An Origin of Prescriptions for Our Mathematical Reasoning (Long version)

Proceedings of 17th Annual Conference on Research in Undergraduate Mathematics Education 312-320 頁 2014 発行
アクセス数 : 690
ダウンロード数 : 70

今月のアクセス数 : 4
今月のダウンロード数 : 3
ファイル情報(添付)
Proc17thAnnConfRUME_312.pdf 1.45 MB 種類 : 全文
タイトル ( eng )
An Origin of Prescriptions for Our Mathematical Reasoning (Long version)
作成者
収録物名
Proceedings of 17th Annual Conference on Research in Undergraduate Mathematics Education
開始ページ 312
終了ページ 320
抄録
To build a supplementary theory from which we can derive a practical way of fostering inquiring minds in mathematics, this paper proposes a theoretical perspective that is compatible with existing ideas in mathematics education (radical constructivism, social constructivism, APOS theory, David Tall’s framework, the framework of embodied cognition, new materialist ontologies). We focus on the fact that descriptive and prescriptive statements can be treated simultaneously, and consider both descriptive and instantiated models in our minds. This indicates that descriptive statements in mathematics come from our descriptions of models, and prescriptive statements come from the instantiatedness of the instantiated models and non-existence of counterexample. As a practical suggestion from the proposed perspective, we point out that careful communication is needed so that students do not recognize the refutation of their arguments as a denial of their way of mathematical thinking.
著者キーワード
Inquiring minds
Prescriptive perspective
Mathematical reasoning
内容記述
This work was supported by Grant-in-Aid for JSPS Fellows No. 252024.
Place; Denver,COLORADO Date; February 27- March 1, 2014
NDC分類
数学 [ 410 ]
言語
英語
資源タイプ 会議発表論文
出版者
The Special Interest Group of The Mathmatics Association of America (SIGMAA) for Research in Underguraduate Mathmatics Education
発行日 2014
権利情報
Copyright (c) 2014 left to authors
出版タイプ Version of Record(出版社版。早期公開を含む)
アクセス権 オープンアクセス