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Comment by SoftTalker | Hacker News Reader

Subject categories such as "math" are also very broad. I struggled with math in elementary school, because it was mostly about memorization. 3 + 5 = 8. 6 x 7 = 42. Learning and being able to spit out those facts as quickly and flawlessly as possible was most of what I remember about math as a young kid. I was never good at that. I still am not good at that. I got Cs and sometimes lower grades in math.

Somehow, though, I passed a test in 7th grade to qualify to take algebra in 8th grade. Suddenly stuff started making sense, and I could see a point to it. You could actually solve an interesting problem. It wasn't just regurgitation of facts. It became more about thinking and connecting concepts and even being creative. I started getting As in math, and continue to do well in High School with geometry, trig, and calculus, but up until algebra was introduced I would certainly not have demonstrated a gifted ability in "math".

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You struggled with math in elementary school because of deeply flawed teaching. Even at that early age, it's not hard to understand that "3 + 5 = 8" is not something that you'd need to literally memorize. Of course, the fact that teaching quality can vary to such an extent is itself noteworthy.

I don't think I agree. 3 + 5 = 8 isn't something you need to literally memorize, but if you don't memorize such facts of basic arithmetic you're at a disadvantage when it comes to doing homework and tests. It's easier and less error-prone to memorize 8*7 than it is to work it out manually every time you see it until it sticks.

For what it's worth, I struggled with math in elementary school and especially high school -- I failed algebra I, then passed it with a D; then I failed algebra II before passing it* with a D. It wasn't until I was forced to take a business calculus class in my 20s that it started clicking, and I assure you the quality of instruction wasn't any better at the college level than it was in high school. (I did eventually graduate with honors with a math degree.)

Agreed. It does need memorization. Anyone who don't think so can try to add and multiply in hexadecimal, what is 0xA + 0xC and what is 0x8 * 0x6? It becomes quite obvious memorization is required when you try it in any other radix other than decimal(which is memorized already).

It might be quite obvious that memorization is convenient, but 'required' means "you can't do it any other way" and that's obviously incorrect.

IDK why we'd assume that there's a different cognitive process for learning mathematics with radix 10 than with radix 16?

Mathematics_education#Methods https://en.wikipedia.org/wiki/Mathematics_education#Methods :

> [...] Rote learning: the teaching of mathematical results, definitions and concepts by repetition and memorisation typically without meaning or supported by mathematical reasoning. A derisory term is drill and kill. In traditional education, rote learning is used to teach multiplication tables, definitions, formulas, and other aspects of mathematics.

I think they mean that it is very useful to “cache” these primitive results, but it is absolutely possible to regenerate them if one is missing or the like.

It should be understood first, and memorized later.

If you do not memorize small things that you frequently need, it will slow you down.

But if keep memorizing things without understanding, at some moment your memory will return an incorrect result, and you will be unable to notice it.

I don't plan to ever need to do math in hexadecimal without a calculator. Far as decimals go, I actually did get away with solving the multiplication problems on the fly...so no, memorization isn't necessary.

I've helped some students that are struggling in secondary math.

They tend to have a surprisingly good handle on the specific topic being studied that they're failing. I can have them tell me what to do on a problem on the whiteboard, and do all the arithmetic and simpler things for them, and they're flawless.

They also tend to have problems in arithmetic and in getting confused on simpler concepts. Context switching is expensive and they lose working memory of the higher order task, and then make silly mistakes.

Most outside tutors work to try and solidify the higher level topic even further, by drilling the heck out of it... this conceals the problem for it to reappear on next unit. (And, it ossifies the new knowledge in a way that compounds the problem for next year).

I don't like the whole "layer cake" model of teaching math that "builds" upon other math in the way we do in the US. But to some extent, it is justified in places. If you struggle with basic arithmetic and integers, algebra is much, much harder.

> it's not hard to understand that "3 + 5 = 8" is not something that you'd need to literally memorize

‘Literally memorize’ as opposed to what? Counting your fingers?

Precisely.

Our entire society is organised so that even university graduates are very rarely called upon to sum two single-digit numbers.

Adding up purchases in a shop? The till does it automatically. Admittedly, the cashier will need to be able to make up change promptly - but a customer needn't check their change.

Paying for parking? There will be a sign listing how much money you need to put in for 1 hour, 2 hours, 3 hours and so on.

Picking 14 items in a warehouse? You only need to count one at a time. There's a chance to speed things up by picking 2 packs of 6 plus 2 singles? Then the computer will print that on the pick list. No computer? Then the boss will print a sign with a lookup table like "14 items -> 2 six packs + 2 singles" and tape it to the shelf.

Trying to figure out whether you can get 9 people to lunch in two cars, one of which is kinda small? Add it up on your fingers, or keep your mouth shut and one of the other 8 people will figure it out.

Just don't get into board gaming :)

> Paying for parking? There will be a sign listing how much money you need to put in for 1 hour, 2 hours, 3 hours and so on.

Then if the maximum parking time is 3 hours, it's 10:15 and you want to know at what time you need to leave you take out a cardboard clock, set the current time, and advanced the small hand one, two, three steps. And to know whether you can afford both the parking and a coffee with the money you have on you you make two piles and keep the parking money in one pocket and the coffee money in another pocket. I got it. [I'm joking, our society is organised in such a way that you don't need to be able to read a clock or handle money.]

Sigh, just happened to me. Booked a room at 1:45 for 3 hours, and was told to leave at 4. The staff insisted so hard that it was like we are the troublesome customer who try to milk out something.

A jaw-dropping moment. Maybe school education is more important than we though.

>Booked a room at 1:45 for 3 hours, and was told to leave at 4.

If you are renting a hotel room by the hour, it is highly likely that the staff are poorly educated

>Maybe school education is more important than we though.

The arguments against schools are generally made[1] by people who do not remember how it was before compulsory education.

[1]At least in Europe.

> Then if the maximum parking time is 3 hours, it's 10:15 and you want to know at what time you need to leave you take out a cardboard clock, set the current time, and advanced the small hand one, two, three steps.

Not at all - you simply count hours using your fingers.

Come on, use the right tool for the job!

Mentally count 5 6 7 8, sure. Why not?

Well, it would be 3, 4, 5 ,6, 7, 8 unless you have memorized the commutative property ;-)

After going around the horn a few times, I expect the student would eventually learn to take the canal :-)

Heck, why even memorize the names of the quantities...

Number line.

You need some amount of this sort of practice to build numeracy. It's great to represent things in more accessible forms but at the end of the day it's useful for citizens to instantly recognize 3+5=8.

Similarly, I got Cs in math in middle school and early highschool. Once I got to calculus something clicked. Now I have a degree in physics and am pursuing a graduate degree in applied mathematics. The math I do now is nothing like the math I was bad at in middle school.

Puberty cannot be understated in terms of its effects...

Probably both ways. Some kids backslide with academics at that age, others seem to gain traction. I didn't mention it but have considered that part of the reason that things became easier for me in the 8th grade is that I was starting to get the mental maturity to think more abstractly and deliberately.

I have a similar story, and puberty was definitely an issue. I didn't get good at math until I was old enough to buy alcohol.

This could be read as "once I needed to figure out how much alcohol per hour I was earning, I learned math".

Which means we just need to make kids play Factorio or Eve Online to instill the desire to be good at arithmetic. Granted, Eve Online would instill other behaviors that might not be so desirable...

I think we do a disservice to mathematics to call calculus "mathematics". Similarly learning alphabet and to write is not called "literature".

We could consider doing the labeling in the other direction where we keep calling calculus, real analysis, algebra, etc. mathematics but treat arithmetic more like we do learning the alphabet (a necessary stepping stone but certainly not the end goal). We could also more typically refer to arithmetic as arithmetic and not math(s), then.

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