Looking back over the quarter's math work, I've come out with a real appreciation for the merits of cooperative groupwork in math education (and all education). In fact, next week I'm going to introduce cooperative groupwork to my 4th graders (I'm using Elizabeth Cohen's Designing Groupwork) -- we'll be engaging in an activity called "Broken Circles." Each group member will have an envelope with circle sections, and each member of the group needs to finish with a complete circle in front of them. They can't talk or take pieces, they can only give pieces. I am very curious to see how this exercise goes. These kids work in partner stations during math right now, but I think the kids would benefit from strategies that foster deeper cooperation.
Our math class also highlighted for me the value of manipulatives (both traditional and online) in "higher order" math...such as algebra. I appreciated learning different strategies for exploring concepts in ways that allow kids to construct their own knowledge, as opposed to being forcefed rules and formulas via direct instruction. The Annenberg videos also gave me good ideas for how kids could construct their own knowledge, such as the video that showed kids developing a rule for calculating the volume and area of rods. Approaching math in this way also allows us to make it more engaging and interesting for kids. I was completely absorbed by the logic puzzle we worked on during our last class. The only danger is how absorbing some of these activities can be -- regrouping students could be challenging if everyone hasn't finished!
The last observation I'd like to make is the value I see in exploring our kids' mathematical identities. Finding ways in which kids can see themselves as mathematicians will help them approach math in a more positive way. As I mentioned in last week's math blog, I found the chart of mathematical activities to be particularly promising for exploring math in our everyday lives. The ideas in Complex Identities are fantastic for both students and teachers to explore their own preconceived ideas about math.
In all, this quarter's math class provided me with good information (via the readings, videos, and class discussion) about how to implement middle level mathematics curricula. The ideas, though, will also be useful to me in my 4th grade main placement class. Thanks to Robin for making math approachable, fun, and edifying!
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