We had a lively discussion at last week’s homeschool math chat about teaching algorithms versus allowing a discovery learning process.
What I can’t help but think about when I reread this discussion is how this compares to teaching a child manners.
Teach kids manners early. Very early.
I know someone who elected to wait until their child understood the concept of appreciation before teaching them how to say thank you. The child is now eight years old and doesn’t say thank you unless prompted.
Daughter, at 18 months old, is being taught please, thank you, ma’am and sir. She has no concept of being polite. Her frontal lobe is about as advanced as the local neighborhood chimpanzee’s. Her favorite phrase these days is, “No. Mine.” I correct this with, “No ma’am.”
At some point it will become habit. Or at least the ritual of, “No,” from her and my “No ma’am” response will become habit.
And at some point shall make the connection that using these polite words will gain her something. She’ll be looked upon favorably, considered one of the “good kids,” or smiled at a little more.
And then she’ll connect it. She’ll see that the concept of politeness is directly tied to the “algorithm” of saying polite words.
Teach kids algorithms early. Very early.
I love the idea of teaching concepts before algorithms in math. But sometimes algorithms have to come first so that the rhythm and habit are in place when the brain is ready to understand the concept.
Each child’s brain is different. One of the beauties of homeschooling and private tutoring is that you can focus on a child and know when they’re ready for algorithms and ready for concepts. As a classroom teacher, it’s a little bit more difficult, but still can be done.
In the classroom you can teach algorithms at the same time as concepts. If you cycle them back and forth, you can catch each student as they are prepared to accept the learning.
If you’re interested in the discussion we had on this, you can see the transcript here. Want to join us for the next one? It’s at 9pm CST every Thursday night on Twitter using the hashtag #HSMath. Jump on in, or get more details about it here.
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Bon,
I think there is overwhelming evidence that focusing on teaching algorithms can be very destructive while, to the contrary, focusing on solving problems through common sense means can be very empowering.
The major work on this was done by Louis Benezet, prior to WWII, but his results and methods got swamped by statistical approaches to assessment after the war.
A comprehensive reference to Louis Benezet’s work has been constructed by Sanjoy Mahajan at http://www.inference.phy.cam.ac.uk/sanjoy/benezet/
I look forward to reading it, Gary. Thanks so much.
I’m not proposing JUST algorithms, though. I do believe that the discovery process is best. The rub is that if there is already panic, trying to get someone calm enough to discover might not work. Giving the rules can be very calming. Once they know that you’re not going to withhold the method they believe they need, then they can free up a little.
Having stumbled upon your blog, I’m not sure if this is an old post and I’m weird to be commenting on it now, but I find your analogy powerful, even though I disagree with the conclusion. Like algorithms, the only sensible reason to learn most manners is to alter people’s perception of you. You can be a good person without ever saying “thank you,” just as you can be a good mathematician without ever multiplying two-digit numbers by hand (for example). But doing either of these would be bucking old traditions that, while of little practical worth, are highly prevalent.
Thanks, R. for your comment.
Although I have to disagree – the sensible reason to learn to say thank you or yes, ma’am is to make others feel good. Of course that will improve the look of yourself. But how wonderful is it to know that you’ve made someone’s day?
I shall continue to consider your refute, though, as I think you have a curious point.