Oct 4 Math Art Project Follow-up Reflection

 

    My group decided to analyze and extend upon the artwork "Between the Devil and the Deep Blue Sea" by Gauthier Cerf, a series of hexagons embedded within each other, where their side lengths correspond to the Fibonacci numbers. Different tasks were broken down and we discussed ways in which such an artwork may be used as an active way to engage students in understanding how the Fibonacci numbers are related to each other through its recursive definition. We extended the Fibonacci pattern using the square, that generated the golden spiral (which is seen in many natural objects) and created a colourful aesthetically pleasing butterfly (credits to Esther). Linking patterns to other mathematical ideas visually allows students to see how some fomulae came to be/makes more sense, such as explaining an infinite geometric series with equilateral triangles.

    This project was initially very entertaining to do because I am intrigued by how Fibonacci numbers are implemented in beautiful artworks. The work distribution was also fair and figuring out who does what wasn't difficult. I loved the analysis by the artist on their artwork and I had to think deep about how it was constructed. Taking the time to reconstruct the artwork was also a fun process, since I love building big things from tiny things ground up. In this case it was the construction of many hexagons with two hexagon blocks. However in hindsight, one hexagon block was sufficient. Tracing objections, joining line segments with a straight edge, and cutting pieces are all activities that I don't do regularly. I also spent a lot of time preparing for my math extension part with the Golden ratio. I thought it was a good way for, say, older high school students to review/utilize some math topics, to help them use what they learned like fractions/ratios, pattern recognition, roots of quadratics, system of linear equations, and limits. Unfortunately, I got to talk about none of that due to time constraints which was frustrating as I put a fair amount of work into it.

    There was a lot of advice I took in from presenting this project. For example, preparing more materials in advance just in case some papers weren't cut to be big enough. It was fortunate to have the art supply room right next to our door, but that won't always be the case for all schools. Giving clear instructions on creating an artwork is crucial too. Many students will have a hard time following the steps if they just hear "this" and "that". It was mostly a stress issue from time constraints, but it was also my first time giving a formal presentation in front of a classroom for over four years. I have been tutoring and TA'ing, but those were less formal. I came into this program to improve my public speaking skills as well, and having some critiques during my UBC-presentations humbles me as I'm able to learn and improve for future presentations/practicum teachings. Teachers should also be taking advice and growing via feedback. For this artwork, I may construct it in front of the class (via screen projection) to let the students see how it relates to the Fibonacci sequence, but I probably will just let them try it out on their own time at home, since time is so limited and there is a rigorous curriculum to go through. I will mostly connect the Fibonacci numbers with the Golden ratio with the set of notes I have written. Visual proofs are very intuitive for students, and I use a lot of geometry to prove certain trigonometric properties, like why exactly is sin(30°) = 1/2. Physics is one direct way to apply math, and in a grade 12 calculus class on the integration topic, teachers can show students how their science 10 kinematics formulae are derived (from constant acceleration) using integration.