This past weekend I had the chance to attend and present at Math In Action, the annual math conference held at Grand Valley. They are six, hour long, sessions throughout the day discussing a variety of topics ranging from cooperative learning, flipping classrooms, using technology effectively, the Adventures with Mathematics series, along with many of topics dealing with math education.
This first session I attended dealt with cooperative learning and how to do this effectively. The presenters were sharing strategies that they used in their classrooms after learning about them from Kagan Cooperative Learning. The first part of the session dealt with what exactly is cooperative learning. The first point they made that really stuck out to me that group work is NOT cooperative learning. As they talked more about this it became clear that it is not, the following quote really hit home on confirming this fact:
This is really true at least in my experience, students work in groups and as you walk around there is always that person who is doing all the work and those who are just piggybacking on the “hog” and they become the “log”. However, at least for me personally I never really know how to address this issue. This session really opened my eyes on how to address you can this. They said you first needed to seat your students based on their test scores for readiness for the content you are going to cover. You need to have four in a group with a “high” (1), “medium high” (2 ), “medium low” (3), and “low” (4) student. Your arrange it so (1) and (3) and (2) and (4) are shoulder partners and will work together. The key is that your students don’t know how your placing them. One activity they suggested having these pairs do, was work on the basic arithmetic skills needed (ie. Adding integers), where each person would have a different problem but it would lead to the same answer. They also suggested the use of task cards where each student would get a card with a problem on it. They would solve that problem and then have the teacher check it and then would become an expert on that problem and then be able to teach that to everyone else as they work around the room to pair up and solve the problem that everyone else has. I think these are both really cool ideas because it allows students to work with everyone in the class, instead of picking their friends, and it also makes sure that every student is doing the work. They also talked about how much easier it is to differentiate with this type of setup because the students that are identified as high achieving for the particular topic can be given material more appropriate for their level without much extra planning and the students don’t know that your doing it. This is definitely something that I want to incorporate into my future teaching.
The next session I attended was on how one Zeeland teacher flipped her classroom. She talked about how to structure the videos for the night before class so they shouldn’t take more that 20 minutes to complete while also making them available as iBooks for the iPads the students are provided as a way to get around the need for Wifi at home. She talked about how she is better able to connect with students in class about what they are doing and seemed to be able to do activities that really made them think. The biggest problem that she talked about was the issue of time to make this switch but overall she said she has really enjoyed it and her students have enjoyed it. Before this presentation I knew the basic premise of a flipped classroom but had never put much thought into it as a teaching method I would use. But after this presentation I think that if I were ever in a situation where a flipped classroom would work I would definitely give it a try.
My next session I was able to swap roles from an attendee to a presenter as I presented with other GVSU math students and one of math education professors on the activities from the K-5 Adventures with Mathematics books. I presented one game that had students work on their division skills to move up and down a pool in a “swim relay” by however much their remainder was. This session was especially fun because I was presenting games that were similar to ones that I wrote in my capstone course and and to an activity I helped create for the Algebra 2 Adventures with Mathematics book. I was able to share not only how to play these games but also talk about how engaged kids get with the math behind them as I have seen in my previous work with them.
My next session dealt with the use of technology beyond the graphing calculator. The first piece that we talked about was using Geogebra. It was nice to see that others are using it as it is something I have already started to use in my teaching. The other piece of technology that was talked about was DESMOS, which is an online graphing calculator. When they first starting talking about it I was thinking how would this be any better that a standard graphing calculator. I soon saw how it was better. As you type in functions the software starts to adjust the graph immediately. It also allows for a decent viewing window to found much easier. With these two features its easy to see how much of an improvement DESMOS is as it will allow for students to see what is happening with graphs much faster than a standard graphing calculator. I don’t know that this is something I will be able to use this semester but I will definitely be using it in the future.
The last session of the day was spent talking about the history of major mathematical topics. We were able to get through two, the quadratic formula and the Pythagorean Theorem. We talked first how an ancient Arabic mathematician was able to find formulas that are very similar to the quadratic formula we use today. This was done without all the technology that we have today and with an aversion to negative numbers. Next we talked about the Pythagorean Theorem and a couple of different geometric proofs for why this is true. These were the most interesting part of this session. (I found out that there are hundreds of different proofs!) The proofs that were shown used a square that was made up of right triangles and a smaller square and showed how to use these with things we already know about triangles and squares to prove the theorem. I think this would be interesting to share with students to show them that what they are working on, people before them figured it out without all the tools they have. I also would like to incorporate one of the geometric proofs of the Pythagorean Theorem with my students as I think this would be much better received than an algebraic proof.
Overall I think the whole experience at Math in Action was great and cannot wait to attend next year. I’m going to try my best to incorporate some of the cooperative learning strategies into my teaching this semester but if not definitely in my future teaching. I also want to incorporate some of the historical information as I think it is important for students to at least see where the concepts they are talking about are coming from.