From speck to story: relating history of mathematics to the cognitive demand level of tasks

It is a challenge for mathematics teachers to provide activities for their students at a highlevel of cognitive demand. In this article, we explore the possibilities that history of mathematicshas to offer to meet this challenge. History of mathematics can be applied in mathematicseducation in different ways. We offer a framework for describing the appearancesof history of mathematics in curriculum materials. This framework consists of four formatsthat are entitled speck, stamp, snippet, and story. Characteristic properties are named foreach format, in terms of size, content, location, and function. The formats are related tofour ascending levels of cognitive demand. We describe how these formats, together withdesign principles that are also derived from the history of mathematics, can be used to raisethe 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 advocatethat this 4S-model can play a role in mathematics teacher training to enable prospectiveteachers to reach higher cognitive levels in their mathematics classrooms.Teaching and Teacher Learning (ICLON