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Ugh I remember my parents quizzing me this shit when I was in grade school.
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Are you smarter than a 4th grader?
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Ugh I remember my parents quizzing me this shit when I was in grade school.
iannis
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At a guess, calculators.
The trouble is in trying to teach logic to gradeschoolers is that they're not logical yet. You -have- to teach them by rote. Once they master the rote they can approach the logic. The rote memorization isn't just a helpful lifelong tool (I still use those fucking Xtables daily), it prepares the mind for logic.
But I can see the argument for why you'd want to go straight to the logic when every child in your classroom has a phone that can tell them immediately what 7x7 is. It's not a particualrly good argument, but I can see how and why someone would make it.
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Let's not kid ourselves. Most people are math idiots now. I run into people in a professional setting in data-driven careers who clearly failed to absorb critical core concepts of numeracy.
I'm fine with this. Rote memorization isn't very useful.
I'd argue the opposite, personally. I've never been able to do anything well until I understood the principles.
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iannis
Musty Nester
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I guess it depends on the individual. It helps me to see that something works before trying to learn exactly why.
There are different types of brains.
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I'm a fan of project-based learning as opposed to one-size-fits-all classrooms for this reason. If you motivate the participants towards a goal and give them tools to self-direct they can experiment and figure out what feels the best for them.
Now if only we could figure out how to manage that in primary schools...
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Definitely helped me to memorize that shit. School back in the late 70s and 80s was all about memorization. And math IMO is key to memorize shit like rules, formulas, and yes the times tables. ITs the basic fundamentals of all math. If you know the formula for xxx, its as easy as plugging in the numbers and solving.
YMMV, I guess. This approach led me to memorize a lot of shit, be able to superficially execute in a battery of intermediate applications, and stop pursuing upper level coursework in college because the conceptual complexity exceeded my ability to memorize and I didn't have an intuitive understanding of what was going on. 20 years later not pursuing advanced math is one of my larger regrets. (I work in simulation and optimization modeling.)
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Your intuitive understanding comes with repetition of doing shit thousands of times in math. At least for me it was not getting it, not getting it, then finally an oh snap moment happened and there it was, completer understanding of that particular exercise.
There is a method in the madness of having you do countless repetitive tasks over and over in mathematics. One is memorization, and second is understanding.
There is a method in the madness of having you do countless repetitive tasks over and over in mathematics. One is memorization, and second is understanding.
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Gurgeh
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If you want your kid to succeed in maths, you have to get them to learn the damn table asap, unless your kid is top 1%, which is probably godamn hard to know at that age, and then making fucking sure they don't use a calculator when doing math until they've finished high school.
The way we're teaching maths in the west is just bad for a vast majority of students.
You're right, but probably not in the way you meant it. In France, a vast majority (I'll need to find the source to have the exact number) of the grade 1-5 teachers don't have a scientific degree, I would guess it's the same in the USA. So end up with a majority of pupils that didn't have a single teacher with a scientific degree during their first 5 years of school. And we're talking a large part of them (teachers) are reaaaaaaaally insanely bad at maths, so all they're able to teach is to press keys on a calculator.
It's devastating. I've seen 21 y/o engineering students write stuff like (1+x)/x = 1 (or 2...) and they aren't shocked by it, because they are extremely bad at mental calculations. It's something that absolutely would never have happened 20 years ago with top 10% students.
There is a minimum of capability you need in both mental calculations and paper & pen calculation if you want to do even half serious maths.
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Siddar
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I agree totally memorization is the key for most students and their ability to memorize things only diminishes with age.
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iannis
Musty Nester
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Maybe they're just comfortable dividing by zero, you shitlord.
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For me it works better in the other order. While it's true that repetition eventually leads to some level of understanding, in the context of academics where students are constantly min/maxing their time investments it's not obviously the case that conceptual fluency is completely achieved by the time repetition allows them to get a good test score and they put the subject aside.
In retrospect that's how it worked for me, anyway, and I went to top-five undergrad and grad programs.
Gurgeh
Silver Baronet of the Realm
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Yeah, they're definitely fine with it. It certainly doesn't bother them to get a "divide by zero" error on a program.
Gurgeh
Silver Baronet of the Realm
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"The value of a teacher is determined by the student who couldn't do without help". I'm not sure who I'm quoting, but it's certainly wise. A top 1% student will figure the best way for him to do things, and teachers are just an annoyance to him. Now for the vast majority of students, it doesn't work. They need to practice a lot in order to understand abstract stuff.
A good example I have, is geometry. In France they've removed most of the geometry to replace it by probabilities and statistics (in high school), which on the paper makes sense. Except that studends haven't practiced much trigonometry, scalar products, geometric transformation. And then when you have engineering school students, you realise they don't understand stuff like Fourier's series or dimension reduction in statistics. Yeah, they didn't spend those hours drawing geometric transformation, or learning trigonometry. It's repetitive and boring, but it's godamn necessary for a vast majority of people to understand more abstract stuff.
zombiewizardhawk
Potato del Grande
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So, like we've all been saying for a while, modern education has turned into a joke?
iannis
Musty Nester
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Yeah, the correct answer is kind of important. Assuming of course that you want to be correct!
But as page1 shows, there are actually multiple ways to get the correct answer to those two questions. We're all utilizing the same idea in slightly different ways.
It did not even occur to me to factor the shit. But that's just less shitty fractions. It's actually a more clever approach than my first impulse.
But as page1 shows, there are actually multiple ways to get the correct answer to those two questions. We're all utilizing the same idea in slightly different ways.
It did not even occur to me to factor the shit. But that's just less shitty fractions. It's actually a more clever approach than my first impulse.
I'd argue the problem is that most people come out on the far side of repetitive, boring work being able to grind out rote computations for structured problems but not grasping the abstract principles enough to pull off improvisational real-world applications and understand what conclusions you can actually draw from the results. In my experience this includes engineers, researchers, coders, economists, and analysts of various flavors. The level of sloppy thinking around numbers is so staggering that you have to think we're doing it wrong at the educational level.
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Hoss
Make America's Team Great Again
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They never tried to make me memorize tables, and it's a good thing because it wouldn't have worked. Never could memorize formulas in college either, but I made the top grade because I remembered the simple formulas and could derive everything else I needed. One teacher in particular would always draw a line on my tests and say things like "You could have started here and done less than half the work".
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I was expecting that test to have one of those BS equations where the answer changes depending on whether you do multiplication or division first. This math is strange, but curious to see how it turns out in the long run.
If it's still a smattering of > 50% fail a standardized math test at graduation, back to the drawing board?
If it's still a smattering of > 50% fail a standardized math test at graduation, back to the drawing board?