At my university, traditionally a few lectures of a course should be tutorial sessions. The idea is that instead of covering new materials, the teacher should go over many exercises so that student learn how to solve problems.

My colleagues do these sessions differently. Some go over some examples and let student work in group themselves for the rest of the time. Some would ask students to come to blackboard to solve problems in the front of the class.

Do you organize such tutorial sessions? What format do you use?

Update, I have arranged office hours, but so far no student has ever come. I suspect very few of them will eventually come to office hours.

Also the lectures are of 105 minutes each time. I usually take 5 minutes break in between.

I am thinking of telling students this next tutorial

  1. You vote to decide which category of problems we will talk about.

  2. A problem from the chosen category will be given, with some hint.

  3. You work by yourself or in group on the problem for 5 minutes.

  4. A random student is chosen to present his/her solution to the class

  5. Name another student to represent you if you don't want to talk.

  • $\begingroup$ What is the size of the class? Effective student-centered learning techniques are possible with various sizes of classes, but the techniques tend to be extremely different for a teacher-to-student ratio of 15 than for 300. $\endgroup$ – Ben Crowell Feb 6 at 16:00
  • $\begingroup$ @BenCrowell I have about 20 students in class. $\endgroup$ – ablmf Feb 6 at 16:38
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    $\begingroup$ Thanks for the info. I would suggest that you just edit that into the question, and then we can delete the comments. $\endgroup$ – Ben Crowell Feb 6 at 17:23
  • $\begingroup$ Do you advertise your sessions as lectures, tutorial sessions, labs? Maybe the students think that this is yet another "we are killing another two hours listening to boring prof talking" kind of thing? I think that simply "covering" problems is not enough, the students have to work themselves, including coming up to the blackboard, I agree with your colleagues. If you want the students to come, declare you sessions mandatory ;) $\endgroup$ – Rusty Core Feb 6 at 20:26
  • $\begingroup$ Oh I just had my first tutorial today. First half I talked. The second half I told them they could stay to work on homework and I will answer questions. 3 students stayed. :D $\endgroup$ – ablmf Feb 6 at 21:27

"Oh I just had my first tutorial today. First half I talked. The second half I told them they could stay to work on homework and I will answer questions. 3 students stayed. :D"

I hope you learned a lesson from that! It's absolutely what I could have predicted. You should have also.

Personally would mix it up some, but emphasize drill/work throughout. Have a handout, do a pop quiz (can be ungraded), do breakouts, do games (Family Feud or Jeapordy knockoffs). Do recitation (student to board).

A very simple way to get things moving is to have a handout that they work on first 25 minutes (make it reasonably short). Then do in class recitation, calling on people, etc. for the solutions. This kills first half of the period. And it gets people using the math, in the mood, etc. Allow self work or partnering/grouping as they choose.

Second half you could pivot to limited lecture time, followed by ad hoc student questions. Keep it light "tricks, hints" during the lecture. Do the horse sound and tap the floor like you are giving them best sooper secret scoop to pass tests. Students love these corny games...life is short, have some fun. Also, the interaction second period will be much better since people have had some recent experience with the material. If they want to bail after the horse secrets during the ad hoc time that is OK. They will have had a good experience for the majority of the time.


I personally do a mix of what you mention, depending on what mathematical maturity is expected of them.

If they are advanced students, I would work our various example problems for them (perhaps leaving some details to them). Most of the time it’s fairly beneficial to let the students work in small groups/pairs so they get the benefit of getting information they might not have gleaned earlier.

For example, in a differential equations class, I might ask the students to form groups of 4-5 and present problems (to the whole class) that cover the different subjects in the course: 1. A group on separable (or exact) 1st order DE, 2. A group working on a variation of parameters problem, 3. A group working on a similar problem instead having to use Laplace operators. By doing this the students will have practice with each type, and see how other students complete it.

This works even if it’s only the first part of a class - simply pick different problems that force students to look at different subtopics.

  • $\begingroup$ Hi, can you expand a bit on your answer? $\endgroup$ – András Bátkai Feb 5 at 19:03
  • $\begingroup$ Do you ask student working groups to work on specific problems? Do they represent the result to the class? $\endgroup$ – ablmf Feb 6 at 8:13

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