Students' Conceptions of the Mathematics of Change and Variation'...

这个研究项目调查了小学，高中， 而大学生们会发展出 微积分在这里广义上是指 数学的变化和变异。 核心假设 从很小的时候起，人们就建立了模型， 一切都变了 数学教学必须建立在 这些直观的模型。 调查法 包括一系列的教学面试， 个别学生提出的问题， 变化的情况，如汽车的运动， 水或植物生长。 他们被给予物质材料 和软件工具来帮助他们进行实验 问题 研究人员观察并录下了 讨论，材料的使用，和学生构建 解决方案的表示。 后续分析 注重学生对问题的建构， 指导他们的预测，他们使用的资源， 他们产生的原则来验证预测， 解释。 该项目的发现将有助于数学 教育工作者重新思考微积分目前 教，以及年龄水平，在关键微积分 思想被引入。 结果也将直接输入 一个主要的小学数学课程，以一个 课程设置围绕“变革”展开。"

This research project examines how elementary, high school, and college students develop intuitive conceptions about calculus--which in this case is broadly defined as the mathematics of change and variation. The central assumption is that, from an early age, people develop models about how things change. Mathematics instruction must build upon these intuitive models. The method of investigation involves sequences of teaching interviews in which individual students are presented with problems about situations of change such as the motion of cars, flow of water, or plant growth. They are given physical materials and software tools to help them experiment with the problems. Researchers observe and videotape the ensuing discussion, use of materials, and student-constructed representations of the solution. Subsequent analysis focuses on students' constructions of the problem, the ideas that guide their predictions, the resources they use, and the principles they generate to verify predictions and explanations. The project's findings will help mathematics educators rethink the ways in which calculus is currently taught, as well as the age levels at which key calculus ideas are introduced. Results will also feed directly into a major elementary mathematics curriculum, in the form of a curriculum strand about "change."