You know when you give a quiz and students do well on one objective, but almost all of them completely bomb the other objective? That's when I know I did not effectively teach the second objective. So, back to the drawing board I go.
The quiz was on solving exponential and logarithmic equations. Most of the students clearly and easily solved the logarithmic equations. But, WHOA, those exponential equations really threw them for a loop!
I had taught the solving exponential equations lesson right before spring break. Normally, I write all of my own lessons, but this time I decided to use a lesson from a textbook (stupid, stupid, stupid!). In this lesson, the textbook had only shown how to solve exponential equations using logarithms as the inverse operation to exponentials. At the time, I didn’t think twice about it. I had already showed them in a previous lesson how to rewrite a logarithmic equation to an exponential equation and vice versa. I assumed they would apply that knowledge too. Ugh…bad assumption.
When we did the practice activities the day before the quiz, I also reviewed the property of equality for exponential equations. I think that is when I started to realize that I did not CLEARLY define the three methods to solving exponential equations, which is not like me at all. If you’ve read this post, you’d know I think one of the best ways for students to understand math is to compare and contrast different methods.
Anyway, the students seemed to be doing okay in the group activity, so I gave them the quiz the next day. Once I began grading them, I immediately realized they were struggling to solve the exponential equations. They were mixing methods all over the place. That’s when you get that pit in your stomach and think oh man, where did I go wrong with this lesson?!
It’s not the textbook’s fault, it’s mine. I so regret not taking a more critical eye to the textbook lesson. Maybe it was me being antsy for spring break or the fact that I had wanted to revamp some of my notes for that unit and I hadn’t had time to do so, so I was wanting an “easy” way out. Whatever the reason, it doesn't matter, I knew I had to fix it with my students.
I decided to create a graphic organizer that CLEARLY states each method and the proper steps to solve. I will be using this with my students tomorrow to review solving exponential equations and then giving a mini retake on this objective.
I’ll update you all soon on how it goes. I imagine it will be MUCH better!!!
In the mean time, I want to share the graphic organizer I created with all of you! Maybe it will prevent you from having an exponential failure like I did.
Click on the picture below to download the file. Enjoy!