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1.
This essay reviews the principles motivating contemporarycritical mathematics discourses. Drawing from varied critical discourses including ethno-mathematics, critical theory, post-structural theory, and situated and ecological cognition, the essay examines the pragmatics of critiques to the privileged role of school mathematics in the era of globalization. Critiques of modern school curricula argue that globalization practices linking education to technological and economic development are increasing, and the curriculum is being re-defined through discourses of privatization, national standards, and global competitiveness. Globalization has reinforced the utilitarian approach to school mathematics and the Western bias in the prevailing mathematics curricula, as well as helped to globalize pervasive mathematical ideologies. In most instances, a newfound status that mathematics is enjoying in this era of globalization is not well deserved, as school mathematics can no longer be considered culturally, socially, politically, nor economically neutral. In particular, school mathematics is increasingly critiqued as a cultural homogenizing force, a critical filter for status, a perpetuator of mistaken illusions of certainty, and an instrument of power. With such concerns it is becoming more evident that mathematics learning and education have implications for building just and democratic societies. As an African female scholar who is now living in Canada, I reflect on what the critical stance might mean for contexts with which I am familiar. I discuss the challenges of school mathematics with a view to improving curriculum and pedagogy so as to raise the awareness of teachers and learners to the questionable assumptions from which mathematics derives its prestige. The mathematics curriculum is central to cultivating values as well as fostering the conscientization of learners.  相似文献   

2.
In this article, I make a case for the inputs that Martin Heidegger's theoretical perspective offers to current concerns about the nature of mathematics, its teaching and learning, and the problem of subjectivity. In particular, I consider Heidegger's notion of positive science and discuss both its applicability to mathematics and its importance to mathematics education. I argue that Heidegger's ontological position is consonant with some sociocultural approaches in mathematics education and that Heidegger's work can shed some light on the problem of knowing and being. Finally, I raise some questions concerning subjectivity and the link between language and mathematical objects.  相似文献   

3.
In this paper I consider the problem of designing strategies for teacher education programs that may promote an aware style of teaching. Among the various elements to be considered I focus on the need to address prospective teachers’ belief that they must reproduce the style of mathematics teaching seen in their school days. Towards this aim, I argue that the prospective teachers need a context allowing them to look at the topics they will teach in a different manner. This context may be provided by the history of mathematics. In this paper I shall discuss how history affected the construction of teaching sequences on algebra during the activities of the ‘laboratory of mathematics education’ carried out in a 2 year education program for prospective teachers. The conditions of the experiment, notably the fact that our prospective teachers had not had specific preparation in the history of mathematics, allow us to outline opportunities and caveats of the use of history in teacher education.  相似文献   

4.
In this report, I examine resources and their use in school mathematics. I do so from the perspective of mathematics teacher education and with a view to the practice of school mathematics. I argue that the effectiveness of resources for mathematical learning lies in their use, that is, in the classroom teaching and learning context. The argument pivots on the concepts of school mathematics as a hybrid practice and on the transparency of resources in use. These concepts are elaborated by examples of resource use within an in-service teacher education research project in South Africa. I propose that mathematics teacher education needs to focus more attention on resources, on what they are and how they work as an extension of the teacher in school mathematics practice. In so doing, the report provides a language with which mathematics teacher educators and mathematics teachers can investigate teachers' use of resources to support mathematical learning in particular and diverse contexts. This revised version was published online in September 2006 with corrections to the Cover Date.  相似文献   

5.
The quality of students' mathematics classroom discussions is an important factor in determining mathematics classroom learning outcomes. Good mathematics classroom discussions provide an opportunity for ideas to be shared and developed, but not all mathematics classroom discussions produce these learning opportunities. In this paper I discuss three constructs (subject, purpose, and frame) and how they can be used to analyze and characterize the quality of students' mathematics classroom discussions in terms of the mathematics learning potential that those discussions provide. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

6.
In this paper I address the question: How is it that people come to choose mathematics and in what ways is this process gendered? I draw on the findings of a qualitative research study involving interviews with 43 young people all studying mathematics in post‐compulsory education in England. Working within a post‐structuralist framework, I argue that gender is a project and one that is achieved in interaction with others. Through a detailed reading of Toni and Claudia’s stories I explore the tensions for young women who are engaging in mathematics, something that is discursively inscribed as masculine, while (understandably) being invested in producing themselves as female. I conclude by arguing that seeing ‘doing mathematics’ as ‘doing masculinity’ is a productive way of understanding why mathematics is so male dominated and by looking at the implications of this understanding for gender and mathematics reform work.  相似文献   

7.
数学教育与人的发展   总被引：3，自引：0，他引：3  
数学教育作为利用数学科学文化知识，从事培养人的一种教育实践活动，具有促进人的发展的功能，而人的发展也离不开数学教育；数学教育要实现人的发展，就要超越数学“学科本位”，关注人的情感体验，改善教与学的方式，加强数学思想方法教学。  相似文献   

8.
Images of mathematics held by university teachers of mathematical sciences   总被引：1，自引：0，他引：1  
For some time now mathematics educators have been studying elementary and secondary school teachers' views of mathematics. A knowledge of university teachers' views of this discipline can provide a useful background to these research endeavours. As part of a national survey of men and women teachers of mathematical sciences in Canadian universities, I included a question concerning the definition of mathematics. In this article I present the themes emerging from a content analysis of the responses obtained and discuss them in relation to research on school teachers' perception of mathematics. I also report the results concerning the university teachers answers to a second question relevant to the image of mathematics, namely identifying up to ten books which, in their opinion, have had the most influence on the development of mathematics.  相似文献   

9.
In this article, I propose ritual as an analytic lens for understanding the persistence of practices in contemporary mathematics classrooms. By foregrounding the cultural nature of the teaching and learning of mathematics in schools, ritual analysis can provide insight about the causes and effects of practices that persist through rounds of “reform.” I begin by considering the legacy of the notion of culture in mathematics education research. I then provide examples of ritual analysis in education research and in mathematics education research. I draw on the scholarship of Quantz (2011) as I articulate a working definition of ritual for use in mathematics education research, considering how this definition may help raise and answer distinct questions apart from more familiar constructs. I list some well-known problems and dilemmas in mathematics education that may be promising domains for a ritual analysis, and I conclude by positioning ritual alongside other constructs and methods that are in use in mathematics education research today.  相似文献   

10.
Research suggests that understanding new images of mathematics is very challenging and can contribute to teacher resistance. An explicit exploration of personal views of mathematics may be necessary for pedagogical change. One possible way for exploring these images is through mathematical metaphors. As metaphors focus on similarities, they can be used to express already-held perceptions about the nature of mathematics. In addition to providing a way of talking about current views of mathematics, the analogous dimensions of metaphors can prompt new ways of thinking about these images. In this article, I consider the use of metaphors as a strategy for explicating elementary teachers’ views of mathematics. I claim that the investigation of metaphors of mathematics helped create a shared communicative space and enhanced the quality of the discussion with the teachers. In particular, our exploration of the metaphor mathematics is a language encouraged a consideration of the humanistic dimensions of mathematics and contributed to a varied re-imaging of mathematics.  相似文献   

11.
Mathematics education researchers have investigated mathematics anxiety in prospective elementary teachers. While many of these studies have focused on the bodily sensations and emotions of mathematics anxiety, particularly those felt in assessment situations, opportunities remain to investigate how prospective elementary teachers interpret their experiences with mathematics anxiety and connect them over time to compose personal histories of mathematics anxiety. Currently, over 90 % of elementary teachers in US schools are women, and women have been shown to suffer more from mathematics anxiety than do men. In this article, I analyze how one woman prospective elementary teacher described, explained, and related her experiences of mathematics anxiety across her personal narratives of learning mathematics as a K-12 student and of learning to teach mathematics as a college student in a teacher preparation program. My research demonstrates that experiences of mathematics anxiety may persist beyond assessment situations to influence women prospective elementary teachers’ larger mathematical histories. I also show that women prospective elementary teachers may interpret mathematics anxiety as specific fears (e.g., loss of opportunities for social participation) and may develop particular coping strategies related to those fears. Finally, I point out that while a coping strategy may be used consistently across K-12 mathematics learning and undergraduate teacher preparation, and may even offer a woman prospective elementary teacher some relief from mathematics anxiety, it may also limit her mathematics learning and professional development. To conclude, I present implications of my research for mathematics teacher educators.  相似文献   

12.
This analysis of the writing in a grade 7 mathematics textbook distinguishes between closed texts and open texts, which acknowledge multiple possibilities. I use tools that have recently been applied in mathematics contexts, focussing on grammatical features that include personal pronouns, modality, and types of imperatives, as well as on accompanying structural elements such as photographs and the number of possibilities presented. I extend this discussion to show how even texts that appear open can seduce readers into feeling dialogue while actually leading them down a narrow path. This phenomenon points to the normalizing power of curriculum. For this analysis and reflection, I draw on mathematics textbook material that I wrote. As a way of modelling an alternative to normalization, I identify myself as a self-critical author and thus invite readers to be critical of their reading and writing of mathematics texts.  相似文献   

13.
Bharath Sriraman 《Interchange》2006,37(1-2):151-178
This paper explores the wide range of mathematics content and processes that arise in the secondary classroom via the use of unusual counting problems. A universal pedagogical goal of mathematics teachers is to convey a sense of unity among seemingly diverse topics within mathematics. Such a goal can be accomplished if we could conduct classroom discourse that conveys the Lakatosian (thought-experimental) view of mathematics as that of continual conjecture-proof-refutation which involves rich mathematizing experiences. I present a pathway towards this pedagogical goal by presenting student insights into an unusual counting problem and by using these outcomes to construct ideal mathematical possibilities (content and process) for discourse. In particular, I re-construct the quasi-empirical approaches of six!4-year old students’ attempts to solve this unusual counting problem and present the possibilities for mathematizing during classroom discourse in the imaginative spirit of Imre Lakatos. The pedagogical implications for the teaching and learning of mathematics in the secondary classroom and in mathematics teacher education are discussed.  相似文献   

14.
数学研究性学习,是当前基础教育改革在数学教育方面的一个亟待解决的十分重要的问题。本文作了实例研究,从两个不同的角度作了如何构想数学问题,如何提出问题并引导学生进行研究性学习的探究。  相似文献   

15.
In this article, I present and build on the ideas of John Threlfall [(Educational Studies in Mathematics 50:29–47, 2002)] about strategy development in mental mathematics contexts. Focusing on the emergence of strategies rather than on issues of choice or flexibility of choice, I ground these ideas in the enactivist theory of cognition, particularly in issues of problem posing, for discussing the nature of the solving processes at play when solving mental mathematics problems. I complement this analysis and conceptualization by offering two examples about issues of emergence of strategies and of problem posing, in order to offer illustrations thereof, as well as to highlight the fruitfulness of this orientation for better understanding the processes at play in mental mathematics contexts.  相似文献   

16.
Research in the didactics of mathematics has shown the importance of the problem of the particular and its relation to the general in teaching and learning mathematics as well as the complexity of factors related to them. In particular, one of the central open questions is the nature and diversity of objects that carry out the role of particular or general and the diversity of paths that lead from the particular to the general. The objective of this article is to show how the notion of semiotic function and mathematics ontology, elaborated by the onto-semiotic approach to mathematics knowledge, enables us to face such a problem. This paper has been elaborated in the frame of the project I+D: MEC-FEDER: SEJ2004-06637/EDUC  相似文献   

17.
My purpose in this article is to contribute tothe conceptualization of the complex terrainthat often is indiscriminately termedmathematics teacher educator development.Because this terrain is largely unresearched, Iinterweave experience fragments of my owndevelopment as a mathematics teacher educator,and reflective analysis of those fragments, asa tool to abstract notions of generalimplication. In particular, I postulate aframework consisting of four stages ofdevelopment that are distinguished by thedomain of activities one's reflections mayfocus on and the nature of those reflections.Drawing on this framework, I presentimplications for mathematics teacher educatordevelopment and for further research.  相似文献   

18.
In this paper I attempt to clarify how the relationship between macro and micro social contexts has been addressed in the Vygotskian and Neo-Piagetian approaches to learning. For each approach I look at how key scholars (Cole, 1977; Perret-Clermont, Perret and Bell, 1991) come to view context as central to their theories of cognitive development. In order to illustrate my review of the dominant strands of empirical research I refer to studies that focus on the uses, learning and understanding of mathematics. I start the paper with the socio-cultural Vygotskian approach. This is closely associated with my own research into the relationship between culture and learning. Not surprisingly, I find biases in this body of research in terms of the macro and micro features of contexts which were analysed. In an attempt to gain insights into alternative ways of conceptualising these relationships I explore work which has adopted a socio-psychological approach. In the final part of the paper I discuss how these insights can be used to broaden our basis for studying interactions in the mathematics classroom and conclude by relating my ideas to new developments in socio-cultural theory.This revised version was published online in September 2005 with corrections to the Cover Date.  相似文献   

19.
认识数学教育惯性下的课程改革   总被引：2，自引：2，他引：2  
数学课程改革应该是数学教育惯性传承下的改革，即数学课程改革应是数学文化惯性的传承，数学精神、思想方法的贯穿，数学家的思维品质的吸纳，数学教学方式的价值流变趋势，以及教师高素质体现下的改革．数学教育惯性下的课程改革应注意：评价改革的先行性；教材设计的典范性与先进性；数学教育研究群体的认同性等几方面的内容．国内外教育改革经验告诉我们，人为地违反惯性发展规律，等待我们的将是惯性“回潮”和惯性“报复”，我们不可不慎思之．  相似文献   

20.
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