To improve understanding of identities and inverses, and to provide a stronger foundation for future mathematics, Sandra Miles designed a two-part lesson that makes the relationship between identities and inverses explicit. This article illustrates Miles' teaching of the first part of the lesson, focused on addition and subtraction, and then gives…

Analogical reasoning has played a significant role in the development of modern mathematical concepts. Although some perspectives in mathematics education have argued against the use of analogies and analogical reasoning in instructional contexts, some attempts have been made to leverage the pedagogical power of analogies. I assert that with a…

Conceptual Metaphor (CM; e.g., Lakoff & Johnson, 1980, 1999; Kovecses, 2020) is central to our thinking and ubiquitously manifested in our language. Given its importance, the teaching of conceptual metaphors has gained much attention in Cognitive Linguistics and Applied Linguistics. While most empirical studies have focused on specific aspects…

This submission contains the Proceedings of the 2014 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at the University of Alberta in Edmonton, Alberta. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of the…