MHF Cycle 2 Reflection

I have previously posted a reflection of our first cycle here.

Here is the plan that we used for our first cycle.
(Most of the activity credits go to Jamie Mitchell and Steph Girvan in the Halton Disctrict School Board - Thank you for sharing your resources - including your blood, sweat and tears guys!)

One of the things we have found as a department is that students often struggle with the algebra portions of this course. Because of this I offered my students an "algebra crash course". I attempted to remind them the core of algebra and solving equations through manipulatives and a clear reminder of what inverse means (i.e. that log is a function, so has an inverse). These should be ingrained ideas that these students have and I find myself often wondering how to best help students at the high school level with these skills. If anyone reading this has any ideas please share!

As you can see in our plan we had two traditional tests in this cycle. We split the algebra portion up into two sections, polynomial & rational functions and logarithmic & trigonometric functions. The last part of the cycle has students explore combinations of functions through investigation of graphs and getting students to do their best to generalize rules for different types of combinations. As a final evaluation in this unit we had student-teacher conferences.

Students had a conference like this one during cycle one as practice (for all of them I was using Google Forms to track and DocAppender to give student immediate access to feedback). For this conference students were given two functions in small groups. They were asked to identify the characteristics of those two functions and then to as a group predict the superposition characteristics of those two functions. On the day of their conferences students rolled a die to get a random second combination. Students were given 5 minutes to prepare and then had 5 minutes to share as much as they could about that combined function. The key was that they were to explain why they believed those were the resulting characteristics, not just to list them.

I found this evaluation very insightful into student reasoning and understanding of characteristics as a whole. It also provided insight into the emphasis that I should consider putting onto the graphical representation of functions in earlier courses. I have started to think that we take for granted what students take away from graphs.

I really enjoyed the experience with conference with these classes and definitely plan to continue working on using them in other courses. Getting students to explain things verbally has an ability to show student learning that reading a written response just cannot do. The power of triangulation of evidence.