Monday, September 05, 2005

Talking math to your child

Does one have to be a mathematician to help someone with math? I believe the answer is no. To know some math is not a bad thing, but it is more important that you know how to talk to your child so he learns how to learn.

Seven ways to respond

I shall never forget my father’s answer when I asked him for help in translating some German words to Norwegian. “Use a dictionary, son!” What kind of help was that? I felt disgusted. He knew the answers and refused to help.

What I did not understand then, and what he might have explained, was that he wanted to put the onus on me. For one thing, because it was my homework, not his, but also because I should get used to use books for help. I have found there are seven ways to respond to a question for help.

1. Accepting the question, but offering no further response.
(“How do I find the volume of a cone?” – “That’s a very good question!”)

2. Encouraging the child to try more on his own.
(“Let’s see what you can find out. Try for another ten minutes.”)

3. Soliciting more information.
(“Please show me what you have tried.”)

4. General problem solving response.
(“Have you solved a similar problem before?”)

5. Specific problem solving response.
(“What do you know about volume of things?”)

6. Specific response
(“What is a cone? Can you draw one?”)

7. Very specific response
(“Study the example on page 54 in your textbook.”)

The aim is to help the child work his mind in such a way that the answer steps forward by itself. A grand order, therefore it is important not to expect miracles overnight.

Some other suggestions.

1. Listen a lot, talk a little. (The important person in the child, not you.)

2. Permit mistakes. (Without them learning can not take place.)

3. Enjoy yourself. (If you don’t value learning, neither will your child.)

4. Know problem solving. (Read “How to solve it” by George Polya. A classic from 1945.)

5. Ask stupid questions. (Ask anything that may help your child learn and have an enjoyable time.)

6. Listen, really listen. (Listen to meanings, not to words.)

You as a math teacher

I believe that to learn is to find answers to questions and to discover new questions. I believe you can help your child to do this even if you are not a math teacher.

The secret lies in the way you communicate with your child. You should aim to be a dialectician, someone who knows how to find truth through dialogue. Your child will not be a self-reliant thinker by accepting others ideas, he has to modify and enlarge his own. To give you a flavour of what I mean, here is a dialogue.

- How do I find 2/3 of 1 4/5? Should I divide or multiply?

- You should do neither. You should think.

- What do you mean?

- If you can't solve the problem, try to solve a simpler problem.

- Like what?

- What is 1/3 of 1 4/5?

- I have no idea!

- What is 1/3 of 21?

- One third of 21?

- That's right?

- That is 7.

- Why?

- Because 7 x 3 = 21.

- You mean, because 21 ÷ 3 = 7?

- That's the same thing.

- Then should not 1/3 of 1 4/5 be 1 4/5 ÷ 3?

- Yes, that makes sense.

- How much is 1 4/5 ÷ 3?

- 1 4/5 = 9/5, so the answer is 9/5 ÷ 3 = 9/5 ÷ 3/1 = 9/5 x 1/3 = 9/15.

- Very good! 1/3 of 1 4/5 equals 9/15. Now what about 2/3's?

- That must be more.

- How much more?

- Twice as much.

- So?

- 2 x 9/15 is 2/1 x 9/15 = 18/15.

- There you are! 2/3 of 1 4/5 equals 18/15.

- OK we found the answer. But, isn't there a faster way!?

- I like your attitude!

- So?

- You tell me! Look back at what we found!

- OK. First we divided by 3 then we multiplied by 2. I don't see a thing!

- 1 4/5 equals 9/5, right?

- Right.

- We found that 2/3 of 9/5 equals 18/15. Do you see any pattern?

- (After a while.) Oh yes! 2 x 9 = 18 and 3 x 5 = 15. So 2/3 of 9/5 = 2/3 x 9/5. All you have to do is to multiply!

- That's interesting. Do you think it always works?

- Come on! Of course it does! Why didn't you tell me right away?

- Because you did not want to know.

- But I did!

- You did not!

- I did.

- Did not.

- I did.

- Then I misunderstood you. I thought you meant "Teach me to think for myself. Teach me self reliance, endurance and self discipline. And most of all, teach me self confidence." That is what I thought you asked me.

- I am confused. I thought we were studying fractions, and not weird thinking and how to gain self confidence!

- To be confused is a good thing.

- Why?

- You don't want to know!

- I do.

- You do not.

- I do.

- It makes you think!

- I knew you were going to say that

One does not become a good dialectician overnight. I have been on it for more than twenty years and I am still learning. However, sometimes I do a good job. Some time ago, after having tried to help Sheena with a problem, she smiled at me and said: “Sir, I hate you!” “Why is that, Sheena?” “Because you make me think!”


Post a Comment

<< Home