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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30
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9answers
8k 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 ...
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2answers
206 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(...
3
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0answers
154 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 ...
6
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1answer
300 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
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2answers
411 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
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1answer
259 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 ...
1
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5answers
250 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 ...
7
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1answer
260 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 ...
9
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1answer
175 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
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1answer
183 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 ...
6
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3answers
809 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 ...
7
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2answers
201 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
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2answers
156 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
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2answers
145 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
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3answers
311 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
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1answer
142 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
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1answer
228 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
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1answer
229 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
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1answer
115 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
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2answers
271 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
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2answers
329 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
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4answers
2k 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
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1answer
169 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 ...
2
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1answer
482 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
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1answer
180 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
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2answers
182 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
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3answers
542 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
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1answer
109 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
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5answers
339 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
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1answer
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
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1answer
84 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
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2answers
130 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
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1answer
200 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
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4answers
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....
5
votes
2answers
152 views

Great Worked-out examples books for Mathematics

I'm studying Mathematics in the UK. Back in Italy, where I am from worked-out problems books are very popular in mathematics and they are always recommended or compulsory at university. Going through ...
2
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0answers
66 views

Request for IBL Script for Putnam-type Problem Solving Course

One of the major benefits of a good IBL script is that it effectively organizes the experience of students so that their effort does not need to be used on such organization. A good script leads from ...
7
votes
1answer
419 views

Polya's "Nearby Problem" Heuristic and Inquiry Based Learning

I've often wondered about the "devise a plan" part of Polya's "How to solve it" outline. What we call "problem solving" can be thought of as what to do when you have no idea what to do. From this ...
9
votes
4answers
363 views

Ideas for math problem solving class for undergraduate students in university

In our university there is a huge gap between two group of students. a group of them came from Math Olympiad competitions and have a very strong background from high school but others, they have just ...
9
votes
5answers
700 views

Problem-Solving Activities that Engage Low-Level Students?

I'm going to be starting teaching a course called algebra COE, which is for students who didn't pass the required state algebra exam to graduate and are now seniors, to do spaced-out exam-like ...
5
votes
2answers
251 views

How should one manage knowns vs unknowns when solving a problem?

I define a known as a variable with a number you can plug in. I define an unknown as a variable without a number you can plug in because none is given. Recently I have taken several classes where ...
13
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1answer
2k views

High-school level algebra textbooks for gifted students

Note. I asked the question below on Math Stack Exchange (link), but didn't get a really satisfactory answer there, so I'm posting it here too. I am looking for high school algebra/mathematics ...
14
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3answers
656 views

The interplay of memory and mathematical performance

As mathematicians and mathematics educators we very often see the Dunning-Kruger effect in action. Our calculus students are certain that they are masters of Calculus because they took the AP exam. To ...
12
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7answers
932 views

Name the heuristic: exploiting the legitimacy of the questioner

As a child, I made frequent use of a particular 'trick' in order to make short work of many different problems. The general form is to be presented a question which wants a definite (numerical) answer,...