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Is learning math exercices by heart actually good ?

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The only possible way I think learning by heart would work is if you memorize the way and not the answer.

So if the excercise is solve 12x+5=17

Dont memorize the answer is 1, but rather memorize the steps:

Subtract the constant part and than devide by the factor.
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I was taught that memorizing the answers deprives you of learning how the process works. It might help in the short term (such as homework) but you lose out in the long run.

Addition, subtraction, multiplication, division, exponents, integrals, derivatives, etc. and all the various techniques in Math are tools. When you fully understand whats happening and why you use a particular process you have that tool in your toolbox.

Like a mechanic knowing when to pull out what kind of tool, you need to learn how each tool works and how to use it and how to make it work with other tools.

I don't think that memorization will help with this.   


Edited:  finished my thought, hit enter too soon
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For me, this wouldn't be effective and it would take a lot of the enjoyment out of doing math.
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Making sure you can walk through and explain every step of a homework problem ain't a bad idea.  If I struggle with an exercise, I try to go back to it and make sure I can do it without looking at the solution.  A step further would be getting ALL the exercises to the point where you can reproduce the solution (and, again, explain the logic) quite quickly.

It's possible that this sort of thing is what your classmate actually means by memorizing the answers.  If you're doing a lot of exercises this approach could take a ton of time, and you may see diminishing returns for the effort you put forth, but it's not an awful thing to do.  Perhaps doing that but only with the hardest problems or the ones with the weirdest solutions would be a good approach!  A step further than that is literally memorizing each step so you can reproduce them without thought.  That would be a waste of time if you can already solve the exercises quickly with some thinking it through, IMO.

Literally memorizing the *solution*, as in just the final step of an exercise, isn't the way.  If *that* is what your classmate is doing I would guess that spending extra time with the work might be helping him out, but that actually memorizing the answer isn't the key.  Or he might have a natural facility for the stuff ya'll are working on, and this extra effort is a waste of time, but he thinks it's helping.  But I'm *guessing* he's doing something more like I described above.  Maybe you know?
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I think a lot of people are thrown off by the word “memorizing” and rightly so, because just memorizing answers gets you nowhere, but if what he means is “do each problem/type of problem repeatedly until you can do them without even thinking” then that is a more viable strategy. You want to make sure you aren’t just memorizing the exact symbols you write, but certainly memorizing the order of logical steps that can solve a particular type of problem will make you a machine at taking math tests. If you pair that with really spending the time to understand where the steps come from / why they make sense the first time you solve the problem, and with some bigger picture thinking where you try to notice and generalize patterns between the different strategies you have learned, you will be an incredibly strong math student.
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Your friend is half-right.

The MOST important thing you can do to get better at math is doing a bunch of different similar problems. So you shouldn’t focus much on memorization, but you absolutely should work on problems so much that you start to recognize patterns.

It’s important to note that this process is not at all about being “smart” or “good at math”, but about a good work ethic and drive.
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I think it depends on what your learning.

There is an element of pattern learning that helps me with maths. For example when I was a kid we had to memorise our times tables up til 10x table by heart in primary 1 (age 4/5) and then up to 12x table by primary 2 (age 5/6).

I've since learned from discussions with age mates that noone else went to a school like this lol. At the time I hated this method with a passion because it was boring and rather too easy but 30+years later and I'm able to run through my times tables like I'm 5 again.

In a non arrogant way I'm often horrified at the lack of basic math skills my age mates or younger people have. It's not a boast more a confirmation that this approach really did work.

So yes I think there are appropriate times to pattern learn and use memorising methods but outside of basic maths I would be concerned that this approach would fall apart as if you have a challenge outside of your memorised parameters will you really have the critical thinking needed to solve it?
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Apparently your classmate is not good at math at all. He is just good at memorization.
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I don't know what he means by learning every exercise by heart? Memorizing the answer to every equation with different variables? Seems tedious and unproductive

Math isn't learnt by rote repeat memorization. Math is learnt by understanding and solving exercises.

You should solve exercises completely on your own and correct yourself afterwards. See where you are wrong, understand why you were wrong, never move on from a question without knowing  *why* you were wrong in the first place, I mean **never**. It is the only way you learn.
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If you have a good enough memory, that will work up to a point, but once you get into the more abstract subjects, you'll hit a wall.

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