Pearla Nesher

Mathematics and Cognition: A Research Synthesis by the International Group for the Psychology of Mathematics Education

Forward Contributors Introduction Efrain Fischbein 1. Epistemology and Psychology of Mathematics Education Gerard Vergnaud 2. Psychological Aspects of Learning Early Arithmetic Jacques C. Bergeron and Nicolas Herscovics 3. Language and Mathematics Colette Laborde 4. Psychological Aspects of Learning Geometry Rina Hershkowitz 5. Cognitive Processes Involved in Learning School Algebra, Carolyn Kieran 6. Advanced Mathematical Thinking Tommy Dreyfus 7. Future Perspective for Research in the Psychology of Mathematics Education Nicolas Balacheff References.

The role of schemes in designing computerized environments

Schemes are said to underly cognitive processes, including problem solving in Mathematics. An attempt to test the impact of schemes in solving 2-step word-problems was made in an instructional study where two computerized environments were compared. In the S.P.A. (Schemes for Problem Analysis) software, the user works with schemes in order to analyze and solve the problems. When using S.P.A., the solver has to fill in the data in a scheme which is presented graphically. From the scheme the operation is derived in a deterministic manner, and the user (solver) can then calculate the solution. A feedback mechanism follows. In the A.P. (Algebraic Proposer) software the user fills in a table with the data given in the word-problem and then has to find out which operation to use in order to find the solution. The effectiveness of S.P.A. vs. A.P. was empirically examined in an instructional experiment which studied two sixth grade classes during a four month period. The results of the experiment concluded that, in solving easy word problems, both of the two software systems were equally helpful. In harder word-problems, however, those who learned with the S.P.A. experienced more success than those who had learned with A.P. It was also found that S.P.A. was more instrumental in helping low achieving students cope with hard word-problems.