Mathematical Inquiry about Factorizing the Polynomial of x<sup>n</sup>-1 and its Phase
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- MOROZUMI Tatsuo
- Education and Human Science, Yokohama National University
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- OGIHARA Fumihiro
- Saku Chosei Junior and Senior High School
Bibliographic Information
- Other Title
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- 整式x<sup>n</sup>-1の因数分解に関する数学的探究とその様相
- 整式xⁿ-1の因数分解に関する数学的探究とその様相
- セイシキ x ⁿ-1 ノ インスウ ブンカイ ニ カンスル スウガクテキ タンキュウ ト ソノ ヨウソウ
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Abstract
<p> The purpose of this paper is to investigate senior high school students’ mathematical inquiry and its phase in factorizing the polynomial xn-1, which focus on producing the irreducible polynomial, discovering and proving mathematical character about the irreducible polynomial xn-1. We investigated students’ mathematical inquiry by teaching units about factorizing the polynomial xn-1 by qualitative methods.</p><p> As a result of our discussions, we obtained several insights:</p><p>(1) By its behavior and its product about factorizing the polynomial xn-1 inductively, a student’s mathematical inquiry is encouraged to connect the properties of the polynomial xn-1 with the properties of the integer n.</p><p>(2) Various interpretations about factorizing the polynomial x6-1 become a foundation of factorizing the polynomial xn-1. For example, students can connect factorizing the polynomial x6-1 with established facts about factorizing when they read the exponential number 6 of x6-1 to 6=2×3 or 6=3×2. Similarly, students advance their own thinking by changing the role of polynomial xn-1 as the base.</p><p>(3) Algebraic matters that students want to prove are generated in inquiry about factorizing the polynomial xn-1 with using a Computer Algebra System (CAS). However, various students’ activities about proving these matters exist.</p>
Journal
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- Journal of JASME : research in mathematics education
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Journal of JASME : research in mathematics education 21 (2), 147-162, 2015-07-28
Japan Academic Society of Mathematics Education
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Keywords
Details 詳細情報について
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- CRID
- 1390845713044989696
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- NII Article ID
- 130007580511
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- NII Book ID
- AA11141495
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- ISSN
- 24333034
- 13412620
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- NDL BIB ID
- 027668489
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- Text Lang
- ja
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- Data Source
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- JaLC
- NDL
- CiNii Articles
- KAKEN
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- Abstract License Flag
- Disallowed