What are pros and cons of requiring students to create their own math questions, and what are some tips to make it work well?

Question

I will teach a special class of 10 high school students who are aiming to study math at top universities. The purpose of the class is to increase students' interest and ability in math. There is competition to be admitted into this class. [EDIT: I will teach this class six lessons, each lasting 90 minutes.]

What are pros and cons of requiring students to create their own math questions, and what are some tips to make it work well?

My plan

Each week I will ask each student to create their own math question (and solution). The question should be challenging but the solution should be explanable in a few minutes using high school math. Examples will be provided.

I will collect and distribute the questions to the students, who will then have a few days to work on them. During the next lesson, each student will explain their solution to a randomly chosen question.

To deter students from just copying a question from somewhere, sometimes I will provide more requirements for their question. For example, their question must be:

• related to one of several geometrical diagrams that I provide;
• posed as an extension question to one of several questions that I provide; or
• inspired by a STEP question of their choice.

I am looking for more such ways to deter students from copying a question from somewhere.

Possible pros

This practice might generate interest in math.

• Students will be encouraged to "play" with math, instead of just trying to answer a question.
• There may be tacit competition to see who can come up with the most interesting question.
• Students personally know the creators of the questions, so they may be more interested in finding the answer (compared to, say, facing Exercise 14.3 in a textbook).
• The questions (which the students will attempt to answer) will probably be neither too easy nor too difficult.

Speaking from personal experience, I have created my own math questions, and this has made me more interested in math. However, I'm not sure if requiring students to create their own questions will make them more interested in math.

Answer 1

It is generally a good idea to have students express their mathematical ideas and thinking for others to see and engage with. Having them create exercises is a way of doing this, and is likely to reveal to you a great deal about the thinking and skills of the students in question.

However, for the purpose of getting good exercises, consider the mathematical maturity and knowledge base of the students and compare to yours. You hopefully have a bit of an edge there. It is much more likely that you can create interesting exercises that are related to real life, concepts that appear later but you can set the stage for now, that are targeted towards a specific idea or technique, that do not have accidental features like misleading wrong ways of getting to the correct solution, and so forth.

Having the students create some exercises, maybe in groups or pairs, and solve each others', can be a good move, but it should be used in moderation.

Also, this activity might be threatening to some students, as they need to show their work to their classmates who might judge them for it; even if this is not the case, it might be perceived as a possibility. Also, some students might used to traditional schooling where the teacher tells what to do and the student just does, no thinking or creativity required. A change to that can be resisted.

For the two aforementioned reasons, and depending on how you frame the activity, there might be resistance.

Answer 2

Pardon my French, but this looks like pure horror to me.

I admit, I express myself in an extreme way, but I think about the following:
You start by saying:

There is competition to be admitted into this class.

So, there already is a form of hostility between the students.

... and now you let students create questions, which might not be solved by their classmates, so this might increase the interpersonal hostility even more?

NO!
Creating math questions is the job of the teacher. If they grow hostile feelings against you, no one cares!
But students amongst each other should not be stimulated into disliking each other.

Answer 3

As a practical matter, I doubt the kids are going to do much out of class work...this sounds like an enrichment activity, ungraded. So, I think any content they prepare for each other, will be pretty weak.

I think you should try to think about what content/activities to do with the kids that is (a) enjoyable, motivational and (b) not too much work for you. This is not a trivial Venn diagram. I do realize your suggestion satisfies (b). I doubt it satisfies (a).

I think some sort of "math team" type activities might work. Hopefully you can find some cheap and easily modified content.

Something like 30 minutes (start of class) math problems, done by the kids. These should by high school math team level problems. Not routine drill from current classes...but not Putnam level craziness. Then exchange papers and grade (maybe have volunteers at the board). Then discuss (maybe you can generalize or give some aenecdotal context on how they relate to college math course.)

Try to keep it interactive (the upfront problems help here, could also bake in some voting or the like..."what question was best, worst"). I would plan in a 15 minute break also. 90 minutes is a long class.

If you can do so, with a modicum of work, you might try to orient the content to some broad themes. I.e. one day of geometry, one of number theory, one of probability, etc. Just...when I did math team, it was mixed...and that was fine. But for your class to look good and to give some focus to the discussion, maybe if you could segregate to themes, it would be good.

I'd also consider bringing in a few guests. E.g. someone in industry (like a stats person from pharma industry) or a math major senior undergrad or senior grad student. Don't make guest carry the whole class...but if you can have some discussion with the kids, it's nice. After all these kids are thinking of going into math (you say). This gives them a chance to hear other voices than your own. And 11th and 12th grade HS kids are starting to transition to adulthood...so nice to hear perspectives form people further on that road. Guests can say if math major was good/bad choice (jobs, socializing, workload, interest, etc.)

I would also think a little about the level of the kids. You said they competed to get in (fine). But what elite are they? I just think it will help ground you in designing, choosing your content. I love them all...it's not like being smart makes you closer to God. And some of the psychology (keep em active, needing a bio break in 90 minutes) applies regardless of brains. But just, think about your audience. Are they little Lisa Randalls or little guest trolls? 10 out of a high school or 10 out of a district?