Foundation, form, and function: the “3F” framework to dialogue within and across theories in mathematics education research
Abstract
There is a pressing need for Mathematics Education Researchers to develop tools and frameworks for scientific communication around theories, to further theory-driven research practices and offer new theoretical advancements. In this theoretical article, we respond by offering the dimensions of foundation, form, and function (3F), which together form the 3F Framework. To advance scientific discourse in mathematics education research, the dimensions provide language to generate dialogue within and across theories and to explore commonalities and key distinctions of theory cultures systematically. Foundation can communicate where theories come from and what their assumptions are. Form can communicate what theories address and how they are structured, and function can communicate where theories may lead. To illustrate the utility of this 3F Framework, we employ Variation Theory to compare and contrast two different theories, Knowledge in Pieces and the Anthropological Theory of the Didactic. We conclude the article with a scientific reflection on the use of the 3F Framework with Variation Theory, and with implications for the practice of mathematics education research.