’s actions makes more sense when these are interpreted in light of the broader context within which the individual is situated. This article is a version of a plenary lecture presented at the Psychology of Mathematics Education conference in 2009, addressing the conference theme “In Search for Theories in Mathematics Education”. In it, I trace the development of my own search for theories to address my wish to understand practices in the field and suggest some tools from linguistics, critical discourse analysis and social theory that can help to make such connections between the various levels of investigation, illustrating with a range of examples.     

The mathematics teacher in shadow education: a new area of focus in teacher education

Journal of Mathematics Teacher Education - This paper presents a discussion on a new focus area in mathematics teacher education, namely the mathematics teacher in shadow education (SE mathematics...     

HF: Working on mathematics education

First an impression will be given of the way Freudenthal worked on mathematics education during the period after WW II, until the early seventies. The sequence of events of that time form the leading principle of that period when important didactic concepts were being developed. In the following section the chronological order is set aside in an attempt to show how Freudenthal approached research, both in education and into mathematics education. In the next two sections two core themes are dealt with in detail: learning mathematics and developing mathematics education. Earlier didactic concepts are completed and further developed into key notions of a science of mathematics instruction.