Why Do Proofs Become Crucial for Understanding Math Concepts?

[Square1]

Hi everyone.

I would like to get some advice I guess in learning strategies for math. Here is my scenario..

I find that in the math classes I've taken so far in university (currently on my second intro calc semester) my typical math learning pattern goes like this...fall behind, do not hand in assignments, study like a dog for the midterms (learn effectively hand "muscle memory" to solve problems or whatever trivial pattern I can grasp), and do class average on the test.

Then, because I AM still to a degree a righteous math student :), I do in fact typically start reviewing the following weekend the things I did not fully grasp. (Note I am restarting my falling behind cycle...) But as I relearn the stuff, I am finding more frequently that I simply can't learn the material unless I TRULY learn it from ground up - notably, that means if there are proofs associated with a concept, one way or another, I do not move forward until I feel comfortable with the proof. The pickle is I can't seem to even approach a proof until I have some greater level of familiarity with a subject ie learn the vague ideas as pressured by an upcoming test.

Now what truly makes me curious to my own situation is that math has been by far my weakest subject. I nearly flunked it in gr 11, flunked in gr.12 (If you're wondering, I got into intro calc at uni by taking a precalc class...whos prereqs weren't too heavily enforced...).

How on Earth is is that someone like myself who has been so mathematically inept throughout his life, discovers he can only truly grasp a concept by struggling through understanding a proof? I don't get it! Everyone I know who is not an honors math student does not give a single droplet of s***t about proofs, instructors tell us not to worry about them, that is, if they even go over them!

Is anyone familiar with my situation? In what ways am I a typical math student and what ways am I not? Can people suggest a learning strategy that they think will help? Thanks a lot everyone.

 

[lurflurf]

You are quite normal. It is much easier and better try and learn things in a systematic way that stresses how each thing relates to the others. The whole point of proofs is that they help us to understand and avoid misunderstanding. The trouble with this approach is it can be difficult and take a long time. You cannot expect to always under everything deeply right away. Trying to learn a jumbled mess of facts you do not understand may seem easier, but it is an unreliable and counterproductive approach.

 

[lavinia]

Hi everyone.

I would like to get some advice I guess in learning strategies for math. Here is my scenario..

I find that in the math classes I've taken so far in university (currently on my second intro calc semester) my typical math learning pattern goes like this...fall behind, do not hand in assignments, study like a dog for the midterms (learn effectively hand "muscle memory" to solve problems or whatever trivial pattern I can grasp), and do class average on the test.

Then, because I AM still to a degree a righteous math student :), I do in fact typically start reviewing the following weekend the things I did not fully grasp. (Note I am restarting my falling behind cycle...) But as I relearn the stuff, I am finding more frequently that I simply can't learn the material unless I TRULY learn it from ground up - notably, that means if there are proofs associated with a concept, one way or another, I do not move forward until I feel comfortable with the proof. The pickle is I can't seem to even approach a proof until I have some greater level of familiarity with a subject ie learn the vague ideas as pressured by an upcoming test.

Now what truly makes me curious to my own situation is that math has been by far my weakest subject. I nearly flunked it in gr 11, flunked in gr.12 (If you're wondering, I got into intro calc at uni by taking a precalc class...whos prereqs weren't too heavily enforced...).

How on Earth is is that someone like myself who has been so mathematically inept throughout his life, discovers he can only truly grasp a concept by struggling through understanding a proof? I don't get it! Everyone I know who is not an honors math student does not give a single droplet of s***t about proofs, instructors tell us not to worry about them, that is, if they even go over them!

Is anyone familiar with my situation? In what ways am I a typical math student and what ways am I not? Can people suggest a learning strategy that they think will help? Thanks a lot everyone.

you learn by thinking a lot. Struggling with proofs is one way to think but not the only way. I like to explore the meaning of theorems or structures by asking questions about them then seeing if I can answer them.

Try proving the theorem yourself first. Don't give up if you can't prove it but keep trying until you know exactly what it is that you can not figure out - usually some missing fact. Then read through the proof in the text.

 

[Square1]

Thank you both for the input. And lavinia that seems like a good, and challenging, tactic (trying to come up with proof and checking how you are off). Thanks.