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Comment by Someone | Hacker News Reader

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This example is overly conservative, but the approach is sound.

Yes, one should expect students to know that you can fit eight five times into 43, but things start being different fast when doing trickier divisions. For example take 903/13. I don't have to think to know 6 times 13 equals 78 and 7 times 13 equals 91, but the average student? Forget it.

I would be happy to see the average student take out a 5 first (903 = 50 * 13 + 253), then another one (903 = 50 * 13 + 10 * 13 + 123). From there, I would have to think a bit to realize that one can take out a 9 (123 is very close to 113). The typical student? Forget it.

And that gets increasingly difficult when the divisor gets larger. What's the first digit of 9230/131?

So, yes, this strategy isn't optimal from a # of operations viewpoint, but for many students, it probably is the best way to get an answer. What would you prefer, a student who doesn't get the answer, or one that gets the right answer in a suboptimal way?

For me, the main question is what the teacher taught: did (s)he only tell students about this slowest, sure-fire way, or did she teach them the 'right' way and told them "if you aren't sure what digit to take next, pick one that you are sure about"?

For the reasons you said, I don't think that this is a general algorithm they are teaching. May be it is a stepping stone to get to understanding of what division means first and then they'll teach them long division. Clearly this is an inefficient method for larger numbers, so I don't see how this can be expected to be useful as a go-to algorithm for calculating division.

I doubt she has been taught to repeatedly take off 10x8s.

I find it more likely she been taught that it doesn't matter what she takes off: as long as she gets to the end without error, her answer will be correct.

I imagine that she has reasoned that taking off 50x8 is difficult because she doesn't yet have instant access to 5x8 (which would be rare for her age group) but she can confidently subtract 8s without error (also rare). Perhaps she reasoned this earlier and has been consistently using an inefficient version of the method when she doesn't need to. In that case, she will likely be able to fix this herself when she realises.

[Edited to add: I interpolate this because I am a schoolteacher who teaches math. It's a big part of my job to recognise what support a student needs: here, most likely she needs 8-times-table support.

The method that I describe is well-enough established in the school system that university entrants use it. Of course, it's possible that her teacher has taught her an inefficient method, but that would be unusual. There are bad math teachers in elementary school, but that's not a typical teaching error.]

That's a bit of interpolation there. I will admit that we are given very little to work on, just a piece of paper with the algo partially done on it by a child... I'm assuming you think that because of the "10x8" on the side and it could be easily "20x8". It looks like they are teaching it by places, and the 10x_ represents the order of magnitude that is currently being operated, and she was to see how many "8"'s in that magnitude are in the number. That was my assumption, at least.

On the contrary: for larger numbers, it is an efficient method, in the sense that one can expect students to do it.

For example, what's the first digit of 1019794644/1457? I would spend a few seconds before taking a guess at 7, compute 71457 to get 10199, conclude "oh, it must be 6", compute 61457, subtract it, etc.

And I can make a good educated guess to get that initial 7 because I know 14 = 1/7 (in the same sense that 27 = 1/37 and 91 = 1/11. It helps to know some factorisations of integers close to 10^n). You can't expect all students to do that, and you don't have to. It turns out that, if they just guess a low end 5, they do better than me, because they only have to compute 51457 (for an expert, a bit easier than either 6 or 7, but for them, likely equally difficult), and, from there, already will have simplified the problem. Their next multiplication will be 11457. After 'my' 71457, I still have to do a more difficult 61457.

Also, looking at it objectively, it turns out that I do the exact same thing as that student that "isn't that good at long division". The only difference it that that student is honest and that I lie, by writing the answer in a way that suggests that that '6' came to me by some divine intervention, and not by correcting an initially incorrect guess.

"or did she teach them the 'right' way and told them" ... there is ONLY the right way to do it. If the kids do it "the wrong way" they don't get credit.

I find this indicative of poor teaching in general, not what standards they are trying to teach. Common core doesn't hurt or help with this issue. Being rigid with methods and not aiming for understanding is the problem.

That is definition of a bad math teacher.

Hansard, record of the UK Parliament's House of Commons, 6 January 2014 http://www.publications.parliament.uk/pa/cm201314/cmhansrd/c...

Question: "Given that the new primary maths curriculum no longer includes the chunking method in division calculations ... assessments in maths will give credit for a pupil’s working?

Answer: "...chunking will not be rewarded in method marks — long division will."

*"Chunking" here refers to the method of the parent article. Chunking has been removed from the curriculum and only the traditional method will receive credit. That's the definition of bad math teaching, from the UK government.

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