A Math(s) consultant from Yorkshire, now working in Ontario and always learning about how students best learn Math(s).
Thursday, November 24, 2011
I took part in a really engaging geometry lesson in a Grade 1/2 split this week. Five centres have been set up and the students work pretty much independently on these; you can see them building their own geometry knowledge as they do the activities. The talk that these activities provoked was impressive and exciting as the students focussed on the geometric properties and relationships.
Compare this approach to the worksheet approach where kids just write the word square next to a picture of a square. Or even worse, cube next to a 2D picture of a cube: how can anyone truly learn about three-dimensions from a two-dimensional worksheet?
The students' use of Mathematical Processes were in abundance including a surprising amount of reasoning and proving ("I think I'll need four sticks to make a cube and I'll show you") and reflecting ("Oh, I needed 12 sticks because a cube is not a square.")
Even a simple question such as 'Usethe two larger triangles (from a set of tangrams) to make different shapes' brought out a wealth of geometric ideas e.g. composing and decomposing shapes, names of different shapes, congruence. The tactile component here was a vital part of the learning: kids need to flip, rotate and move shapes to learn about them.
After all, if the world's best geometer, Donald Coxeter, used manipulatives and concrete materials to help him better understand geometry, then why shouldn't all our students do so?