This book brings together leading researchers in mathematics education to share personal narratives of key mathematical moments or ideas that inspired, surprised, or helped direct their research. While the fruits of research activities and products are shared at scholarly conference and journals, the footprints of mathematics that ignited the…

This paper uses a comparative methodology to examine the teaching of abstraction in two mathematics lessons, in Denmark and England. In doing so it aims to extend previous work by the authors, examining the effect of local, cultural issues on the form of teaching in order to understand how these also affect the subject content too. The analysis…

Learners of English as a foreign language often find it difficult to understand figurative speech, which relies heavily on metaphor. This article explores why metaphors challenge learners and presents ways to incorporate metaphors into EFL instruction to help learners understand figurative speech. Topics discussed include cognitive metaphor,…

Lectures, outlines, and class exercises are collected from 16 experienced teachers of general semantics in colleges, adult education, and management training. Among the subject areas explored in the sample lessons are high-level abstractions, extensional-intensional meanings, the "is" of identity, listening, classification, labeling, general…