Last Friday was the first quiz-buffet of the year in each of my classes. Some of my fifth graders really took this metaphor to heart and rhapsodized over whether they would be picking up some of the “chicken wings” or “roast beef” and deciding that they would come back later for “dessert.” In all of my classes the quizzes went really smoothly. I feel much more adept at putting together quizzes and practice packets and keys than I did a year ago. It’s also nice being able to dip into the materials I made over the course of last year.
In my high school classes—Geometry and Calculus—most of my students quizzed for almost the whole period. (Our periods are forty-five minutes.) Those who finished before the period was over continued working on their first Investigation about defining geometrical objects (Geometry) or a new sheet about limits of sequences and series (Calculus). I’ve only had a brief conversation with my Calculus students about what Fridays might look like in the future (free-choice time to work on problem sets and projects, with quizzing as an option) and haven’t had a chance yet to discuss this with my Geometry students. For now I’m just happy to get my high schoolers into an assessment rhythm that feels comfortable to them. I figure that opportunities for self-direction will open up as the material of these courses unfolds. Also, there’s a whole lot of self-directed, choice-but-not-free-choice time in my Geometry class throughout the week already—more on that another time. Still, for my high schoolers I’m currently in a place where I view free-choice time as purposeful but in a supporting role. It’s an important opportunity for students to direct their own learning of course content and to personalize it, but it’s something that while good in itself is also a means to an end—getting at the content of a field of study.
With my fifth graders, it’s easier for me to see free-choice time as an essential component of the course that can stand on its own. It’s an opportunity for kids to explore a huge variety of mathematical activities, to help them find some that they love, and to help them build identities as mathematicians and as individuals. It’s an end in itself that has its own set of goals built in. I wouldn’t let a high schooler investigate a mathematical game that she was into during calculus class—at least not for any significant duration—no matter how excited she was about it. Because it’s calculus class. But for my fifth graders, it doesn’t matter to me whether strategizing about that game is in any way related to the other content that we’re exploring in the course. It doesn’t need to be laying groundwork for making factor trees or subtracting integers. Having a kid build up her own relationship with math is at least as important as anything I could teach her.
Writing this makes me want to make high school more like middle school. Think, think, think…
I decided that introducing the quiz structures and the free-choice structures in the same week would be too much to dump on fifth graders all at once. (At the very least, it would mean way too much of me over-explaining all at once.) So I had several activities available for kids to choose from in an informal way once they were done with their quizzes. These are some of the activities that I’ll “announce” for this coming Friday in a more formal way, and this time around my kids will have the chance to journal about what they’d like to pursue ahead of time. (They’ll also journal about what quizzes they’re preparing to take.) I reasoned last week that having some prior experience with the activities in question would make that first planning/reflection this week more grounded and thoughtful.
Anyway, the activities I had for last Friday were: some books to peruse, a collection of metal puzzles, some pattern blocks, Geofix shapes, Hex boards, chess boards, and a logic puzzle—one of those grid ones. In one class, the first few students to be done with their quizzes quickly took up the Geofix shapes. (These are so fabulous, fun, and mathematically rich!) As other students finished with quizzes, they one by one joined the Geofix festivities. As they built I was able to entice, with minimal prompting—“Hey, could you get this off of here for me?”—several students to become obsessed with some of the metal puzzles.
In the other class, the choices were more varied. The first wave of students that finished their quizzes also went for the Geofix shapes and grabbed some metal puzzles as well. A pair of students got to a point in quizzing where they felt stuck, so I told them that they could work on this quiz together as practice. They promptly plopped themselves down over by the door and dove into the quiz together. I thought that this was a great use of time for them. It arose so naturally and reinforced the low-pressure atmosphere that I’m trying to cultivate around quizzing. They ended up doing a second quiz together as well. Some other kids played Hex, and the last two to finish quizzing asked me if I had any origami books, which I did. They had started in on some folding as the bell rang to end the period.
Free-choice lasted between twenty and ten minutes, depending on the fifth grader. How long each student quizzed was entirely up to them, although I had asked ahead of time that they come prepared to take at least two of the eight that would be on offer. Most of them took at least four; several were determined to take all eight, and did. If you’re interested, you can look at their first list of skills here.
Last Friday was a lot of fun, and I got a lot of positive feedback from the kids about both the quizzes and the activities afterwards. They’re already looking forward to this Friday, and so am I.
I Choose Math 