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I disagree about the repetitive calculation being "entirely unnecessary". Background: I (probably like many here) excelled at high school and undergraduate mat

I disagree about the repetitive calculation being "entirely unnecessary". Background: I (probably like many here) excelled at high school and undergraduate mathematics. I have a graduate degree in a heavily mathematics-focused branch of engineering (digital signal processing) and much of my work involves applying that math at a conceptual level. I'm currently tutoring an adult I'm close to who is approximately at GP's starting level and has a strong anxiety reaction to math. I'm finding that the repetitive calculation aspect is important to being able to developing an intuition for the concepts. The process that's working well for us so far involves alternating between practical word problems (to establish a motivation for learning the material), theoretical/background explanations (to hit the understanding at a high level) and repeated simple problems (to practice the mechanics). I'm finding that, in terms of process, the repeated problem-solving is critical for two reasons. 1) It helps to build a sort of mental "muscle memory", and 2) it helps with developing intuition, since your mind eventually gets bored with the mechanics and starts to notice patterns. Remember that mathematics at that level is all about building blocks. Every concept/problem-solving practice you learn is part of a tower of strategies; if earlier mechanisms aren't almost mindless, it's MUCH harder to build on top of that knowledge.

zenhack 9y ago
One of the earliest memories I have of really enjoying math was a unit on modular arithmatic from my 6th grade math class. The teacher introduced the concept with a hands of a clock metaphor, gave us a whole bunch of drill problems, and told us to watch for patterns. We had an easel in the class room where he collected the insights students had gained. Discovering the relationship with remainders by ourselves was incredibly cool.
- InitialLastName 9y ago
  I had a similar experience when I learned about factoring (not sure what age). I got a little obsessed with finding prime numbers by hand, and eventually figured out that I only had to search for factors up to the square root. I distinctly remember that as the first time I realized how powerful a simple mathematical insight can be to speeding up a process. Now, of course, I use mathematical insight to speed up processes occupationally; I guess that experience stuck with me.
princeb 9y ago
> 1) It helps to build a sort of mental "muscle memory", and 2) it helps with developing intuition, since your mind eventually gets bored with the mechanics and starts to notice patterns. muscle memory is super important in math. the last thing you want is to be struggling with foundation when you're trying to progress through concepts. everything needs to be available to you at the snap of your fingers. trying to progress math knowledge without the basics is doable, but it's a ton of mental overhead and frustration that you can cut down if you just get the practice out of the way. plus it's super cool if you're one of those guys who have the ability to quickly apply 10-20 different models on a real world problem. that's what we think of when we think "good at math".

zenhack 9y ago

One of the earliest memories I have of really enjoying math was a unit on modular arithmatic from my 6th grade math class. The teacher introduced the concept with a hands of a clock metaphor, gave us a whole bunch of drill problems, and told us to watch for patterns. We had an easel in the class room where he collected the insights students had gained. Discovering the relationship with remainders by ourselves was incredibly cool.

InitialLastName 9y ago
I had a similar experience when I learned about factoring (not sure what age). I got a little obsessed with finding prime numbers by hand, and eventually figured out that I only had to search for factors up to the square root. I distinctly remember that as the first time I realized how powerful a simple mathematical insight can be to speeding up a process. Now, of course, I use mathematical insight to speed up processes occupationally; I guess that experience stuck with me.

princeb 9y ago

> 1) It helps to build a sort of mental "muscle memory", and 2) it helps with developing intuition, since your mind eventually gets bored with the mechanics and starts to notice patterns. muscle memory is super important in math. the last thing you want is to be struggling with foundation when you're trying to progress through concepts. everything needs to be available to you at the snap of your fingers. trying to progress math knowledge without the basics is doable, but it's a ton of mental overhead and frustration that you can cut down if you just get the practice out of the way. plus it's super cool if you're one of those guys who have the ability to quickly apply 10-20 different models on a real world problem. that's what we think of when we think "good at math".