Enroll in the Freudenthal Institute’s summer school program on Math Education in Utrecht, Netherlands, to help students excel at math and inquiry-based learning, and develop a Math-driven interdisciplinary project for the school at large.
Middle school students often struggle with abstraction as algebra is introduced. Attending this 2-week course transformed my understanding of how kids mathematize, expanding my notion from merely horizontal (real world to math world) to include a vertical direction as well (referential math to formal math) and augment my definition of “realistic” to include anything imaginable. By reordering concepts to build on students’ embodied experience, I will bolster new ideas with previous understanding.
From my experiences at the Freudenthal Institute, I gained a deeper appreciation of the importance of embodied cognition and the ways in which physical movement can support deeper learning of mathematical concepts. I plan to purchase motion detectors so students can experience the challenge of recreating a graph of motion over time by moving their bodied towards and away from the motion detectors. This kinesthetic experience of the graphs will give students new insight into time-distance graphs
During my tour of the cultural repositories of the Netherlands, I was drawn to artwork that played with perspective, especially M. C. Escher’s work. His art manipulated mathematical properties, like perspective, to create impossible objects. Imagine my surprise when our study of geometry at the summer school course was rooted in perspective and exploring multiple sight lines for the same scene! I was inspired to root students’ geometrical explorations in their experiences of spatial relations.
Two big changes: students will experience more problems to solve that are non-routine and “messy” so they appreciate the power of math to organize. By giving students the experience of a Wiskund (Dutch math competition), they will begin to understand how to pull on all of their knowledge to think mathematically. Additionally, we will study inquiry projects, like “How do we move people through dense urban environments?”
Our units on Quadratics will be launched with a task I piloted in Utrecht. Students will multiply lines to discover new math: quadratics/parabolas. This will provide them insight into the connections between graphs and equations, linear and quadratics. Our geometry study will connect to art and perspective. My students will also create a Mondrian-style piece in Desmos, using graphs to create images similar to the photos I share with them.
I plan to develop a parent workshop, demonstrating how Realistic Mathematics Education impacts a student’s ability to mathematize their world. In these workshops, parents will experience a small taste of this type of mathematics instruction to understand the benefits first-hand. To provide them with an imaginable problem, I will pose the elevator problem that I worked on this summer. I will also share these problems at Math for America, as a facilitator of professional learning.
Attending an international college course with people from around the world allowed me to discover the common challenges in math education and the unique challenges to the US. Math is often described as the universal language, but through this cultural exchange, I discovered some of the mathematics I assumed was universal is actually US-specific notation. This gave me a greater appreciation of human impact on mathematics, noticing which aspects really are universal and which ones aren’t.
Most teachers complete their coursework prior to entering the classroom, or within the first few years of their career. Through Fund for Teachers fellowships, we are able to gain new insights into better ways to educate students, stay current with changes in technology and research, and develop a deeper, more personal understanding of our subject matter, outside of the classroom. This can reignite our enthusiasm and remind us why we got into teaching in the first place!
Having never studied abroad before, I gained a deeper type of empathy for my students who are learning English, as I now have first-hand experience being in a country where I don’t speak the local language. Spending three weeks in the Netherlands developed my understanding of Europe in a way that a quick tourist trip would never have done so. Additionally, the summer math course expanded my understanding of what it means to mathematize.