An Instructional Complexity Approach to the Science of Learning by Analogy

灵活的、可转移的、跨主题联系的数学教学是高质量教学的关键。这个探索性项目通过一种潜在的变革性方法解决了这一目标，该方法利用并扩展了类比学习研究的科学，类比是一种支持灵活和联系的数学思维的有前途的模式。这项研究提出了一种不同于大多数基于实验室的研究的方法，该研究旨在将特定的学习机制分离出来进行研究。取而代之的是，研究人员将有意识地对多种学习过程进行组合检查，并将其置于教室中。在自然主义的课堂环境中，许多学习机制同时运行，可能相互增强，也可能相互削弱。因此，迫切需要更多的理论来解释学生是如何从认知原则/过程的相互作用中学习的。更好地与课堂环境中的学习保持一致的研究也将使研究结果更适用于使用，使教师能够更容易地将基于研究的建议用于课堂实践。研究人员将利用一套“翻译准备”原则来测试这一方法，以“在STEM学习期间在空间上支持类比”。这些原则可以产生很高的学习效果，而且有课堂证据证明它们的可用性和有效性。由于这些原则是在自然主义的课堂环境中实施的，本研究认真考虑了这些原则在课堂上实际实施(或不实施)的不同方式，不同的组合和顺序可能会改变预期的结果。本研究中支持数学课堂类比的原则是由美国国家科学基金会支持的空间智力与学习中心(SILC)提出的，包括：同时视觉表征、空间对齐、连接手势和对儿童认知资源的敏感性。研究一是对现有数据的新分析，以比较美国和香港和日本这两个成绩较好的地区的教师在用类比方法教授8年级数学时如何使用和结合这些原则。研究2将对一组专家教师进行深度访谈，以传播这些原则及其组合频率的结果。将征求教师对这些替代方案的反馈，以及他们对自己学生的类比最佳实践的意见。研究3将对基于视频的课程的三个版本进行实验比较-一个涉及多个支持策略作为高成就地区的模式，一个涉及美国支持或违规的模式组合，以及一个与SILC预测的最佳组合。还将实施WM和EF措施，以探索组合支架是增加还是减少处理负荷。总而言之，这些研究将提供丰富的数据，说明空间类比原理1)通常在实践中结合在一起，2)最佳整合以支持学生在数学课堂上的学习。这些数据将支持理论的产生，该理论阐述了认知机制如何相互作用来支持学生的数学思维。广泛的影响：该项目可能对数学教学以及学习科学研究产生广泛影响。该项目采用了一种创新的方法，将理论驱动的研究重点转变为在不失去严谨性的情况下纳入复杂性，使学习理论能够更好地解释和指导日常课堂中的教学实践。类比教学最佳做法的广泛传播计划已经到位。

Mathematics teaching that is flexible, transferrable, and connected across topics is crucial to high quality instruction. This exploratory project addresses this goal by a potentially transformational approach that leverages and extends science of learning research on analogy, a promising mode for supporting flexible and connected mathematical thinking. This study proposes an approach different from much of lab-based research designed to focus on isolating specific mechanisms of learning for study. Instead, the researchers will intentionally examine multiple learning processes combinatorially and as situated in classrooms. Many mechanisms of learning operate simultaneously in naturalistic classroom situations, and may either augment or undermine each other. Therefore, more theories that explain how students learn from the interaction of cognitive principles/processes is urgently needed. Research that is better aligned with learning in classroom settings will also make research findings more applicable for use, enabling teachers to more easily adopt research-based recommendations for classroom practice. The investigators will test this approach by leveraging a set of "translation ready" principles" for spatially supporting analogy during STEM learning. These are principles that produce high learning outcomes and for which there is classroom evidence for their usability and efficacy. As these principles are implemented in naturalistic classroom settings, this study takes seriously the diverse ways in which they may be realistically enacted (or not) in the classroom, in different combinations and sequences that may change the expected outcomes. The principles for supporting mathematics classroom analogy in this study were developed by the NSF supported Spatial Intelligence and Learning Center (SILC), and they include: simultaneous visual representations, spatial alignment, linking gesture, and sensitivity to children's cognitive resources. Study 1 is a new analysis of existing data to compare how teachers in the U.S. versus two higher achieving regions: Hong Kong and Japan, use and combine these principles when teaching 8th grade mathematics by analogy. Study 2 will be deep interviews with a set of expert teachers for dissemination of these principles and the results about their combinatorial frequencies. Teacher feedback on these alternatives will be elicited, as well as their input regarding best practices of analogy for their own students. Study 3 will experimentally compare three versions of a video-based lesson - one involving multiple support strategies as modal in the high achieving regions, one involving the modal U.S. combination of supports or violations, and one with the optimal combination predicted by SILC. WM and EF measures will also be administered to explore whether combined supports increase or reduce processing load. Together, these studies will provide rich data on the way spatial analogy principles are 1) typically combined in practice, and 2) optimally integrated to support students' learning in mathematics classrooms. This data will support the generation of theory that addresses how cognitive mechanisms interact to support students' mathematical thinking.Broader Impacts: The project has the potential for broad impact on mathematics teaching as well as on research in the science of learning. The project takes an innovative approach to shifting the focus of theory driven research to incorporate complexity without losing rigor, making learning theory better able to explain and inform teaching practice within the complexity of everyday classrooms. A broad dissemination plan for best practices of analogy instruction is in place.