- I felt I was too inexperienced to take it on.
- I felt the curriculum didn't lend itself nicely to projects.
- I didn't have the resources and infrastructure to execute it.
- I hadn't heard of many who believed in it.
- Couldn't elegantly explain why I felt it was necessary.
Slowly, over the last little while, these barriers have begun to weaken. I began by implementing smaller project work in my classes. It taught me some of the pitfalls that a fully project run class may encounter. My province went through an entire curriculum overhaul and pioneered a set of courses targeting the workplace and skilled trades. My indoctrination to twitter and blogs has provided a healthy repertoire of projects and inspiration for many more. Included with the ideas, twitter introduced me to many people who also held my vision for the potential of mathematics projects. Administrative support and my experimentation with wikis are reducing the logistical issues. All these factors culminated in a post last month where I gave my initial vision. (http://musingmathematically.blogspot.com/2011/10/proper-workspace-for-workplace.html) It has since been shifted and tweaked as my ideas grow.
Despite all these advancements, I have not been able to sit down and write exactly why I felt that a project-based course could benefit the students at my school. (I had bits and pieces, but no unified point) This problem took a major leap toward resolution this morning when I watched a TED Talk by Dan Meyer (@ddmeyer). I have used, and modified, some of Dan's ideas in class as a litmus for project-based math; his speech perfectly embodied why I have been working toward project-based math. Watch below:
The presentation contains many valid points, but the one that struck me as the inspiration behind my vision was Dan's use of the term "intuition". I haven't been teaching for long, but have spent that time watching students hunting for answers from information sources other then themselves. All 5 symptoms mentioned in the talk could describe my students' behaviour. Even the best lessons were met with the one question that told me something had to change:
"Is this right?"
The project-based approach will not eliminate the learning of incremental skills. It does not outlaw me from taking a group of students aside to explain a particular mathematical concept. It is not about abandoning my students so they can practice formulating questions on their own. I want my class to be set-up as a launching pad for student intuition. I want to equip my students with the tools to follow their own intuition.
In previous keynotes, I have heard the term "low-floor". Here, Meyer uses the term "level playing field". In both cases, the terms describe a math room that allows all students to become involved. Even a room, like my own, that is filled with students who think they cannot do math. Projects are built around familiar contexts to protect the dignity of all; every student has filled a container with water. Students can then use their intuition as the road map toward the solution. As they go, they will not only learn the incremental skills, they will use them in the most authentic situation possible--a situation they create. The math becomes the vocabulary for their intuition.
The projects provide the perfect weapon against impatient problem solving. It lessens the pressure that every student feels to "play the game". My hope is to provide a setting where students are looking for a solution to a problem, but don't mind spending time doing the math along the way.