This trimester in precalculus I’m taking a bit of a risk and trying an alternative final exam for the trigonometry unit. Students are building concept maps including each topic that we covered in the trig unit and the connections between them. (Full disclosure, I’m borrowing the format and rubric for this activity from @cheesemonkeySF and you can read the post here.)
I put a great deal of thought into why I think this exam is more effective then a traditional multiple choice test (like I did last year). Steve and I put a lot of time into trying to get students to see connections between concepts and to get them to truly understand the mathematics behind each individual concept. My goal is to help students become mathematical thinkers, not just people who can memorize certain steps in time for the final exam only to forget (or never actually learn) the concepts. Because of this I have issues with giving a multiple-choice final exam which tests them over the exact thing that isn’t my main objective. I understand they are easier to grade, but for the last year I’ve been looking for some alternative to the traditional multiple-choice final exam.
Enter the concept map idea. At its core the concept map forces students to find connections between topics and think deeply about how those topics fit together in mathematics. In addition to just finding the important concepts maybe the most important part of it is justifying the link between the concepts. This should provide me a window into the reasoning skills and their grasp of the big ideas in the from the course.
Students got started on working on outlines for how their concept maps were going to look. Some students started sketching concept maps on the mega whiteboards, others made outlines, and some stared for a while not knowing where to start. It was awesome to see all the different methods and reasoning for how each concept map was going to be designed. There was already thinking about the “big picture” connections between topics. This was a great start and every student was engaged all hour.
Many students came ready to begin putting their concept maps together. Once again
engagement was at a very high level. One student said, “I think this is the hardest we’ve worked as a class all year.” Just this fact alone makes me think this style of exam is worth hanging on to. To have full engagement with every concept in trigonometry and constant conversations about the meaning of concepts for two days straight is great. I’m starting to see how students made connections throughout the trimester and I’m excited for their final products.
Students came in and went to work without me saying anything and worked hard the entire hour. It was fun to watch all of their ideas come together. By the end of the hour there was no doubt that I would be doing something similar for my final exam next year.
Thoughts and Reflections
I couldn’t have been happier with the outcome of this project. There are a number of reasons I deem this project a success and worth doing again next year. First, students were forced to think about the context of all the concepts. It happens so often in math class where students just chug through the course without seeing the bigger picture. I think there is a tremendous amount of value in creating activities where students can step back and look at the context of the concepts they’re learning. If my goal is for students to see mathematics as more than just pushing around numbers and symbols then I have to incorporate this type of activity.
In addition to seeing the bigger picture, this also gives students a chance to collaborate on a project that has more meaning then a final exam. They have to collaborate and analyze the course together, and think critically about the connections between concepts. This is a skill that students will most certainly use in college and in the work force.
Also, this style exam creates a learning experience for students. Over the course of three months concepts become fuzzy or connections are lost and this forces students to go back and really decipher the meaning of the concepts and connections between them. Often as students move through content they miss the connections (even though I try to create activities to help with this). Reflection allows students see the connections (maybe for the first time) and they’re more likely to have really learned them because the learning moments are happening in the context of the concept map project. I don’t see how this could happen with a traditional exam.
Finally, my favorite quote of the last day convinced me that this activity was worth keeping: “Mr. Cresswell, I’m actually really proud of this. This so much more meaningful than regular assignments.”
As I alluded to above, my goal is to create individuals who are mathematically minded and critical thinkers. I think this activity does a far better job of pushing students in that direction then a traditional exam.