Something I love about mathematics is the wealth of things it can describe. Throughout the first week of VAMPY, we have explored complex shapes, patterns in nature, and probability. Campers discovered unique ways in which these topics describe the world around us.
As one of the hottest weeks of June came to a close, the campers’ curiosity was piqued as we discussed Archimedean solids, spherical geometry, and their effects on air travel around the world. Using blow-up beach balls and globes (that I blew up myself), students explored spherical geometry and some hard questions that brought a new light to their current mathematical understanding of air travel. Though the temptation to play volleyball with the beach balls was there, we took a more applicable route. Students used dry erase markers on the beach balls to describe curved triangles that have total angle measurements of greater than 180 degrees. Kind of crazy! Application to abstract math is everywhere, and this is just one example. Whether people like it or not, our world is run by math and our students are getting a taste of that throughout our class.
During our study hour sessions, I introduced the students to the magic of probability – as applied to some classic games like poker and blackjack. Don’t worry though, we didn’t gamble! Understanding how the probability of certain hands impacts the game, we all played against a computer simulation to answer an age-old question: Can human intelligence beat out a simulation? I was so proud to see that using our various math skills and teamwork, we beat the computer every time we played.
So, what is next for our mathematics class? This week we are exploring incident geometries and phi, which is the ratio of terms in the Fibonacci sequence. In study hours, we will be exploring Russell’s paradox, derivation of some incredible equations in math such as Euler’s formula, and experimental versus theoretical probability using a plastic wrap ball filled with candy! Catering to students’ sense of fun and play has created a great learning experience that benefits their understanding of high-level mathematical topics.
My goal is to expose the students to mathematics topics that they may not see in high school, or even until their late undergraduate career (if they were to major in math). I could tell the topics would be a hit when I saw their faces light up as I told them about my plans. At VAMPY, students get to learn something new and challenging with others that have the same passion as them. As one of my very first mathematics professors said, mathematics is our way of describing the natural world; studying it not only improves our understanding of nature, but also encourages appreciation for the complexities of our world.
— Sarah H. Mathematics teaching assistant
