An exploration in the space of mathematics educations

A mathematical metaphor frames the intentions of this paper. Imagine that we know how to construct an N-dimensional space, ME, in which each point represents an alternative mathematics education -or ame -and each dimension a feature such as a component of content, a pedagogical method, a theoretical or ideological position. Each "reform" of mathematics education introduces new points and each fundamental idea a new dimension. Thus, if one considers a particular point (an ame) in ME, among its many "coordinates" are a (metaphorical) measure that runs from informal to formal and another that runs from instructionist to constructivist. In the paper I shall define seven more such oppositional principles that have not been recognized in the past as structuring choices in mathematics education.

[1]  Seymour Papert,et al.  Mindstorms: Children, Computers, and Powerful Ideas , 1981 .

[2]  Robert W. Lawler,et al.  The Progressive Construction of Mind , 1981, Cogn. Sci..

[3]  A. Tversky,et al.  Judgment under Uncertainty , 1982 .

[4]  P. Ross.  TURTLE GEOMETRY The Computer as a Medium for Exploring Mathematics , 1987 .

[5]  S. Weir.  Cultivating minds: A logo casebook , 1987 .

[6]  S. Papert,et al.  LEGO, Logo, and design. , 1988 .

[7]  John Lansdown,et al.  Visual modelling with Logo: a structural approach to seeing , 1990 .

[8]  U. Wilensky.  Abstract Meditations on the Concrete and Concrete Implications for Mathematics Education , 1991 .

[9]  J. Shaughnessy.  Research in probability and statistics: Reflections and directions. , 1992 .

[10]  Celia Hoyles,et al.  Learning mathematics and logo , 1992 .

[11]  Yasmin B. Kafai,et al.  Minds In Play: Computer Game Design as a Context for Children''s , 1994 .

[12]  W. Dörfler.  Computer Use and Views of the Mind , 1993 .

[13]  Uriel Joseph Wilensky,et al.  Connected mathematics : builiding concrete relationships with mathematical knowledge , 1993 .

[14]  C. Unsworth.  The Concept of Function , 1993 .

[15]  S. Papert.  The children's machine: rethinking school in the age of the computer , 1993 .

[16]  Mitchel Resnick,et al.  Turtles, termites, and traffic jams - explorations in massively parallel microworlds , 1994 .

[17]  A. Sfard.  Reification as the birth of metaphor , 1994 .

[18]  Celia Hoyles,et al.  Computers and exploratory learning , 1995 .

[19]  U. Wilensky.  Paradox, programming, and learning probability: A case study in a connected mathematics framework , 1995 .

[20]  Mitchel Resnick,et al.  New Paradigms for Computing, New Paradigms for Thinking , 1995 .

[21]  Jere Confrey,et al.  A critique of the selection of “Mathematical objects” as a central metaphor for advanced mathematical thinking , 1996, Int. J. Comput. Math. Learn..

[22]  Seymour Papert,et al.  The Connected Family: Bridging the Digital Generation Gap , 1996 .

[23]  Uri Wilensky.  Modeling Rugby: Kick First , Generalize Later? , 1996 .

[24]  Uri Leron,et al.  Just give me a computer and i will move the earth: Programming as a catalyst of a cultural revolution in the mathematics classroom , 1996, Int. J. Comput. Math. Learn..

[25]  Celia Hoyles,et al.  Windows on Mathematical Meanings: Learning Cultures and Computers , 1996 .