Mother Function!

Reflection for Thursday, 8/1/2013

Today, we opened with a graph matching activity that I found particularly interesting, because I have learned that my students have a few particular weaknesses heading into my calculus class:  (1) anything involving exponential or logarithmic functions, (2) problem solving involving trigonometry, (3) algebraic manipulation including factoring, solving, rationalizing, manipulating expressions, (4) graphing (or having a feel for the shape of a graph without a calculator).

In my school, we have a six period, seven day rotating schedule, which means I see classes for six days in a row (with one long period during lunch), and then drop the class for a day.  We also, for AP Classes, have an extra flex-block period after school, once every seven days.  This year, I’m thinking about using those flex-blocks (at least at the start of the year) to reinforce some of these skills, and I think that working with graphs of functions might be a good way to start that.

What I particularly like about the graph connection activity, is the oddness of the basic graphs–not ln(x), but ln(x^2), not 1/(x-2), but (x^2-3)/(2x-4).  I like the review of what I call mother functions (they especially like the ones that are BAMFs (bad asymptote mother functions)).  I think this works in a couple ways–first, gives me a chance to see how students functional thinking (sans calculator) is working after a summer off, and perhaps focus in on specific student weaknesses without taking significant time away from class; second, it gets students ready to work together throughout the year, which is an important skill not always developed in earlier math classes.