Great success with Mistakes

Some of the best moments of the school year have been those during which I can stand back, watch my students, and actually see their curiosity, engagement, or determination while trying to solve a problem. These moments have definitely been few and far between, but in the last week I stumbled upon one of the best instances of this that I've seen all year.

I've been thinking for a while that I needed to incorporate some type of practice in my classroom involving "proofreading" math work. After all... editing paragraphs in English class is a very common lesson plan, why can't it work in Math? So, last week, bravely scheduled for the day that I was being observed by my Teach for America program director, I copied mistakes from the most recent quiz onto transparencies, made up a graphic organizer and proceeded full steam into a new classroom activity. It was a HUGE success! The lesson was not focused on simply correcting the mistakes, but identifying them, describing/analyzing them, and concluding each little mistake with a statement or rule that would prevent the students from doing the same thing in the future. At no point did we actually say "The answer should have been this..." That was implied by all of the other analysis. (If anybody is interested in the graphic organizer, I would be very excited to share it with you!)

During this lesson I saw the "problem-solving spark" that I have lamented the absence of all year. As I moved from one example to the next on the board, uncovering each on the overhead with a little played up fanfare, I didn't need to remind students to pay attention, keep their head up, or not talk to their neighbors. They were intent on finding the mistakes on their own. When I asked the analytical questions following this, instead of getting blank stares I got really thoughtful answers - some of which I had never thought of myself. These attitudes toward this mistake activity have continued to be positive this week as they have used the same organizer to analyze mistakes they were making on their own. "Ms. Breeden... I've been making the same mistake on all of these, I just need to remember this..." It's been great.

There are a couple of different things I can take from this experience... First, with the analysis of the mistakes I asked my students to move up Bloom's taxonomy and they responded amazingly. Why have I not been doing this all along?? Their previous boredom with the material is not necessarily a result something intrinsic, but a result of them not being pushed to the higher levels of understanding that inspire motivation and curiosity. The second realization comes from what I've seen this week... after being pushed to the higher level, almost every student has shown mastery of the topic this week. In addition to that, about half the students (much more than normal) have been successful at taking this knowledge and applying it to different, more challenging problems. (Problems that are even a step beyond NM state standards!) Maybe they're just a little smarter this week, maybe I did a great job of explaining something, but I think it's more an issue of them finally being challenged and pushed. My expectations have not been high enough so far, but maybe this experience will get me a little closer.