We recently covered Area in Geometry and instead of employing a usual teaching format (follow lessons in book with nightly homework in between) I tried a “blended classroom” approach. I started the chapter with a project, a BIG project. Students were told they had to design a house, make the blueprints, determine the total surface area of the house, and put it on the market (not really on the market, but they had to decide where they were going to build the house, come up with an address and based on “comps” in that neighborhood (i.e. houses with the same total area or square footage) set a price and create a realtor’s brochure). The house had to have at least five of the shapes we had studied this year: square, rectangle, triangle, parallelogram, rhombus, kite, trapezoid, any regular polygon, and circle. It had to have at least two stories and they had 1 acre of land on which to build.
They had 2.5 weeks to get this done. Class time, with the exception of the first 10 minutes or so was theirs to do what they wanted. They could work anywhere on campus they wanted (I created a google form where they could tell me where they’d be) and in the course of those 2.5 weeks, they had to check in with me two times each week. Homework was minimal. Each night they had to derive, visually, a new area formula that I assigned. We spent the first 10 minutes of each class sharing our derivations and after that the time was theirs to work.
Let me tell you a little about this class: it’s a bear to teach. I don’t know if it’s the mix of girls I have or the fact that it’s a seventh period class but the group as a whole would rather be pretty much anywhere else but my class, doing anything else but Geometry on a daily basis. Fun, right? Part of me thought it was a big risk to give these seemingly unmotivated girls so much freedom, and during seventh period no less! The other part of me thought it really couldn’t get much worse, and we all needed a change of pace.
Once the project started, I was pleasantly surprised by a few things: [1] I could always find the students when I would circulate the campus and, amazingly, they were usually excitedly working. It seemed I had finally found something that they liked! [2] Over and over again I heard, “I was working on this last night with my dad” or “My mom was helping me look up the area formulas.” To me this is awesome. I gave them something that they shared, voluntarily, with their families at home! [3] the nightly homework assignments in which they had to derive the area formulas on their own were amazing: creative and thoughtful, they showed me that the students were really thinking and using their reasoning skills to figure them out. Here are a few samples:
Look at all of that amazing thinking and reasoning?
When the project finished, I noticed a couple of other small observations that may or may not mean anything. The project was due at the beginning of class on Wednesday. That day no one was absent and everyone was excited, I might even say proud, to hand in their project. No one needed an extension, and at first glance, they all looked amazing.
I gave an evaluation about how they liked this project and this way of learning a topic. Here are some of the results:
I found this next result particularly fascinating: look how hard they worked! I totally let go, I removed the usual scaffolding of a typical chapter and the micromanaged assignments, and they actually worked harder.
Finally, I share with you some anecdotes from the evaluation:
I enjoyed being able to work anywhere it gave me a different vibe then sitting in the classroom like I do in every other class. I liked how we needed to check in with you. I wish we could’ve done it as a group if we liked to, and needs a little bit more time maybe another 3 days since it’s a lot of small projects into one. It was a nice break from writing down on paper taking notes doing regular problems. It also opens me to think about how to find the are of a shapes I didn’t know and how I could use the area of shapes I already knew to solve for the shape. I think it would’ve been better to go over all the areas we might need first then give the project.
I really enjoyed this project, which is saying a lot because math is neither my strong suit nor my passion. This was a great opportunity for me to learn about what Area is and how it is solved while simultaneously incorporating my creativity. Instead of sticking to the routine of homework, quizzes, and tests, I was able to show the little skill I have in math. I also am better at learning when the material is applied to real-life situations. It gave me a lot of confidence as well.
I loved the project
I loved how this is something relevant that we can actually use in real life
It was actually fun making the floor plans and the brochure
it was a fun engaging project that made me look forward to this class.
There were some skeptics. And, you can see from above there was a mixed review when it came to the question of whether they learned what they needed to know by doing this project. What was so interesting to me were the comments by students who thought they didn’t learn what they needed to simply because I hadn’t traditionally taught them:
I didn’t really enjoy it because it didn’t help my understanding of area, it only tested my abilities to look up and follow the formulas. I didn’t really know what I was doing during this project and I would not feel confident or prepared if I took a quiz on area after completing this project
I feel like the project was a nice way to get immersed into the area section of geometry. However, I don’t think that the project was very efficient in teaching me the most about area. I also don’t think it prepared me very much for any tests/ quizzes we will have concerning area in the future.
I did learn how to do the area and stuff but I often found myself looking up the formula for specific shapes. I feel I might of retained the information better if we would of learned it from the book but I did like the project.
I really liked this project and i thought that it was the most enjoyable project. I think that learning about are and perimeter could have been accomplished in a different way. I think that i would have learned about area better if we did followed the book and did it like a normal class. (Normal meaning that the teacher teaches us the lesson and then the students do the problems in class and for homework and ask the teacher questions).
I would argue that having to look up and figure out formulas yourself makes you much more likely to remember them. How can we convince our students that learning doesn’t need to happen with the teacher at the board and students passively receiving the information? And, that perhaps this isn’t the best way to learn? How do we teach our girls to be resourceful and to value that resourcefulness? This has been a really awesome experiment for me and despite some mixed reviews, I truly believe that this is the way that real, sustaining, learning happens. I look forward to continuing this free, blended style of project based learning and hope to see the culture shift where my students learn to trust this process and trust themselves and all that they’re capable of.
