Explicit language objectives are included in the Swedish national curriculum for mathematics. The curriculum states that students should be given opportunities to develop the ability to formulate problems, use and analyse mathematical concepts and relationships between concepts, show and follow mathematical reasoning, and use mathematical expressions in discussions. Teachers’ competence forms a crucial link to bring an intended curriculum to a curriculum in action. This article investigates a professional development program, ‘Language in Mathematics’, within a national program for mathematics teachers in Sweden that aims at implementing the national curriculum into practice. Two specific aspects are examined: the selection of theoretical notions on language and mathematics and the choice of activities to relate selected theory to practice. From this examination, research on teacher learning in connection to professional development is proposed, which can contribute to a better understanding of teachers’ interpretation of integrated approaches to language and mathematics across national contexts.
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.
Using the past to orientate on the present and the future can be seen as one of history’s main contributions to educating future citizens of democratic societies. Because teachers often lack useful methods for pursuing this goal, this study explores three pedagogical approaches that may help them making connections between the past, the present and the future: working with longitudinal lines (LL), with enduring human issues (EHI) and with historical analogies (HA). The efficacy of these approaches was examined in three case studies conducted in two Dutch secondary schools with eighth- to tenth-grade students (N=135) and their teachers (N=4) as participants. Explorations took place within the boundaries of the existing history curriculum and in close collaboration with the teachers who participated because they felt a need to motivate their students by means of a pedagogy to make history more useful. Findings suggest that implementing the LL- and EHI-approaches in a traditional history curriculum with chronologically ordered topics is more complicated than implementing the HA-approach. The HA-approach appears to have more potential to encourage students to use historical knowledge in present-day contexts than the other two approaches. In terms of students’ appraisals of the relevance of history, the application of the EHI-approach showed positive effects.
