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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.

3
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1answer
80 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 ...
6
votes
4answers
324 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
1answer
147 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 ...
4
votes
0answers
90 views

Why is problem solving important for all of us?

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 ...
3
votes
1answer
219 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, ...
8
votes
2answers
148 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
3answers
484 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! ...
3
votes
1answer
116 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 ...
6
votes
1answer
104 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
5answers
292 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 ...
26
votes
9answers
7k 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 ...
-2
votes
1answer
63 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.
5
votes
1answer
134 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, ...
8
votes
2answers
118 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....
12
votes
1answer
178 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 ...
5
votes
2answers
117 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 ...
7
votes
1answer
151 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 ...
10
votes
4answers
6k 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....
2
votes
0answers
58 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
344 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
5answers
560 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
141 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
votes
1answer
850 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 ...
9
votes
4answers
298 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 ...
13
votes
2answers
261 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 ...
12
votes
7answers
872 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,...
13
votes
3answers
559 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 ...