I love today's word from the OED

[conuly]

https://www.oed.com/view/Entry/64193431

And since I'm posting one dictionary-related link I may as well post another:

https://www.arrantpedantry.com/2021/11/08/i-am-begging-you-to-learn-how-dictionaries-work/

Comments

[pauamma]

*wince* I hear you. (I was unable to make sense of long division until someone explained not how to do it, but why that apparently pointless sequence of piecemeal operations worked.)

[conuly]

In the US, at least, a lot of people were taught arithmetic by the "memorize the algorithm" method.

Which means they can't explain why it works, and often will get infuriated at the idea that newer curricula are making an active attempt to teach that part.

(These people also have bizarre ideas of how long it takes to teach things. "I learned long division in a week!" No, you didn't. There are 36 weeks in the school year. It took more than a week.)

[kengr]

I got lucky. In 6th grade (1966) they introduced The New Math and working with different number bases caught my attention.

Then the Asimov books I referred to in another comment got me thru algebra. and from there I could mostly handle it myself.

[pauamma]

Here too (late 1960s France, equivalent of US grade school - I think grade 3). That approach may have worked with others; I don't remember. I only know that for whatever reason, it didn't for me.

[conuly]

It "works" superficially well because kids can memorize algorithms a heck of a lot faster than they can gain a total conceptual understanding of arithmetic - right up until they can't. But when they hit the wall, they hit it hard, and they have no way of going back and fixing their bad habits.

[pauamma]

In hindsight, that may very well be. I was taught how to extract square roots using pen and paper, but if I ever learned it, it didn't stiuck even for the maybe 2 years before I started using precomputed numerical tables and a slide rule.

[kengr]

Something that most teachers never knew helps a *lot* with both multiplication and division.

What they really are is repeated addition or subtraction respectively.

So 12 time 13 is actually "what do you get when you add 13 12s together.

Likewise, 159/12 is actually "how many times can you subtract 12 from 159"

Those explanations make many things much clearer.

My standard recomendations for folks who have trouble with math are Isaac Asimov's Realm of Numbers and follow that up with Realm of Algebra.

Alas, Asimov hit calculus and bounced, so there's no equivalent that I know of for higher match than algebra. But at least those two will get you through high scholl in most places.

[pauamma]

The explanation I got (not from my teacher - it was an adult family friend) was along the lines of "It's the same steps as for multiplying numbers with more than one digit, but in reverse. Here's an example using the multiplication steps for (mumble); try reversing them."