One of the things that has frustrated us with our 10 year old’s current school is that he has no text books. This makes it hard for us to look up how he’s learning things. It’s especially frustrating in math as they now learn different methods we did.
Recently, I was struggling to show him how to divide. (Well, I wasn’t struggling to show him how to divide but my way seemed to be completely foreign to him, as if he’d never learned it before. So I was struggling to build on what he already knew.)
So I asked his teacher how he had taught the class to divide, and he sent me back this work sheet with the “4 methods he had taught them”.
Nevermind that those are 3 methods and one explanation on how to write problems – I will admit that at times I’m a bit too pedantic about saying exactly what you mean. (But really, it’s math, you have to say 3 when you mean 3!)
While it seems like a good way to understand what division is all about, it seems to be lacking in ways to easily come up with the exact answer. But it does work to teach them how multiplication and division are related.
I also really liked that it was immediately followed up with word problems, i.e. “Mike has 32 cookies. He wants to share them equally with his 6 friends. How many cookies does each friend get?”
I hope there’s a next step where they learn how to divide the “good old-fashioned way”. 
Whether or not they do, I’ve already taught my 10 year old that way, although I had to teach him decimals as well. (I’m sure that when I first learned to divide, they very conveniently left out all problems with remainders and then added them in later.)
Which way do you think is the best way to teach kids about division?
Hi Stormy,
My teacher taught long division (the old fashioned way). I struggled with long division, but was advised by my mother to get close by guessing multiplication and then figure out the remainder. The teachers disliked this approach, though, because I would only use scratch paper to calculate the remainder, and thus didn’t show most of my work.
I didn’t care. Long division took forever, and mental math is fun and easy.
*Four different methods?* Wonderful! When I was ten, only two kids in the class owned calculators, but all of us knew that being able to divide 146547 by 465 was NOT going to be a skill we needed in life.
I try to sit in on my 9 year-old’s maths class once a week to keep in touch with what she is learning. It strikes me that perhaps fewer students will be able to *do* long division but more stand a chance of being able to *invent* long division.
Digital electronics has afforded us the luxury of being able to think more strategically, and less tactically, about maths. Four methods of division provides those points of view that Alan Kay assures us is worth 100 IQ points.
The one downside to this “new approach” (other than the undeniable risk of leaving some students utterly bamboozled -when they could have been only somewhat bamcoozled by more time on one method) -is that it eschews pen and paper. The rationale is that pen and paper is a crutch -and forcing students into estimation and “strategies” makes them think and learn more. Fair enough -but I love the way that you can make a MACHINE out of your brain and paper. What is a Turing machine with no tape after all….
hello
Pete
sent from my windows computer -hey, at least its not an iPhone
I agree with Pete. There is absolutely no point trying to teach calculations to kids. What they need to learn is to apply math, using tools/computers, to real-world problems. So they become real engineers if needed.
A separate math class should exist for probabilities/statistics so people learn to do their finances — which is something that people do use in their every day life.
I wrote a blog post about education a few days ago, but the only reason I link this here is about the 3 TEDTalks videos I embed there. They’re much more on-topic for the questions you are facing rather than my article.
All the comments thus far strike me as “How do we feel about division (or math in general)?” rather than “Is my child being taught correct math concepts and principles for applying those concepts?”
I was appalled by the “strategies for division.” If you learn the concepts then the “mental math” is easy by definition (ref. Ryan S.)
I disagree utterly with the notion that there is no point teaching children to perform “calculations” — the ability to perform “calculations” are at the core of analytical thought. Tools/computers have nothing to do with analytical thought; they are merely tools.
And what’s that about probability & statistics in my daily finances? Am I going to determine the probability of a correct checkbook balance INSTEAD OF BALANCING MY CHECKBOOK? WTF?
I admit I was non plussed when our children seemed to be doing such basic maths in unfathomable ways that I could not help them with. Division was the hardest by far and I could only attempt to explain with long division and got quite ‘stressy’
However on reflection I realised I actually applied the more heuristic methods myself in daily problems (like how much of each ingredient do I need if I have 1/3 the number of eggs called for in the recipe).
So yes I now think these methods have a value, but long division does as well. These methods are good for early stage learning, and I suspect fit the concept of multiple intelligences (eg the picture or learning line methods).
So to answer your question – lets teach as many useful tools as we can do without over doing it.
1) I disagree with an above commenter. Just because we don’t use a skill in life doesn’t mean it should be removed from school curriculum. The most valuable thing children glean from their schooling is not information… information will largely be forgotten. What they take away – in theory – is the ability to learn and teach themselves for the rest of their lives.
2) I feel that it would be detrimental to skip over the “basics” of doing math by hand, replacing that instead with the skill to aptly use a calculator to achieve the desired results. I’m a PC tech and while I may never use the skill of knowing how a CPU interfaces with the North and South bridge (and how those in turn interface with other devices), having basic knowledge like that helps me understand more fully the big picture.
TLDR; Knowing the basics helps exponentially in understanding and applying the complex.