Latest Research News on Mathematics education : Feb 2022

Mathematics education in its cultural context

This paper presents the results of a series of analyses of educational situations involving cultural issues. Of particular significance are the ideas that all cultural groups generate mathematical ideas, and that ‘Western’ mathematics may be only one mathematics among many. The values associated with Western mathematics are also discussed, and various issues raised by these analyses are then presented.[1]

Epistemologies of Mathematics and of Mathematics Education

This chapter addresses issues concerning epistemology, as they relate to mathematics and education. It commences with an examination of some of the main epistemological questions concerning truth, meaning and certainty, and the different ways they can be interpreted. It examines epistemologies of the ‘context of justification’ and of the ‘context of discovery’, foundationalist and non-foundationalist epistemologies of mathematics, historico-critical, genetic, socio-historical and cultural epistemologies, and epistemologies of meaning.

In the second part of the chapter, after a brief look at epistemology in relation to the statements of mathematics education, epistemologies in mathematics education become the main focus of attention. Controversial issues within a number of areas are considered: the subjective-objective character of mathematical knowledge; the role in cognition of social and cultural context; and relations between language and knowledge. The major tenets of constructivism, socio-cultural views, interactionism, the French didactique, and epistemologies of meaning are compared. Relationships between epistemology and a theory of instruction, especially in regard to didactic principles, are also considered. [2]

Error Analysis in Mathematics Education

A review of the literature on error analysis in mathematics education and an extensive investigation of errors made by German schoolchildren suggests a classification of errors and their causes in terms of information-processing mechanisms. Pupils’ errors may be caused by semantic differences between mathematical language and natural language, by individual differences in spatial abilities, by deficiencies in the mastery of prerequisites, by incorrect associations or failure of cognitive control, and by the application of irrelevant strategies or rules. Implications for research and practice are suggested.[3]

Critical Variables in Mathematics Education: Findings from a Survey of the Empirical Literature.

This survey represents an attempt to indicate how much is known about all aspects of research in mathematics education. For each topic, a brief description of the variable is provided and the kinds of experiments or other empirical studies which have been used to investigate them are indicated. At the end of each chapter is a bibliography and a list of illustrative research reports. The final chapter contains suggestions as to priorities for more extensive reviews of the available factual information on various aspects of mathematics education and for further research. Topics covered include teachers, curriculum, student variables, environment, instruction, tests, and problem solving.[4]

Integrating Science and Mathematics Education: Historical Analysis

A number of national science and mathematics education professional associations, and recently technology education associations, are united in their support for the integration of science and mathematics teaching and learning. The purpose of this historical analysis is two-fold: (a) to survey the nature and number of documents related to integrated science and mathematics education published from 1901 through 2001 and (b) to compare the nature and number of integrated science and mathematics documents published from 1990 through 2001 to the previous 89 years (1901–1989). Based upon this historical analysis, three conclusions have emerged. First, national and state standards in science and mathematics education have resulted in greater attention to integrated science and mathematics education, particularly in the area of teacher education, as evidenced by the proliferation of documents on this topic published from 1901–2001. Second, the historical comparison between the time periods of 1901–1989 versus 1990–2001 reveals a grade-level shift in integrated instructional documents. Middle school science continues to be highlighted in integrated instructional documents, but surprisingly, a greater emphasis upon secondary mathematics and science education is apparent in the integration literature published from 1990–2001. Third, although several theoretical integration models have been posited in the literature published from 1990–2001, more empirical research grounded in these theoretical models is clearly needed in the 21st century.[5]

Reference

[1] Bishop, A.J., 1988. Mathematics education in its cultural context. Educational studies in mathematics, 19(2), pp.179-191.

[2] Sierpinska, A. and Lerman, S., 1996. Epistemologies of mathematics and of mathematics education. In International handbook of mathematics education (pp. 827-876). Springer, Dordrecht.

[3] Radatz, H., 1979. Error analysis in mathematics education. Journal for Research in mathematics Education, 10(3), pp.163-172.

[4] Begle, E.G., 1979. Critical Variables in Mathematics Education: Findings from a Survey of the Empirical Literature.

[5] Berlin, D.F. and Lee, H., 2005. Integrating science and mathematics education: Historical analysis. School Science and Mathematics, 105(1), pp.15-24.