In my Keynote Address to PME-NA 45, I offer an embodied framework for naming what makes mathematics powerful for mathematicians and scientists, yet intractable for many learners. The essential claim is this: Students reside in the Real World, where math is grounded, embodied and meaningful, while mathematics resides in the ungrounded, disembodied…

This project seeks to understand the emergence of mathematical meanings mediated by learners' interactions with multiple artifacts. Extending our prior work which took an enactivist approach and revealed the dynamics of embodied interactions fundamental to understanding fraction division, we now employ a semiotic lens to illuminate how learners…