"定理说......":工科学生理解常微分方程解的意义

IF 1 Q3 EDUCATION & EDUCATIONAL RESEARCH
Paul Hernandez-Martinez , Svitlana Rogovchenko , Yuriy Rogovchenko , Stephanie Treffert-Thomas
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引用次数: 0

摘要

对于学生微分方程的学习,特别是在高等本科和研究生课程中,还需要进一步的研究。对工程师数学教育的研究表明,学生对实践性、情境化教学法的需求与对抽象推理和适当使用数学结果的需求之间存在冲突。很少有论文关注工程专业学生对定理的解释以及它们在论证和解决问题中的应用。本文从社会文化的角度看待学习,并采用了一种根植于巴赫金主义理论的方法论——对话探究。新开发的协作探究和定性数据分析-调查高级工程学生在完成一项旨在评估他们对微分方程解的存在唯一性定理(EUTs)理解的任务时所产生的意义。我们确定了两个重要的认识论脱节,这两个脱节解释了我们的一些学生在理解微分方程和微分方程解的意义时所面临的困难。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
“The theorem says…”: Engineering students making meaning of solutions to Ordinary Differential Equations

There is a need for further studies on students’ learning of Differential Equations (DEs), especially in advanced undergraduate and graduate courses. Research on the mathematical education of engineers shows a conflict between students’ demands for practical, contextualized pedagogies and the need for abstract reasoning and appropriate use of mathematical results. Few papers focus on engineering students’ interpretation of theorems and their use as tools in argumentation and problem-solving. This paper takes a sociocultural stance on learning and employs dialogical inquiry – a methodology rooted in Bakhtinian theory, newly developed for collaborative inquiry and qualitative data analysis – to investigate the meanings that senior engineering students made while working on a task designed to evaluate their understanding of Existence and Uniqueness Theorems (EUTs) of solutions of DEs. We identified two important epistemological disconnections that explain the difficulties that some of our students faced in making meaning of solutions of DEs and the EUT.

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来源期刊
Journal of Mathematical Behavior
Journal of Mathematical Behavior EDUCATION & EDUCATIONAL RESEARCH-
CiteScore
2.70
自引率
17.60%
发文量
69
期刊介绍: The Journal of Mathematical Behavior solicits original research on the learning and teaching of mathematics. We are interested especially in basic research, research that aims to clarify, in detail and depth, how mathematical ideas develop in learners. Over three decades, our experience confirms a founding premise of this journal: that mathematical thinking, hence mathematics learning as a social enterprise, is special. It is special because mathematics is special, both logically and psychologically. Logically, through the way that mathematical ideas and methods have been built, refined and organized for centuries across a range of cultures; and psychologically, through the variety of ways people today, in many walks of life, make sense of mathematics, develop it, make it their own.
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