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Questions tagged [problem-solving]

For questions related to creating, categorizing and identifying appropriate problems as well as the benefits of problem solving and related pedagogy including motivation.

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4 votes
2 answers
679 views

Parkour and Mathematical Practice?

Learning mathematics and learning parkour seem to have a lot in common. Both can be done on varying levels, but to progress in either one needs to overlearn and build basic skills so that these skills ...
15 votes
1 answer
192 views

Having students assess what problems they're ready for

Does anyone have experience with giving students a collection of problems where they have to assess which ones they have the knowledge to solve? I was exploring the connection between video games and ...
2 votes
8 answers
699 views

Practical case for solving with system of 2 equations

When I teach basic math I want to emphasize on it's power (algebraic part for starters) as a tool for solving certain problems you cannot solve with naked brain, so that one models a problem with ...
4 votes
1 answer
393 views

Problem of the Week for College Students

Trinity's Problem of the Week and Purdue's Problem of the Week were both weekly problems that were excellent for college math clubs to tangle with at their weekly meetings. However, both of them are ...
0 votes
2 answers
317 views

What will happen if someone doesn’t make it to the IMO team?

I am highly interested in mathematics, and solving Olympiad maths problems has been a type of hobby for me. But due to my age, I will never be able to give the olympiads a go again. I want to know ...
-1 votes
1 answer
126 views

Why do problems should be solved by pen and paper before coding? [closed]

I heard that before you can handle data automatically, you have to know how to handle it manually. Why is it impossible to find a problem and build some machine learning algorithm to find a proper ...
-1 votes
1 answer
240 views

Learning, exams, math degree

I have only passed the one fourth of my courses so far, which means like one year of the maths undergraduate studies. I live in a different place from where the university i study at is and try to ...
6 votes
1 answer
621 views

Theory-practice order vs practice-theory

I heard that there were some studies on what is the best order for teaching math. But I cannot find any papers (probably my English is too poor to google this paper correctly). As I heard idea was: ...
9 votes
2 answers
520 views

Native language, writing, and mathematical problem solving

This question is meant to explore the intuition that mathematical thought does not most naturally proceed from writing in one's native language. The hackneyed and not entirely satisfying slogan that ...
-2 votes
1 answer
124 views

On doing scientific research [closed]

What I want to ask is: can I use the results of others when doing scientific research, whether it is math, physics or other science, without trying to prove them myself or try to verify them? For ...
1 vote
0 answers
125 views

Quality of a solution in mathematics

How can you determine a quality of a solution for a mathematics problem in general ? If you try to explain too much then solution becomes bit longer and it takes time to go through causing less ...
6 votes
1 answer
314 views

What are some ways that one can progress from stage 2 to stage 3 of the rigor stages that Terry Tao has described?

Terry Tao describes 3 stages of one's mathematics education on his web blog. 1: Pre-rigorous 2: Rigorous 3. Post-rigorous I know how one can progress from stage 1 to stage 2 (this simply can be done ...
-1 votes
1 answer
55 views

Problem solving or question answering

What can be the most appropriate way of asking , Solve the problem or answer the question ? As common usage in examinations we have question papers for all subjects. Therefore like in other subjects ...
5 votes
4 answers
529 views

Doctorate and examples of difficult solved problems

Okay. My questions are: How do some people do doctorates in mathematics and spend so much time like three to six years trying to answer one or two open problems? How do they have the patience, ...
0 votes
1 answer
122 views

Problem solving and independent scientific research [closed]

Is analogy a way to solve problems when doing research in math and physics? Is it very important?How important is it? Could i do independent scientific research on some open problems perhaps having ...
-2 votes
2 answers
185 views

Is applying maths a 'hard problem' and how does the profession help?

Question: Is there such a thing as an Applied Maths profession? In my engineering experience we were often at a loss as to which mathematical approach to take, and there seemed no obvious way to find ...
0 votes
0 answers
97 views

Problem solving approach to learning and psychology

I try to have a problem solving approach to learning math. What i mean by this is if someone sets some questions or problems regarding the material i am reading how should i answer or what questions ...
1 vote
1 answer
205 views

Math outside of undergraduate studies and proofs

I read sometimes mathematical works of others outside my undergraduate studies. I think i can not follow the understanding of the proofs of theorems sometimes. What should i do? Should i read other ...
2 votes
0 answers
139 views

Solved , open problems and levels of difficulty

What are the advantages and wins of solving already solved problems? Does it help me know how to become better at problem solving and test my abilities on it? Does it help me become better and have ...
30 votes
9 answers
9k views

Can mathematics be learned by ONLY solving problems?

Here is the concept: Student is presented with a problem. He/she may not even understand what is being asked, or may attempt. Students reads a solution to the problem. In it there may be ...
1 vote
2 answers
436 views

Should I do all the proof practice problems in How to Prove It, an intro to proofs book?

Like the title says. I am self studying intro to proofs(How to prove it by velleman) so I can start an introduction to analysis. I am wondering if I should complete all the exercises in the textbook(...
6 votes
1 answer
347 views

Combinatorial problems which can be solved with polynomials

Can someone please post some (relatively easy, high school level) combinatorial problems which can be solved with polynomials (but not generating functions). Here is an example of one such problem: We ...
3 votes
2 answers
675 views

How actually are prime numbers taught in elementary school in United States and how easily do students learn what they're being taught about them?

I read the question https://math.stackexchange.com/questions/1593091/how-to-explain-why-study-prime-numbers-to-5th-graders and according to the body of the question, some students sigh. Also according ...
5 votes
1 answer
297 views

How important is it to come up with or learn an elementary solution?

Note: by "elementary" I mean "without using more advanced theory and tools". Students are sometimes required or encouraged to solve very difficult problems using limited number of ...
8 votes
1 answer
181 views

What is a good place for teachers to share self-created content?

I am a high school mathematics teacher and I regularly create problems and their solutions for my students. It has always lingered in my mind that this content can also benefit others. What would be a ...
3 votes
1 answer
193 views

Help finding good deep mathematics problems

Once, when I Was doing calculus 2, someone challenged me to calculate and prove the Gaussian integral, with a few hints, and a few days, I managed to. It was a great feeling to solve a “deep” multi ...
7 votes
3 answers
2k views

Looking for a HIERARCHY of math subjects

If you were to "map" mathematics onto a tree structure where the top is "Mathematics", and then below it the different branches, then sub-branches, etc. What do you suggest is a good structure, for ...
8 votes
2 answers
219 views

Do you teach different proofs or calculations of same question?

Recently I asked a question on math.stackechange about the most ways to differentiate the same function and it didn't seem to generate any interest - rather, the reason why I'd ask such a question was ...
3 votes
2 answers
219 views

More intermediate steps or check well-understanding

I work as a math tutor mostly for talented high-school students that are passionate about mathematics and want to learn more of it beyond school programs. They are very smart kids, but I noticed that ...
5 votes
2 answers
240 views

Are there any more mathematical journals or websites with the "problems and solutions"?

Are there any more mathematical journals or websites with the "problems and solutions"? such as , the American Mathematical Monthly and Crux Mathematicorum
4 votes
3 answers
393 views

Are some people unteachable at mathematical problem solving? [closed]

This is a concise description of what happens if I attempt any problem solving task with numbers: [1] I never work out where to start. [2] If by some miracle [and I'm talking Moses parting the waves ...
5 votes
1 answer
188 views

Developing abductive (problem-solving) skills

I am looking for long-term (over the course of many semesters) strategies, including specific types of in-class activities, for developing the abilities of students to come up with intermediate steps ...
5 votes
1 answer
266 views

Why is problem solving important for all of us? [closed]

I am looking for academic references related to this questions. In fact, I need to write a paper which shows the importance of problem-solving approach for everyone. Certainly, this should include ...
1 vote
1 answer
383 views

How to improve mathematical skills(University level)?

I am doing Ph.D in Mathematics, I feel I lack few of the skills, if I can improve those skills I think I can do better as a Math scholar. I need some suggestion on these following(below I am talking ...
2 votes
1 answer
134 views

Student-friendly / efficient approach to computing Taylor coefficients of infinite binomial series expansions?

I’m working on a section of a course covering Taylor expansions, and have found that, although there is great notation for simplifying the formula for the coefficients of a general infinite binomial ...
6 votes
2 answers
286 views

A question from a young student to mathematicians

I'm a young math student. And I live with the effort of always wanting to understand everything I study, in mathematics. This means that for every thing I face I must always understand every single ...
14 votes
2 answers
356 views

Is there a framework to study the mathematical competence in problem-posing?

I've read some articles about it and those papers show us that there are some facts to understand the mathematical competence in problem-posing. Besides that, those investigations show that there are ...
7 votes
4 answers
3k views

Students understand during course but can't solve exam

I am teaching a math class where the students, most of them, tell me that they can understand the materials given by me during the course. I test them during the course too and they seem to get it. ...
3 votes
1 answer
255 views

Can we solve math just by speaking and not using any other extra devices?

I have been thinking, is it possible, or a good thing to do when learning from a textbook without ever writing anything down. But have to verbally give out the solution from beginning to the end with ...
3 votes
1 answer
615 views

Why do the stages of rigorousness have specific timestamps?

This is a reduced quote from There’s more to mathematics than rigour and proofs of Terrence Tao (emphasis mine): The “pre-rigorous” stage, in which mathematics is taught in an informal, ...
3 votes
1 answer
437 views

"Seeing" GCD and LCM in Word Problems

Last year, I taught GCD and LCM and then gave my students word problem relating to these concepts ("Two runners with given different speeds; when will they meet again?", "Having three kinds of flowers ...
8 votes
2 answers
216 views

Problem based learning (PBL) for pupils with educational difficulties

I taught IT in an engineering school during three years in problem based learning (PBL) only. Now I teach maths to pupils between 10 and 15 years old who have a lot of educational difficulties. I'm ...
6 votes
3 answers
561 views

Stating identity is not the same as knowing value

A discussion with a frustrated 10th grade student sent me here. I had provided two linear function expressions, $f(x)=2x+2$ and $g(x)=-\frac{1}{2}x-2$, now find the intersection of the two lines! ...
6 votes
1 answer
122 views

What are the fundamentals of writing practice questions for early teen students?

I have to write some practice questions, or toy problems for some students in the age range 11 to 14. This is for a workshop I will be running. The students are encouraged to work on these questions ...
10 votes
5 answers
366 views

Drumming up interest in journal-problem-solving and competition prep

I teach at a small liberal-arts college and advise our Math Club. In past years, I have talked a few students into taking the Putnam Exam. I've found that I pretty much have to "coerce" them into ...
5 votes
1 answer
139 views

How is this problem categorised?

I'm trying to find some online questions and training material related to this sort of question. It's not something that I can identify the name of: A raffle has these prizes (ending 00 @ £12, ...
-2 votes
1 answer
101 views

How do I solve this ratio problem? [closed]

Here is the problem: If Bill takes 3 hours to paint a room and James takes 5 hours to paint a room, how long will it take to paint a room if they work together? Show your working. Thank You.
8 votes
2 answers
140 views

How to retain the key points of an exercise?

I'm a student majoring in maths. The sole reason I chose mathematics is that I like mathematics. I'm sure I do not belong to that "gifted" category. I haven't participated in maths competitions either....
13 votes
1 answer
216 views

Question about the process of creation of problems and exercises in Mathematics

I have a question about formulating problems and exercises in Mathematics. When attempting to create a problem of Number Theory or Real Analysis, for example, in this process, is the problem first ...
10 votes
4 answers
9k views

Is it possible to improve logical thinking and problem solving abilities?

I'm from Italy and I'm 13 years old. I'm good in Math and I'm good in languages (I know Italian, English and Russian and I think I'm good at them). I'm a programmer and I know HTML, CSS, JS and Python....