Examples for Habit 3 Identifying Similarities and Differences

Critical thinking across all disciplines is one of our school initiatives.  We looked specifically at our questioning strategies this past year.

I was attracted to Pearse and Walton's book, Teaching Numeracy: 9 Critical Habits to Ignite Mathematical Thinking, because I want to incorporate habits that promote high levels of mathematical thinking. Their book is written with K - 8 in mind, so as I read, I'm interpreting their habits for the secondary  math class. 

This third habit, identifying similarities and differences, clearly connects to Marzano's work on high-yield instructional strategies.  There are four ways to identify similarities and differences: by comparing or classifying and creating metaphors or analogies.

I teach Algebra 2.  We spend most of our year on functions, identifying key attributes of each function, paying attention to transformations, and then applying those functions to problem situations.  Learning to note similarities and differences is essential to our work.

One go-to strategy is I notice, I wonder.  It is so easy to jump into a lesson without pausing, giving time for students to examine a graph, an equation, a situation.  It is in that pause, students can notice similarities, wonder about differences.

Another task that I used several times this past year is "Odd One Out."  I gave students four functions, expressions, equations and asked them, "Which one doesn't belong?"  We started with the Sesame Street clip to activate prior knowledge.  Students enjoyed the clip and sang along. I created a couple of my own "odd one out" activities and found a few of them in the book, The Algebra Teacher's Activity-a-Day, Grades 6-12: Over 180 Quick Challenges for Developing Math and Problem-Solving Skills.  Then sometime this year, MTBoS teachers started talking about the activities and Mary Bourassa created this website, Which One Doesn't Belong.  Check it out!  Add to it!  Invite your students to add to it!  One particular feature of the Odd One Out activities that worked best in my classroom and a definite difference from the Sesame Street version is that there are multiple correct answers.  Here is one example I used this year:

Student responses included:

1. The quadratic function because it is the only one symmetrical about the y-axis.
2. The exponential function because it is the only one with an asymptote.
3. The exponential function because it is the only one that does not pass through the origin.
4. The linear function because it is the only one with an unrestricted range.
5. The linear function because is the only "straight" line.
6. The linear function because it is the only one that can be found in the third quadrant.
7. The square root function because it is the only one that is only found in the first quadrant.
8. The square root function because it is the only one with a restrict domain.

Other comparison activities from this past year include:
Systems problems ... how are these alike and different

Factoring methods - I wrote about that activity here

A problem I didn't use this past year but one I want to use to use this year is "Intersections" at NRICH Maths. It gives 2 sets of simultaneous equations and asks: Explain why the solutions are so different and yet the pairs of equations are nearly identical. Can't wait to listen in on these discussions! I'm hoping that by looking at the equations more critically students will understand the significance of accuracy.  Minor changes in math can make huge differences!

Comparison activities fit well in the course I teach.  I struggle with creating metaphors and analogies.  If you use an activity for creating metaphors or analogies in secondary math will you share?

Pearse, M., & Walton, K. (2011). Habit 1: Monitor and Repair Understanding. In Teaching numeracy: 9 critical habits to ignite mathematical thinking. Thousand Oaks, Calif.: Corwin Press.