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…

Hands-on science activities and first-hand experiences of kindergartners studying trees demonstrate the true meaning of authentic assessment. The activities and teacher interactions had several things in common: (1) they asked students to perform or create something; (2) they invoked real-world applications; (3) they showed that there is more than…

This book describes inquiry learning during a year-long classroom exploration with 4th graders, which began with setting up a bird feeder and a journal for students to record observations. The authors argue that schools have been organized to make things easy for learners, shielding them from the messiness, ambiguity, and change of intellectual…