In Julia Campbell and Christine von Renesse’s (2019) study, the experience was situated in a liberal arts university course focused on mathematical explorations. The class differs from typical mathematics classrooms in that it does not require specific content goals (p. 132). It was led through inquiry-based learning, and von Renesse writes that the type of enthusiasm found in her classroom would not typically be found in other math classrooms, painting a picture of just how different, special, and unique the context of this study was.
Julia Campbell was a student in von Renesse’s class, and she shares her personal mathematical journey, describing how her perspectives toward mathematical capability shifted throughout the course. The paper hones in on maypole dancing, a traditional folk dance at European festivals. The students engaged with and explored different types of representations and various patterns, counted ribbon patterns, and mathematically wondered about the structures that emerged from the maypole dancing ribbons.
My first stop was on page 132, where von Renesse lists the meta-goals of the class. I have included them here:
• Students will appreciate mathematics as a human endeavour which is one of our mostfundamental intellectual pursuits.
• Students will strengthen their reasoning skills and become better problem solvers.
• Students will strengthen their skills in reading, writing, argumentation and speaking.
• Students will become more self-monitoring, reflective learners and take greater personal
responsibility for their learning.
• Students will approach mathematics more positively and gain a balanced perspective of
mathematics.
• Students will improve their mathematical confidence.
• Students will develop awareness of the negative impact of broadly held societal views.
• Students will be capable of and interested in considering mathematics outside of the
confines of the classroom, understanding the value of lifelong learning in mathematics.
These meta-goals are all goals that I feel we have been working toward in our own classrooms. In high school classrooms, however, it often feels as though content goals are prioritized over these “meta-goals.” While there are systemic and structural layers that contribute to this prioritization, I really value these meta-goals and believe math teachers ought to strive toward them.
Have you integrated these goals into your own curriculum? If yes, how so? If not, why not?
Personally, the way we react as teachers and talk about mathematics and success has a significant influence on our students’ perceptions of the subject. By remaining positive-neutral, avoiding the rigid binary of right or wrong—while still acknowledging mathematically correct and incorrect reasoning—we can lessen the pressures that often lead to adversity toward mathematics.
My second stop occurred toward the end of the paper, in the recapitulation of the entire study. Countless types of representations were created from a relatively simple inquiry into understanding how maypole dance patterns work. This reminds me of the mathematical curiosity that Francis Su (2020) discusses in relation to being a mathematical adventurer. It is inspiring to see how dancing around the maypole extrapolated into such complex-looking mathematical patterns.
What conditions need to be present in a classroom for a simple inquiry—like exploring maypole ribbon patterns—to evolve into rich and complex mathematical representations?
Hello Anna,
ReplyDeleteThank you for your questions; they are thought-provoking. Although mathematics plays a crucial role in everyday life, I have not always connected it to deeper aspects like self-reflection, confidence, and positive attitudes due to curriculum constraints, time pressures, and standardized testing. Within these limits, I have used word problems, group discussions, and visual aids to promote reasoning skills. With the shift toward embodied learning, I am now eager to implement inquiry-based lessons that move beyond rote memorization by integrating real-life scenarios and movement-based activities to make math more engaging. For these explorations to succeed, it is essential to cultivate a safe, supportive environment where students feel encouraged to take risks, experiment, and collaborate. By using open-ended prompts, scaffolding, and multiple representations, I aim to help students uncover patterns and link experiences to abstract concepts like symmetry, transformations, and combinatorics, creating a classroom where learning math becomes an exciting journey of discovery and empowerment.
Hi Anna,
DeleteThank you for the great summary and sharing of your stops and wonder.
Your first stop regarding von Renesse’s meta-goals really resonated with me. In secondary school, we often treat confidence and self-monitoring as "side effects" of learning math rather than the primary goal. I completely agree with your point about being "positive-neutral." When we stop acting like the sole judge of right and wrong and instead become facilitators of reasoning, the students’ fear of the subject begins to melt away. It suggests that our job isn't just to teach math, but to heal the negative relationship students have with it.
I also loved your second stop on the complexity of the ribbon patterns. It is amazing how a simple folk dance can lead to deep explorations of combinatorics and group theory. It reminds me of the Vogelstein reading where a collective "ensemble" creates a mathematical proof through movement. The Maypole acts as a physical recording of the group's history, and every cross and under-pass is a data point. It shows that math isn't just something you do - it is something you leave behind in the world.
To answer your question about what conditions are needed for this kind of evolution, I think Clementina hit the nail on the head: it requires a safe environment for risk-taking. But it also requires the teacher to have the "courage to be bored" or to sit with the "not-knowing." If we rush to provide the pattern formula too early, we kill the inquiry. As you noted, shifting from a binary of right/wrong to a space of exploration is what allows a simple dance to become a complex representation.