Math-art Project Reflection

We decided to analyze and extend upon the artwork "Between the Devil and the Deep Blue Sea" by Gauthier Cerf, a series a hexagons imbedded 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 asthetically pleasing butterfly. Linking patterns to other mathematical ideas visually allows students to see how some fomulas came to be/makes more sense, such as explaining an infinite geometric series with equilateral triangles.

As a non-artistic person, this project allowed me to get creative. I personally did not do most of the art itself, but it was certainly interesting and satisfying to dive into the connections, especially the one between the fibonacci sequence, the hexagonal art, and the golden ratio. I found it pretty cool to see that two different geometric shapes had such similar properties yet a completely different pattern. One thing I found challenging is the time constraint. I did not anticipate the length of time it took to do the interactive artwork. If I were to change something about the project, I would have probably have students create the golden ratio spiral instead, telling them to look at the side lenghts of the squares. Doing so will allow them to see the fibanacci as well, and since a square is a simpler shape, it would certainly require less time to do so. In addition, I would extend the artwork by using maybe an octagon. I am not sure if there would be a pattern, but it would be a fun experiment to do trial and error, and if it doesn't work, that is okay. Math and science is all about experimentation and taking risks, and that is somehting that I want to instill in my students as a teacher, that it is okay to make mistakes and that it is part of the learning process.

Curricular Competencies Covered: 

1) Develop thinking strategies to solve puzzles and play games

2) Develop, demonstrate, and apply mathematical understanding through play, story

3) Visualize to explore and illustrate mathematical concepts and relationships

As seen above, part of the BC curriculum is to get students to problem solve and critically think. Part of this includes pattern recognition and the ability to visualize between mathematical concepts. I think that our project is an excellent and intriguing way to demonstrate that. Projects like these allow students to extend their knowledge beyond the intrumental mathematics and develops a better sense of creativity in mathematics. Students will realize that mathematics is not just formulas and numbers, but that it surrounds us. I think I would incorporate a shortened version of today/s project in a sequences and series unit, along with providing more examples and visual proofs of other types of sequences and series. In addiiton, I would like to explore a combination of mathematics and science as well in my classes. For example, I would like to collaborate with the physics department and perhaps do a lab for my Calculus class. This would allow them to apply what they know in the context of Physics, extending their knowledge beyond numbers alone and helping them see application in the real world.