PERSPECTIVE article
Front. Educ.
Sec. STEM Education
Foundation, Form, and Function: The "3F" Framework to Dialogue Within and Across Theories in Mathematics Education Research
1. University of Bremen, Bremen, Germany
2. University of Colorado Denver, Denver, United States
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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.
Summary
Keywords
Dialogue about theories, Form of theories, Foundation of theories, Function of theories, Learning about mathematical functions and graphs, mathematics education research, Networking of theories, variation theory
Received
22 December 2025
Accepted
17 February 2026
Copyright
© 2026 Bikner-Ahsbahs and Johnson. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Angelika Bikner-Ahsbahs
Disclaimer
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