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Context:

Because of organizational mess, there is a high chance that I'll be preparing a ~3h class for gifted students during a spring-camp (a week-long gathering full of all kinds of nice things to do) which will be split into two 90-minutes chunks on two different days (hopefully consecutive).

I have very little experience concerning such setting (previously it was either one-shot or at least semester-long courses) and I'm afraid that with all the activities available, they won't remember anything for the next day.

What I would like to achieve:

  • Although they need to declare which of the classes they want to attend (that is, either all the 3h or nothing), I don't want to tie them up with some sort of assignments, homeworks, problems to think about, whatever.
  • This cannot be two different one-shot classes. The topic is set and based on previous experience, for this audience I need at least 2.5h to deliver it in an understandable manner.
  • I would like avoid repeating myself, as this audience gets bored fast.

The quesion:

How to plan the class so that it will be relatively easy to bring students up to speed again when starting the second chunk?

My baseline plan was:

  • prepare a few memorable (if I can manage) problems for the three most important concepts of the first day,
  • give some handouts that the could refer to the next day,
  • at the end of the first chunk go over the handout and summarize the most important concepts,
  • at the beginning of the second chunk go over the notions in the handout and give a small task for each important concept,
  • solve each together, in the process referring to the memorable problems from the first bullet.

The problem with this plan is that it feels clumsy and will probably take more than 0.5h I can spare. Perhaps I could try interweaving the summary and the material of the second day, but that is hard and I'm afraid they might get lost.

What would you suggest?

Topic (edit):

This will be a part of lectures on computer science (think algorithmic contests), and the topic is associative operators. It is about why and how to represent partial problem/solution information in a way that can be combined by associative operators. A simple example is exponentiation by squaring. That can be combined with matrices to calculate Fibonacci numbers with logarithmic number of operations.

In fact this topic is not preset, but the intersection of what fits and what I can prepare on short notice is small, which means any other will be much worse.

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  • $\begingroup$ What is the topic that is preset? It seems much depends on the topic, and whether there is a natural partition. $\endgroup$ – Joseph O'Rourke Apr 17 '15 at 11:21
  • $\begingroup$ @JosephO'Rourke I've added some info on the topic. Unfortunately I don't see any natural partitions. Normally it takes less time, but here I cannot rely on the material from previous classes - these are high school students from different backgrounds - I will have to do everything from scratch. $\endgroup$ – dtldarek Apr 17 '15 at 11:57
  • $\begingroup$ I am too far from this topic to provide useful suggestions, so take this with a grain of salt. I would consider dividing the two sessions into: (1) associative operators, and (2) non-associative operators. For the latter, you could use vector cross product, which is noncommutative as well (but satisfies the Jacobi identity). The contrast between the two might enhance the appreciation of associative operators. $\endgroup$ – Joseph O'Rourke Apr 17 '15 at 23:57
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I think you should prepare it as if it were a special topic presented in a course in an undergraduate college. Although you don't mention age in the post, your post suggests these are college-bound high school students. I imagine one of the benefits of this camp is to give them a taste of what college classes are like, in an ideal sense. Don't repeat; review. Assume that they will behave like proper students, who are interested in learning because they opted to take the course. Give them an outline of the material, mention time will be tight, make yourself available outside of class for questions, spend two minutes or less reviewing the outline at the beginning of the second class, and prepare to triage if things go not according to plan.

Gerhard "Show Them You're Having Fun" Paseman, 2015.04.17

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