Bernd Zimmermann

Identification and fostering of mathematically gifted students: Rationale of a pilot study

In a three year research project, annual mathematics talent searches for highly able and motivated twelve year old students were conducted. Of these, 150 took part in a long term Saturday enrichment program to train their mathematical abilities in problem finding and problem solving. The article first discusses the educational and organizational constraints of programs for gifted children. Mathematical giftedness is defined by high achievement in two tests: The Scholastic Aptitude Test (SAT-M) and the HTMB, a set of seven problems specially devised for the talent search. The philosophy of the teaching program is explained and illustrated by examples. Preliminary results indicate the considerable success of the program. Possible consequences for normal classroom teaching are indicated.

Investigating Mathematical Beliefs by Using a Framework from the History of Mathematics

In the theoretical part of the article a framework of eight activities and motives is sketched (calculate, apply, construct, argue, order, find, play, evaluate), which proved to be successful along the history of mathematics. Furthermore, some arguments are presented and discussed why this framework is useful for studying mathematical beliefs. The empirical part is about two case studies using this network carried out in Joensuu (FIN) and Jena (GER). The goal of the first study was to compare mathematical beliefs of student mathematics teachers in Finland and Germany. The second part is about the influence of using a handheld calculator on the belief of a pupil. The first study reveals that neither in Finland nor in Germany the school mathematics seems to give much support for these activities, in Finland university mathematics even less. The only exception is calculating, for which the both institutions seem to give overdose. On the other hand, the finding of the second study that voluntary playing with progressive technology, even during a short period of time, might shift mathematical beliefs in a positive way.