So far I've tried building my presentation from elements, each of which is differently paced.

A lot of tutorials are given just by rapidly writing fully worked solutions on the board, thereby leaving little room for actual discussion of concepts. I don't like that kind of tutorial.

The last tutorials I taught were based on the fact that the maths school would release fully worked solutions electronically at the end of the week and encouraged their tutors to have a more "lesson" based presentation.

I ended up with a presentation based on putting skeleton solutions comprising a list of sub questions that just referred to the appropriate concepts from the lectures. Then I asked the class to come up with the answer to each sub question so that they could see how a solution was built up and could contribute to its construction.

Then of course, even though you are keeping the ones who want to move faster happy by giving them the opportunity to participate and thus not get bored, you still have to regulate who's answering and how often and how to encourage the weaker students to have a go.

Any thoughts from others on how they handle this are welcome.


This situation sounds very similar to many of the classes that I have taught. Like you, I dislike the kind of tutorial that is just based on worked solutions - but, what I found was that the worked solution, could be a part of a dynamic tutorial.

This is what I have done - initially, I go through a worked example on the board (interactive whiteboard tends to work well), all the time encouraging questions about each of the steps. (I colour code the processes as well).

Then, I have the students in small mixed ability groups (i.e. I choose the groups based on abilities) go through separate questions, following the worked example as a guide. Gradually, having the groups determine solutions without a worked example on the board - using the skills, they have acquired.

I found that the smaller groups were less confronting as the quieter students started to become more vocal within the groups (and occasionally in front of the class) with more tutorials. Also, I found that the students became more confident to tackle questions on their own for practice/homework.


Perhaps the real solution to the conundrum is to take out one of the restrictions. Limit the material (it is just impossible to cover much material in any depth in 50 minutes), stretch time (perhaps by asking the students to prepare beforehand, or leave homework(ish) questions for later), or match abilities (ask the more quick students to help out others, perhaps by setting up work groups for each class).


Get them to work on problems in small groups (4 to 6 students) and walk around watching/listening and giving advice. This works best if they are working at a white/black board. If you don't have enough board spaces, dark whiteboard markers work well on windows, and butcher's paper is ok at a pinch.

You need to make your expectations clear on what is supposed to happen. I also tell them that no-one is allowed to move on without helping the others to understand. (EDIT based on recieved comment: Perhaps a better thing is to tell them they need to check if everyone is ok with moving on before moving on, rather than requiring that people help others to understand.) I also tell them it's always ok to ask someone to how/why they did something, as long as they're polite about it. When you are watching/listening, look for problem-solving strategies you can help them with, misconceptions you can fix, and also good things you can point out to them to increase confidence. If everyone is stuck at the same place, tell them to leave that one for later and you'll do it at the board at the end of the class.

At the end of the class, do some presenting to the whole class, perhaps doing a problem they all struggled with. Another thing to do in the whole-class time is ask them to volunteer things they learned today. This sort of "cognitive closure" is good for them.

One practical advantage of doing group work is that once you've set up how it works, students can start working even before the other students arrive, in some cases even before you arrive, so you don't have to waste time waiting for people to turn up.

In terms of learning, you get to actually see what their understanding is and have a hope of fixing misconceptions. This can't happen very well in any whole-class setting. Imagine the situation where you "got through" the wole amount of content but half the class lost you at the first example. All the rest of the examples are wasted. This way what they work on is more easily targeted at what they need. Also, students at different ability-levels can engage at different levels, sometimes by self-selecting into different groups, sometimes by the stronger students acting as teachers for the others.

Finally, it's more fun for everyone!

  • $\begingroup$ A quibble: might be a little too much to declare that everyone has an obligation to help others understand. Yes, doing so is "a good thing", but to declare it a (moral?) obligation will alienate some students, and also tend to delegitimize the teacher. Instead of "requiring" it, "recommend" it, for all the pursuant virtues. $\endgroup$ – paul garrett Jul 17 '14 at 23:16
  • $\begingroup$ @paulgarrett Fair point. "Recommend" is probably better. However they should still as a group come to a concensus that it's ok to move on, even if some students don't fully understand. I'll make an edit. $\endgroup$ – DavidButlerUofA Jul 17 '14 at 23:20

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