Collaborative Research: Re-Crafting Mathematics Education: Designing Tangible Manipulatives Rooted in Traditional Female Crafts

嵌入符号系统的标准数学教育往往无法吸引学生，特别是女孩，因为数学与真实的世界背景脱节。这种缺乏参与延伸到缩短课程和潜在的终身避免数学。这个项目将建立在学习理论的基础上，假设设计经验（即，具体化学习）可以在学习过程中发挥至关重要的作用，以及更形式化的建构学习。具体来说，研究人员将探索传统女性的手工艺（针织，钩编，缝纫和绗缝），使用工艺设计创建数学学习模型，特别是在物理环境中修复错误的过程，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，突出了传统妇女手工艺社区中发挥作用的日常数学，并向中学青年介绍了新的数学思想。目标是设计和确定可以长期利用的工具，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连接民族志，以理论化数学和传统女性手工艺之间的联系;（2）开发关键工具，材料（即，一套新的有形的操作方法）和支持活动，通过设计和体现的学习方法在数学教学中具有潜在的高效用;和（3）实地测试这些早期原型与一系列青年（5-9年级），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。核心重点将是突出新的方法，让学生和教育工作者通过动手的工艺品，数学思维，一种方法，利用一系列的数学思想，为学生提供新的有形的操作作为“对象，以思考”在数学教育。

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.