How do/did you go about learning math?

Question

I have wanted to improve in math, so I could do computer science, and generally develop math skills. However, the process has been chunky. I can summarize it into these three issues: Understanding, Slow learning, Note taking. But i'd like to hear more about how you handled these things.

Understanding: I'm not good at figuring out problems myself, and things often go over my head. I need to get what i'm thinking about to be able to take my notes, so often i'll write something and not have a clue what it means or what i'm doing. For example, I was learning how to multiply decimals. 3.2 x 3.9. The answer was 12.48, but I kept getting 60. For weeks I didn't know what I was doing wrong. I crossed multiplied like they asked, but I kept getting 45 + 15 = 60. I asked for help online, and realized- I forgot place value. It was quite disappointing to figure out that I couldn't figure something like that out myself, but it wasn't asking about it that made me sad; It was the fact that I was trying to improve my problem solving/intuition skills by figuring out how to solve the problem, and everything went over my head, again. What would you suggest for developing intuition, or being able to figure out what you're doing wrong yourself? Did you struggle with this, and what did you do?

Slow learning: I take more time to learn something than I do to forget it. I often take weeks/months to get a snippet of a topic, and that doesn't usually work when the curriculum needs you to get it in 2 weeks for the test, so I try to cram and-fail. This has more to do with Understanding + Note taking, however, but I wanted to know if there are any slow learners here and what you do to be able to be sharp and progress in math, while still being legible for college snap-snap curriculum pace. What would you/do you do?

Note taking: Memorization is near impossible for me because my notes are horrible. I have to take them by hand, and generally there's a lot of problems with them. My teacher goes quite fast (or, more likely-i'm too slow) so my notes are often scribbly, or don't have text to explain them at all. I'll simply copy what my teacher wrote on the board, yet not getting a single part of the concept or why it works. I won't know where to place certain types of knowledge so the placement of my notes is also difficult, I might write something incoherent in a panic in some random page and not be able to retrieve it, tips and tricks are placed in irrelevant spaces, it's just generally difficult and unusable. While no one writes their notes the same way, my notes generally seem to not work for me. How do you write your notes, what would you say defines terrible notes for you, and what do/did you do to improve and prevent them?

How do you go about with learning how to learn math? What is your process, what do you believe defines a bad math learning process, and how would you improve that process? I'd like to hear what you would do. Thank you for reading, your input is welcome.

Answer 1

My guess is that this question isn't a good fit for this site. You are asking for advice and this advice can be very subjective.

That said, a few general comments and thoughts for you:

1) There is nothing wrong with memorization and I am guessing that you are no worse at this than most. Have you memorized the small multiplication table? Try memorizing some formulas for areas and such.

2) Don't worry about note taking. Yes, in school we focus on having students take notes, but it is often way over emphasized. You need to internalize what you are learning. Having a nice well organized notebook can be helpful, but it means nothing if you can't do much without it.

3) Instead of trying to memorize your way out of everything, try to understand what is really going on. Take your time. It is better to spend a lot of time on one problem/concept and then fully understand this, than memorizing some "method" that you are just going to forget again. If you are having a hard time with multiplying two two digit numbers, then focus on the one digit numbers and get those down to a point where you feel comfortable. Then work you way up this way. This is take time, but you wouldn't have to start over and over again.

4) Don't worry about being a slow learner. I am a slow learner. I have often been in situations where a problem is posed. Everyone else gets the answer quickly and I still don't get it. But when I do get something I typically get it very well. The key thing is to not be satisfied with just knowing the answer to a problem. You have to understand the methods involved.

For example: You are trying to learn how to multiply $3.2 \cdot3.9$. You might have learned to do like $3$ times $3$ plus $3$ and the $9$ and so on... Instead, maybe try the following $$\begin{align} 3.2\cdot 3.9 &= (3 + 0.2)\cdot(3 + 0.9) \\ &= 3\cdot 3 + 3\cdot 0.9 + 0.2\cdot 3 + 0.3\cdot 0.9 \\ &= \dots \end{align} $$ It is exactly the same as the rule you have learned, but it shows why you are doing it like that. You have to write a lot more, but that is ok.

Or: if you don't like the decimal, then maybe do the following $$ 3.2\cdot 3.9 = 32\cdot 39 \cdot 10^{-2} = \dots $$

Play around with the multiplication. To to rewrite the expression in various ways and you will see that you always get the same thing.

One last note: I know that many students struggle with the rigour of mathemtics. It is unforgiving. You make a simple mistake and your answer is completely wrong. Don't let this get to you. Keep trying and identify your mistakes and repeat repeat and repeat over and over again until you can do the same problem in your sleep. After you can do $3.2\cdot 3.9$, then do $3.3\cdot 3.9$, then $2.9\cdot 3.8$ and so on. Don't be afraid of repeating!