Designing an Equitable Approach to Multiplicative Reasoning through Dynamic Measurement for Area (DYME-A)

该项目利用技术作为教学工具和民主化力量，扩大学生对面积测量和乘法数学的了解，并支持这些主题与学生日常生活之间的有意义的联系。该项目建立在以前的工作与动态测量面积（DYME-A），一种方法，让学生在探索面积的模型作为一个动态扫描的线段在一段距离。先前的结果表明，这种方法支持学生的乘法推理面积作为一个连续的量，可以动态变化的基础上两个线性措施：长度和宽度。研究结果还表明，DYME-A的潜力，支持学生的乘法和除法的推理。为了使DYME-A方法能够为不同的学生群体所用，该项目旨在通过设计动态区域模型将其扩展到四年级的整数乘法，该模型关注学生的文化相关性和适合背景的学习经验。该项目的指导问题是：（1）学生的DYME-A推理如何支持他们乘法推理的发展？(2)什么类型的干预设计DYME-A可以达到更多样化的学生群体，并扩大其影响？(3)设计实验方法如何通过公平研究来设计更公平的设计和理论？该项目通过一个专业发展计划与导师，涉及（a）深入研究乘法推理研究，以描述与DYME-A的相互作用，（B）问题化目前使用的设计实验方法，并找到方法来合并既定的方法用于公平研究工程师更公平的设计和理论的能力建设的主要研究者。DYME-A方法为在测量和乘法之间建立更强的联系开辟了新的途径，这些联系可能支持K-8数学的其他领域，如分数和比例推理。努力制定更公平的设计实验原则也将有助于创新方法的研究。该项目得到了NSF的EDU Core Research Building Capacity in STEM Education Research（ECR：BCSER）项目的支持，该项目旨在培养研究人员开展高质量STEM教育研究的能力。该奖项反映了NSF的法定使命，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 uses technology as both a pedagogical tool and a democratizing force to expand student access to the mathematics of area measurement and multiplication, and to support meaningful connections between these topics and students' everyday lives. The project builds on prior work with Dynamic Measurement for Area (DYME-A), an approach that engages students in exploring models of area as a dynamic sweep of a line segment over a distance. Prior results suggest that this approach supports students' multiplicative reasoning about area as a continuous quantity that can dynamically change based on two linear measures: length and width. Findings also showed DYME-A's potential for supporting students' reasoning about multiplication and division. To make the DYME-A approach accessible to a diverse population of students, this project aims to expand it to multiplication of whole numbers in fourth grade through the design of dynamic area models that attends to students' culturally relevant and context-appropriate learning experiences. The project's guiding questions are: (1) How can students' DYME-A reasoning support their development of multiplicative reasoning? (2) What type of an intervention design for DYME-A can reach a more diverse population of students and broaden its impact? (3) How may the design experiment methodology be informed by equity research to engineer more equitable designs and theories? This project builds the capacity of the principal investigator through a professional development plan with mentorship that involves (a) delving deeper into the multiplicative reasoning research to describe the interplay with DYME-A, and (b) problematizing the current use of design experiment methodology and finding ways to merge established methods used in equity research to engineer more equitable designs and theories. The DYME-A approach opens novel avenues toward establishing stronger connections between measurement and multiplication that may support other areas of K-8 mathematics, such as fractions and proportional reasoning. Working to develop principles for more equitable design experiments will also contribute to research on innovative methodological approaches. The project is supported by NSF's EDU Core Research Building Capacity in STEM Education Research (ECR: BCSER) program, which is designed to build investigators' capacity to carry out high-quality STEM education research.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.