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Colin Foster

Solving linear equations, an important mathematical technique at the core of the Algebra 1 curriculum, forms an essential foundation for more advanced work. Too often, developing fluency with linear equations entails plowing through pages of repetitive exercises. How can students master this topic while using their mathematical sense-making faculties?

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Colin Foster

Exploring even something as simple as a straight-line graph leads to various mathematical possibilities that students can uncover through their own questions.

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Matthew Inglis and Colin Foster

Mathematics educators have been publishing their work in international research journals for nearly 5 decades. How has the field developed over this period? We analyzed the full text of all articles published in Educational Studies in Mathematics and the Journal for Research in Mathematics Education since their foundation. Using Lakatos's (1978) notion of a research programme, we focus on the field's changing theoretical orientations and pay particular attention to the relative prominence of the experimental psychology, constructivist, and sociocultural programmes. We quantitatively assess the extent of the “social turn,” observe that the field is currently experiencing a period of theoretical diversity, and identify and discuss the “experimental cliff,” a period during which experimental investigations migrated away from mathematics education journals.