教員養成課程の教科「数学」専門科目における「証明」の扱いに関する考察 I

概要

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In Mathematics the reasons that some Theorem or Proposition is true are assured by"Proof under Logical Deduction". Strictness, rigidity and rightness are essential demands ofMathematics. In Education of Mathematics in teachers' training course it is important tomake many students understand the reasons of mathematical statements while meetingsuch demands of Mathematics. I will study concretely the instruction of "Proof" by turningmy attention to various features of the structures of proofs.In the first part of this series I will consider in detail the instruction of "Proof" in thecase of Fundamental Theorem of Simple Algebraic Extensions Fields on Galois Theory inthe subject "Advanced Algebra". Since this theorem has essentially different variousproofs I am first interested in such case and tend to make a deep consideration about itsproofs.
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