Questions tagged [problem-design]

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

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18
votes
3answers
949 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 ...
20
votes
4answers
7k 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 ...
18
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 ...
6
votes
4answers
187 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 ...
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 ...
12
votes
7answers
886 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
3answers
721 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 ...