Subject: Learning Math

Posted by Bob Gorman on 10/14/2010
In Reply To:Creativity, innovation, intuition and discovery Posted by Sharon Villines on 10/13/2010

Message:

On 10/14/2010 9:54 AM, Sharon Villines wrote:
On 14 Oct 2010, at 1:19 AM, Connie Woodberry wrote:

The best thing a teacher can do is put every possible resource, opportunity and support in place for learning to happen and then get out of the way.

A question. Can mathematics be taught/learned this way? Without al the repetition? For example, without the forced march to memorize the times tables?
IMHO every subject has multiple parts necessary for mastery. Mathematics, the simplest & most fun to teach shows these off fairly clearly. You're quite right, the basic 'facts' in arithmetic are the addition & times (multiplication) tables. If you have them memorized, cold, you can do everything else (in arithmetic) much quicker. But like with your genius niece there are alternatives. I taught math in 2 special ed high schools. Most of the learners did not know their "+" & "x" tables.
I addressed it in 2 ways, since they would need these 2 tables of 'facts' readily available for my favorite activity which was solving Cryptarithms which is totally about thinking the primary skill I was really teaching. ;-)

First, I got the 2 charts on big posters, about 30" x 30" and put then on the walls - permanently! If they needed 6x7 they could look it up. This creates a natural repetition, & after a few weeks most students no longer needed to look at the charts; but a few did. It also showed some of the patterns that certain numbers exhibit.

Second, I realized that while the 1st method helped my visual learners, it did little to nothing for my strong audio & kinesthetic learners. One day, on the spur of the moment, I tried the following and it worked so well I used it for the rest of the year. In the middle of almost any other topic I would shout out like a drill sergent: Count to 100 and back by 3's! It gave them a more intuitive grasp of multiplication.

If you want to experience this first-hand, for free, stop reading this post for a moment and count to 100 and back by 7's!



Perhaps I'm being too literal about "get out of the way." I'm curious because I'm comfortable saying this about children under 12 and adults over 21 but in the great in-between in think you would have to bar the door if you weren't standing in front of it.

Again, IMHO, there are fundamentally only 2 ways to learn anything:
1. Experiment & form your own conclusion.
2. Ask someone - an Authority.

Many Individuals have a strong preference. I very strongly prefer Experimenting, since I have a deep seated distrust of almost all authorities.

However, many tasks are learned far better by asking an authority than by experimenting. Examples: I fly gliders and learned by doing whatever my instructor told me to do, and I'm still alive. I also learned Aikido, a martial art, by following, exactly, what my instructor demonstrated. The best Sensei I ever had did not speak a word of English!

I doubt age has much to do with it, but due to a strange upbringing, I didn't go thru my terrible 2's till I was 62. IMO in adolescence from 10-20 our primary task is to review all the stuff we learned by authority from 0-10 and accept it, reject it, or modify it. A primary strategy is to reject an idea and see if the world collapses as our authorities told us it would!

Bob

Follow Ups:

Learning Math - Connie Woodberry 10/14/2010