Dietmar Küchemann

Learning Experiences Designed to Develop Multiplicative Reasoning: Using Models to Foster Learners' Understanding

Successful progress in learning mathematics depends on a sound foundation of the understanding of multiplicative structures and reasoning. This includes not only the properties and meanings of multiplication and division, but also their many links with ratio and percentage and with rational numbers both fractions and decimals. Yet these connections take time to establish and primary teaching can sometimes emphasise facility in calculation rather than the building of conceptual connections. This chapter draws on our experiences from the Increasing Competence and Confidence in Algebra and Multiplicative Structures (ICCAMS) study in order to discuss how learning experiences can be planned to promote this kind of conceptual understanding. In doing so, the authors discuss the ways in which representations can be introduced and how formative assessment may be used.

Learning Experiences Designed to Develop Algebraic Thinking: Lessons from the ICCAMS Project in England

Algebra provides powerful tools for expressing relationships and investigating mathematical structure. It is key to success in mathematics, science, engineering and other numerate disciplines beyond school as well as in the workplace. Yet many learners do not appreciate the power and value of algebra, seeing it as a system of arbitrary rules. This may be because teaching often emphasises the procedural manipulation of symbols over a more conceptual understanding. In this chapter, we will draw on our experiences from the Increasing Competence and Confidence in Algebra and Multiplicative Structures (ICCAMS) study in order to look at ways in which learning experiences can be planned. In doing so, we will discuss how representations can be used, and the relationship between algebra and other mathematical ideas strengthened. We will also discuss how formative assessment can be used to nurture a more conceptual and reflective understanding of mathematics.