Area Of Mathematics Education Research Articles

Unraveling the Relationship Between Students’ Mathematics-Related Beliefs and the Classroom Culture

Over the past 2 decades the study of students’ (and teachers’) mathematics-related beliefs has gradually received more and more attention from researchers in the field of educational psychology as well as from scholars in the area of mathematics education. In this article positive beliefs about mathematics and mathematics learning are considered as a major component of competence in mathematics. Results of empirical studies are presented showing that primary school students often have negative and/or naive beliefs about mathematics learning, focused on the phenomenon of “suspension of sense-making” in mathematical problem solving. A design experiment is then described in which a learning environment was developed and implemented, which was intended to improve students’ performance in problem solving as well as their mathematics-related beliefs. This and related work support the hypothesis that changes in the classroom culture and practices can foster students’ mathematical thinking and learning as well as their beliefs, but they do not provide a more in-depth understanding of how the interaction processes and patterns in the classroom influence students’ math learning in general and their mathematics-related beliefs in particular. Using a socioconstructivist perspective as a theoretical framework, the article then discusses a recent investigation that precisely attempts to contribute to unraveling the reciprocal relationship and impact between students’ beliefs, on the one hand, and crucial components of the learning environment, especially teachers’ beliefs and the classroom culture, on the other hand. The article concludes with some critical reflections and suggestions for future inquiry.

Mathematics teaching/learning in basic and senior secondary schools

In spite of much improvement in the academic staff of training colleges in the area of Mathematics Education as well as yearly organisation of maths and science clinics, little evidence is found in the improvement of performance of pupils/students in our schools. Improvement is measured by the performance of students at the BECE, and SSCE the results, of which seem to be very low over the years. Studies done, however, suggest that the improvement in mathematical attainment of pupils/student does not only depend on good staffing in our schools. There is therefore the need to explore factors that will help to improve upon the performance of pupils/students. Mathematics Connection Vol. 4 2004: 52-55

Yueh-Gin Gung and Dr. Charles Y. Hu Award to Hyman Bass for Distinguished Service to Mathematics

The Yueh-Gin Gung and Dr. Charles Y. Hu Award for Distinguished Service to Mathematics is the most prestigious award made by the Association. This award, first given in 1990, is the successor to the Award for Distinguished Service in Mathematics, awarded since 1961, and has been made possible by the late Dr. Hu and his wife Yueh Gin Gung. It is worth noting that Dr. Hu was not a mathematician. He was a retired professor of geology at the University of Maryland. He had such strong feelings about the basic nature of mathematics and its importance in all human endeavors that he felt impelled to contribute generously to our discipline. This year's award goes to Professor Hyman Bass of the University of Michigan. Professor Bass has compiled an outstanding record as a research mathematician, he has served with distinction on numerous boards and committees within our profession, and he has worked hard and effectively in the area of mathematics education. Hy cites the honors calculus course he took from Emil Artin at Princeton as the birthplace of his career as a mathematician. From Princeton, he went to the Graduate School at the University of Chicago just as Cartan and Eilenberger's Homological

Toward a Pragmatic/Contextual Philosophy of Mathematics: Recovering Dewey’s Psychology of Number

The philosophy of mathematics education is unnecessarily depriving itself of a potent source of material and inspiration. While John Dewey is regarded as a towering figure in the philosophy of education, he is conspicuously absent in contemporary conversations within the philosophy of mathematics education. This state of affairs is particularly interesting in that, early in his career, Dewey co-wrote a book in the area of mathematics education. The Psychology of Number and its Applications to Methods of Teaching Arithmetic (PN) was written by Dewey and James A. McLellan and first published in 1895. PN receives little attention from Dewey scholars, philosophers of mathematics, and mathematics educators. For example, Paul Ernest’s The Philosophy of Mathematics Education is regarded as a leading work in the field. It is telling that he refers to Dewey mostly in passing. His references paint Dewey with the broad and stereotypical brush of the romantic progressive (in the most generic and inaccurate sense). This lack of regard is not uncommon.

A First-Person Perspective on Problem Solving in a History of Mathematics Course

Although problem solving is one of the most studied areas of mathematics education, researchers have not systematically studied the experiences of problem solvers. This article provides a first-person perspective on problem solving in an undergraduate History of Mathematics course. The authors officially enrolled in a course to document problem-solving experiences. Through this self-study, this article highlights social and material resources for problem solving. Based on personal experiences, the authors generalize 4 primary factors that affected perceptions of problem difficulty in the course: categorization, interpretation, resource relevance, and complexity. The personal perceptions of problem difficulty were also influenced by the interrelatedness of these 4 factors over time, which is called stabilization. The detailed analyses of resources for problem solving and the descriptive theory of problem difficulty from the authors' perspectives as problem solvers complement cognitive and situative analyses of problem solving.

Mathematics and Narrative

Recent work in the area of mathematics education has been informed by the process writing movement in language education and by challenges to dominant literacies in school subjects including mathematics and science. Specifically, writers concerned with the exclusion of many children and adults from dominant mathematical practices have argued that narrative approaches to mathematics are both desirable and possible. An examination of mathematics writing in historical perspective suggests, however, that mathematicians operate within a number of non-narrative genres through which mathematical meanings are constituted; this paper argues that the solution to underachievement in mathematics lies in explicit teaching of such genres and a recognition of a mathematical tradition which lies outside of individual authorship.

Moving away from the illusion of a scientific theory of mathematics education research

Questioning Fundamental Assumptions What ismathematics education research? One could argue that, for researchers in the area of mathematics education, this is a question which ought to have been resolved long ago. But has it? In Gilleleje, Denmark, a symposium on "Criteria for Scientific Quality and Relevance in the Didactics of Mathematics" was held in 1992, and in May, 1994, an international workshop, sponsored by the International C;:ommission on Mathematics Instruction (ICMI), was conducted at the University of Maryland in the United States on the theme "What is mathematics education research and what are its resultsr' Mathematics education researchers around the world have begun to question, in fundamental ways, the assumptions and methodologies associated with their research (see, for example, Kilpatrick, 1993; Sierpinska, 1993; Mason, 1994). Eight criteria for evaluating the scientific quality of education research in general, and mathematics education research in particular, were identified by Kilpatrick (1993) and Sierpinska (1993). These papers discussed whether these criteria-validity, objectivity, originality, rigour and precision, predictability, reproducibility, and relatedness-have been, and should continue to be, fundamental in examining the relevance of mathematics education research. . .. I believe that, despite this underlying questioning of research in mathematics education, at least three false assumptions still prevail, namely, that: . 1. Theory-driven research is the most powerful form of mathematics education research, and should receive more attention than theory generating research; 2. Mathematics education research is or should become a science; and therefore 3. Criteria .for evaluaing mathematics education research should align closely with criteria used for evaluating scientific research.

Concept Learning and Retention in Mathematics

RECENTLY many experiments have been con ducted in order to investigate the different ways by which children learn mathematical concepts. There is a growing concern as to what methods of instruc tion are most appropriate for children of all levels of mathematical and academic ability. Questions of what can be and what should be taught at the differ ent levels of mathematics education have been raised, and there now seems to be some agreement that children are capable of mastering more mathe matics and more complex mathematics, than was previously possible. One has only to review the findings'of a researcher such as Suppes, and read the reports of well-known mathematicians, psychol ogists, and educators such as those who composed the Cambridge Report, in order to learn of recent advancements and proposals for the future. Some of the recent experiments have been con cerned with how children employ newly learned con cepts in a problem-solving situation. This area of mathematics education is beginning to undergo much experimentation, but as yet, there is not much that can be put together in the form of well-defined pro cedures and widely accepted ideas. Many psychologists and mathematics educators, considering the above concern, have investigated the effectiveness of the use of programed materi als as a means of testing various instructional theo ries. One can find opposing views as to the effec tiveness of such materials in an instructional situ ation, but the least that can be said is that pro gramed materials allow the researcher to more nearly duplicate the normal teaching situations than did the classical laboratory methods.