Stack Exchange Network

Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [problem-design]

For questions how to design and create questions, exercises and examples.

2
votes
1answer
167 views

Using tensegrity structure to teach high school math?

I am exploring ideas to design a secondary-level-project-based-10-lessons-unit-learning-plan which can end with a creation from the students involving a tensegrity structure. such as or My general ...
2
votes
2answers
46 views

Project Based Learning or Applied Math involving modular arithmetics?

I am searching for ideas to construct Project Based Learning type that involves Modular arithmetics with eventually geometry and could fit in High School level What could a nice research question ...
7
votes
3answers
437 views

Interesting but very easy epsilon-delta problems?

I am teaching a real analysis class. Students in the class have inconsistent high school algebra skills. They now have a complete but tenuous understanding of $\varepsilon$-$\delta$ limits. I want to ...
0
votes
0answers
135 views

Does this problem enhance mathematical creativity?

There are an equal number of red, yellow, green, and blue cards. Take one of them and put it in the box. Suppose that red cards was most selected, followed by yellow, green, and blue when we selected ...
5
votes
4answers
297 views

A question about Vector Analysis problems

Why is it difficult to find really challenging vector analysis problems (problems about Green's, Stokes' and Gauss' theorems in a Calculus 3 course) in Calculus books? Most of the problems are ...
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 ...
11
votes
2answers
223 views

Can number theory help me create equations with nice solutions?

I'm teaching a remedial algebra class, and I recently put a radical equation on a quiz. At this point, the students had only solved polynomial equations by factoring, so the equation had to turn out ...
12
votes
1answer
179 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 ...
18
votes
8answers
746 views

Good Examples of Questions to have Students Ponder Over Without Paper

A few times now I've found myself in a situation where I want to give a precalculus-level undergraduate student something to think about that's kinda fun and that's well outside of their coursework. ...
11
votes
1answer
596 views

How does Project Euler come up with such good problems so rapidly?

Ever since I learned about Project Euler, I have been astonished and wondering about how Colin Hughes (the creator of Project Euler) manages to come up with such problems at such a rapid pace (once a ...
7
votes
3answers
155 views

Mathematical Task with Various Solutions

I need to come up with a mathematical task for middle school (9th grade), which involves either algebra, functions, probability or statistics (anything but geometry actually). My problem is, that the ...
19
votes
1answer
205 views

Problems which require interpreting definitions

I'm trying to find more problems suitable for early college students (students who know algebra and calculus) that involve translating words into mathematical notions. A nice example is this one: ...
0
votes
0answers
79 views

How to formulate math problems? [duplicate]

I always had doubts about how to formulate difficult problems (high-level problems) in mathematics? Is there any rule (a pattern) for this? Or is it a matter of level of knowledge and background? or ...
20
votes
7answers
1k views

Good examples of functions defined as definite integrals of elementary functions?

I am writing some Calculus content, and I would like a "big list" of useful functions which are defined by definite integrals, but are not elementary functions. Two examples of such functions are $$ ...
13
votes
3answers
541 views

How to use false theorems or proofs?

I would like students to be critical and not believe that every proof they see is correct. Lecturers make mistakes and students should not think: "That must be a valid argument/proof/syntax because it ...
1
vote
2answers
129 views

Create Problems for Polynomial Interpolation

I want to create problems concerning polynomial interpolation for students. However, I need those problems to differ in difficulty for the different students. What I could always do is solve some ...
18
votes
5answers
1k views

Good examples of Lagrange multiplier problems

I've noticed that most Lagrange multiplier problems I've seen can be solved with other methods. Often the method of Lagrange multipliers takes longer than the other available methods. I don't like ...
12
votes
3answers
941 views

Challenge questions for extremely bright kids

I suppose this is the place for my questions as much as any place is: I'm a math student coming on my 3rd year of undergrad, and I am working as a counselor at a Summer math camp. The camp is for 12-...
7
votes
4answers
171 views

Topics for Discovery-based Projects

Are there any existing sources for topics or projects which are: Suitable for first and second year undergraduates taking introductory math classes (possibly with some prompting or a couple pages of ...
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
876 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,...
7
votes
2answers
445 views

Examples where it easier to prove more than less [duplicate]

Especially (but not only) in the case of induction proofs, it happens that a stronger claim $B$ is easier to prove than the intended claim $A$ since the induction hypothesis gives you more information....
7
votes
1answer
300 views

Is there a repository with K-12 math exercises and problems written in LaTeX (English or Spanish)?

I've been searching for a repository or a database with math problems (K-12 levels) written in LaTeX, but with no luck. Neither in Spanish (my student's language) ...
11
votes
5answers
367 views

Grade 8 “Question of the Day” Ideas

I've begun a "Question of the Day" (QOTD) contest in my grade 8 class where I post a problem solving question on the wall each day and students are challenged to answer it in their own time. I need ...
8
votes
3answers
539 views

How to address struggling readers in the mathematics classroom?

I am currently in a course titled "teaching reading in a content area." While there are plenty of examples of different strategies that can be used in different subject areas, there are little ...
7
votes
3answers
976 views

Arithmetic / Algebra problem generation software?

I'm struggling to find any good "problem generation" software or sites. I want a program that will do the following: Generate typical problems at all sorts of levels (from toddler age through to teen,...
29
votes
3answers
1k views

Are there any benefits to having an entire course's homework problems available from day one?

I am designing a course for the upcoming fall semester, and I am tossing around an idea in my head. While planning which topics to cover each week and how to set the pacing of the course, I figured I ...
9
votes
5answers
1k views

Applications of Calculus 2 to Physics

I'm teaching a section of Calculus 2 (integration techniques, arc length, surface area, improper integrals, parametric & polar functions, sequences, and series ) next semester and would like to ...
19
votes
6answers
6k views

Examples and applications of the pigeonhole principle

The Pigeonhole Principle (or Dirichlet's box principle) is a method introduced usually quite early in the mathematical curriculum. The examples where it is usually introduced are (in my humble ...
19
votes
4answers
5k views

How does one create “good” math problems?

As lifelong students of mathematics, we find problem-solving to be absolutely essential to enhance our understanding of the subject. Teaching others what we know serves to reinforce our existing ...
6
votes
3answers
167 views

Where can I inform me about experiences with exam tasks heading for deeper understanding?

In a traditional exam, there is a strong focus on facts and techniques. For instance, in a course on linear algebra, students are asked to diagonalize matrices and they have to check whether a given ...
18
votes
3answers
880 views

Good problems that uncover difficult points in a theory

There is a great quote of Yitz Herstein: The value of a problem is not so much coming up with the answer as in the ideas and attempted ideas it forces on the would-be solver." A number of such ...
17
votes
7answers
1k views

“Correct the following mistake”-style questions?

Does anyone have any experience giving students incorrectly "solved" math problems and asking them to identify this error? Being self-critical is one of the skills that I would like my students to ...
18
votes
4answers
298 views

Multiple Solutions Methods vs. Encouraging a Particular Approach

It happens frequently in math that problems have multiple possible solutions. This might become troublesome, e.g. when students use some other approach, hence, not learning the current topic. One ...