The status and context of change in mathematics education in Malawi

This article analyses the context and status of mathematics education reform in Malawi. It describes four interrelated developments in the reform of secondary education in general, and mathematics education in particular, in Malawi. These developments are concerned with attempts to increase access to secondary education for a majority of Malawians and to provide a mathematical education that is relevant to the needs of the current society. Although these are promising developments in line with the political context of Malawi, and although they aim at developing a more suitable curriculum for Malawi, I suggest that they are limited in two ways. First, participation in these reform processes has involved only a few individuals and neglected teachers and students from distance education centres who comprise the majority of participants in secondary education in Malawi. Secondly, the reform processes have proceeded with little empirical justification and qualitative understanding of the realities of schooling in general, and mathematics education in particular, in Malawi. The analysis in this article suggests that these limitations in the reform process are a function of an inadequate understanding of the social-contextual aspects of mathematics learning and what it means to provide an education that more broadly recognizes its democratic nature.This revised version was published online in September 2005 with corrections to the Cover Date.     

Embodied cognition and curriculum construction

The disembodiment of cognitive science has resulted in curricula with disembodied concepts and practice. The emergence of the embodied cognitive science provoked public reflections on the nature of the curriculum. This has elevated the body from the ‘peripheral’ position to the ‘central’ position, acting as the subject in action and becoming the bridge to experience transformations. Meanwhile, the nurturing role of the environment for the mind is attracting increasingly more attention, and the environment, the body, and the mind jointly constitute a dynamic system that prompts the transformation and restructuring of learners’ experience. The reshaping of the relationship between the body and education and the integration of physical experience and mind-building have led us to examine curriculum from a completely new perspective, and curriculum construction is thus transformed to the dynamic generation of interaction among the body, the mind, and the environment based on group experiences. To be precise, there are three basic dimensions in the construction of an embodied curriculum: (1) returning to the life-world and promoting the integration of the curriculum narrative framework and the student’s learning trajectory; (2) introducing the embodied experience and realizing the continuous interactions among the learner’s body, mind, and environment; and (3) integrating the functions of technologies to provide a powerful mediating tool for the construction of embodied curriculum.     

Unpacking personal identities for teaching mathematics within the context of prospective teacher education

This article explores the personal identities of two prospective elementary teachers as they progressed from mathematics methods coursework into their capstone student teaching semester. Results indicate that both prospective teachers perceived contrasting obligations of effective mathematics teaching in the teacher education and student teaching contexts, yet came to reconcile these differences in different ways. Whereas one prospective teacher was able to oppose the obligations set forth in the student teaching context, the other complied with obligations in both the teacher education and student teaching contexts. Implications for teacher education include differentiated experiences and placements, methods design, and explicit foci on students’ mathematical thinking.     

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     

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 -     

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.     

"假性理解"原因浅析

“假性理解”是中学生数学学习中比较普遍的现象，也是老师们一时难以找到真正原因而无法很好解决的问题，它严重地影响了中学数学的教学质量。本以现代认知理论中数学学习过程理论为主要依据，探讨分析了中学生在数学学习中可能造成假性理解的几点因素：感知因素、数学思维因素、原数学认知结构因素等。     

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.     

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.     

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.     

Preparing teachers for realistic mathematics education

A shift in mathematics education in the Netherlands towards the so-called realistic approach made it necessary to prepare prospective teachers for a type of curriculum different from what they experienced as pupils. This article describes the characteristics of a preservice programme aiming at this goal and presents an analysis of the development of the student teachers' views of mathematics and mathematics education during the programme as well as their classroom behaviour. This analysis is based on two research studies. The first was a longitudinal study in which the student teachers were followed during years by means of questionnaires and interviews. The second was a study in which graduates from this programme were compared with graduates from a more traditional preparation programme by means of two teacher questionnaires and a pupil questionnaire, the latter measuring the pupils' perceptions of the actual teaching behaviour of the graduates. The teacher education programme appeared to be successful in changing the student teachers' views of mathematics education, especially in the direction of a more inquiry oriented approach, and in promoting effective teacher behaviour in the classroom. As far as their facilitating role as a teacher is concerned, the student teachers seemed to go through a two-stage learning process. Most of them reached the first stage, in which they realize that pupils have different preferences for learning and that a variety of possible explanations for problems should be offered. However, only a small number of student teachers seem to reach the second stage, in which they recognize the principle of building on pupils' own constructions, an important feature of realistic mathematics education. Possible explanations for the low impact of the programme, as well as solutions are discussed.     

The modern mathematics reform movement in Brazil and its consequences for Brazilian mathematics education

This paper reports on the conclusions drawn from an investigation of the modern mathematics reform movement in Brazil. The focus of the study was an analysis of the mechanisms of transfer of knowledge from developed to developing countries, through a case study of Brazil and its adoption of the modern mathematics curriculum.The report presented here focuses on the dynamics of the reform movement and on the consequences of the movement for Brazilian mathematics education. The movement is studied as to how ideas about modern mathematics reform were disseminated to the Brazilian mathematics education community and the consequences due to misinterpretations of the intended curriculum in the implementation process. The intent of the study is that future initiatives in curriculum change proceed more efficiently in light of previous experiences, without repeating the mistakes committed in the past.     

Teaching units as the integrating core of mathematics education

How to integrate mathematics, psychology, pedagogy and practical teaching within the didactics of mathematics in order to get unified specific theories and conceptions of mathematics teaching? This problem—relevant for theoretical and empirical studies in mathematics education as well as for teacher training—is considered in the present paper. The author suggests an approach which is based on teaching units (Unterrichtsbeispiele). Suitable teaching units incorporate mathematical, pedagogical, psychological and practical aspects in a natural way and therefore they are a unique tool for integration.     

高职高专教育高等数学课程建设的研究与实践

随着高职高专教育形势的变化,重新审视了高等数学课程在整个高职高专教育中的地位和作用,对高等数学的教材建设、教学方法和手段、提高学生学习兴趣等问题进行了深入地研究,并将研究成果及时运用到教学实践中,化解了教学中的矛盾,提高了教学质量.