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，尤其是女孩，因为数学与现实世界的背景脱节。这种参与度的缺乏延伸到课程的缩短和可能的终身回避数学。该项目将建立在学习理论的基础上，该理论假设设计经验（即具体化学习）可以在学习过程中与更形式化的结构学习一起发挥关键作用。具体来说，研究人员将探索传统的妇女手工艺（针织、钩针编织、缝纫和绗缝），利用工艺设计为数学学习创造模型，特别是在物理环境中修正错误的过程，以教授基本的数学概念，如比例推理、分数和几何。这项工作的更广泛影响在于，它有可能扩大女童和妇女对STEM活动的参与，进而扩大她们的职业生涯，既突出了传统妇女手工艺社区中日常数学的作用，也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，以改变学校内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关联民族志，以理论化数学与传统女性手工艺之间的联系；(2)通过设计和具体的学习方法，开发在数学教学中具有潜在高效用的关键工具、材料（即一套新的有形教具）和支持活动；(3)在一系列青少年（5-9年级）中对这些早期原型进行实地测试，以加深理解，为课程开发的下一阶段和更广泛的采用提供必要的基础。此次活动的核心重点将是强调通过动手制作工艺品吸引学生和教育工作者进行数学思维的新方法，这种方法利用一系列数学思想，为学生提供新的有形操作工具，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.