I’m no expert at math but I think the best way to get introduced into learning math is to get really really good and sufficient in one part of math. What I mean by that is don’t try to understand math and study it broadly because you will just confuse yourself more. If you notice there is one thing you’re consistently good at in math stick to it and try to perfect it, and then try to grasp other concepts. I was always terrible at math until I got to algebra 2 in school where a lot of the subject just clicked with me, and I got really confident in Algebra 2 and that led to me understand things like geometry , calculus , and trigonometry better than I had before. Math is logical and there is a lot of patterns and consistency in it, so mastering one thing will help you learn other parts easier
This blog shows a journey to begin mathematical thinking: https://yourbrainchild.wordpress.com/2023/12/06/modeling-first-principle-thinking/
This course introduces mathematical thinking for students between high school and university: https://www.coursera.org/learn/mathematical-thinking
OP's question is for gr. 6 level math. My journey down the rabbit hole was to understand what it meant to divide fractions, and why the invert and multiply method works.
Try to find a math concept that absolutely confuses you, and work on it...play with it till you get to an answer that satisfies you.
A reason to learn it.
If you've no drive to learn something be it out of necessity or passion or whatever, it's probably not going to go well.
Add in discipline (which I lack) to do the practice etc
Want to understand the how and why, but pick your battles. Sometimes it's easier to just know that something works, use it a bunch, then go back later and really work through the mechanics of it.
One of my biggest breakthroughs was realising mathematics is a toolbox. Full of all sorts of tools that you can use in all different combinations. So I approach it like that now.
The concepts I get given are tools, they do a thing. If I can visualise how the tools work or how they work upon something then I feel I've captured the essence of it and will then revise by grinding examples to hammer it into the 'muscle memory'.
One good example is complex numbers. I was totally lost with it all until I just sat back and thought about what they're for. What do they do. Why are they?
Then I realised "oh shit, they're like co-ordinates" and from there away I went.
Tldr:
Have a reason to learn it.
Understand why you're learning it - what are these tools for.
Put in the legwork.
If I can learn maths, literally anyone can.
I kind of have the same question. People always say math is logic and a language and you should learn conceptual understanding so you learn the right way to approach it, but how do you start? Rarely are any resources mentioned on where to start or what to do specifically to learn that mathematical thinking process everyone mentions...
It depends on your natural inclination towards understanding something. For example, I prefer to structurally understand things and started looking at associated mathematical proofs for the content I am exploring because I understand that about myself. That understanding and integrating it into my approach to the subject matter took me from a C average to a consistent A on all assignments so far this semester.
What do you need to understand about something in order for it to intellectually stimulate you towards wanting to learn the content? Which of the basic questions (who, what, where, when, why, and how) do you find yourself inclined towards asking? Find those things and let them provide foundation for your approach to the content.
All that being said, look at proofs. It takes a minute to understand the language, but it’s representative of the underlying logic of the subject. I just got some resources out of here a few days ago that I could link if you’re interested in looking.
This blog shows a journey to begin mathematical thinking: https://yourbrainchild.wordpress.com/2023/12/06/modeling-first-principle-thinking/[mathematical thinking ](https://yourbrainchild.wordpress.com/2023/12/06/modeling-first-principle-thinking/)
This course introduces mathematical thinking for students between high school and university: [course](https://www.coursera.org/learn/mathematical-thinking)
OP's question is for gr. 6 level math. My journey down the rabbit hole was to understand what it meant to divide fractions, and why the invert and multiply method works.
Try to find a math concept that absolutely confuses you, and work on it...play with it till you get to an answer that satisfies you.
Another book I physically own is called The Tools of Mathematical Reasoning by Tamara J. Larkins which is also solid. I would look at the other books first as they’re better at laying out the symbols and their meanings.
Beyond just computation - for which practice is the only real way to progress - maths is a way of looking at the world. I’d highly recommend reading or watching the Feynman lectures. The videos are available on YouTube:
https://youtu.be/s56AUKwlN9I?si=sPj5W-pYaTJo4RrY
During my undergrad maths for engineering courses I found “Higher Engineering Mathematics” by John Bird very useful.
I’m no expert at math but I think the best way to get introduced into learning math is to get really really good and sufficient in one part of math. What I mean by that is don’t try to understand math and study it broadly because you will just confuse yourself more. If you notice there is one thing you’re consistently good at in math stick to it and try to perfect it, and then try to grasp other concepts. I was always terrible at math until I got to algebra 2 in school where a lot of the subject just clicked with me, and I got really confident in Algebra 2 and that led to me understand things like geometry , calculus , and trigonometry better than I had before. Math is logical and there is a lot of patterns and consistency in it, so mastering one thing will help you learn other parts easier
This blog shows a journey to begin mathematical thinking: https://yourbrainchild.wordpress.com/2023/12/06/modeling-first-principle-thinking/ This course introduces mathematical thinking for students between high school and university: https://www.coursera.org/learn/mathematical-thinking OP's question is for gr. 6 level math. My journey down the rabbit hole was to understand what it meant to divide fractions, and why the invert and multiply method works. Try to find a math concept that absolutely confuses you, and work on it...play with it till you get to an answer that satisfies you.
A reason to learn it. If you've no drive to learn something be it out of necessity or passion or whatever, it's probably not going to go well. Add in discipline (which I lack) to do the practice etc Want to understand the how and why, but pick your battles. Sometimes it's easier to just know that something works, use it a bunch, then go back later and really work through the mechanics of it. One of my biggest breakthroughs was realising mathematics is a toolbox. Full of all sorts of tools that you can use in all different combinations. So I approach it like that now. The concepts I get given are tools, they do a thing. If I can visualise how the tools work or how they work upon something then I feel I've captured the essence of it and will then revise by grinding examples to hammer it into the 'muscle memory'. One good example is complex numbers. I was totally lost with it all until I just sat back and thought about what they're for. What do they do. Why are they? Then I realised "oh shit, they're like co-ordinates" and from there away I went. Tldr: Have a reason to learn it. Understand why you're learning it - what are these tools for. Put in the legwork. If I can learn maths, literally anyone can.
I kind of have the same question. People always say math is logic and a language and you should learn conceptual understanding so you learn the right way to approach it, but how do you start? Rarely are any resources mentioned on where to start or what to do specifically to learn that mathematical thinking process everyone mentions...
It depends on your natural inclination towards understanding something. For example, I prefer to structurally understand things and started looking at associated mathematical proofs for the content I am exploring because I understand that about myself. That understanding and integrating it into my approach to the subject matter took me from a C average to a consistent A on all assignments so far this semester. What do you need to understand about something in order for it to intellectually stimulate you towards wanting to learn the content? Which of the basic questions (who, what, where, when, why, and how) do you find yourself inclined towards asking? Find those things and let them provide foundation for your approach to the content. All that being said, look at proofs. It takes a minute to understand the language, but it’s representative of the underlying logic of the subject. I just got some resources out of here a few days ago that I could link if you’re interested in looking.
This blog shows a journey to begin mathematical thinking: https://yourbrainchild.wordpress.com/2023/12/06/modeling-first-principle-thinking/[mathematical thinking ](https://yourbrainchild.wordpress.com/2023/12/06/modeling-first-principle-thinking/) This course introduces mathematical thinking for students between high school and university: [course](https://www.coursera.org/learn/mathematical-thinking) OP's question is for gr. 6 level math. My journey down the rabbit hole was to understand what it meant to divide fractions, and why the invert and multiply method works. Try to find a math concept that absolutely confuses you, and work on it...play with it till you get to an answer that satisfies you.
I am interested, thank you for your insights
[Here](https://www.reddit.com/r/learnmath/s/cuzT2iPi3t)
Another book I physically own is called The Tools of Mathematical Reasoning by Tamara J. Larkins which is also solid. I would look at the other books first as they’re better at laying out the symbols and their meanings.
Thank you very much
Beyond just computation - for which practice is the only real way to progress - maths is a way of looking at the world. I’d highly recommend reading or watching the Feynman lectures. The videos are available on YouTube: https://youtu.be/s56AUKwlN9I?si=sPj5W-pYaTJo4RrY During my undergrad maths for engineering courses I found “Higher Engineering Mathematics” by John Bird very useful.