Learning Mathematical Problem Solving

[tuxscholar]

So far it seems to be the case that to learn math one inevitably needs to learn problem solving for the sake of developing mathematical intuition. I tried to solve some elementary level algebraic math problems on my own especially as discussed in the book elements of algebra by Euler, but i still find most of the time clueless to solve even problems whose concepts I've previously learned and constantly referring back and forth to find the proper solution. I realized that first of all i need to develop mathematical problem solving skills in a more comprehensive way. So for that purpose I've decided to work with these books in specific order :
For elementary coverage : Welchons Algebra, Geometry by Keiselev and Gelfands works in Basic Mathematics

Then for having a decent ground in mathematical problem solving :

• How to Solve It by George Polya
• Mathematics and Plausible Reasoning by George Polya
• The Art and Craft of Problem Solving by Paul Zeitz
• Problem Solving Through Problems by Loren Larson
• Problem-Solving Strategies by Arthur Angel
• Geometry Revisited by Coxeter & Greitzer
• Putnam and Beyond by Gelca & Andreescu
• Winning Ways by Berlekamp, Conway & Guy
• Problem Solving Through Recreational Mathematics by Bonnie Averbach et al.

Do anyone struggling with problem solving in math? How they manage to develop a decent intellectual grounding when it comes to problem solving of various kinds of mathematical topics?

 

[PeroK]

So far it seems to be the case that to learn math one inevitably needs to learn problem solving for the sake of developing mathematical intuition. I tried to solve some elementary level algebraic math problems on my own especially as discussed in the book elements of algebra by Euler, but i still find most of the time clueless to solve even problems whose concepts I've previously learned and constantly referring back and forth to find the proper solution. I realized that first of all i need to develop mathematical problem solving skills in a more comprehensive way. So for that purpose I've decided to work with these books in specific order :
For elementary coverage : Welchons Algebra, Geometry by Keiselev and Gelfands works in Basic Mathematics

Then for having a decent ground in mathematical problem solving :

• How to Solve It by George Polya
• Mathematics and Plausible Reasoning by George Polya
• The Art and Craft of Problem Solving by Paul Zeitz
• Problem Solving Through Problems by Loren Larson
• Problem-Solving Strategies by Arthur Angel
• Geometry Revisited by Coxeter & Greitzer
• Putnam and Beyond by Gelca & Andreescu
• Winning Ways by Berlekamp, Conway & Guy
• Problem Solving Through Recreational Mathematics by Bonnie Averbach et al.

Do anyone struggling with problem solving in math? How they manage to develop a decent intellectual grounding when it comes to problem solving of various kinds of mathematical topics?

Isn't the idea that you pick one book and work through that? You can't need all those books.

 

[tuxscholar]

Isn't the idea that you pick one book and work through that? You can't need all those books.

Indeed, that is quite a decent idea. After all there is no royal road to mathematics one can do nothing better than wrestling with plenty of problems painstakingly with exhaustive efforts and deliberation. Thank you.

 

[MidgetDwarf]

Read topic. Follow examples with paper and writing tool. Ask why such and such line is true.
Finish topic. Go to exercises. Do a few until you get stuck. Think of why you are stuck. Do problems(mainly techniques) used to solve other problems help? If so, solve it and proceed to next problem. If not, throw kitchen sink at problem. If you solve it, continue on to next. If not, go back to reading topic. Rinse and repeat the above algorithim.

 

[MidgetDwarf]

Although keiselev both books are excellent. I would have found them extremely difficult to study from them on my own when I was first learning mathematics. If it works for you great. If not. Find another book.

 

[gleem]

Did you have any issues with math before college?

 

[tuxscholar]

Did you have any issues with math before college?

Well I'm not studying math in college, but for the sake of perceiving the beauty of the subject and to contribute something worthwhile in the realm of mathematics. But so far when it comes to do problems i always felt a sense of intellectual friction which most of the time leads me to procrastinate learning mathematics so to tackle that I'm solely focusing on having a decent grasp in the act of probelm solving thoroughly.

 

[gleem]

So you are trying to study math on your own. I think this would be challenging for most people and would benefit greatly from having a teacher to guide and act as a model for them. The teacher provides a structure to follow and helps you avoid pitfalls. The teacher provides a cadence for your progress, forcing you to keep pace during your learning. By yourself, you may get discouraged and frustrated pershaps developing behaviors that are counterproductive.

You did not say if you have taken advantage of the multitude of videos online, from which you can see how math is done, including those on physics. Not everybody can learn math from books and benefit from them to the same degree.

 

[tuxscholar]

So you are trying to study math on your own. I think this would be challenging for most people and would benefit greatly from having a teacher to guide and act as a model for them. The teacher provides a structure to follow and helps you avoid pitfalls. The teacher provides a cadence for your progress, forcing you to keep pace during your learning. By yourself, you may get discouraged and frustrated pershaps developing behaviors that are counterproductive.

You did not say if you have taken advantage of the multitude of videos online, from which you can see how math is done, including those on physics. Not everybody can learn math from books and benefit from them to the same degree.

Well indeed watching videos can be helpful but when it comes to mentoring I can't find one or it's emotionally demanding, especially if one is terrible in human communication. I rather prefer to make my own self my mentor and books my companion. I've considered about videos but it all seems to be time consuming and distracting but I'll reconsider about it. Anyways thanks for your concern.

 

[gleem]

I've considered about videos but it all seems to be time consuming and distracting but I'll reconsider about it.

I can appreciate the difficulty with finding someone to guide your effort. One approach is to take a math course, even a non-credit one, or to audit an online one. You have some indirect guidance. What seems to be consuming your time is your inability to make progress with your current approach.

 

[MidgetDwarf]

Well indeed watching videos can be helpful but when it comes to mentoring I can't find one or it's emotionally demanding, especially if one is terrible in human communication. I rather prefer to make my own self my mentor and books my companion. I've considered about videos but it all seems to be time consuming and distracting but I'll reconsider about it. Anyways thanks for your concern.

WHat level are you currently at?

Arithemetic?
Algebra?
Geometry?
Trig?

Last math class taken and level.

 

[tuxscholar]

WHat level are you currently at?

Arithmetic?
Algebra?
Geometry?
Trig?

Last math class taken and level.

I've studied math all the way upto high secondary school (mpboard, Class 12th) in india, which was highly mechanical and exam centric approach and I've never really learned math but studied it for the sake of having good marks in exam and that's it. After that comes a hiatus of seven years and I've forgotten a lot of math and then now I've suddenly got a profound intellectual urge to learn this elegant subject. So I've decided to hone first problem solving skills and relearn math from algebra II to precalculus. The only difficulty seems to be lack of consistency and academic discipline which is something I'll going to overcome.

 

[MidgetDwarf]

JUst work through am algebra book and stop overthinking. Start doing instead of thinking.

 

[symbolipoint]

After that comes a hiatus of seven years and I've forgotten a lot of math and then now I've suddenly got a profound intellectual urge to learn this elegant subject. So I've decided to hone first problem solving skills and relearn math from algebra II to precalculus. The only difficulty seems to be lack of consistency and academic discipline which is something I'll going to overcome.

Problem-solving skills and relearning intermediate algebra through Pre-Calculus need to be learned together. Trying to separate them is basically not good.

edit: What I just wrote could be misunderstood. Those are two things to be learned or relearned, which are:

• Problem-solving skills
• Intermediate Algebra through Pre-Calculus

 

[tuxscholar]

Problem-solving skills and relearning intermediate algebra through Pre-Calculus need to be learned together. Trying to separate them is basically not good.

edit: What I just wrote could be misunderstood. Those are two things to be learned or relearned, which are:

• Problem-solving skills
• Intermediate Algebra through Pre-Calculus

Indeed, I'm simultaneously learning and relearning both.

 

[gleem]

Indeed, I'm simultaneously learning and relearning both.

You are indicating that you are learning math and problem-solving as separate endeavors. This will probably not be productive. Early studies of problem-solving courses have not delivered the benefits sought. What is fundamental is a thorough knowledge and understanding of the math topic and the effective use of that knowledge.

The mathematics itself will train you to solve problems. You learn the rules of the subject, which will provide strategies for solving problems.

Mathematics builds on itself in an ever-expanding array of concepts and relationships. To solve a problem in a specific topic, you must know the topic and any prerequisite topics well. It will take time just to get up to the point where you will be able to try topics beyond high school. Patience and discipline are essential.

 

[symbolipoint]

You are indicating that you are learning math and problem-solving as separate endeavors. This will probably, etc., etc.,...

In fact he does seem to understand that the two do work together and are learned together. I too wanted to clarify to him so the problem of unlinking is likely not really something he's trying to do.

 

[tuxscholar]

Well surely I've understood that math is a deductive subject where every concept builds upon the other like an interlinked conceptual chain, also after considering about the arguments of you decent intellectuals' I've no intention of learning problem solving and math which is rather absurd. What one need is a thorough conceptual understanding of fundamental topics in math. One can have such conceptual clarity by using those ideas for practical purpose like in finance or computing or in physics then after that one can deep dive in pure math to learn math for its own sake like an artist, which is what my intention is to become a mathematical artist. Again thank you for your decent advice.