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Tuesday, November 22, 2005

The value of projects

Are projects valuable for students in a high-school math class? I suppose the answer must inevitably be, “Sometimes they are, sometimes they aren’t.”

OK, so we need to shift the terms of the question. We should ask, What kinds of projects are valuable? Which students are they valuable for? And how does their value compare to other learning experiences such as lectures, discussions, computer activities, homework, and tests (yes, tests)?

I have a healthy skepticism about projects. (At least I think it’s healthy.) Too often a student spends lots of time on flashy posters and flashy PowerPoint presentations to the exclusion of mathematical content. Too often the student merely cites and rearranges the work of others, usually from websites. (Actually, the work is often not even cited and not even rearranged.) Too often 90% of the work in a group project is done by a single student. And too often a significant chunk of the work isn’t even done by a student at all, but rather by a tutor or perhaps a parent.

And yet...and yet...there are all those times when a student has gained important or even essential knowledge from the process of creating a project. This knowledge might range from new mathematical content to the research process itself to the skills involved in working collaboratively in a group. If there’s a presentation component, everyone can benefit from the experience of standing up in front of a class and trying to explain a mathematical concept. And surely some students benefit from the change of pace and from the different modalities involve in creating and presenting a project — as opposed to homework, tests, etc.

There was one project I still remember back from when I was an 11th-grader. It was an investigation of 4- (and higher) dimensional vectors. I’m hesitant to draw any conclusions from this one example, especially since I don’t want to commit the fallacy of assuming that my students are like me. Not many are, I’m sure.

Perhaps it’s possible to ensure that a large majority of students will experience the potential benefits of project work while minimizing the negatives. Here are a few suggestions:
  1. The project should involve researching and learning some mathematical content that is genuinely new to the student.

  2. A presentation to the class should be required.

  3. After the presentation, all members of the group should be quizzed, both orally and in writing, about the content of the project.

  4. A significant amount of the work should be done in school, in order to minimize contributions by tutors and parents.

  5. The rubric should clearly emphasize content first, clarity of presentation second, and appearance a distant third.

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