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I am an undergraduate applied math student. In about a month, I will be teaching two nine-hour math courses (one precalculus, one calculus) to a small group of motivated high school students. My broad objective is to refresh their existing skills and to give them an opportunity to present and work interesting problems together. This is why I am planning on using the problem sequences from Mahavier's Trigonometry and Calculus notes. In addition, I will encourage them to see me during some regular office hours that I will hold. I prefer this style of teaching given that we only meet for an hour two times a week and also because I really enjoyed a full math class.

However, I think now I face the conflict of using these resources with them and not knowing how far we will get, or perhaps switching over to a more lecture-based format and being more certain about this. Then there is the issue of assessment, because I have spoken to the former teachers of these classes and they have typically devoted one class for a traditional exam and another at the end for a cumulative exam.

My question is, does my preferred way of running the class fit in with the short time we have with each other?

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    $\begingroup$ The class meets for a total of nine hours, and historically they've spent 30% of that class time on exams? And it's for credit, for high school students? Unless there's a significant amount of homework, it seems difficult to teach enough to evaluate them on the usual things, especially if class time is devoted primarily to interesting problems. (I say this because nine hours is about 2.5 weeks of class for (pre)calculus, at my university). $\endgroup$
    – pjs36
    May 31, 2017 at 3:17

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I think the answer to this question boils down to how concerned you are about "how far we will get". Like, it's certainly easier to set a pace if you're lecturing, but you only need to do this if you have a mandated list of topics to cover. Without such a mandate though, you can run the class exactly as you prefer; that's your prerogative as the instructor. :) Then using all the class-time for this is depends on what you're comfortable with. Do you need to have a class meeting to hold an exam, or are you comfortable with the students taking an assessment on their own? Do you need to need to have the whole class meet to give a lecture, or can you record a lecture for them to watch (asynchronously) on their own?

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