[论文解读] Beyond deficit-based models of learners' cognition: Interpreting engineering students' difficulties with sense-making in terms of fine-grained epistemological and conceptual dynamics

Ayush Gupta, Andrew Elby|arXiv (Cornell University)|Mar 22, 2010

Educational Strategies and Epistemologies参考文献 49被引用 31

一句话总结

本研究将工程专业学生在数学意义建构上的困难重新解释为认识论障碍，而非知识内容的缺陷——具体而言，是学生认为数学方程比直觉推理更可信。通过与一名工程专业学生的临床访谈，作者表明，吉姆在解决流体静压力问题时出现错误，源于其认识论立场：他视数学与常识脱节，拒绝调和形式化表达与日常推理。本研究的关键贡献在于提出一种细致入微、情境敏感的认识论动态模型，揭示了学生推理中可教的契机，为教师提供了基于现有积极认识论种子的支持路径。

ABSTRACT

Researchers have argued against deficit-based explanations of students' troubles with mathematical sense-making, pointing instead to factors such as epistemology: students' beliefs about knowledge and learning can hinder them from activating and integrating productive knowledge they have. In this case study of an engineering major solving problems (about content from his introductory physics course) during a clinical interview, we show that "Jim" has all the mathematical and conceptual knowledge he would need to solve a hydrostatic pressure problem that we posed to him. But he reaches and sticks with an incorrect answer that violates common sense. We argue that his lack of mathematical sense-making-specifically, translating and reconciling between mathematical and everyday/common-sense reasoning-stems in part from his epistemological views, i.e., his views about the nature of knowledge and learning. He regards mathematical equations as much more trustworthy than everyday reasoning, and he does not view mathematical equations as expressing meaning that tractably connects to common sense. For these reasons, he does not view reconciling between common sense and mathematical formalism as either necessary or plausible to accomplish. We, however, avoid a potential "deficit trap"-substituting an epistemological deficit for a concepts/skills deficit-by incorporating multiple, context-dependent epistemological stances into Jim's cognitive dynamics. We argue that Jim's epistemological stance contains productive seeds that instructors could build upon to support Jim's mathematical sense-making: He does see common-sense as connected to formalism (though not always tractably so) and in some circumstances this connection is both salient and valued.

研究动机与目标

• 挑战将学生意义建构困难归因为知识或技能缺乏的缺陷模型。
• 探究认识论信念——学生对知识与学习的看法——如何影响工程专业学生调和数学形式化与常识推理的能力。
• 分析像吉姆这样的学生，尽管具备正确的概念与数学知识，仍因认识论限制而得出错误答案的原因。
• 开发一种精细的认识论与概念动态模型，避免将学生推理简化为单一缺陷。
• 识别学生推理中可促进意义建构的积极认识论种子，供教师加以利用。

提出的方法

• 对一名高年级工程专业学生（吉姆）进行临床访谈，观察其在导论物理课程中解决流体静压力问题的过程。
• 运用精细的认识论框架分析吉姆的推理，识别其在解题各阶段认识论立场的转变。
• 追踪吉姆如何将数学方程视为权威，同时否定常识推理的可靠性或相关性。
• 利用视频与音频转录稿，分析解题过程中概念知识、数学形式化与认识论信念之间的互动。
• 应用一种动态的认识论立场模型，以解释学生推理取向在不同情境下的变化。
• 识别出吉姆推理中显现的潜在意义建构契机，特别是在常识与形式化短暂一致的时刻。

实验结果

研究问题

• RQ1 为何一名具备完整内容知识的工程专业学生在物理问题中会得出违反常识的错误答案？
• RQ2 学生的认识论信念——尤其是对数学方程权威性与意义的看法——如何影响其在物理问题中的意义建构？
• RQ3 学生推理如何被理解为并非缺陷，而是蕴含可促进意义建构的积极认识论种子？
• RQ4 认识论立场在解题过程中如何动态变化，其在调和形式化与常识推理方面发挥何种作用？
• RQ5 哪些认识论动态使学生能暂时将形式化与直觉推理联系起来，教师又如何利用这些时刻？

主要发现

• 吉姆具备正确解决流体静压力问题所需的所有概念与数学知识。
• 尽管如此，吉姆仍否定了常识推理的可靠性，将数学方程视为内在可信，即使其结果违背直觉。
• 吉姆的认识论立场阻碍了其调和数学形式化与日常推理，导致其接受了一个违反常识的错误答案。
• 他相信方程与意义及常识无关，使得通过直觉推理进行意义建构显得不必要或不可信。
• 尽管如此，吉姆偶尔也意识到常识与形式化之间的联系，表明积极的认识论种子确实存在，且可被培育。
• 本研究揭示，认识论动态并非单一不变，而是情境敏感的，学生在被引导或其推理与已有信念一致时，有能力转变其立场。