| Budget Amount *help |
¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 1996: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1995: ¥1,300,000 (Direct Cost: ¥1,300,000)
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| Research Abstract |
The study finally aims to describe the progress of 8th graders' proof-conception by proof instructions based on relative concept of truth in mathematics in Japan. The aim involves the following goals.
Goal 1 : Clarifying the theoretical background to developmaterials for proof instruction based on relative concept of truth in mathematics.
Goal 2 : Developing materials for proof instruction based on relative concept of truth in mathematics.
Goal 3 : Collecting data of some small groups of 8th grader throughout proof instruction based on relative concept of truth in mathematics by natural observation.
Goal 4 : Describing the progress of 8th graders' proof-conception by analyzing the data by sociological / psychological method.
Regarding Goal 1, I discussed the following points.
Discussion 1-a : Background & significance of relative concept of truth in mathematics.
Discussion 1-b : Movement of curriculum in school mathematics of Japan.
Discussion 1-c : Introduction of proof in textbooks of junior
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high school mathematics in Japan.
Discussion 1-d : Conceptions of truth of a proposition in proof instruction following tectbooks of junior high school mathematics in Japan.
As to Discussion 1-c, I got the following conclusion. In textbooks of junior high school mathematics in Japan, there is no consistency between regulations of argument in a definition of proof and a set of arguments of proof, or we cannot judge whether there is a consistency or not. As a reason of no consistency, One criterion of correctness (correspondenceto facts students can acquire) is applied for a proposition before the field of geometry in 8th grade, and the other criterion (coherence to comewhat assumptions) is applied intentionally for the same proposition in the field. Furthermore, the application of two criterions is causedby adapting not only justification or explanation as functions of proof, but also local systemization of the propositions learned before the field of geometry in 8th grade.
As to Discussion 1-d, I got the following conclusion. Regarding the meaning of truth, two conceptions is possible to brought up : the applicability of propositions in the range students can recognize, and the dependence of their truth on the proved propositions. Regarding the criterion of truth, the following conception is possible to be brought up : it is pre-established which criterion should be applied to a proposition, the correspondence to the facts students can recognize or the deduction from assumptions under the pre-established distinction of usage. Less
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