How color and creativity transform the way students connect ideas in calculus

By Megan Reeves, Upper School Math

There is never a dull moment in math class. Literally. The whiteboards are never left white, and at any moment, I have between 5 and 10 different colored markers at my disposal. I use color to help the students SEE the connection between ideas. Specifically, during curve sketching in calculus, information can get lost in translation. As you transition between a function, the first derivative, and the second derivative, the presentation of the information morphs. While ideas, vocabulary, and processes are repeated, each representation tells you in a “new” way. To aid in the presentation of this new information, I tried to incorporate color to draw the connections and highlight the distinctions. 

The approach I use stems from my experience as a student teacher. One of my students had an Individualized Education Plan (IEP) that included color coding to highlight important information. This strategy has since become a fundamental part of my teaching, and I believe it positively benefits all students. Every learner processes information differently. The moment that one student has an “aha” could be the moment another student loses all their momentum. So, I try to present the content in many different ways. Mathematically, this means showing the students the algebraic, numerical, and visual representations. To SEE the connections, we create color codes and utilize our vocabulary. Additionally, I incorporate metaphors and activities that translate the math concepts from the rigid mathematical world and relate them to new contexts. 

This engagement with the curriculum starts on the first day of class and continues throughout the year. The border of my whiteboard is lined with monsters from the first day of class. Affectionately called “Descriptive Monsters,” this activity is an ode to my mentor from my first year of teaching. With the monsters, we set the tone by stepping into a silly, low-stakes activity that seems more creative and artistic than mathematical. However, the purpose of the activity is rooted in skill building, specifically communication. Effective communication is a foundational skill in mathematics. In the context of proof, we think about using words to express our process and explore the validity of a statement. However, algebraic proofs show up everywhere. Every time students set out to solve problems and show their work, they are communicating their thinking by making valid statements connected to mathematical algorithms — proving how they got there. The activity connects the idea of an effective description: one that can be followed to recreate a monster similar to the original. We look for things like color, quantity, location,  and shape. Then, we explore what constitutes an effective description when we translate back to describing functions by their characteristics (intercepts, increasing/decreasing behavior, maximums/minimums, concavity, etc.). There is fun, creativity, and collaboration working towards reinforcing the skill of effective communication. 

Taking “the math out of math class” might sound counterintuitive, but I have seen the opposite in my practice. Students’ success in math is often limited not by their ability or whether they see themselves as math students but by their own limiting beliefs. Students often enter my class with preconceived notions about their math ability; my goal is to shift their mindsets and show them that they are capable. Shifting the mindset of teenagers is no small task; however, when broken down into smaller, more attainable goals it can be accomplished. Every day, I aim to assist my students in building their resilience, reinforcing their problem-solving skills, and ultimately boosting their confidence.  If students believe they are capable and trust their teacher to help them get where they need to be, there is no limit to what can be accomplished together.