ABSTRACT

Integrating mathematics content into science usually plays a supporting role, where students use their existing mathematical knowledge for solving science tasks without exhibiting any new mathematical meanings during the process. To help students explore the reciprocal relationship between math and science, we designed an instructional module that prompted them to reason covariationally about the quantities involved in the phenomenon of the gravitational force. The results of a whole-class design experiment with sixth-grade students showed that covariational reasoning supported students’ understanding of the phenomenon of gravity. Also, the examination of the phenomenon of gravity provided a constructive space for students to construct meanings about co-varying quantities. Specifically, students reasoned about the change in the magnitudes and values of mass, distance, and gravity as those changed simultaneously as well as the multiplicative change of these quantities as they changed in relation to each other. They also reasoned multivariationally illustrating that they coordinated mass and distance working together to define the gravitational force. Their interactions with the design, which included the tool, tasks, representations, and questioning, showed to be a structuring factor in the formation and reorganization of meanings that students exhibited. Thus, this study illustrates the type of design activity that provided a constructive space for students’ forms of covariational reasoning in the context of gravity. This design can be used to develop other STEM modules that integrate scientific phenomena with covariational reasoning through technology.

摘要

将数学内容融入科学通常起到辅助作用，即学生利用现有的数学知识解决科学任务，在此过程中不会表现出任何新的数学意义。为了帮助学生探索数学与科学之间的相互关系，我们设计了一个教学模块，促使他们对引力现象中涉及的数量进行协变推理。对六年级学生进行的全班设计实验结果表明，协变推理支持学生对重力现象的理解。此外，对重力现象的考察为学生构建关于共变量的意义提供了建设性的空间。具体来说，学生们对质量、距离和重力的大小和值的变化进行了推理，因为它们同时变化，以及这些量在相互变化时的乘法变化。他们还进行了多变量推理，说明他们协调了质量和距离，共同定义了引力。他们与设计的互动，包括工具、任务、表示和提问，表明是学生表现出的意义的形成和重组的结构因素。因此，这项研究说明了设计活动的类型，它为学生在重力背景下的协变推理形式提供了建设性空间。