The first challenge to the belief that multiplication is repeated addition appears when students start working with fractions. From the mathematical point of view, multiplication as repeated addition can be extended into fractions. Feb 9, 2025 · The axiom we seek is typically hidden behind this strange idea that a function is “well-defined”. Let’s keep running with our example of the additive group of integers mod 10. If we want to define a function to this set, it’s very easy. This research paper critiques the current definition of multiplication, arguing that it fails to adequately address the multiplication of negative numbers. The author proposes a new definition based on ancient Indian mathematics that applies universally to both positive and negative examples. Terence Howard explores the deep-rooted beliefs surrounding multiplication and questions the identity element in mathematics. He challenges the conventional ... Jul 1, 2001 · Thus, this study supports the hypothesis that the origin of the concept of multiplication is in the schema of correspondence rather than in the idea of repeated addition. Nov 24, 2020 · This chapter addresses the problematics for the conceptualization of multiplication in school mathematics and fundamental difficulties, which include semantics for defining multiplication meaningfully, syntax in relation to languages, and difficulties that originate from historical transitions. This article aims to explore how two primary mathematics teachers cope with the changes of meanings in the process of making sense of multiplication. It presents a divergence of personal conceptions of multiplication across different contexts between two primary school mathematics teachers.
