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Mathematical Connections and Their Relationship to Mathematics Knowledge for Teaching Geometry

机译：数学几何关系及其与数学知识的关系

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Effective competition in a rapidly growing global economy places demands on a society to produce individuals capable of higher-order critical thinking, creative problem solving, connection making, and innovation. We must look to our teacher education programs to help prospective middle grades teachers build the mathematical habits of mind that promote a conceptually indexed, broad-based foundation of mathematics knowledge for teaching which encompasses the establishment and strengthening of mathematical connections. The purpose of this concurrent exploratory mixed methods study was to examine prospective middle grades teachers' mathematics knowledge for teaching geometry and the connections made while completing open and closed card sort tasks meant to probe mathematical connections. Although prospective middle grades teachers' mathematics knowledge for teaching geometry was below average, they were able to make over 280 mathematical connections during the card sort tasks. Curricular connections made had a statistically significant positive impact on mathematics knowledge for teaching geometry.
机译：在迅速发展的全球经济中，有效的竞争对社会提出了要求，要求他们培养具有高阶批判性思维，创造性的问题解决能力，建立联系和创新能力的个人。我们必须考虑我们的教师教育计划，以帮助准中级教师建立数学思维习惯，从而促进概念性索引的，广泛的数学知识基础的教学，其中包括建立和加强数学联系。这项并发的探索性混合方法研究的目的是检查预期的中年级教师的数学知识，以教授几何学以及完成开放式和封闭式卡片排序任务以探究数学联系时所建立的联系。尽管预期的中级教师在几何教学方面的数学知识低于平均水平，但他们在卡片分类任务中能够进行280多次数学连接。在数学教学中，建立的课程联系对数学知识具有统计学上显着的积极影响。

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