How we think about teaching, with citations.

What four decades of research say about online algebra for Classes 6–10.

Dragging to discern invariants, constructing up the van Hiele levels, and proof as explanation — and the case for Play With Geometry.

Ratio invariance discovered by scaling a triangle, the triangle/ratios/wave as one linked object, and concept before SOHCAHTOA — and the case for Play With Trigonometry.

Game and simulation gains are largest in biology and for younger students; the cure for the abstract topics is making the invisible visible and manipulable — the design case for a play-first biology.