We began the session by listing together some of the challenges or barriers to using project-based learning in math. The main two challenges seemed to be time (how to fit such projects into an already-overcrowded curriculum) and the test (mathematical discovery and real-world applications will not be tested, so they get bumped in favor of tested material). To address these, Ms. Texas advised viewing a project in a different way: not as something to be added in at the end where students apply a mathematical tool after it has been taught, but instead as an overarching framework that bridges many standards/concepts and drives students to learn those concepts. Students can be introduced to the project idea at the start of a unit, then work on it in pieces over the length of the unit, and the project will create the need (or at least motivation) for the relevant mathematics to be learned/taught.
The most inspiring part of the presentation was when Ms. Texas described a project she did with her students in a combined math & science class. She had students design and build a model of a bridge, which incorporates the physics of forces, and the math of similar triangles, trigonometry, and vectors. But most important was her idea by which she created an audience and a purpose for the project. She had read an article in her newspaper about plans to build a new bridge across the Ohio River near her town. And the local Department of Transportation was soliciting proposals from engineering firms in the area. So she called up the DOT and asked them if her students could be part of the proposal process. After some discussion and convincing, they agreed, and she asked if they could send an official request for proposals to her class. So then, at the start of the unit, she was able to show that letter to the class, and pass it around to convince the students it was real and they were really being asked to submit designs! Students created designs to the specifications of the real project, as well as slightly-less-accurate balsa-wood or spaghetti bridge models. They were asking Ms. Texas to teach them about the math and science of forces, so they could have a better design. In the middle of the project, Ms. Texas brought in engineer volunteers to look at the progress and give real critique/feedback. At the end, the students had a final product (report/design brief) of high quality and had learned lots of math and science.
In closing, she provided us with a list of resources that can be used for math projects, of which the following were interesting enough for me to write down:
- Engaging algebra videos by The Math Dude (site)
- Math raps at educationalrap.com (their math page, listen to a sample of “Circumference (It Just Makes Sense)”)
- The National Math Trail, where students map out a path, including pictures and worked solutions, of math problems in their local community (site, Kay Toliver explaining her use of the Math Trail)
- West Point Bridge Designer, a free software where students design and load test bridges while striving for cost efficiency (download page)
- Eeva Reeder’s geometry project where students design a school of the future (overview, project details, article by ER on applied learning)
Over the past four years of teaching math courses, I have moved to include more (and hopefully better) projects each year. This is partly influenced by my transition to teaching half-engineering, where the curriculum is almost entirely projects (with direct instruction as needed to aid the projects). But it is also due to my philosophy of teaching: I believe students learn better when they discover the ideas for themselves and when they engage hands-on in doing of mathematics. I have posted most of my Geometry and Algebra 2 with Trigonometry projects online.
What I would like to do this year is move away from including lots of projects interspersed within my math classes, to having the projects drive the math. I need to sit down and pick out maybe four-six major projects (either extensions of mine or from other sources) that have enough heft, and bring together enough concepts, to drive the curriculum. In addition to choosing them, I need to think about how I can work to make them have a real purpose for the students and a real audience beyond the teacher, whenever possible.