Representations are often used in instruction to highlight key mathematical ideas and support student learning. Despite their centrality in scaffolding teaching and learning, most of our understanding about the tasks involved with using representations in instruction and the knowledge requirements imposed on teachers when using these aids is…

Several studies have documented prospective teachers' (PSTs) difficulties in offering instructional explanations. However, less is known about PSTs' learning to provide explanations. To address this gap, we trace changes in the explanations offered by a purposeful sample of PSTs before and after a mathematics content/methods course sequence.…

This article describes a study in which measures of mathematical knowledge for teaching developed in the United States were adapted to measure mathematical knowledge for teaching in Ireland. When adapting the measures it was not assumed that the mathematical knowledge used by Irish and U.S. teachers is the same. Instead psychometric and…