Abstract

A current research problem in mathematics education is the characterization of the role of teachers in the processes of technology integration in mathematics classrooms. This article shows how two secondary mathematics teachers taught the concept of derivative of a function at a point and the concept of derivative function, one of them using digital technology and the other one without using it. Their teaching was characterized by describing their hypothetical learning trajectories (learning goals, learning activities and the hypothetical learning processes). APOS theory (which stands for Action, Process, Object and Schema) was used to describe the hypothetical learning processes. The results showed that the use of digital technology in class may promote reflection among students without excessive computations, thus helping them to construct the concept of derivative.

摘要

数学教育中当前的研究问题是数学教室技术集成过程中教师角色的表征。本文介绍了两位中学数学教师如何在某一点上教授函数的导数概念和导数函数的概念，其中一位使用数字技术，而另一位则不使用数字技术。他们的教学以描述他们假设的学习轨迹（学习目标，学习活动和假设的学习过程）为特征。APOS理论（代表动作，过程，对象和模式）用于描述假设的学习过程。结果表明，在课堂上使用数字技术可以促进学生的反思，而无需进行过多的计算，从而帮助他们构建派生概念。