Are all brains good at math?

Re:Are all brains good at math? by jrgoff on Thursday September 01, 2022 @02:33PM (#32680921)

I'm curious what value you consider understanding long division to hold? In my mind it has some value in training how to follow an algorithm and obviously has some value in being able to divide arbitrary integers (and beyond). But of course as you point out there's not much point in forcing long division when there are ubiquitous computers available to do the job better. And while I think following an algorithm carefully can be a valuable skill, if that is the primary goal then I'm not sure teaching long division is a particularly good way to go about it.

I agree with your general point that math curriculum builds on itself and if students fall behind it can make things worse and worse for future classes. But in general I think, at least when I was in school, there was probably too much focus on algorithms and not enough on conceptual understanding. I think part of the reason is that algorithms historically were necessary to know before calculators were ubiquitous, and also I think algorithms are much easier to teach and evaluate so there's probably a tendency to focus on them for that reason.

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Re:Are all brains good at math? by CivBase on Thursday September 01, 2022 @04:31PM (#32682705)

It's not necessarily the algorithm that matters. There are a few different algorithms you can follow for division and a few ways you can accurately represent the results. For example, kids these day commonly learn something called the "lattice method" for multiplication. It's a different algorithm from what I learned, but that doesn't necessarily matter.

The point is not for students to learn how to follow an algorithm (or master doing it quickly), but that they learn why the algorithm works and how to interpret the result.

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Re:Are all brains good at math? by knaik94 on Thursday September 01, 2022 @05:34PM (#32683587)

Honestly, I hadn't come across the lattice method until you mentioned it. I would strongly argue that it hinders learning because it's hard to draw an association between the numbers you are writing down and how the lattice method is set up. It is equivalent to long division after you recognize that the lattice method removes the shifting to the right as you multiply by the next digit. With the standard long multiplication method, you recognize that what you were really doing is splitting the multiplier by powers of 10 once you learn the distributive property. The lattice method is actually weirder because you don't move by increasing powers of 10, you go in the reverse direction. You still have to carry and you still add up numbers in column/power of 10 order, starting with the smallest power at the very end. If anything, the lattice method represents everything about the common core math approach that many parents and teachers dislike.

The algorithm matters and I argue that once students can naturally derive the algorithm on their own, there's no place for human calculations. Computers and calculators should be used. We're no longer living in a society where students will have to worry about "what if you don't have a calculator on you". It seems as weird as memorizing unit conversions to me.

What's interesting is that the purpose of implementing the common core standard was exactly what I am arguing for. A shift away from algorithmic memorization to a number sense way of doing math. The failure lies with the teachers not being able to teach well much more than students not learning.

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