Why Use Multiple Representations in the Mathematics Classroom? Views of English and German Preservice Teachers

Dealing with multiple representations and their connections plays a key role for learners to build up conceptual knowledge in the mathematics classroom. Hence, professional knowledge and views of mathematics teachers regarding the use of multiple representations certainly merit attention. In particular, investigating such views of preservice teachers affords identifying corresponding needs for teacher education. However, specific empirical research is scarce. Taking into account the possible role of culture, this study consequently focuses on views about using multiple representations held by more than 100 English and more than 200 German preservice teachers. The results indicate that there are culture-dependent aspects of preservice teachers’ views, but also that there are common needs for professional development.

     

Teaching the Pursuit of Assumptions

Within the school of thought known as Critical Thinking, identifying or finding missing assumptions is viewed as one of the principal thinking skills. Within the new subject in schools and colleges, usually called Critical Thinking, the skill of finding missing assumptions is similarly prominent, as it is in that subject's public examinations. In this article we examine how school‐ and college‐focused texts explain and teach ‘this very important skill’. The same texts also deal with the nature of assumptions, validity and the role of stated reasons in arguments, and the way these matters are tackled will also be examined in our inquiry. In addition we explore what respected contributors to the critical thinking movement have had to say about some of these issues.