[论文解读] Inquiry-Based Mathematics Education: a call for reform in tertiary education seems unjustified

Tanya Evans, Heiko Dietrich|arXiv (Cornell University)|Jun 24, 2022

Visual and Cognitive Learning Processes参考文献 79被引用 6

一句话总结

本文批判性地评估了探究式数学教育（IBME），认为该运动呼吁对本科数学教育进行激进改革的主张缺乏依据。基于认知科学和教育心理学的研究，本文主张：缺乏指导的发现式学习会损害学生的学习效果——尤其是对初学者和代表性不足的群体而言——而通过认知参与提示进行的显性教学则能取得更优的学习成果。

ABSTRACT

In the last decade, major efforts have been made to promote inquiry-based mathematics learning at the tertiary level. The Inquiry-Based Mathematics Education (IBME) movement has gained strong momentum among some mathematicians, attracting substantial funding, including from some US government agencies. This resulted in the successful mobilization of regional consortia in many states, uniting over 800 mathematics education practitioners working to reform undergraduate education. Inquiry-based learning is characterized by the fundamental premise that learners should be allowed to learn 'new to them' mathematics without being taught. This progressive idea is based on the assumption that it is best to advance learners to the level of experts by engaging learners in mathematical practices similar to those of practising mathematicians: creating new definitions, conjectures and proofs - that way learners are thought to develop 'deep mathematical understanding'. However, concerted efforts to radically reform mathematics education must be systematically scrutinized in view of available evidence and theoretical advances in the learning sciences. To that end, this scoping review sought to consolidate the extant research literature from cognitive science and educational psychology, offering a critical commentary on the effectiveness of inquiry-based learning. Our analysis of research articles and books pertaining to the topic revealed that the call for a major reform by the IBME advocates is not justified. Specifically, the general claim that students would learn better (and acquire superior conceptual understanding) if they were not taught is not supported by evidence. Neither is the general claim about the merits of IBME for addressing equity issues in mathematics classrooms.

研究动机与目标

• 批判性评估探究式数学教育（IBME）在本科数学教育中的实证与理论基础。
• 评估IBME是否真正提升了数学教育中的概念理解与教育公平性。
• 挑战‘减少教师指导可提升学习成果’这一假设。
• 提出基于证据的IBME替代方案，以在传统讲授模式中促进主动的认知参与。
• 引导未来研究将重点放在改进传统教学，而非以未经证实的探究模式取代它。

提出的方法

• 对认知科学与教育心理学研究文献进行了范围综述。
• 综合分析了六十余年关于直接教学与探究式教学的实验研究发现。
• 分析了关于主动学习、工作记忆限制与认知负荷理论的元分析证据。
• 回顾了关于探究式与传统课堂中性别表现差异的实证研究。
• 运用分层线性模型与加权回归分析，评估IBME中公平性主张的实证依据。
• 提出一种改进的讲授模式，整合自我解释提示与认知参与策略。

实验结果

研究问题

• RQ1 探究式学习是否比显性教学更有效于促进本科生的深层数学理解？
• RQ2 探究式学习是否促进了数学教育中的公平性，特别是对女性和代表性不足群体？
• RQ3 工作记忆限制在多大程度上削弱了初学者在发现式学习中的有效性？
• RQ4 社会动态因素（如课堂参与率）在探究式课堂中对性别表现差异起到了何种作用？
• RQ5 通过认知参与提示增强传统讲授，能否实现与IBME相当或更优的学习成果？

主要发现

• 在以探究为导向的抽象代数课程中，学生平均表现劣于传统课堂学生，且男性表现优于女性，这与IBME声称的公平性优势相矛盾。
• 女性在课堂讨论中的参与率显著与性别表现差距相关，表明社会动态在探究式环境中对女性构成不利影响。
• 认知负荷理论与实验证据一致表明，由于工作记忆限制，对初学者而言，最小指导的教学方式无效。
• 学生通过独立重新发现数学而学得更好的说法，缺乏实证研究支持，尤其对先前知识水平较低的学习者而言。
• 在显性教学中补充自我解释提示与认知参与任务，比无指导的探究式教学更有效且更具公平性。
• 尚无充分证据支持大规模用IBME取代传统数学教学，未来改革应聚焦于改进传统讲授，而非采用未经验证的探究模式。