ABSTRACT
Multiplicative reasoning is a cornerstone to success in other mathematical topics and a potential gatekeeper to success both in and out of school. This chapter describes multiplicative reasoning in two ways: mathematically and from a teaching and learning perspective. It examines the general concept of initial multiplicative understanding. The chapter focuses on why multiplication and division are not simply an extension of addition and subtraction and the difference between additive (absolute) reasoning and multiplicative (relative) reasoning. Additive reasoning involves situations in which sets of objects are joined, separated, or compared. When thinking about the skills and concepts that help to support the development of strong multiplicative reasoning, it is important to consider both procedural fluency and conceptual understanding. It further talks about the characteristics of strong multiplicative reasoning and the importance of both conceptual understanding and procedural fluency in multiplicative reasoning. The chapter also provides an introduction to the OGAP Multiplication and Division Progressions.
