In the book Beechick says there are a few modes of thinking that our brains move through as we learn math concepts. They are Manipulative (hands on), Mental Image (like a drawing on paper or in your head), and Symbolic (1+1=2).
"Piagetian theory says this [Manipulative Mode] thinking predominates up to about ages six or seven." She also says that we can't expect kids to do something in the next modes before they are ready to move on, and that they will let us know by certain things they do.
For example we can't expect kids to write and understand the meaning of 1+1=2 until they've had sufficient time to learn that one apple in this hand and another apple in the other hand makes two apples all together, and then they have to be able to imagine the apples in their head. Only after both of those are firmly in their minds, will they be able to understand the symbols with complete understanding.
She gives a good list of ideas how parents can foster this kind of learning (playing games, at the grocery store, in the dining area, yard, garage, workshop, kitchen, car or even by the TV.)
I can't help but ponder my Math Methods courses in college. I never considered myself a math whiz, and maybe I missed something, but this book has laid it out most clearly for me. I now have more confidence in teaching my son math and am excited about learning alongside him!
I am trying to make a mental habit to be conscious of the little opportunities throughout our days to inject some simple mathematical thinking.
Fresh Tomato Soup (from this cookbook, which I love!)
8 medium tomatoes, peeled and seeded, if desired
4 cloves of garlic, minced
Combine in saucepan and cook over medium heat, stirring occasionally, until tomatoes are soft.
3 c. water or vegetable stock
2 chicken boullion cubes
1 tsp. sugar
2 sprigs of fresh basil, chopped
Add, bring to boil, simmer 5 minutes. Run through a blender, if desired.
I served ours with Ultimate Grilled Cheese Sandwiches (with bacon and 3 cheeses), tall glasses of milk, and homemade Granola Bars.
One more thing, I'm also excited about this Pre Math-It program/game my friend borrowed us too. Dominoes are always a hit here.
Got any fun math ideas you'd care to share?