Another one added to the toolbox

Just a quick post on a strategy I recently used so I don’t forget to use it again in the future.

We were working on law of sines (LOS) in trig. We spent one day deriving the law of sines and one day solving basic triangles. At this point, about 30% of the class was ready to move on to complex LOS applications (the next lesson) while the rest of the class needed more practice solving triangles using LOS. Without planning it all the way through, here’s what I decided to do.

The next day I placed students that were ready for the application questions together in two small groups. Let’s call this the “advanced” students. I provided them with instructions, materials, and let them go explore the problems in their groups. I provided minimal scaffolding. For the most part they were able to work their way through the first few problems, which was what I hoped for.

As for the students that needed reinforcement and more practice, I placed them together in a few groups and provided heavy scaffolding and detailed attention to their needs. I’ll call these the “developing” students. I floated, sat and worked with them individually, and clarified any misconceptions that came up. By the end of the period, I was pretty confident that almost all of them could solve a triangle using LOS.

The following day, I brought the groups back together by using the advanced students to teach the developing students the complex LOS problems that they had already solved. I placed 1-2 advanced members with 2-4 developing members, depending on their levels. I found it to be a pretty good proportion. Of course, I was around to help and answer questions, but the kids ran the show and worked independently of me. The advanced students reinforced their understanding of the problems while the developing students shared a private tutor. And because the developing group got to practice more of the basic stuff the day before, they were much more fluid with the new material. It worked so well that I had them continue this peer tutoring for a second day.

What I loved about this stretch of days was that it promoted independent thinking and allowed me to reach the kids that needed it most. It also incorporated peer tutoring and kickstarted some great discussion amongst the kids. To top it off, it all required minimal prep. It was a win across the board.

Although we were studying the law of sines, I don’t see why I couldn’t use this strategy somewhat regularly with other topics. It could work well with anything that starts off fairly straightforward and gets complex, but still is obtainable without much scaffolding. Even if it does require a bit more guidance, I could provide more detailed scaffolding to the advanced group to help get them off the ground. And, of course, the advanced students could change based on the concept so one would get too comfortable.

Another collaboration strategy added to the toolbox.

Boy, do I need them.

 

bp

Two-Stage Exam

 

My kids have been struggling this spring and their exam scores have been pretty sad. Its been one of those years. To help matters, I began adjusting my pace, but I also wanted to implement some sort of structure for collaborative learning. Idea: group exams.

Sadly, I’ve never really used group exams. To be honest, the collaboration aspect of my lessons is usually pretty lackluster as a whole. I may have used group exams once or twice before, but it wasn’t significant enough for me to remember the experience. So, I had no idea on how I was going to structure it now. Brian Vancil mentioned that I try a two-stage exam.

It was amazing.

During a two-stage exam, you first have students take an exam independently, like they normally would (this is stage one). Immediately after you collect it, you get them in groups and give them the same exact exam  (this is stage two). They collaborate and submit one document with everyone’s name on it. Their final grade: 80% stage one and 20% stage two. These percentages can certainly be adjusted.

Student discussion during stage two was rich and completely focused on the mathematics. The kids were consumed with sharing their ideas, strategies, and misconceptions. Even my more introverted students were voluntarily sharing their thoughts in the groups. As I was walking around observing, part of me felt like I was dreaming. It was that good.

Their scores didn’t disappoint, either. I’ve given these exams a few times over the course of this spring and, overall, the results have been better than my traditional exams. But their scores are the least of my concerns. And two-stage exams do way more than merely inform me about how well my students understand something.

Students actually LEARN from these exams.

They’re driven by the students, reduce anxiety, and afford the kids a great opportunity to communicate their thoughts in a meaningful way. I’ve polled my kids after each of the exams and their attitudes towards the experience were overwhelmingly positive. The kids loved the immediate feedback and the ability to learn what they did wrong (and right). They were teaching and learning from each other in ways I’ve never seen. There were so many “ah-ha!” moments during stage two that they were hard to count. The groups were reflecting about what they did and didn’t do and unifying these thoughts to really learn from each other.

My kids are looking forward to the next exam. I’ve never heard that before.

 

bp

 

P.S. There’s also some introductory research on two stage exams conducted by Carl E. Wieman, Georg W. Rieger, and Cynthia E. Heiner. A good read!