arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1904.08751math.HOcs.HCcs.LO
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教育中的“完全、透明和交互式数学模型”技术

Technologies for "Complete, Transparent & Interactive Models of Math" in Education

Walther Neuper

摘要:

ThEdu和其他学术团体正在计算机数学方面形成新一代的教育数学软件。相应的概念和技术在一定程度上得到了澄清,这就要求与教育科学合作,以优化新一代对教育实践的影响。本文针对教育科学家,他们希望研究特定的软件功能,并估计在大学和随后的高中STEM教育中的各自影响。其主要特点是“完整,透明和互动的数学模型”,在数学的所有相关方面提供互动体验。交互使用几层形式语言:术语语言、规范语言、证明语言和程序语言,这些语言通过提供“下一步指导”的Lucas-Interpretation连接起来,并提供证明器功能来检查用户输入。因此,本文是从计算机数学的角度出发,不能对计算机数学对教育实践的影响进行认真的描述,这取决于与教育科学的合作;这种合作是由一系列问题准备的,其中一些偏向于软件可用性(主要由计算机数学家解决),其中一些偏向于教育科学的真正研究。

英文摘要:

A new generation of educational mathematics software is being shaped in ThEdu and other academic communities on the side of computer mathematics. Respective concepts and technologies have been clarified to an extent, which calls for cooperation with educational sciences in order to optimise the new generation's impact on educational practice. The paper addresses educational scientists who want to examine specific software features and estimate respective effects in STEM education at universities and subsequently at high-school. The key features are characterised as a "complete, transparent and interactive model of mathematics", which offers interactive experience in all relevant aspects in doing mathematics. Interaction uses several layers of formal languages: the language of terms, of specifications, of proofs and of program language, which are connected by Lucas-Interpretation providing "next-step-guidance" as well as providing prover power to check user input. So this paper is structured from the point of view of computer mathematics and thus cannot give a serious description of effects on educational practice -- this is up to collaboration with educational science; such collaboration is prepared by a series of questions, some of which are biased towards software usability (and mainly to be solved by computer mathematicians) and some of which are biased towards genuine research in educational sciences.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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