What makes a good project? Teachers argue over how much they should be predetermined or up to student direction, the difference between problem-based learning and project-based learning and other aspects. The summer capstone course I just finished teaching had an opportunity for maximum openness. It had the context of the history of mathematics, so any mathematical topic is fair game. One of my weaknesses as a teacher is not giving students enough structure - I'm so interested in what they'll do with freedom that I provide more than many want.

The condition of learning that this connects to the most, for me, is employment. Brian Cambourne explains

*employment*:

Employment. This condition refers to the opportunities for use and practice that are pro- vided by children’s caregivers. Young learner-talkers need both time and opportunity to employ their immature, developing language skills. They seem to need two kinds of opportunity, namely those that require social interaction with other language users, and those that are done alone.The project directions were minimal - instead I tried to communicate the idea in discussion, having the whole class talk about the kinds of things into which they might look, and who might be interested in that also. This worked pretty well

Parents and other caregivers continually provide opportunities of the first kind by en- gaging young learners in all kinds of linguistic give-and-take, subtly setting up situations in which they are forced to use their underdeveloped language for real and authentic pur- poses. Ruth Weir’s (1962) classic study of the presleep monologues of very young children is an example of the second kind of opportunity. Her work suggests that young learner-talkers need time away from others to practice and employ (perhaps reflect upon) what they’ve been learning.

As a consequence of both kinds of employment, children seem to gain increasing control of the conventional forms of language toward which they’re working. It’s as if in order to learn language they must first use it.

Brian Cambourne,Towards an Educationally Relevant Theory of Literacy Learning,Reading Teacher, v 49 n3, Nov 1995.

Project Possibilities: a project should show an investment of 16 or more hours. You might want to keep a log.Since this capstone class had an emphasis on writing for an audience and sharing work, more of this is available to share than in a usual semester. So... here's some student work! Hope you enjoy it, and that it gives an idea of what the exemplars are about.

- developed mathematical writing on content of your own working
- historical profile of period in mathematics or of significant mathematician
- series of lessons that includes historical connection or context or connects significant math content to the Common Core.
- video or video series on any of the above
- mathematical art that explores any of the above

Several of the teachers in the class put together lesson plans or a unit. For example, Erika, Kyndra and Kelsey made a website, the 3rd Grade Brigade, with lessons and resources for the 3rd grade common core in mathematics.

Bre Zielinski and Jessica Bracey went the farthest out there. One got interested in the platonic solids and the other in tessellations so they tried to combine the two to make tessellated polyhedraa. Lots of neat photos of their results in what was definitely the most artistic project.

Jeff Holt investigated something near and dear to my heart as he tried to make a new statistic for studying Magic: the Gathering. I may have egged him on, but he was genuinely interested in studying this or World of Warcraft. (He also did a history of the mathematician who invented Magic, Richard Garfield, for a weekly assignment.)

The project that had the most impact on their colleagues was this dandy from Ryan Garman and Joe Kargula. Ryan is a baseball coach at Grand Valley, and a former star player. He had the idea to dig into Sabermetrics and got some fascinating results:

If you enjoyed these you might be interested in the student-chosen exemplars from this same course.

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