# Day 78: Not All Mistakes are Bad, IF You Learn From Them!

I’ve been reading the book, Total Participation Techniques: Making Every Student an Active Learner by Persida Himmele and William Himmele, published by ASCD (can also be found online and downloaded if you are a member of ASCD).  The authors talk about getting your students actively engaged AND cognitively invested in the learning rather than being “listening objects” in the classroom.  One quote that resonated with me was:

At any age, people need to pause and process what they are learning. They need to chew on concepts, jot down their thoughts, compare understandings with peers, and articulate their questions…and celebrate the learning that is happening right now in my head.

As a follow-up to solving trig equations, I had my students create posters, but I wanted them to do more.  I found a great idea from Rebecca Peterson called the Mistakes Game.  I adjusted the directions some and came up with this activity:

SOLVE CORRECTLY:

2. Once you have the correct answer(s), write out the solution process neatly on a poster paper.
3. Include a graph of the original function and the location of the solutions (color-code by principle solution and symmetry solution.)

INTRODUCE A COMMON MISTAKE:

1. Now work the problem incorrectly, hiding your mistake as cleverly as possible.  Your “mistake” must be a true pitfall of the given problem (i.e., what kinds of conceptual errors would students likely make?).  Your error cannot be a simple arithmetic or algebraic mistake unless it is related to using an Algebra Trick incorrectly.
2. When you’re happy with your “lie”, put it on the back of your poster paper. Post this side for all to see.

FIND THE ERRORS:

1. When every group is done, you will find the errors on the other posters and vote on the group with the sneakiest mistake.
2. Be prepared to discuss/defend your results.

I really like the idea of coming up with a mistake.  This causes the students to use higher-order thinking skills to analyze and synthesize.  This is cognitive engagement at its best.  I heard lots of discussion around the process, with students correcting others and helping them understand their error; but then the magic happened!  Trying to think of a mistake one could make when solving a trig problem, and the idea that they need theirs to be “tricky” led them to go through many of the common errors.  They were talking about what would be an error and by deciding if it was “tricky” enough, they had to understand the nature of the error.  I am really excited to see if this process helps students to think more carefully while they solve trig equations and to avoid those common pitfalls.