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

该项目使用技术作为教学工具和民主化力量，以扩大学生接触面积测量和乘法数学的机会，并支持这些主题与学生日常生活之间有意义的联系。该项目建立在以前使用面积动态测量(DYME-A)的基础上，该方法使学生能够探索面积模型，即对一条线段进行一段距离的动态扫掠。以前的研究结果表明，这种方法支持学生关于面积的乘法推理，认为面积是一个连续的量，可以根据长度和宽度这两个线性度量动态变化。研究结果还表明，Dyme-A有潜力支持学生关于乘法和除法的推理。为了使DYME-A方法能够为不同的学生群体所接受，该项目旨在通过设计动态区域模型来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)学生的动态A推理如何支持他们发展乘法推理？(2)什么样的动态A干预设计可以接触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性研究来设计更公平的设计和理论？该项目通过有导师指导的专业发展计划培养首席调查员的能力，该计划涉及：(A)更深入地研究乘法推理研究，以描述与DYME-A的相互作用；(B)使设计实验方法论的当前使用出现问题，并找到方法合并在公平性研究中使用的既定方法，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。努力为更公平的设计试验制定原则也将有助于研究创新的方法方法。该项目得到了NSF的STEM教育研究EDU核心研究能力建设计划(ECR：BCSER)的支持，该计划旨在建设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，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 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.