Line Dancing

 The idea of embodying Euclidean proofs is frankly quite fun and cool. I find it interesting and wonder about the challenges of making the movement fluid when the proof gets difficult. The decision-making process in creating the dances is quite exciting and I wonder if this can be achieved with most if not all of Euclid's proofs. How would add more dancers look like and how that would simplify or make the proof more challenging?  I also found the representation and imagination aspect of this brilliant. Proofs are not everyone's cup of tea and it feels like a very abstract concept sometimes. Representing proof which is a logical explanation in a physical way is brilliant. I think it makes the proof more accessible. Sometimes you need to visualize how something would look physically to understand and Euclidean proofs are a great way to do that. I wish we did this when I was doing real analysis in topology. 

 I find that is quite challenging yet creates a deeper understanding of the proof than just reading it. As you start to understand how the proof can be performed physically, you begin to make deeper connections and try different methods. I know with my group Tim and Duncan, decided to use the joining of two circles from the given points to display the perpendicular line. And this was just a different way to understand the same proof. We have to be aware of our spatial awareness of us, the circles, and points. This kind of learning can be incorporated with more than just proofs. I think we can do this with graphing, sine cosine functions, and parabolas. Especially with y=x, y=-x^2 and such. Having a very visual lesson or aid would be great. It makes students think about how to move their bodies or how to represent something physically rather than on paper. Within the context of math history in secondary, I like the idea of proof starting from basics and working our way up. It reminds students how all these complex topics started and it's a very real and physical way of working up from basic ideas. Collaboration and creativity are always welcomed in math and this activity is great for that. 

The constraints and challenges that I see, which I noticed during my short practicum can be in the class. Classroom management is really, and you really do have to know your students. Not everyone is comfortable with activities such as this, I was not either when we did this in class. You have to be ready to change and restructure the activity based on your class. Some students need very structured boundaries and instructions and for some, you can give them a general idea to build around.