Mathematical education and democracy

Is it possible to develop the content and form of mathematical education in such a way that it may serve as a tool of democratization in both school and society? This question is related to two different arguments. The social argument of democratization states: (1) Mathematics has an extensive range of applications, (2) because of its applications mathematics has a “society-shaping” function, and (3) in order to carry out democratic obligations and rights it is necessary to be able to identify the main principles of the development of society. The pedagogical argument of democratization states: (1) Mathematical education has a “hidden curriculum”, (2) the “hidden curriculum” of mathematical education in a traditional form implants a servile attitude towards technological questions into a large number of students, and (3) we cannot expect any development of democratic competence in school unless the teaching-learning situation is based on a dialogue and unless the curriculum is not totally determined from outside the classroom. The social argument implies that we must aim at “empowering material” which could constitute a basis for reflective knowledge i.e. knowledge about how to evaluate and criticize a mathematical model, while the pedagogical argument implies that we must aim at “open material” leaving space for decisions to be taken in the classroom. Will it become possible to create materials at the same time open and empowering? To answer this question we have to analyse the concept ‘democratic competence’, which can be related to ‘reflective knowledge’ characterized by a specific object of knowledge and a specific way of knowledge production. The ultimate aim will be to unify these characteristics in an epistemological theory of mathematical education. This paper is a revised version of \ldDemocratization and Mathematical Education\rd, R. 88-33 Department of Mathematics and Computer Science, Aalborg University Centre.     

Mathematical education versus critical education

This paper concentrates upon the relationship between mathematical education (ME) and critical education (CE) connected with the Frankfurt School and Critical Theory. To make the discussion as precise as possible a distinction is made between three alternatives in ME: Structuralism, pragmatism, and process-orientation. These alternatives are related to the key terms of CE in order to show the extent to which ME and CE contradict each other. The conclusion is that there does not exist any integration — nor even any close relationship-between ME and CE. Finally, this result is discussed in the light of the following two theses:

1. It is necessary to increase the interaction between ME and CE, if ME is not to degenerate into one of the most important ways of socializing students into the technological society and at the same time destroying the possibilities for developing a critical attitude towards precisely this technological society.
2. It is important for CE to interact with subjects from the technical sciences, and among these ME, if CE is not to be taken over by the technological development and fade away into an unimportant and uncritical educational theory.

     

国家教育体制改革领导小组办公室负责人就教育体制改革试点有关问题答记者问

日前，国务院办公厅印发了《关于开展国家教育体制改革试点的通知》（国办发[2010]48号），确定了国家教育体制改革试点的主要任务和试点单位，各地各校申报的国家级试点项目即将全面启动实施。针对社会各界广泛关心的教育体制改革试点有关问题，记者采访了国家教育体制改革领导小组办公室负责人。     

Mathematical history,philosophy and education

History of mathematics occupies itself describing processes of growth and development, whereas philosophy of mathematics is concerned with questions of justification. Both play an essential role within the educational context. But there is a problem because genuine historical studies necessitate ever greater particularity whereas mathematics and philosophy require generality and abstraction. The paper offers some methodological reflections about these matters together with two case studies from nineteenth century history of arithmetic and integration theory, respectively, which try to strike a balance between the directly opposed requirements.     

中学的数学文化与数学教育

根据中学的数学实践，探讨中学数学化的主要内容及数学在素质教育中的意义．     

American Indian and Taiwan Aboriginal education: Indigenous identity and career aspirations

This article investigates the interactions between identity and career aspirations among Taiwanese Aborigines and American Indians. While many similarities exist between the two indigenous groups, several differences remain as well. In comparing the identity issue between these two groups, this study shows that American Indians generally live in a more multicultural society than Taiwanese Aborigines. American Indian students do not experience the same degree of stereotype or racial discrimination from their teachers and peers as experienced by Taiwanese Aborigines. However, affirmative action policies are more favorable in Taiwan than they are in the United States. Drawing from a critical standpoint theory, we argue that families, tribes, and communities should play a more prominent role in the education of indigenous peoples.     

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.     

Mathematical problem solving and young children

Educators of young children can enhance the development of a problem-solving thought process through daily activities in their classrooms. An emphasis should be placed on the actual thought process needed to solve problems that occur in everyday living. Educators can follow simple suggestions to create problem-solving situations for all ages of children. The process of thinking through a problem and finding a solution is more important than traditional mathematics counting and memorizing useless facts. Even very young children are capable of a problem-solving process that is on the appropriate developmental level. The problem-solving process is constructivist in nature, as each individual perceives problems according to her or his background and developmental levels. Educators need to make a conscious effort to capitalize on all stages of problem-solving thinking to enhance future mathematical development.     

Pushing the entrepreneurial prodigy: Canadian Aboriginal entrepreneurship education initiatives

Globally, neoliberal education policy touts youth entrepreneurship education as a solution for staggering youth unemployment, a means to bolster economically depressed regions, and solution to the ill-defined changing marketplace. Many jurisdictions have emphasized a need for K-12 entrepreneurial education for the general population, and targeted to youth labeled ‘at risk’. The Martin Aboriginal Education Initiative’s Aboriginal Youth Entrepreneurship Program (AYEP) has been enacted across Canada. This paper applies critical discourse analysis to a corpus of texts, exposing how colonial practices, deficit discourse, and discursive neoliberalism are embedded and perpetuated though entrepreneurial education targeted at Aboriginal students via AYEP.     

数学文化与高职数学教育

数学文化扎根于社会实践,随着人类文明的兴衰而荣枯;信息时代也就是数学时代,高新技术在本质上是一种数学技术,数学文化是现代文化的一个重要支柱;传播和普及数学文化是高职教育的重要任务,高职数学应发挥文化与应用两大功能,从文化层面重新审视高职数学课程改革,建立“以人为本,以学生为中心”的教改新构架。     

加拿大原住民与非原住民的收入差异

从加拿大2001年的人口普查中抽取3％的样本数据,分析了原住民和非原住加拿大人之间工资和薪金的差异,发现注册印第安人、梅蒂斯人与非原住民的年收入和周薪在跨组和组内都有显著差异。这种差异在很大程度上是由于人口、人力资本、职业以及这三种人口的区域差异。     

“概率论与数理统计”在双语教学中的教与学

双语教学是在我国少数民族地区为了使少数民族学生既能学好汉语,又有利于保留少数民族语言,在教学中使用的两种语言．《概率论与数理统计》作为一门理论性很强的数学课程,具有自己独特的概念和方法,内容丰富,结论深刻,对学生来讲是一门比较难学的数学课程．在双语数学教学中既要从本课程的特点出发,又要考虑到学生的实际,选取恰当的教学方法．     

Improving the participation and engagement of Aboriginal and Torres Strait Islander students in business education

Most Australian universities have among their goals to increase the number of Aboriginal and Torres Strait Islander students at their institutions. In the Australian higher education context, Aboriginal and Torres Strait Islander students are seriously under-represented, particularly in business education compared to other disciplines. An understanding of why a larger proportion of Aboriginal and Torres Strait Islander students do not choose to study a discipline that provides promising employment opportunities, is fundamental to improving the status quo. This paper reviews the literature to identify key barriers to Aboriginal and Torres Strait Islander students’ participation and engagement in business education. Apart from multiple general barriers to participation in higher education, factors specific to business as a profession and as an academic discipline are also considered. The paper then discusses a number of strategies Australian educational institutions could pursue when seeking to increase participation and engagement of Aboriginal and Torres Strait Islander students in business. Drawing on the review, the paper concludes with recommendations for higher education institutional policy to further improve Aboriginal and Torres Strait Islander student participation and engagement in business studies.     

Mathematical problem solving by pre-school children

In this article we provide new evidence for mathematical problem-solving abilities of pre-school children. These problem-solving behaviours occurred in a study of sharing of discrete items by dealing, in which we examined the abilities of three categories of counters to solve a discrete re-distribution problem. We detail the problem solving strategies used in the context of sharing by dealing as a common action scheme of pre-school children in clinical interviews.     

高职数学文化教育与高职数学教育改革的思考

高职教育是我国高等教育的重要补充,高职教育的特点决定了高职教育的实践性和技术性,在高职教育中,高职数学教学长期以来缺乏文化教育,数学教学成为了干涩的职业性教育,这不仅无法提升高职数学教育的质量,同时也无法发挥高职数学教育的功能和价值。鉴于此,在高职数学教育中,通过融入文化教育来实现教学改革,在提升高职学生数学职业技能的同时,还能够培养学生的数学思想。     

The contribution of Aboriginal epistemologies to mathematics education in Australia: Exploring the silences

Epistemology is a conceptual template for how we think about the world, and the study of how we come to know the world around us. The world does not dictate unequivocally how to interpret it. This article will explore this position on the fluidity of epistemic constructs through two prominent philosophical perspectives, those being derived from the works of Ludwig Wittgenstein and Michael Foucault, respectively. These insights will be used to more deeply unfold the current situation for Aboriginal students within dominant approaches to mathematics curriculum in Australia, and the subsequent approaches to the inclusion of Aboriginal knowledge and epistemologies. It is suggested that the epistemic constructs most valued and thus credited as conveyors of ‘truth’, and therefore positioned as powerful forms of knowledge within dominant curriculum and education policy, are those derived from Western, Eurocentric origins. This privileging of particular epistemological constructs over others is reinforced unconsciously through the articulation of educational goals deemed most appropriate, or ‘socially just’, for the Aboriginal student population. The place of Aboriginal knowledge within such constructs is therefore reflective of broader ideation around the role of education within society and its failure to challenge existing structures of power and injustice.     

Tracing spectres of whiteness: discourse and the construction of teaching subjects in urban Aboriginal education

The author traces how discourse functions in the context of a school-based, urban Aboriginal education initiative, with a focus on the construction and organization of teaching subjects. Critical discourse analysis that traces spectres reveals some of the ways that whiteness and Eurocentrism create the possibilities for, and the conditions in which teachers take up, the positions: victim of racism, arbiter of authenticity, and rescuer. Consideration of the multiple, complex, and shifting positions teachers occupy within whiteness in general, and in colonial systems of education in particular, offers unique possibilities when untangling and reconfiguring teachers' constructions of Aboriginality/Indigeneity and responses to Aboriginal/Indigenous education. This theory building also contributes to the larger field of curriculum studies by demonstrating how consideration of ‘unheroic tales’ can aid in theorizing teacher identity and difference, both within and beyond the markers Indigenous/non-Indigenous.