How do I think more mathematically?

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In summary, the conversation discusses tips for becoming more mathematically inclined, including practicing lots of problem-solving exercises, studying algebra and applying it to other subjects, and understanding concepts rather than just memorizing formulas. Additionally, the conversation mentions helpful resources such as tutors and online forums for problem-solving practice.
  • #1
STS816
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I'm trying to figure out how to think more in terms of mathematics rather than going to straight to some formula or equation. I'm a junior in high school and I have a 97 in Pre Calculus so I'm not really having trouble with formulas and equations but I can't really seem to figure out problems that I don't know a specific formula for. I took the ACT today and I think this may have really hurt me on the math part.

Any tips on how I can become more mathematically inclined? Thanks.
 
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  • #2
Just do lots and lots of problems (ones about problem-solving, not about plugging things into formulas) -- that's how one prepares for things like the SAT or ACT as well.
 
  • #3
i can relate to you i have a high grade in pre cal to and wen i first took the act i had a 19 i just kept on practicing and now I am at a 30 around. its just practicing and timing, try getting a act or sat tutor if you are having difficulties its worth it in thne long run
 
  • #4
STS816 said:
I'm trying to figure out how to think more in terms of mathematics rather than going to straight to some formula or equation. I'm a junior in high school and I have a 97 in Pre Calculus so I'm not really having trouble with formulas and equations but I can't really seem to figure out problems that I don't know a specific formula for. I took the ACT today and I think this may have really hurt me on the math part.

Any tips on how I can become more mathematically inclined? Thanks.

In one word: ALGEBRA.

Also study a laboratory science in which you will apply the introductory and intermediate levels of Algebra. If your intermediate course on Algebra includes some exercises on modeling, this can be very helpful in learning to think mathematically.

Back to the answer, "ALGEBRA"; this is the coursework in which you learn to derive formulas for yourself.
 
  • #5
Another tip - Never set out to memorize a formula or an equation you see. Try to understand what the statement really means, explain it in simpler terms to yourself, know how to prove the statement. I often forget many identities but I remember how to prove them, I quickly prove them on the spot and I get them again. And don't memorize the proof either - just read a proof, several is possible, pick the one you find that makes most sense to you, it you understand what the proof did to achieve that result, you will remember it =]
 
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  • #6
Memorization will ultimately fail you, and the only suggestion I can give is to try and engage yourself outside of your textbook math. You KNOW when you understand something and when you're just trying to memorize because you're in panic mode. I have developed over the years to reject not being able to understand something, and it drives me nuts when I can't because my memory sucks! Just an example of questions you might come across that I think help out mathematical thinking if you do enough of: Prove n^3-n is divisible by 3 (or the more difficult prove n^5-n is divisible by 5). I won't give you the answer, but there are all sorts of random problems out there.

I get some minimal practice by answering questions on this website! You never know what kind of weird questions people will ask that are thought provoking.
 
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  • #7
  • #8
symbolipoint said:
In one word: ALGEBRA.

Also study a laboratory science in which you will apply the introductory and intermediate levels of Algebra. If your intermediate course on Algebra includes some exercises on modeling, this can be very helpful in learning to think mathematically.

Back to the answer, "ALGEBRA"; this is the coursework in which you learn to derive formulas for yourself.

I'm doing exponential modeling in pre cal right now and surpising enough, I think I may really understand it.

And thanks Edgardo for that link.
 

1. How can I improve my problem-solving skills in mathematics?

The key to improving your problem-solving skills in mathematics is to practice regularly. Start by reviewing basic concepts and techniques, and then try solving a variety of problems from different sources. Don't be afraid to make mistakes, as they can help you learn and improve. Additionally, try to approach problems with a logical and organized mindset, breaking them down into smaller and more manageable steps.

2. What are some strategies for thinking more logically in math?

Some strategies for thinking more logically in math include breaking down problems into smaller steps, looking for patterns and connections between concepts, and using logical reasoning to solve problems. It can also be helpful to take a step back and approach problems from different angles, as well as seeking out different resources and perspectives.

3. How can I improve my critical thinking skills in mathematics?

To improve your critical thinking skills in mathematics, it is important to actively engage with the material and think critically about the concepts and techniques being used. This can involve asking questions, seeking out alternative solutions, and evaluating the validity of your own reasoning. It can also be helpful to discuss problems with others and consider different perspectives.

4. What are some techniques for visualizing and conceptualizing mathematical problems?

One technique for visualizing and conceptualizing mathematical problems is to draw diagrams or create visual representations of the problem. This can help you better understand the relationships between different variables and concepts. Another technique is to use real-world examples or analogies to help make abstract concepts more concrete and relatable.

5. How can I overcome my fear of math and approach it with confidence?

To overcome your fear of math and approach it with confidence, it is important to recognize that making mistakes is a natural part of the learning process. Focus on your progress and celebrate small victories, rather than getting discouraged by setbacks. It can also be helpful to seek out support and resources, such as tutors or study groups, to build your skills and confidence in mathematics.

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