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接触，并支持这些主题与学生日常生活之间的有意义的联系。该项目建立在先前的动态面积测量（DYME-A）工作的基础上，DYME-A是一种让学生探索面积模型的方法，作为一段距离上线段的动态扫描。先前的结果表明，这种方法支持学生的乘法推理，即面积是一个连续的数量，可以根据两个线性测量：长度和宽度动态变化。研究结果还表明，DYME-A具有支持学生进行乘法和除法推理的潜力。为了使DYME-A方法适用于不同的学生群体，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，以关注学生的文化相关和上下文适当的学习体验。该项目的指导问题是：(1)学生的DYME-A推理如何支持他们的乘法推理发展？(2) DYME-A的哪种干预设计可以覆盖更多样化的学生群体并扩大其影响？(3)公平研究如何为设计实验方法提供信息，以设计更公平的设计和理论？该项目通过专业发展计划和指导来培养主要研究者的能力，包括(a)深入研究乘法推理研究，以描述与DYME-A的相互作用，以及(b)对设计实验方法的当前使用提出问题，并找到合并公平研究中使用的既定方法的方法，以设计更公平的设计和理论。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研究创新的方法方法。该项目得到了美国国家科学基金会EDU STEM教育研究核心研究能力建设（ECR: BCSER）项目的支持，该项目旨在培养研究者开展高质量STEM教育研究的能力。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识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.