A study of problem posing under the technology environment: Analysis of problem solving process using "Cabri-Geometry"
Tadayuki KISHIMOTO
takishi@ningen.human.tsukuba.ac.jp
Graduate School of Education
University of Tsukuba
2-177-22 Iriya Zama-City Kanagawa-Pref. 228-0024
Japan
Abstract
The purpose of this paper is to clarify the factors needed for problem posing under computer environment(Cabri-Geometry), and to describe the relation between such factors and problem posing. At first, "problem posing" was defined as "to make a new question during the process of solving a question(original problem) asked by the others or during the process of investigation". In this paper, the factors needed for problem posing are as follows: "analysis of problem", "mathematical knowledge, "heuristics", and "computer environment".
In addition two processes of problem solving while two graduate students posed the same problem, were analyzed based on the framework.
As a result, it is found that:
(1)Problem posing was influenced by the conditions which subjects add implicitly, or the conditions involved in the original problem.
(2)Problem posing was influenced by mathematical knowledge of subjects.
(3)Heuristics was selected based on the idea that making condition to be general.
(4)Problem posing was influenced by operation of drawing tool.
Generally, students need to enrich heuristics and mathematical knowledge or understand problem itself so that they can pose many problems. Students need to consider selection of heuristics, conditions which they add implicitly, conditions involved in an original problem, and operation of drawing tool.
© Asian Technology Conference in Mathematics, 1998. |
