## Math

Teach children the concrete before the abstract no matter how old they are. When they are young always have them use counters such as dry beans or buttons rather than cubes. Give them story problems and let them use their counters to solve them. When they can add or subtract up to 20, introduce multiplication and division using beans. They will see right away multiplication is the same as addition only faster.

Let them use counters as long as they want. No child should use a multiplication table until he has created one and it might take months to make one. Let the child learn through experience faster and easier ways to do any type of math.

Daily mental effort, one step at a time, will give the child the habit of concentration. Encourage clear thinking and rapid, careful execution. Do not redo incorrect problems; move on to the next problem.

To learn money, use real money

To learn weights and measures, weigh and measure. Weigh out 4oz of sand or rice. Have them guess the weight of an object such as a book and then weigh it. Learn fractions while learning measurements. Use a yard stick and measure objects around them. When learning place values, say “two tens” instead of “carry the two”.

Great resource book: Applying Algebra by Garlic Press

Source: A Charlotte Mason Education; A Home Schooling How To Manual by Catherine Levison

Thanks for your post. I think it got me to understand a bit more of what some of the “math wars” are about.

I understand your point, and I think it is true, but

onlyin the case that you are teaching math for daily, pragmatic goals. In other words, if the be-all and end-all of your reason to teach math is so that children can manipulate numbers and pay bills, do the daily things we need math for well, etc, then I think it is true that you should, “Teach children the concrete before the abstract no matter how old they are.”On the other hand, if you are teaching for thinking skills in general, Then focusing on concrete skills first might not be the best way to go.

You might be interested in reading a post I made my blog concerning exactly this subject. It’s at:

The Math Mojo Chronicles

in that post and the one after it, I explore both sides of the issue.

But after reading your post, I think I should make some additions, because of some of the interesting points you have made. Your point about daily mental effort is absolutely on target. Consistency is a great teacher, just ask any athlete.

I especially liked your point about learning money using

realmoney. I want to cringe every time I see people using play money. Do they think their children are dolts?Anyway thanks for the interesting post.

All the best,

Brian (a.k.a. Professor Homunculus at MathMojo.com )