Cultivating Knowledge of Mathematical Equivalence

这个项目将开发和测试一个学期的概念为基础的指令，促进数学等价和代数思维的相关收益的理解的有效性。研究对象为中小学生.虽然许多简短的单次实验室研究提出了在短期内促进等号知识的有效方法，但这些研究通常未能产生可供常规课堂教师使用的实用指南。该项目将应用较长时间的实验室研究结果，目的是为课堂教师提供一种培养学生等号知识的实用方法。假设是，改进的等号知识将导致更好地获得代数，这是进入高等数学和科学的重要途径，提供了进入科学，技术，工程和数学（STEM）领域的机会，有助于推动现代社会。这个项目将探讨有效的间隔，概念为基础的教学，促进理解数学等价和相关收益的代数思维。多项实验研究表明，简短的，基于概念的教学干预可以导致儿童的等号知识的改善。拟议中的研究将测试随着时间的推移，间隔这种干预是否会导致等号知识的更实质性和长期收益，以及这种知识是否反过来促进代数推理。研究的一个组成部分将旨在优化基于概念的干预。另一个组成部分将是一项研究，调查随着时间的推移，干预的影响，使用交叉设计。该研究将采用一种比最常用的措施更敏感的等号知识的措施，允许检测相对细粒度的收益，以响应教学干预。总的来说，这项工作将有助于该领域对如何提高等号知识的理解，以及对等号教学对学生代数能力的因果影响的理解。该项目由探索研究preK-12计划（DRK-12）共同资助，该计划旨在显着提高科学，技术，工程，该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

This project will develop and test the effectiveness of a semester-long conceptually-based instruction for promoting understanding of mathematical equivalence and associated gains in algebraic thinking. Participants in the research will be elementary- and middle- school students. Although many brief, single-session laboratory studies have suggested effective ways to promote equal sign knowledge in the short term, these studies have generally failed to produce practical guidelines for use by regular classroom teachers. This project will apply findings from laboratory studies over a longer time period with the goal of packaging a practical approach to developing students' knowledge of the equal sign for classroom teachers. The hypothesis is that improved equal sign knowledge will lead to improved access to algebra, an important pathway into higher mathematics and science that provides access to Science, Technology, Engineering, and Mathematics (STEM) fields that help power modern society. This project will explore the effectiveness of spaced, conceptually-based instruction for promoting understanding of mathematical equivalence and associated gains in algebraic thinking. Multiple experimental studies have shown that brief, conceptually-based instructional interventions can lead to improvements in children's equal sign knowledge. The proposed research will test whether spacing such interventions over time can lead to more substantial and long-term gains in equal sign knowledge, and whether such knowledge, in turn, fosters algebraic reasoning. One component of the research will aim to optimize the conceptually based intervention. The other component will be a study that investigates the effects of the intervention over time, using a crossover design. The research will employ a measure of equal sign knowledge that is more sensitive than most commonly used measures, allowing for detection of relatively fine-grained gains in response to the instructional intervention. In total, the work will contribute to the field's understanding of how to improve equal sign knowledge and understanding of the causal impact of equal sign instruction on student competence in algebra.This project is co-funded by the Discovery Research preK-12 program (DRK-12) that seeks to significantly enhance the learning and teaching of science, technology, engineering, and mathematics (STEM) by preK-12 students and teachers, through research and development of innovative resources, models, and tools.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.