Week 8 Reflections

Campbell, J., & von Renesse, C. (2019). Learning to love math through the exploration of Maypole Patterns. Journal of Mathematics and the Arts, 13(1–2), 131–151. https://doi.org/10.1080/17513472.2018.1513231

Summary

This paper serves as a narrative documenting the journey of liberal arts students as they delve deeply into mathematics. Professor Christine von Renesse's course, "Mathematical Explorations," is designed to provide a foundational class for students majoring in non-mathematical subjects. Therefore, this research not only examines the maypole dance through a mathematical lens but also offers insights from one student in the course, Julianna, who shares her personal struggles with math, her decision to give it one last chance, and how she overcame the challenges encountered during mathematical explorations. 

For many liberal arts students, math can feel like a nightmare. However, in this class, comprised of students from various majors, they approached math with a different mindset. Together, they brainstormed questions they were curious about and collectively decided which ones to pursue. The class employed various pedagogical approaches, including inquiry-based learning, ambitious teaching, problem-based learning, constructivist learning, and discovery learning, all aimed at encouraging deeper thinking and exploration. Additionally, the teacher provided challenging academic tasks and activities to promote the student's learning potential. Furthermore, by integrating math and English writing, students were encouraged to document their problem-solving process, fostering a sense of self-affirmation. For instance, when they encountered difficulties calculating permutations, a classmate suggested cutting the ribbons vertically on the pole to observe the patterns.

Initially, their guiding question was based on a desire to understand how the maypole dance worked. They hope they can predict the ribbon pattern for any given dance without having to dance it. Therefore, they narrow down the study to 4 and then 6 dancers in total. As they began to better understand the intricacies of the over-under dance, they wondered how many different ribbon patterns there were given the number of ribbons. Taking the example of 6 ribbons with 2 colors, they determined that there were 26 = 64 possibilities in total for this category. Excluding the two possibilities of having only one color (6 black ribbons or 6 red ribbons, totaling 2 possibilities), the final count was reduced to 62 possibilities with two colors.

                                                    

They designated black as the dominant color and red as the secondary color, attempting various permutations across different categories as follows:

- 5 black ribbons, 1 red: 6 possibilities

- 4 black ribbons, 2 red: 15 possibilities

- 3 black ribbons, 3 red ribbons: 20 possibilities

- 2 black ribbons, 4 red: 15 possibilities

- 1 black ribbon, 5 red: 6 possibilities

Subsequently, they also explored permutations for scenarios involving 6 ribbons with 3 colors and 6 ribbons with 4 colors, presenting open problems for future research.

The patterns and explanations provided in this paper are somewhat brief and ambiguous. Therefore, I sought out some of the students' assignments from this class to gain a clearer understanding of how they navigated this mathematical journey.

Stops

“I did not care if I was wrong, because each mistake led me closer to an answer. In our learning community, there were no right or wrong answers, there were just answers – proven in pages of proofs written like an essay in English class.” (p. 134)

I can relate to Julianna's experience in math. Coming from a liberal arts background, I often hesitated to find the right answers and had doubts about being right or wrong. However, I still maintained a curiosity about math. As a student, my math learning experience led me to believe that every problem had a definitive solution, and if I couldn't arrive at the correct answer, then I was simply wrong. It wasn't until I became a teacher that I realized the importance of showing the entire problem-solving process to students. It's probably considered stupid by some of the people who are good at math, however, for me and some of my students who struggle with math, it provided an opportunity to observe our logic and reasoning processes

“Everyone has the capability to be ‘good’ at mathematics, but it is all in how you look at it. ” (p. 134)

I always used to prefer liberal arts over math because I felt confident with words, sentences, and structures. Additionally, art offers various avenues of expression without necessarily pointing to a single correct answer, making every response acceptable. However, this study has truly changed my perspective on inquiry-based math learning. It has reminded me that math is not just about preparing for exams and aiming for higher grades but is instead an approach to solving real-life problems and an opportunity to enhance logical thinking skills.

Question

Have you ever presented math in the way demonstrated in the example? If so, would you like to share some thoughts or feelings about your experience?