COLLABORATIVE RESEARCH: Re-Crafting Mathematics Education: Designing Tangible Manipulatives Rooted in Traditional Female Crafts

嵌入到符号系统中的标准数学教育往往无法吸引学生，特别是女孩，因为它将数学与现实世界的背景相分离。这种缺乏参与感的情况延伸到缩短了选课时间，并可能终身回避数学。这个项目将建立在学习理论的基础上，这些理论假设设计经验(即具体化学习)可以在学习过程中发挥关键作用，以及更形式化的构造学习。具体地说，研究人员将探索传统的女性手工艺(编织、钩编、缝纫和缝纫)，以创建数学学习模型，使用工艺设计，特别是在物理环境中纠正错误的过程，以教授基本的数学概念，如比例推理、分数和几何。这项工作的更广泛的影响在于它有可能扩大对STEM活动的参与，以及后来对女孩和妇女的职业生涯的参与，突出传统妇女手工艺社区中正在使用的日常数学，并向中学生介绍新的数学思想。其目标是设计和确定可长期利用的工具、材料和活动，以改变跨越校内和校外学习空间的数学方法。PI计划(1)对女性手工艺圈进行一系列认知和联系的民族志，以理论性数学与传统女性手工艺之间的联系；(2)开发关键工具、材料(即一组新的有形操作)和支持活动，通过设计和具体的学习方法在数学教学中具有潜在的高实用性；以及(3)在一系列青年(5-9年级)中实地测试这些早期原型，以加深理解，并为下一阶段的课程开发和更广泛的采用提供必要的基础。核心重点将是强调通过实践技能让学生和教育工作者参与数学思维的新方法，这种方法利用一系列数学思想为学生提供新的有形操作，作为数学教育中的“思考对象”。

Standard mathematics education that is embedded in symbol systems often fails to engage students, especially girls, by divorcing mathematics from real world contexts. This lack of engagement extends into truncated course taking and a potentially life-long avoidance of mathematics. This project will build on theories of learning that postulate that design experiences (i.e., embodied learning) can play a crucial role in the learning process alongside of more formalized construct learning. Specifically, the researchers will explore traditional women's crafting (knitting, crocheting, sewing, and quilting) to create models for mathematics learning using craft design and especially the process of fixing mistakes in physical contexts to teach basic mathematical concepts such as proportional reasoning, fractions, and geometry. The broader impact of this work lies in its potential to broaden participation in STEM activities and, later, careers for girls and women, highlighting both the everyday mathematics at play in traditional women's crafting communities as well as introducing middle school youth to new mathematical ideas. The goal is to design and identify tools, materials, and activities that can be leveraged in the long term to transform approaches to mathematics spanning both in- and out-of-school learning spaces.The PIs plan to (1) conduct a series of cognitive and connective ethnographies of female crafting circles to theorize the connections between mathematics and traditional women's crafts; (2) develop key tools, materials (i.e., a set of new tangible manipulatives) and supporting activities with potentially high utility in teaching mathematics through design and embodied approaches to learning; and (3) field test these early prototypes with a range of youth (grades 5-9) to deepen understanding and provide the necessary foundations for the next stages of curriculum development and broader adoption. The core focus will be on highlighting new ways to engage students and educators in mathematical thinking through hands-on crafts, an approach that leverages a range of mathematical ideas to provide students with new tangible manipulatives as "objects-to-think-with" in mathematics education.