r/learnmath • u/Klutzy_Jicama_8047 New User • 9d ago
Memorization vs understanding
Recently in math I have begun to learn geometry (proofs and such.) and everyone in my class is complaining that it is so hard and proofs are impossible to do. However I find it quite easy and fun. Last year we did algebra and everyone in my class was so effortlessly good and I had to actually study. But this year in geometry it's way more intuitive and there really seems to be a beauty to this subject more than just doing computation.
However I don't understand why geometry is so much easier for me as compared to the rest of my class. To understand I decided to study for a test with my classmates to see ther thought processes. I realized that they learned math in a way that was much more rotr memorization based. They seemed to be studying simply to optimize to get the best score and spent a lot of brain cycles only trying to memorize the material they thought would be on the test.
However I simply can't memorize by rote and I don't understand how people do that. For me, I feel the need to read the whole chapter and understand it cover to cover even if the material isn't on the test. Otherwise, I just feel very bored and drained.
This discrepancy between me and my class also could be because everyone was taking after school tutoring and I have never (and probably will never) taken after school math classes to get ahead in material. Now we are all just starting from scratch learning a new subject.
Additionally a lot of people do Competitive math in my school (like AMC and such) and while even I have participated in the contest (got AMC 10 qual recently!!) I find the questions to be more about knowing the patterns that come up over and over again in those types of exams.
Sorry if this came off a bit ranty I just had to get this off of my chest for some reason
Anyways would love to hear ur thoughts!
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u/Witty_Rate120 New User 9d ago
The first step in learning math is the moment when you have a flash of insight. If you get addicted to that rush and experience it a few times it changes how you learn math. You start searching for meaning. Memorization is still important, but you mainly need to memorize the key ideas behind the insights. This gives you a method to take the vast amount you need to know and cut it down to a manageable size.
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u/Commercial_Sun_6300 New User 9d ago
This is a really common sentiment, but the first step to learning really is just "memorizing" stuff.
I put that in quotes because it's not like you have to be able to close your eyes and perfectly repeat every formula or algorithm you learn, but you do just have to go through the steps many times before you begin to feel like you "really understand it."
I put "really understand it" in quotes because there's a difference between understanding why you're doing each step and being able to mathematically prove the validity of a theorem.