paper folding

Last week in math class I learned that paper folding is very mathematical! It was really interesting to see how the simple act of folding an origami box uncovered so many mathematical challenges. It was a truly rigorous way to explore geometry and proofs - I personally had difficulty expressing the reasons why I knew a given shape was what it was! Particularly challenging was finding a way to articulating why one folded line was parallel to another.

One question I have is how best to elicit the proofs. Is it best to have the whole class work independently and volunteer answers? Or would it be better to have students work in teams or groups? I'm personally inclined to say groups, because I know I could have used someone to bounce ideas off of when we did this in class.

I think this is a great way to explore geometry and practice articulating mathematical proofs in the classroom. While we engaged in this activity as a way to explore and provide proofs, I'm personally planning to adapt this activity into a lesson for 4th graders. My kids had some trouble with geometric shapes when they were learning about them last fall. I think (and my master teacher agrees) that examining geometric shapes while folding an origami box will help them better understand and remember what they learned. It helps that most of my class is rather origami obsessed, too!

engaging math

Last week in math class, I learned strategies for creating group math lessons that engage students and are inquiry focused. Since so much of the math in my main placement classroom seems to be whole class direct instruction, it's refreshing to see ways that math concepts can be taught -- and taught intuitively -- without being stultifyingly boring. The group work we did in class the last two Mondays using the online statistics generator was fun, interesting, and engaging. It didn't really feel like we were learning, but we were using math skills such as statistical analysis and data graphing.

My ongoing question about group work seems to be how to best implement group lessons. Exactly how much groundwork will be required to familiarize my students with group roles? With a pacing guide, will I have that time? Will students in my groups really be responsible for the learning of everyone on his team?

I believe the implications for classroom practice are that group inquiry lessons, if implemented thoughtfully, can greatly enhance our math curriculum. Using absorbing, thought-provoking lessons like the one we experienced in our class the last two weeks can be an effective alternative to more "traditional" methods.