Analysis of Slow Learners in the Calculation of Symbolic Fractions and Development of an Online System to Support them

符号分数计算学习速度慢的分析以及支持他们的在线系统的开发

• 批准号: 13680269
• 负责人: NISHIZAWA Hitoshi
• 金额: $ 2.62万
• 依托单位: Toyota National College of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13680269/
• 关键词: Algebra; Computer Support; Slow Learner; Support Function; WWW; Symbolic Calculation; 国際研究者交流; オーストリア; オーストラリア

Slow learners do not learn the calculation of symbolic fractions easily even if they have enough skills to calculate numerical fractions. The suspected reason is that symbolic calculations depend on several mathematical rewriting rules, which are usually hidden in black boxes at numerical calculations, and the slow learners cannot use the rules properly. They can calculate numerical fractions automatically according to a few patterns they have learnt from experience and without thinking of the mechanism of the calculating steps.We have been developing a Web-based online exercise system to support such slow learners in symbolic calculation. The system analyzes the input symbolic expressions sent by the students, categorizes the calculating errors into careless mistakes, fatal errors, and other errors. The fatal errors are mostly caused by incorrect rewriting rules that look similar but are not equal to any mathematical rewriting rules, and show that the student do not calculate upon mathematical rules. The system has two special Web pages: step-by-step instruction page and the explanation page. The instruction page shows one step of the calculation to the student according to the selected rewriting rule. By using this page, the student is accustomed to use rewriting rules in his/her symbolic calculation. The explanation page shows itself when the student makes a fatal error on his/her calculation in the exercise page. It explains that the exact calculating step is lead by an incorrect rule, and shows a numerical counter example to show the incorrectness.Slow learners who used the system showed better recognition than other students in the post-test, which demonstrates the effectiveness of the method and the system developed in this project.

学习慢的人即使有足够的技能来计算数字分数，也不会轻易学会符号分数的计算。怀疑的原因是符号计算依赖于几个数学重写规则，这些规则通常隐藏在数值计算的黑盒子里，而慢学习者无法正确使用这些规则。他们可以根据他们从经验中学到的一些模式自动计算数字分数，而不考虑计算步骤的机制。我们一直在开发一个基于网络的在线练习系统，以支持这些慢学习者进行符号计算。系统对学生输入的符号表达式进行分析，将计算错误分为粗心错误、致命错误和其他错误。致命的错误大多是由于错误的重写规则，这些规则看起来很相似，但不等于任何数学重写规则，这表明学生没有根据数学规则进行计算。本系统有两个专门的网页：步骤说明页面和说明页面。指令页根据所选择的重写规则向学生显示计算的一个步骤。通过使用这个页面，学生习惯了在符号计算中使用改写规则。当学生在练习页的计算中出现致命错误时，解释页就会显示出来。说明了精确计算步骤是由一个不正确的规则引导的，并给出了一个数值反例来说明其不正确。使用该系统的慢速学习者在后测中表现出比其他学生更好的识别能力，证明了该方法和本项目开发的系统的有效性。

项目成果

西澤一, 吉岡貴芳: "誤解解消を支援する分数式計算演習システム"論文集・高専教育. 27号. 549-554 (2004)

Hajime Nishizawa，Takayoshi Yoshioka：“支持误解解决的分数公式计算练习系统”论文集和技术大学教育第27期，第549-554号（2004年）。

S.Matsui, H.Nishizawa, T.Yoshioka: "Similarity of Two Fractional Expressions and the Relation with Careless Mistakes"Proceedings of the International Conference on Computers in Education/SchoolNet2001. Vol.3. 1263-1266 (2001)

S.Matsui、H.Nishizawa、T.Yoshioka：“两个分数表达式的相似性以及与粗心错误的关系”国际教育计算机会议论文集/SchoolNet2001。

H.Nishizawa, T.Yoshioka, F.J.Fuchs, A.Dominik: "A Knowledge-Sensitive On-line Exercise for Developing Algebraic Strategies"Proceedings of the 8th Asian Technology Conference in Mathematics. 118-126 (2003)

H.Nishizawa、T.Yoshioka、F.J.Fuchs、A.Dominik：“开发代数策略的知识敏感在线练习”第八届亚洲数学技术会议论文集。

Y.Kajiwara, H.Nishizawa, T.Yoshioka: "Effectiveness of the Hints Given at a WWW-based On-line Exercise System"Proceedings of the International Conference on Computers in Education/SchoolNet2001. Vol.1. 186-189 (2001)

Y.Kajiwara、H.Nishizawa、T.Yoshioka：“基于 WWW 的在线练习系统中提示的有效性”国际教育计算机会议记录/SchoolNet2001。

H.Nishizawa, S.Matsui, T.Yoshioka: "A Method to Find Calculating Errors Based on Misconceptions at a On-line Exercise System"Proceedings of 7th Asian Technology Conference in Mathematics. 192-199 (2002)

H.Nishizawa、S.Matsui、T.Yoshioka：“一种基于在线练习系统误解的计算错误的方法”第七届亚洲数学技术会议论文集。