Math Art Projects

1. We 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, which generated the golden spiral (which is seen in many natural objects) and created a colorful aesthetically pleasing butterfly. Linking patterns to other mathematical ideas visually allows students to see how some formulas came to be/make more sense, such as explaining an infinite geometric series with equilateral triangles.

 2. There were many challenges when creating this project. We struggled to find a way teachers could connect Fibonacci sequences and golden ratios to the math curriculum. Although the Fibonacci sequence may be a simple sequence of the sum of two preceding numbers, there is much more students can learn about, including the golden ratio and the proofs. However, we thought proofs would be too complex at their level, so we focused on students and their ability to observe and identify patterns. Having two different shapes that represent the Fibonacci sequence allows students to identify patterns and visualize the sequence. Further, the golden ratio exists in many of our surrounding artworks and nature. So we thought it would be a good activity for students to understand the Fibonacci sequence and connect it to their lives. Finally, I personally got to develop a better understanding of the topic and it helped me understand the importance of implementing math art projects in a classroom. Not only did I learn something new, but I had fun and was engaged!

 3. As our group was presenting, we realized it would be challenging for students to create the hexagon artwork as it took up so much time and lots of explanation was needed. Further, we thought it was important for our classmates to play with the hexagons because it could be difficult to visualize the Fibonacci sequence right away. However, it would have been better if our classmates were given pre-cut hexagons to play with and identify the pattern themselves. Further, providing them with the three triangles would've helped them realize that the diagonals of the hexagon are twice the side length. I realized that I need to be flexible in the future and be aware that my lesson plan could not go the way I intended. Further, I need to be aware of seating arrangements as cutting and tracing paper in a group did not go well in the way my classmates were seated. Nevertheless, I would keep the golden ratio artwork because it extends the idea of the Fibonacci sequence in a different shape. I could implement this activity/assignment in many ways. I can allow students to go outside in the garden to see if they can find the golden ratio themselves and allow them to create an artwork. Finally, I can even connect this topic to other subjects such as the history of art because the golden ratio exists in many famous artworks. Overall, this project helped me reflect on my teaching behavior and I was able to learn how to implement engaging projects in a math curriculum.