There have been some great discussions going on in some of my homeschooling groups about just how a child learns math. This is a discussion that is important to me as I still have one more child to educate. Well, I can’t teach him as I don’t believe you can make anyone learn that which they don’t want to learn so I guess I should rephrase that as one more child to guide or facilitate along his journey.
So what have my homeschooling groups been discussing? Well, one topic is about the essay Just Do the Math excerpted from Have Fun. Learn Stuff. Grow. Homeschooling and the Curriculum of Love, by David H. Albert . In this essay
We did the same thing (skipping ahead). Actually it wasn't my idea at all. My son insisted because he only can learn math through higher level conceptual thinking. He would make up little algebraic ways to learn arithmetic. Anything rote stumped him. Higher level stuff...no problem. I wonder how many kids learn in a similar way. If you're right than quite a few.
If I had tried to make him learn math "in order" he would have hated it. So I just let him do what he liked and skip the stuff that annoyed him.
Years later I don't think he is any worse for it. He can do "the annoying stuff' most notably long division and long multiplication problems. He doesn't usually make mistakes and he seems to know his times tables. I did make a point to eventually walk him through long division so he would understand it but the other stuff he picked up mostly from working with algebra.
Its interesting to read opinions on math education. The debate is so impassioned. It never fails to surprise me how invested people get. There are many educators out there that strongly believe that children need hours of drilling basic math in order to ever be mathematically literate.
Seriously. Algebra should be part of math instruction from the beginning. Since it's *in there* anyway.
The Teaching of Arithmetic I: The Story of an experiment by L. P. Benezet, Superintendent of Schools, Manchester, New Hampshire, 1929. In this article Mr. Benezet tells of an experiment he conducted and the findings of this experiment. Mr. Benezet in Part III writes:
‘They saw what we were trying to do and were surprised at the ability to reason and to talk, shown by children whose minds had not been chloroformed by the dull, drab memorizing of tables and combinations.’
In this article, arithmetic wasn’t formally taught till seventh grade! Instead, the teachers concentrated on teaching the children to "read, reason, and recite”. When I read this, it made me think of some of the reading I’ve done about the Thomas Jefferson approach to education and the Charlotte Mason approach. I’m not an expert at either of these approaches but from what I’ve gathered, they focus on literature and building up the character through these readings. By teaching the child to think and reason, the child learns and can apply concepts to more areas of understanding. Hmmm…That explains quite a bit about how my son is learning.
My youngest son’s unschooling math journey:
My youngest really didn’t enjoy the repetition system. He felt that once he read it, he had it. I must say, that seemed to be the case. My oldest was a firm believer in the repetition system as that’s how she learned. I was tired of the fussing so I went looking for other ways. At first, my spouse was adamant that I could unschool everything except math. So I did what every practical Mom does and I turned that subject over to him! He wanted it his way, so I let him at it. That didn’t last long. In fact, I don’t even think it went two consecutive days! Being me, I wasn’t going to just ignore the situation so I went to the unschooling groups and learned some more.
The Life of Fred series was suggested and since I love books, I went looking. The books are suggested for about fifth grade and up so I had time. I finally bought the complete series last year when my son, by age, would be considered fourth grade. They sat on the shelf for a period of time after the initial interest and the opening giggles the Story of Fred creates. Then one day, my son came to me and asked if he could just read them as a novel and skip the problems. I told him of course!
He sat down with the first book and giggled his way through it. Then he moved on to the next book and while reading that one, he went back on his own, and started re-reading the first one, doing all the equations along the way! I must add, he got them all right, too! He has since moved on to the third book ‘Beginning Algebra as serious as it needs to be’. This book really caught his attention and he ran to me to share what he had just read:
Here in print, was EXACTLY how he was feeling about ‘normal’ math books! WoW! This author gets it! So here I am, with an unschooling ten year old, who loves math! He always DID love math but those redundant math books would have beaten the love of math out of him. Do I assign him a certain amount of pages he must cover in a given day? Absolutely not! Why would I set limits? Sure there are some weeks that he doesn’t open up a math book and that’s OK. There are days he does. Besides, just how advanced do I need him to be? If without prodding, he is still learning at an accelerated rate, why would I interfere? No. I see my job as always being on the lookout for more interesting things that will continue to enrich his world.