An Instructional Complexity Approach to the Science of Learning by Analogy

灵活、可转移、跨主题的数学教学对高质量教学至关重要。这个探索性项目通过一种潜在的变革性方法来实现这一目标，该方法利用和扩展了类比学习研究的科学，这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许多基于实验室的研究的方法，旨在将学习的具体机制分离出来进行研究。相反，研究人员将有意地将多个学习过程组合起来，并在课堂上进行研究。在自然的课堂环境中，许多学习机制同时起作用，可能相互增强，也可能相互破坏。因此，迫切需要更多的理论来解释学生如何从认知原则/过程的相互作用中学习。更好地与课堂学习相结合的研究也将使研究结果更适用于使用，使教师更容易在课堂实践中采用基于研究的建议。研究人员将利用一套“翻译准备”原则来测试这种方法，以在STEM学习过程中进行空间支持类比。这些原则可以产生高的学习效果，并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的课堂环境中实施的，本研究认真考虑了它们在课堂中可能实际实施（或不实施）的不同方式，以及可能改变预期结果的不同组合和顺序。在本研究中，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能与学习中心（SILC）开发的，包括：同步视觉表征、空间对齐、连接手势和对儿童认知资源的敏感性。研究1是对现有数据的一项新分析，以比较美国教师与两个成绩较高的地区：香港和日本，在类比教授八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入访谈，以传播这些原则及其组合频率的结果。教师对这些替代方案的反馈将被引出，以及他们对自己学生的最佳类比实践的投入。研究3将实验性地比较三种版本的视频课程——一种涉及多种支持策略作为高成就地区的模态，一种涉及支持或违规的模态组合，另一种是由SILC预测的最佳组合。还将采用WM和EF措施，以探索组合支持是否增加或减少处理负荷。总之，这些研究将提供丰富的数据，说明空间类比原则是如何在实践中典型地结合起来的，以及如何最佳地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，以解决认知机制如何相互作用，以支持学生的数学思维。更广泛的影响：该项目有可能对数学教学和学习科学的研究产生广泛影响。该项目采用了一种创新的方法，将理论驱动研究的重点转移到结合复杂性而不失去严谨性，使学习理论能够更好地解释和指导日常课堂复杂性中的教学实践。关于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.