Thursday, October 11, 2007

Better math, better learning (John Mighton and JUMP Math)

Do you know what neuroplasticity is?

What do you think about recent discoveries about the way our epigenetic system helps us process information?

University of Toronto professor Dr. John Mighton slung some of this around last night to a roomful of teachers and interested others, in between demonstrating why we invert and multiply when dividing fractions, and giving some hints about teaching the nine times table. (Funny, I just reminded one of my own Squirrelings about that yesterday, the fact that the digits have to add up to nine. Teachers don't know this?) He also shared the (to me) appalling information that, according to his research of provincial math curricula across Canada, there is not one province that specifically, in its curriculum guidelines, says that children must be taught to solve questions like "what is 2/3 of 9."

What he had to say went well beyond pushing his math program or his books, although he was there specifically to promote his book The End of Ignorance. As I listened I kept mentally hearing quotes from Charlotte Mason overlapping with some of the scientific findings Dr. Mighton was describing along with his own experiences tutoring children. (You can read the appendix to his book here.)

The most recent discoveries about our brains show that they can develop new abilities, rewire themselves and learn material beyond what was previously expected. It's not so much that you're born a math genius or not. The evidence points to the fact that most kids can learn anything.

So why don't we all learn way more than we do?

Dr. Mighton mentioned a Scientific American article, "The Expert Mind," that points out that you can learn the rules of chess, and play chess as an amateur for the rest of your life, not ever getting any better than a beginner. (Yep, he's got my chess-playing style nailed.) On the other hand, players who are taught small groups of powerful moves and so on become very good, very fast. (Wouldn't the same thing also apply to those who are taught to bang out songs on the piano but never go beyond that?)

He also described being inspired by a volume of letters by Sylvia Plath, in which she explains how she learned to write: by imitating great writers. He pointed out that Plath developed one of the most original voices in 20th century American poetry, so it obviously was no handicap to begin with imitation.

The problem in schools today is that kids are often expected to do without some simple training in basics that they need if they're to seriously develop their abilities--specifically in math, but in the other areas as well. The issue of whole language vs. phonics is one example; spending too much time on discovery-based math learning (including overuse of manipulatives) without teaching the needed basic skills is another. (Remember Mr. Person's blog post, Hands-On, Brains-Off?) Just because kids can work with models or manipulatives doesn't mean they can generalize enough to answer questions that are given in another context; and conversely, just because they haven't been able to learn something by playing with pizza pieces or whatever doesn't mean they can't learn those concepts if they're presented with a more "guided discovery" approach. (Some people apparently read The Myth of Ability and get the idea that John Mighton completely eschews manipulatives; this isn't so, he does use chocolate bars and other concrete examples when it helps to demonstrate a point.)

Add to this the fact that our working memories aren't always that great; you might "discover" something during a lesson, but forget it later. And this is not limited to children; Dr. Mighton mentioned (I think it was in The Myth of Ability as well) that he was once impressed by some mathematical discovery, and then realized that he himself was the one who had published the article some time before.

We need to pay more attention to the ways that kids learn and behave in groups; this might not apply so much to homeschooling (and might be a reason we're homeschooling), but it's still important to understand. Actually most of us know it instinctively already: when you were in school, didn't you have a pretty good idea who the "smart ones" and the "dumb ones" were? And if you thought you were one of the "dumb ones," the odds are that you started to limit your own ability to learn because you thought you couldn't.

And in our most of us also's socially acceptable to laugh, wince and say "I just never could do math."

So we need to change that.

We need to find ways to increase students' confidence in themselves--no matter what their background, no matter how they've been labelled. [UPDATE: sorry if that sounded a bit too much like the I'm-so-special-boost-my-self-esteem thing. I'm talking only about helping students understand that they do genuinely have the ability to learn.] We need to avoid making the faulty assumption that certain parts of the population are born with less ability to learn than others. (Charlotte Mason's methods were used with children of all classes and backgrounds, blowing the Victorian idea of only-wealthy-children-can-learn to pieces.)

We need, according to Dr. Mighton, to have more confidence in teachers' reports of success with these methods. He talked specifically about the fact that his JUMP Math program has been accepted more in Western Canada than in Ontario, in spite of the fact that classroom teachers who have tried it have been more than satisfied with the results they've seen. Bureaucracy rules and change is slow.

We need to use "guided discovery" methods, especially in cases where manipulatives did not work well; where it would really make more sense to just teach what needs to be taught rather than expecting students to keep reinventing the wheel. We need to teach subjects such as mathematics in short, progressive steps, always "raising the bar" (a favourite Mighton phrase) just a little--or even just making the next step seem a little harder; never rushing ahead or adding in a lot of extra clutter. Dr. Mighton talked about one special-needs student who understood 1/4 + 1/4, and then 1/7 + 1/7, and then 1/36 + 1/36 and so on; but got agitated when asked to add 1/4 + 1/4 + 1/4. However, after being given more opportunities to add things like 1/400 + 1/400 and 1/855 + 1/855 (my examples), he suddenly asked to go back and try 1/4 + 1/4 + 1/4 again; and this time he was successful.
"Here we may, I think, trace the solitary source of weakness in a surpassingly excellent manual. It is quite true that the fundamental truths of the science of number all rest on the evidence of sense but, having used eyes and fingers upon ten balls or twenty balls, upon ten nuts, or leaves, or sheep, or what not, the child has formed the association of a given number with objects, and is able to conceive of the association of various other numbers with objects. In fact, he begins to think in numbers and not in objects, that is, he begins mathematics. Therefore I incline to think that an elaborate system of staves, cubes, etc., instead of tens, hundreds, thousands, errs by embarrassing the child's mind with too much teaching, and by making the illustration occupy a more prominent place than the thing illustrated."--Charlotte Mason, Home Education
Is this just a return to rote learning? No. Even Charlotte Mason had her students practice times tables, and insisted that learning in subjects such as mathematics and grammar must be continuous--that each bit must build on the next. As Charlotte Mason said--look at the evidence. I have personally seen our 10-year-old's success with Mighton's JUMP Math fractions unit this fall, at a time when she particularly needed to rebuild confidence in her math ability.

If kids stumble through school not being able to read, to spell, to do basic math--then is it their fault for being stupid, or our fault for not teaching them properly, or for making them think they are incapable? (I don't think Dr. Mighton blames classroom teachers but rather the system in general.) If we have astonishing success with children who were thought unable to learn--how did that happen? (Some educators could learn a lot from homeschoolers.) If we discover, or rediscover, some method that works well for a wide range of students--can we put down our prejudices and simply use what works? Don't we want all children to be good readers and writers, to go beyond the minimum, to enjoy all learning including mathematics? Shouldn't we be doing whatever it takes to reach those goals?

You can decide.


Anonymous said...

Thanks for posting that information, and for the related article links as well. I found them quite helpful to read up on. My 11 year old is really enjoying the fractions unit.

Anonymous said...

My daughter is loving the fractions unit as well. She is actually quite good at math, but was struggling with some of the fractions concepts. She is very happy. I would recommend that unit to anyone, and am looking into the moving to the JUMP math for Jocelyn for the rest of her program. Thanks for sharing.

Anonymous said...

Thank you for taking the time to post this information. I would have liked to attend the event but couldn't swing it!

walking said...


My eighteen daughter has autism. We were told that, if we did not make huge strides by age six, all was lost! Wrong! When she was fifteen and verbal with very confused jumbled up syntax, we found the right speech therapy program (which was very CM like). In the past three years, she has made huge leaps in language. Just before her eighteenth birthday I found out about a program for social connectedness (also very CM like) and now she is also making wonderful strides in that arena, too!

The neural plasticity scare is a lot of hoo-ey!

Anonymous said...

Interesting information!
I've printed up The Expert Mind to read later.

JacciM said...

Interesting stuff there, Mama Squirrel. Have you ever read the Bluedorn's take on abstract mathematics?? Just wondering. Math is the one area in which I don't use Miss Mason methods. I think I could read article after article on teaching math to children and come up with over a dozen different "bests". It's maddening ;)

I do agree, though, that those who try to squash all children of a certain age into a neat little "stage" where they can do this but can't do this are often selling children short. One of the popular theories out there says that children *might* be able to start working through mathematical problems mentally (without concrete manipulatives) at around age 7 or 8. Never mind my 5 year old does mental addition, subtraction, multiplication, and division in everyday scenarios. I tell her I have 12 jellybeans and each of the children needs the same amount. How many should they have? She thinks for a second or two and tells me like it's no big deal. Glad no one told her she wasn't old enough yet ;)

Thanks for more math info to mull over :)

Anonymous said...

JUMP Math is doing more workshops:
April 12, May 17th, June 7th in Toronto. They are in the evening and conducted by John Mighton. Just go to and you will see it on the "What's New" home page. Just in case you are interested. The programme is recommended for home schoolers and anyone who is interested, you don't have to be proficient at math at all.

Anonymous said...

How can I find information on the JUMP program for homeschool, individual use? I live in the United States, and the Jump website doesn't really explain how to purchase the program privately. I'm very interested in this method for my 8 year old daughter who has learning disabilities.