Critical Issues in the Distance Teaching of Mathematics and Mathematics Education

Distance modes of teaching and learning have proved to be increasingly popular, worldwide, during the last three decades of this century, especially in the areas of mathematics and mathematics education. This chapter critically examines the distance education phenomenon in relation to several key variables: the nature and purposes of both mathematics and distance teaching; the current and potential roles of computer technology in the flexible delivery process; and the particular implications of these factors in relation to interactions between so-called ‘developed’ and ‘developing’ countries. Case studies of current practice are presented to exemplify several of these key issues in relation to course development and delivery. Finally, a framework for future discussion is provided in the form of eight possibly contentious propositions which call for stronger theoretical and practical relationships to be developed between educators in the fields of distance education, mathematics and mathematics education.

[1]  M. A. Clements,et al.  Expanding the modes of communication in mathematics classrooms , 1990 .

[2]  S. Stodolsky.  The Subject Matters: Classroom Activity in Math and Social Studies , 1988 .

[3]  I. Lakatos,et al.  Proofs and Refutations: Frontmatter , 1976 .

[4]  Knowledge, Partitioned Sets and Extensionality: a refutation of the forms of knowledge thesis* , 1983 .

[5]  Celia Hoyles.  Mathematics in prime time television: the story of fun and games , 1990 .

[6]  Geoffrey Howson,et al.  School Mathematics in the 1990s , 1987 .

[7]  J. Stigler,et al.  Culture and Mathematics Learning , 1988 .

[8]  B. Greer,et al.  New Directions in Mathematics Education , 1989 .

[9]  Gilah C. Leder,et al.  School Mathematics: The Challenge to Change , 1989 .

[10]  Thomas Tymoczko.  New Directions in the Philosophy of Mathematics , 1985 .

[11]  A. Bishop.  Western mathematics: the secret weapon of cultural imperialism , 1990 .

[12]  Stieg Mellin-Olsen.  The politics of mathematics education , 1987 .

[13]  B. Simon.  Twentieth Century Education , 1981, History of Education Quarterly.

[14]  Paul Ernest.  Values, gender and images of mathematics: a philosophical perspective , 1995 .

[15]  R. Goodstein,et al.  Remarks on the Foundations of Mathematics , 1957, The Mathematical Gazette.

[16]  Ruth Merttens,et al.  Sharing Maths Cultures: IMPACT: Inventing Maths For Parents And Children And Teachers , 1990 .

[17]  Philip J. Davis,et al.  The Mathematical Experience , 1982 .

[18]  S. Shanker,et al.  Godel's Theorem in Focus , 1990 .

[19]  Larry Cuban.  How Teachers Taught: Constancy and Change in American Classrooms, 1890-1990 , 1984 .

[20]  C. Marsh.  Producing a National Curriculum: Plans and Paranoia , 1998 .

[21]  M. Kline.  Mathematics: The Loss of Certainty , 1982 .

[22]  M. A. Clements,et al.  Mathematics in language : a review of language factors in mathematics learning , 1991 .

[23]  Fred Lockwood.  Open and Distance Learning Today , 1995 .

[24]  Rudy Rucker,et al.  Infinity and the Mind , 1982 .

[25]  Elizabeth J. Burge,et al.  Electronic Highway or Weaving Loom? Thinking about Conferencing Technologies for Learning. , 1994 .

[26]  J. P. Kahane,et al.  The Popularization of Mathematics: Frontmatter , 1990 .

[27]  B. Russell.  History of Western philosophy , 1949 .

[28]  Issues for the Popularization of Mathematics , 1995 .

[29]  Mary Tiles.  Mathematics and the image of reason , 1991 .

[30]  J. Mousley.  Learning about teaching , 1996 .

[31]  Susan J. Lamon,et al.  Integrating research on teaching and learning mathematics , 1988 .

[32]  Melbourne Studies in Education 1965 , 1966 .

[33]  M. A. Clements,et al.  Mathematics education research : past, present and future , 1996 .

[34]  John Bigelow,et al.  Science and Necessity , 1991 .

[35]  G. Lakoff,et al.  Women, Fire, and Dangerous Things: What Categories Reveal about the Mind , 1988 .

[36]  W. B. Carver,et al.  Mathematics in Western Culture. , 1954 .

[37]  J. R. Newman.  The World of Mathematics , 1961 .

[38]  Paul Ernest,et al.  The Philosophy of Mathematics Education , 2003 .

[39]  E. Glasersfeld.  Cognition, Construction of Knowledge, and Teaching , 1989 .

[40]  P. Freire.  Education for Critical Consciousness , 1973 .

[41]  W. G. Perry.  Forms of Intellectual and Ethical Development in the College Years: A Scheme. Jossey-Bass Higher and Adult Education Series. , 1970 .

[42]  Imre Lakatos,et al.  On the Uses of Rigorous Proof. (Book Reviews: Proofs and Refutations. The Logic of Mathematical Discovery) , 1977 .

[43]  A. Thompson.  The relationship of teachers' conceptions of mathematics and mathematics teaching to instructional practice , 1984 .

[44]  Peter Sullivan,et al.  Quality mathematics teaching: Describing some key components , 1994 .

[45]  Valerie Walkerdine,et al.  The Mastery of Reason , 1988 .

[46]  M. A. Clements,et al.  Reshaping School Mathematics in Australia 1788–1988 , 1988 .

[47]  Ole Skovsmose,et al.  Towards a philosophy of critical mathematics education , 1994 .

[48]  D. Keegan.  Foundations of distance education , 1986 .

[49]  P. Harris.  Mathematics in a cultural context : aboriginal perspectives on space, time and money , 1991 .