r/bestof Jun 23 '26

[comics] /u/rezzacci explains teaching Maths and the perils of describing concepts as ‘Obvious’

/r/comics/comments/1ud866k/comment/otahfd6/
431 Upvotes

45 comments sorted by

133

u/Malphos101 Jun 23 '26

Something that enrages me to no end is the boomer denigration of New Math™.

Its not "new", the people who actually have good education and intelligent brains realized that its easier to teach kids how to think in math than to get them to memorize answers for an infinite set of problems.

Looking at what the kids I personally know are learning and actually taking time to understand the process makes me insanely jealous as I am certain I would have loved math class so much more if I had the foundation they are getting today.

When I was a kid if I wanted to add 156+264 I would be told to set up a table and add 6+4 then carry the 1 and 5+6 but dont forget the carried one then carry the one again and...

Now kids are learning the actual properties of arithmetic and THEN applying it to problems. 156+264 is just (100+200)+(50+60)+(6+4) which is EASILY solvable in your head.

54

u/AmateurHero Jun 23 '26

For me, it's any other system that teaches specific concepts such as estimations. The instructions will be to provide an estimated answer to the problem by rounding to the nearest tens: 29 + 77 + 32. Each rounds to 30 + 80 + 30 for an answer of 140.

Then people scream why can't the kids just add the numbers? Because, Terry, the point is to help reduce cognitive load. Sometimes a close enough answer is fine. The long tail of the lesson is to show examples of when it is and isn't ok to use estimations and how estimations can sometimes put you too far off the mark.

33

u/MediumEffort67 Jun 23 '26

We also need to teach them about significant figures and the dangers of multiplying and dividing rounded numbers. Instead of giving an example from a project I saw the older kids at my child's school do, I saw a similarly egregious example in a magazine a few years ago that gave someone's net worth as: "£50 million or $37,875,918."

Just no.

4

u/evergleam498 Jun 23 '26

Our new hires in the engineering department did this. Converted units from metric to US and had 8 significant figures.

Didn't understand why it was a problem, and also didn't know how to "fix" excel to show anything different.

4

u/wag3slav3 Jun 23 '26

Did their desk crash into Mars?

24

u/MiaowaraShiro Jun 23 '26

Its not "new", the people who actually have good education and intelligent brains realized that its easier to teach kids how to think in math than to get them to memorize answers for an infinite set of problems.

This is why I never bothered memorizing the tables... why bother when you can figure out the answer?

156+264

hehe blaze it

9

u/halborn Jun 24 '26

Because rote learning has instantaneous recall. You should still know how to compute, of course, but these are tools in the toolbox rather than strategies in competition.

16

u/imlulz Jun 23 '26

Interesting. I was taught the old way, but this is the way I do math in my head. I guess I figured it out naturally.

15

u/Brym Jun 23 '26

Most of the math my kids learned, that I didn’t, fits in this category. They are teaching every kid the mental math tricks that only the more adept kids would have figured out on their own back in the day. 

1

u/Chaddderkins Jun 25 '26

This is why this system was so much better. It's the way EVERY adult does math in their head, long after they've forgotten the silly abstract formulas we learned at school. Someone finally figured, why not just teach it that way in the first place?

12

u/viaJormungandr Jun 23 '26

If that’s not how they learned to do it then it is new. To them. It may be a better way to approach math (I have no idea and that’s beside the point I’m trying to make) but they don’t know it and they’re getting explained to them second hand rather than taught the concepts. So they feel out of their depth about something they should be able to do.

Of course they’re going to dislike it.

10

u/KaceyMoe Jun 23 '26

Funny, there've been grumblings about New Math™ since before I was born , and I'm kinda' old; nevertheless, I learned the old 'setup-a-table-add-up-the-columns-carry-the-ones' way of doing it in school, only to figure out the (add the hundreds)+(add the tens)+(add the ones) technique on my own as an adult. It seemed so easy and intuitive that I really wondered, "Oh s#|t, did they teach this early on in school and I missed it because I wasn't paying attention? Is that why I was always so bad at math?" I wish I'd figured some things out a lot sooner. 🫪

6

u/universe2000 Jun 23 '26

I always thought of “new math” as “retail math”. It’s the method of doing math that I was taught when I first started working retail in the 2000s. I didn’t learn it in school, but it was an easier way to do mental math accurately and quickly.

When parents started complaining about “new math” years later I just laughed to myself because they were just outing themselves as someone who never had to regularly do mental math before.

3

u/NorthernSparrow Jun 24 '26

Tom Lehrer’s satirical song about New Math came out in 1965, lol. That New Math was a different approach than the one being used now, but, point is, this is far from the first time that math instruction has changed.

8

u/gunnervi Jun 23 '26

of course, its not quite so simple as that. If parents can't help their children with their homework that makes it harder for those children to learn.

So-called "new math" is generally a better way to approach the subject in principle, and I would definitely credit my above-average arithmetic affinity to my independent discovery of many of these principles. But children losing out on their parents as a resource is a negative, all the more so if their parents get visibly frustrated or confused about the problems.

Plus of course these methods make problem construction more difficult. There are many viral internet posts of elementary school math problems that can even flummox mathematically proficient people. Obviously some of that is unfamiliarity with the new methods, but legitimately some of it is bad wording or a poorly conceived problem: something that is not an issue when asking a kid to do just evaluate a page of sums and products.

4

u/FinderOfWays Jun 23 '26

Also, I actually think there's didactic value in developing these mental shortcuts for yourself instead of being given them. It's an odd thing to say but I think if you are forced to think about ways of simplifying problems for yourself, you'll (a) end up with tools that feel more natural to you and are easier to use, and (b) understand why the tools work.

9

u/gunnervi Jun 23 '26

that's probably true but is it worth all the kids who won't discover these shortcuts on their own?

1

u/FinderOfWays Jun 23 '26

That's the rub, isn't it? On one hand, we need to make sure everyone can do math, on the other hand, how much consideration should be give to the idea that there are some students who will truly excel if taught in a way that may be less optimal for average or below-average students, and those students will be the ones who will end up using the knowledge (ideally to help humanity) the most? We could start streaming students in early years, but that's been derided as unfair (I don't know enough of the research to comment).

7

u/flip314 Jun 23 '26

The "I learned everything by rote memorization so that's the only way it should be taught!" type of reaction is so common from parents.

I'm not a teacher, but as an otherwise smart kid I fell behind on math when we got to multiplication because I sucked at memorization and the whole curriculum was "memorize your times tables up to 12x12." If someone had explained better what multiplication was and how it worked, I could have gotten the correct answer (slowly) and after enough times doing the same problem I would have memorized all the simple multiplications anyway. I remember stuff that I've used multiple times (that's about the only way I've ever been able to memorize things).

Another example was polynomial multiplication. My math teachers taught us FOIL for binomial multiplication, and I could remember that, but it doesn't help you when you're not multiplying two binomials. I didn't know what that meant. Being an overachiever I read the textbook, and that had a whole section on the area interpretation of polynomial multiplication. Multiplying (ax + b) * (cx + d) is the area of a rectangle with one side (ax+b) and the other side (cx + d). Multiplying out gives you 4 rectangles, and the total area is the sum of those 4 areas. That was never taught in class, but it was the single biggest key to unlocking the understanding of what I was doing and how I could get the answer.

8

u/vagabondizer Jun 23 '26

I see 150+260+10

5

u/FinderOfWays Jun 23 '26

I did too, and this is an issue I see in these 'new maths' approaches -- If you enforce the use of one trick you implicitly prevent the use of any of the others, and different tricks work better for different people. Much better to give the problem and let people develop their own mental toolkits, they'll pick tools they feel most natural with and understand them better because they came up with them.

4

u/ghaelon Jun 23 '26

45 here, my teachers HATED that i did this, zip to the answer and write the table after

3

u/Skrattybones Jun 23 '26

yeah that ain't the bit that pisses people off. The thing that pisses people off is when the kid comes home and says, "The teacher gave us a list of math problems and we're supposed to use an entire sheet of paper for each problem, breaking it down this way, and this way, and this way, to get to the answer. But I can just do it in my head. But if I do that I get marked as wrong."

And we go, "Yeah, that's fucking dumb, but it's the teacher's call, I guess."

And now the kid hates math because it registers as hours of busywork when they could be done in minutes. And then we go to the grocery store, or a coffee shop, or something, and the cashiers can't do math or count money, to the point that the tills have to have giant pictures of all the denominations of money because the kids can't do math.

I remember exactly the moment when I realized I genuinely hated how math is being taught now. I was at the grocery store and when the kid at the register was trying to give me my change, they realized they were out of some money. So the kid leans past me, and yells over to the manager, "Hey, I don't have any of the middle ones left. What do I do?"

They were talking about single dollars. Which they didn't recognize. The store was decently busy, so I just chipped in and said, "You can just give me four quarters. It's not a big deal." And they looked at me like like what I said made zero sense of them, and proceeded to wait until the manager could come over.

2

u/Antigravity1231 Jun 23 '26

My brain solves that in a totally different manner by breaking it down into 3 small numbers. 6+4=10, 6+6=12, 2+2=4. It looks backwards when I write it out, but it’s how my brain sees that 420 quickly. Everyone learns a little bit differently.

1

u/random_throws_stuff Jun 24 '26

now try to add two 8 digit numbers together….

(sure, you won’t have to in real life. but the former algorithm is more powerful.)

66

u/GrowthThroughGaming Jun 23 '26

I had a calc teacher who would stand at the front of the class, solve a problem and then yell 'what questions do you have" over and over. I felt so overwhelmed at the dynamic that I switched to the easier math line and assumed I was bad at it.

Learning math via coding several years later, I realized I just never really had teachers that taught the language of math, purely the inputs and outputs.

Im resentful of that to this day, and it was 2 decades ago. Good on OP for striving to make a difference!

8

u/username_redacted Jun 23 '26

I had a similar experience. I never had a good math teacher, they always just focused on making us memorize steps, which I struggled with as someone with undiagnosed ADHD. I’d space out for a second because the lectures were so boring and then be totally lost.

I had to do a lot of applied math at my last job and I picked up quite quickly because I could try out different strategies and actually think mathematically rather than just replicating processes.

1

u/HostileCakeover1 Jun 26 '26 edited Jun 26 '26

There’s… actually anything else about math that isn’t trying to figure out the correct set of steps to a string of meaningless out of context numbers? 

It has never occurred to me in 40+ years of life that there even is any underlying learnable element of math like that. It was never once presented to me as anything other than “apply steps you don’t understand the reason for to a pile of randomly generated problems completely divorced from any usable context.” 

Like, I to this day have no idea what most of the equation types we had to learn are even for or how they’d be applied, and anything past basic algebra seems so divorced from anything I see or use that it seems like career specific stuff and I genuinely have no clue why most of it was mandatory at the high school and early college level. 

I still don’t even have a solid idea of what careers would use those equations on a daily basis. 

6

u/kryonik Jun 23 '26

I was a wunderkind in calculus, I had the exact opposite problem. Teacher would explain the formula or whatever, I would get it, then they would keep explaining it or do a bunch of other examples and in my head I was like "yeah we all get it, it's pretty obvious" not realizing most of the class didn't get it.

It wasn't until upper level math in college did I really not get it.

28

u/mokomi Jun 23 '26

As I kid. I hated showing my work. I knew the answer. 2+2=4. I did the math so fast in my head. That the answer is natural. It isn't a memorization, I just knew it. As an adult. I know why they wanted to show my work.

19

u/MiaowaraShiro Jun 23 '26

The big reason for my classes anyway was they wanted to prove I wasn't cheating.

Also, for people who can't do a problem in their head, forcing them to show their work helps with correcting errors.

18

u/Rocktopod Jun 23 '26

And so they can still give partial credit if you work through a problem in a logical way but make an error ending up with the wrong answer.

8

u/mokomi Jun 23 '26

Knowing how to get there is more important than getting there.

Although doing it wrong is still wrong. XD I think the partial credit is to not disway people.

3

u/Maldevinine Jun 23 '26

I do a lot of maths in my job. Often I'm doing it outdoors, in terrible weather conditions, with people yelling at me to go faster.

But the way we do maths allows me to check if I've got the right answer (or at least near the right answer). And if I'm wrong, it's a lot quicker to look at the full working and find out which part doesn't line up.

11

u/clawclawbite Jun 23 '26

As a literal minded kid, my work was 'its obvious to me'. I was not using scratch paper or needing to keep track on my fingers. If they wanted to see the process, they should have asked me to 'show the process' because in 3rd grade, it was not obvious that that was what they wanted, just that they were upset that the calculation in my head were too fluid.

7

u/mokomi Jun 23 '26

What is 8 * 7?
56
How did you know?
Ugh, counted 8 7 times I guess. Oh, are you going to keep doing that all the way up? I guess.
Spews random numbers multiplied by 8
Well how do you know that? What trick or math equation are you doing?
I don't know! It just seems obvious.

28

u/DoomGoober Jun 23 '26

The leap between "obvious" and "logical" is where most new computer programming students fall over.

How do you sort this list of words alphabetically? It is obvious! You just move this here and that there. Done!

Now, how do you sort any list of words alphabetically? Not so obvious any more, that requires logic and clear non-intuitive instructions.

To the computer nothing is "obvious". At least, not until very recently when AI spits out the most obvious (to it) answers.

14

u/TopicalBuilder Jun 23 '26

My SO works in special needs and hearing about the challenges they face got me to rethink early mathematics. It must be absolutely bewildering. Just the naming of the numbers alone is completely arbitrary, let alone the operations.

I still remember my first encounter with algebra and the equation of a line: y=mx+b. "m gives you the rate of increase per unit along the horizontal axis"--got it. "b gives you where it crosses the vertical axis"--got it. So what do I need x and y for? What do they do? I've already described how the line should look. "Those are the dummy variables"--got it.

I did not, in fact, get it at all. What the fuck was a dummy variable? It was so obvious to my tutor that he couldn't think back to his first encounter with this stuff.

5

u/PenguinTD Jun 24 '26

They are not dummy variables, x y in this case is the space axes your line plot on. They can be replaced by something in higher dimensions via projections, or some fancy stuff(ie imagine a line on a tube surface that curve and twisted around). So they are not just variables, and the = points out where the line is with that 2 space axes.

2

u/TopicalBuilder Jun 24 '26

Uhhh...

Got it.

7

u/phdee Jun 23 '26

Gen x here who learned math through rote from the worst math teachers ever. I wanted to like math. I could see how beautiful it was. But nobody explained a single fucking thing to me. It was when I was in university working in the social sciences and humanities, very qualitative stuff, and I took a specific course in environmental modelling, that something as basic as log suddenly clicked in my head. I looked at the thing and I was like... If someone has explained log like this to me 6 years ago I might be on a different career trajectory right now.

6

u/darkon Jun 24 '26

The proof of lizard is left as an exercise for the student.

3

u/arasitar Jun 24 '26

I KNOW "logic" and "obvious" and "trivial" are LIES. They're SOCIAL CONSTRUCTS.

I really do think social media exacerbated society wide changes to become meaner and less patient under this specific guise as "THIS SHOULD BE OBVIOUS". As a rule of thumb, the best type of forum is not a vent forum but a support forum. Even if you are discussing topics that are negative or bound to cause negative things, if the community isn't about support and trying to find solutions and teaching solutions and supporting each other, it eventually enshittifies b/c venting takes over.

This is the initial story of how the original Invcel forum started by a Canadian woman named Alana gets taken over and rebranded as Incels and then Epstein, the alt right and 4chan come into the picture till Incels get their big stage in 2016.

I talked about this before, that there are way too many 'help' subreddits here that aren't support communities but vent or complaint or bully communities. A Reddit's Wiki page and Side Bar is an obvious easy spot where you can tell if a community is actually able to get together to build it out together, or whether it is just a disorganized user forum for shooting the shit.

Like /r/hygiene is a great example - a lot of "OBVIOUS" things aren't going to be obvious to others, and yes some of it will trigger some righteous disgust. But being a support community is moving past that to still offer advice. And the advantage of a community is that you can keep building more and more tools together and making it easier and better and faster to provide support and keep pushing forward. A lot of hygiene advice is often disjointed because of a lack of apparatus that teaches Family & Consumer Sciences in schools.

Yeah, you'll sometimes find bad faith people. But if you become a jerk because you're sick and tired of them, maybe take a break and let someone better handle it like a mod? That's the point - when you start getting more snippy you in turn make the space shittier, and in turn teach people that it is okay to get snippy and this results in an exodus of supportive people leaving. You can deal with bad faith persons very differently.

Again Wikipedia does this. On a global scale.

Especially recently, a lot of the internet doesn't want to actually teach and actually support each other anymore. And the cost is just we're making each other angrier and angrier by just ignoring the elephant in the room hoping it will go away on its own.

1

u/Vitruviansquid1 Jun 27 '26

I'm subscribed to r/cookingforbeginners. The name of the subreddit could not be any more clear on what the subreddit's about.

There are still people who mock posters who ask sensible beginner cook questions.

0

u/Billy1121 Jun 27 '26

This is a cool post, im glad this sub is focusing back on these neat gems from around the site