More Articles/Papers/Talks

Please note that although these articles have been roughly classified into two broad categories of Mathematics Education and Mathematics there is sometimes considerable overlap between the two categories. They have also not been arranged in chronological or any other specific order.

The articles below may be used for non-profit, educational

purposes only, provided that their source/origin is properly referenced at all times.

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Mathematics Education

THE ROLE AND FUNCTION OF PROOF WITH SKETCHPAD ('99, pdf) (The traditional view that the only function of proof is that of verification is criticised, and it is argued that other important functions of proof such as explanation, discovery, systematization, etc. ought not to be neglected in the classroom).

http://mzone.mweb.co.za/residents/profmd/proof.pdf

THE ROLE AND FUNCTION OF PROOF IN MATHEMATICS ('90, pdf) (From *Pythagoras*, No. 24, Nov. 1990, pp. 17-24) (Original version of above article).

http://mzone.mweb.co.za/residents/profmd/proofa.pdf

EL PAPEL Y LA FUNCION DE LA DEMOSTRACION EN MATEMATICAS ('93, pdf) (Spanish translation of above article from *Epsilon*, No. 24, 1993, pp. 15-30)

http://mzone.mweb.co.za/residents/profmd/proofb.pdf

PAPEL E FUNCOES DA DEMOSTRACAO NO TRABALHO COM O SKETCHPAD ('01, pdf) (Portuguese translation of '99 Proof article from *Educacao e Matematica*, No. 62, April 2001, pp. 31-36)

http://mzone.mweb.co.za/residents/profmd/proofc.pdf

CHILDREN'S ACCEPTANCE OF THEOREMS IN GEOMETRY (pdf) (Some empirical data from a questionnaire regarding the grounds of children's acceptance of the truth of some geometric theorems. Poster paper presented at PME 16, 1992).

http://mzone.mweb.co.za/residents/profmd/accept.pdf

WHY PROOF IN DYNAMIC GEOMETRY? (pdf file) (A short discussion of why proof is still necessary and useful in a convincing environment such as dynamic geometry).

http://mzone.mweb.co.za/residents/profmd/why.pdf

PUPILS' NEEDS FOR CONVICTION & EXPLANATION WITHIN GEOMETRY (pdf) (Revised and expanded version of PME 15 paper, 1991)

http://mzone.mweb.co.za/residents/profmd/needs.pdf

LEARNERS' NEEDS FOR CONVICTION AND EXPLANATION WITHIN THE CONTEXT OF DYNAMIC GEOMETRY, 2000 (An empirical study related to students' experience of a Sketchpad activity).

http://mzone.mweb.co.za/residents/profmd/vim.pdf

THE HANDLING OF GEOMETRY DEFINITIONS IN SCHOOL TEXTBOOKS (Short editorial from Pythagoras criticising the direct provision of definitions in textbooks.)

http://mzone.mweb.co.za/residents/profmd/geomdef.htm

TO TEACH DEFINITIONS IN GEOMETRY OR TEACH TO DEFINE? (PME '98 paper) (Distinguishes two different types of defining and present some empirical data related to a teaching experiment that focussed on defining as a process).

http://mzone.mweb.co.za/residents/profmd/define.htm

THE ROLE OF AXIOMATIZATION IN MATHEMATICS & MATHEMATICS TEACHING ('86, pdf) (Two different types of axiomatization are analysed in relation to their functions in mathematics and mathematics education).

http://mzone.mweb.co.za/residents/profmd/axiom.pdf

ALTERNATIVE INSTRUCTIONAL STRATEGIES FOR GEOMETRY EDUCATION: A THEORETICAL STUDY (1977/8) (The theoretical background to the USEME project in 1977/1978 in the Cape Province).

http://mzone.mweb.co.za/residents/profmd/usewo1.htm

A FIBONACCI GENERALIZATION: A LAKATOSIAN EXAMPLE (PME '97 paper - pdf file) (Describes a generalization of the Fibonacci series which followed a Lakatosian path, and includes some philosophical comments).

http://mzone.mweb.co.za/residents/profmd/fibo.pdf

FUTURE OF SECONDARY SCHOOL GEOMETRY (SOSI '96 Plenary, pdf) (Outlines recent developments in geometry research, the Van Hiele theory and the impact of dynamic geometry on the possible future of secondary school geometry).

http://mzone.mweb.co.za/residents/profmd/future.pdf

FUTURE OF SECONDARY SCHOOL GEOMETRY (Sosi '96 Plenary, from *Proof Newsletter*, Dec 1999, html)

http://www-didactique.imag.fr/preuve/Resumes/deVilliers/deVilliers98/deVilliers98.html

EL FUTURO DE LA GEOMETRIA EN SECUNDARIA ('99, pdf) (Spanish translation by Martin Acosta of above article "The Future of Secondary School Geometry" from *Proof Newsletter*, Nov/Dec 1999)

http://mzone.mweb.co.za/residents/profmd/future.htm

COMPUTER VERIFICATION V.S. ALGEBRAIC EXPLANATION (pdf file) (A simple junior high school example to illustrate the difference between verification and explanation).

http://mzone.mweb.co.za/residents/profmd/alge.pdf

OLYMPIC MATHEMATICS: IS IT FAIR? ('96, pdf) (Discusses the 1996 Women's 100 m. final at the 1996 Atlanta Olympic Games and whether the gold medal was awarded fairly).

http://mzone.mweb.co.za/residents/profmd/olympic.pdf

TRANSFORMATIONS: A GOLDEN THREAD IN SCHOOL MATHEMATICS, 1993 (pdf) (Discusses and illustrates various examples of the application of transformations such as isometries, similarities and affinities to the study of the symmetry of border patterns, tessellations, graphs and the production of alternative proofs and definitions). (Apologies for poor quality of reproduction & some typos)

http://mzone.mweb.co.za/residents/profmd/transform.pdf

THE ROLE OF TECHNOLOGY IN MATHEMATICAL MODELLING (pdf) (Various examples of the use of technology such as graphing calculators, *Sketchpad* and symbolic algebra software in the modelling and solution of some real world problems are given).

http://mzone.mweb.co.za/residents/profmd/techmod.pdf