Abstract
It is a challenge for mathematics teachers to provide activities for their students at a high level of cognitive demand. In this article, we explore the possibilities that history of mathematics has to offer to meet this challenge. History of mathematics can be applied in mathematics education in different ways. We offer a framework for describing the appearances of history of mathematics in curriculum materials. This framework consists of four formats that are entitled speck, stamp, snippet, and story. Characteristic properties are named for each format, in terms of size, content, location, and function. The formats are related to four ascending levels of cognitive demand. We describe how these formats, together with design principles that are also derived from the history of mathematics, can be used to raise the cognitive level of existing tasks and design new tasks. The combination of formats, cognitive demand levels, and design principles is called the 4S-model. Finally, we advocate that this 4S-model can play a role in mathematics teacher training to enable prospective teachers to reach higher cognitive levels in their mathematics classrooms.
Highlights
Research shows that the majority of time in mathematics classes is spent on performing tasks (Roth & Givvin, 2008)
History of mathematics (HoM) can be seen as a source of inspiration for mathematics teachers to make their lessons more meaningful and cognitive demanding for students
Stein and Lane (1996) introduced the cognitive demand framework to differentiate between mathematical tasks based on the level of mathematical thinking evoked by the task
Summary
Research shows that the majority of time in mathematics classes is spent on performing tasks (Roth & Givvin, 2008). The first two levels are considered to be low in terms of cognitive demand, while the second two are defined as high cognitive demand activities This taxonomy can be used to classify mathematical tasks (Stein & Smith, 1998) and has been used in practice and empirical research. History of mathematics (HoM) can be considered as an effective tool to design lessons of a higher cognitive level. HoM can be seen as a source of inspiration for mathematics teachers to make their lessons more meaningful and cognitive demanding for students. With this approach, HoM is “not a primary tool for learning mathematics better and more thoroughly....,” HoM “serves to illustrate other historical aspects of the discipline” The possible application of the model in teacher training programs will be discussed, in order to arrive at the designoriented approach we pursue for the educational practice of mathematics teachers
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