It was great.

We’ll see what they came up with when they took it home to finish it for homework.

This book is nice, too. I go to it often when my ideas get stale: http://www.amazon.com/Cooperative-Learning-Mathematics-School-Activities/dp/1879097575

In our calculus class, we won’t cover sign analysis, but we will probably look at asymptotes vs holes pretty soon. This is what I’m thinking we’ll do: I’ll give them a table with several functions, and columns for recording holes, asymptotes, etc. They’ll fill out the table with their groups using calculators, record any patterns they find, and share out. As long as I pick the functions carefully, I won’t have to explain what it is that makes some functions have holes and others have asymptotes – they’ll figure it out.

In general, I try to tell the students as little as I can – the less information they start with and more carefully I choose the starting information, the more the students get out of coming to big conclusions on their own. Plus, they often end up making some amazing connections that I never would have thought of if I was straight up lecturing!

Ooh – one last thing that helps. Whenever possible, I try not to answer their questions directly. So, I answer “Why is that point located at (pi/2, 1)” is answered with, “Good question! Can someone help explain why that point is (pi/2, 1)?”

First off, let me say that I love your SMART board presentation…”check yo’ self before you wreck yo’self.” *smile* As for the teacher-centered/student-centered questions, that is something that has been a goal of mine for this year, too.

Something that I suggested to Anne (@msgregson) at one point was a partner review/practice activity…you have 2 forms of similar style problems…partners get different forms, solve a problem, then the switch and check each other. This could possibly work with new concepts, too, where students take the responsibility of (your quote-ish) “Making something they don’t know look like something they know”. Pulling the class together at the end can bring up some conversation about how the partner thing worked, what mistakes they saw in each other. You can also partner with someone, esp. if there’s an odd number of students.

You inspire me with your reflections and transparency. Keep it up!

First of all, don’t sweat it – it’s only day 4! Secondly, try some problem-based approaches. You don’t have to go all in the way I have, but give them some problems to work, an exploration or a lab that they have to work through together which gives you a chance to watch them work rather than direct them. If you aren’t sure what to do, there is a series of calculus books by MAA with labs and applications that are pretty handy (I can send you exact titles if you are interested), and for a little more structured exploration I recommend a book by Paul Foerster. It’s an exploration book designed to go along with his textbook, but I have been using it independently for years.

Good luck!