Posted in Homeschooling
I wrote a while ago about how so far my children don't like math (here's the link if you want to read it). Mary, who is almost 10, especially does not like it and seems to have some sort of acute math phobia. She has been working lately on subtraction with borrowing and just could not get when she needed to borrow. She would take a problem like 9300-1500, and say the answer is 8200. She subtracts the zeros, looks at the 3 and the 5, and even though the 5 is below the 3, will subtract 3 from 5 and get 2, and then subtract the 1 from the 9 to get 8.
I kept saying, "If you can't subtract the five from the three, you need to borrow" but it didn't help at all. Illustrations did not seem to help. She just couldn't understand. Then, this past weekend, I was researching TPR a bit more (which I mentioned in my last entry) and found some articles by Dr. James Asher, who founded the method. I was intrigued by the article Some Mysteries of Arithmetic Explained: Secrets Revealed that May Help Parents and Teachers clarify mathematics for youngsters (link here) for two reasons; one, my problem with Mary, and two, why is a guy who founded a language teaching method writing about math?
So I didn't find the answer to my question, but I did find an idea that helped the situation with Mary. Dr. Asher says, "I discovered that the standard arithmetic we learned in school has some severe limitations that are hidden until one begins to doodle with arithmetic. Here are some examples:
Multiplication is nothing more than repeated addition
With utmost confidence, teachers present to their students this premise: Multiplication is repeated addition. If this premise is true, I believe it only holds for whole positive numbers. It certainly does not explain negative numbers or fractions."
It had bothered me to tell Mary that you couldn't subtract 5 from 3, because of course you can. The answer is negative 2. And it wasn't helping her know when to borrow anyway. So this week I have been saying, "If the bottom number is bigger than the top number, then you need to borrow." Clear. Simple. True. And now she seems to be getting it!
Thanks, Dr. Asher!