One of the fun activities we bandied about in the Talk Less session at TMC16 was to ask students to create the best mistake for a particular problem. Each year in my Algebra I classes, my students (9th graders) have had some portion of Algebra I the year before. Many have had courses that didn’t take them all the way through, some experienced all of it but didn’t do so well, and some had PreAlgebra. We are a private 9-12 school, so we are in charge of placing them after an assessment. This is all to say that while my students need a year of Algebra I, many of them also need a fresh look at the subject–especially the intro topics that they most definitely hit last year. This activity is perfect for this situation.
Introducing this activity was as simple as can be. I gave them one equation to solve and asked them to create the best mistake they could. I had each table (3 or 4 students per table) put their mistake worked out on the board. After they were all done, a representative needed to explain their mistake. Here were all the results from one period.
I’ll tell you what, as happy as I was with these results, the next period wasn’t so great. As much as I don’t want to degrade or judge a mistake that a student thinks is relevant, they started going down a road of simply dropping numbers or introducing new ones. Responses weren’t as thoughtful. A lot of that is on me. Maybe the setup required more work than I indicated before. Maybe I need to respond to the specific combination of students in that room. Regardless, I’ll be coming back to this activity.
This year I am using mistakes to prompt discussion in class and make homework dissection more engaging. In my AP Calculus AB class, I use Active Calculus as the text, and many of its activities and exercises are perfect for an Activity Builder conversion. Such was the case when I assigned this activity to work on section 1.3 Ex 1 in Active Calculus.
The very first slide has students drawing some secant and tangent lines on a function. Most students in all three sections did pretty well with it, but I saw a few common errors I wanted to address. So channeling my Talk Less course from TMC16, I made up these two slides.
We have been playing around with the prompt “What is the best mistake?” in Algebra I lately. Today we did another similar exercise where I gave them two flawed solutions to a homework problem and the prompt “Which is the best mistake?”
Like in past iterations, students buzzed about what that means, and I was predictably quiet save for my warning that they have 60 seconds to formulate an argument.
Anyone in this field will tell you that a good answer is one with a solid reasoning, a good warrant. I heard a few that I liked. The best argument all day–all year so far–was when a student said “#1 is the best mistake because it is a mistake I would make.”
At TMC16, I attended a 3 day class led by @stoodle and @Plspeak. For reference, here are their materials on the wiki and a collection of the tweets from the class.
Chris started the class by demonstrating how he uses Claim/Warrant statements to structure class discussion. He models formal debate by forcing students to present a solution or opinion in terms of “My claim is ______. My warrant is ______.” The warrant is the justification.
Another strategy they demoed was in presenting two solutions (and sometimes two errors) and having students pick which they liked best.
So today, on the 3rd class day with my Algebra I students, I gave it a whirl.