Summer vacation is over for me as well as for other local educators; still, the cusp of summer and fall is a nice time to hit to the books and get back to instructing local students in mastering important math skills that will last a lifetime.
During the summer I relaxed and did some needed professional reading. My wife and I spent more time playing with our grandchildren and we also had more friends over to the house to break bread and enjoy some laughs. One proud summer moment was when we watched a cousins daughter graduate from Middlebury Colleges language school. These thingsplus the chance to tutor some wonderful math students between the ages of 6 and 14made the summer of 2007 very special, but not surprisingly the season went by far too quickly.
When I was an elementary school principal, and even now as a busy math tutor, what I enjoy most about students and their math understanding is discovering how they learn. For example, I was told that one of my students could easily count by fives; even though this was true, the child was still having trouble telling time. How this relates to telling time on an analog clock is a puzzle to me.
My experience indicates that most children can count by ones but many cannot count by other groupingsthey never actually do it.
Young students often recite by a variety of numbers. Reciting is very different from counting. Counting is an action that requires a student to actually get a group of five objects. Lets use pennies as an example
After getting a set of five pennies, students must keep getting these sets as they recite the amount. I had an incident like this not too long ago. A child told me she could count by twos but really had no idea how to count; she could recite the numbers by twos. I then wondered why putting 18 to 22 children in one class was the best way to teach mathematics? Of course I dont have a good solution to our traditional classroom approach to education; an approach that seems to need so much fixing.
Next week, Ill muse more on classroom size and the way some educators teach new math.