Cultivating Knowledge of Mathematical Equivalence

这个项目将开发和测试为期一学期的基于概念的教学的有效性，以促进对数学等价性的理解和代数思维的相关收获。研究的参与者将是中小学生。尽管许多简短的、单节的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制定出供正规课堂教师使用的实用指导方针。这个项目将在更长的时间内应用实验室研究的结果，目的是为课堂教师包装一种实用的方法来发展学生的等号知识。这个假设是，等号知识的改进将导致获得更好的代数知识，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，这些领域有助于为现代社会提供动力。这个项目将探索基于概念的间隔教学的有效性，以促进对数学等价性的理解和代数思维的相关收获。多项实验研究表明，简短的、基于概念的教学干预可以提高儿童的等号知识。这项拟议的研究将测试，随着时间的推移，这种干预措施的间隔是否可以导致等号知识获得更实质性和更长期的收益，以及这些知识是否反过来促进了代数推理。这项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，采用交叉设计，调查干预随时间的影响。这项研究将采用一种比大多数常用方法更敏感的等号知识测量方法，允许检测相对细粒度的收益，以响应教学干预。总而言之，这项工作将有助于该领域理解如何提高等号知识和理解等号教学对学生代数能力的因果影响。该项目由发现研究PRE-12项目(DRK-12)共同资助，该项目旨在通过研究和开发创新资源、模型和工具，显著提高Pre-K-12学生和教师的科学、技术、工程和数学(STEM)的学习和教学。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.