# Providing interesting problems for all students in heterogeneous groups

Sometimes students from different programmes take the same course together. They may have a different background and/or different interests in the course. One example could be a basic mathematics course which is taken by physicists, mathematicians and teacher training students.

Is there a reasonable way of providing all these groups with (e.g. homework) problems without boring the other students. Would it be acceptable if in addition to a common body of problems each group gets additional "special" questions? Is there any research on the question of how such a strategy might influence the students' motivation and their learning outcome? How to deal with the problem that some students might think that the "special" exercises of (one or more) of the other groups are too easy in comparison?

• I tend to give the same base homework to everyone but occasionally throw in extra credit problems which I anticipate will be interesting to some but not all students. I try to mix more applied problems which are likely to appeal to engineering or science students as well as more mathematical questions which target the math majors. – John Coleman Jul 5 '16 at 2:13

• Instead, I would ask "hard" problems and separately give a "hints" document. The purpose of the hints document is to guide students through the steps. For example, let's say that deep into a Calculus II class, after seeing the bulk of the integration techniques, I would ask $$\int \sqrt{x^{2} + 1}\ dx$$ and then on a hints page, I would give a series of hints, starting with a trig substitution, perhaps. The general instruction / philosophy would be, "If you get stuck, take a look at the hint and try to continue from there. If you are still stuck, look at the next hint." Thus, by going through the hints, they (ideally) automatically fall into the right bucket of ability.