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.
Mastering academic language (AL) by elementary school students is important for achieving school success. The extent to which teachers play a role in stimulating students’ AL development may differ. Two types of AL stimulating behavior are distinguished: aimed at students’ understanding and at triggering students’ production of AL. As mathematics requires abstract language use, AL occurs frequently. The instructional methods teachers use during mathematics instruction may offer different opportunities for AL stimulating behavior. In our first study, based on expert opinions, instructional methods were categorized according to opportunities they offer for stimulating students’ AL development. In the second study, video-observations of mathematics instruction of elementary school teachers were analyzed with respect to AL stimulating behavior and instructional methods used. Results showed that actual AL stimulating behavior of teachers corresponds to the expert opinions, except for behavior shown during task evaluation. Teachers differ in time and frequency of their use of instructional methods and therefore in opportunities for stimulating AL development. Four teaching profiles, reflecting different AL stimulating potential, were constructed: ‘teacher talking’, ‘balanced use of methods’, ‘getting students at work’ and ‘interactive teaching’. Teachers showed more types of behavior aimed at students’ AL understanding than at production.
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Numeracy and mathematics education in vocational education is under pressure to keep up with the rapid changes in the workplace due to developments in workplace mathematics and the ubiquitous availability of technological tools. Vocational education is a large stream in education for 12- to 20-years-olds in the Netherlands and the numeracy and mathematics curriculum is on the brink of a reform. To assess what is known from research on numeracy in vocational education, we are in the process of conducting a systematic review of the international scientific literature of the past five years to get an overview of the recent developments and to answer research questions on the developments in vocational educational practices. The work is still in progress. We will present preliminary and global results. We see vocational education from the perspective of (young) adults learning mathematics.
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