The Math All Around Us
The math team at my school never lets a single activity or event pass by without drawing attention to important or interesting mathematical connections. This includes everything from morning assemblies to field trips. Even though few if any of these events were meant to support the mathematics curriculum, we find methods to make them function.
Morning assemblies, for example, can be a wonderful time to introduce a programme of fast creative boosters that can be repeated throughout the day. For example, important historical problems and their current applications, logical puzzles and riddles, and counterintuitive problems are all topics that could be explored further.
A programme of this nature can be run by a group of teachers or students working together. If your school has a Math Club, the problems can be chosen by the club, or the winners of one round can be requested to propose the next problem if your school has one. In a nutshell, this can be as entertaining and imaginative as the folks who come up with the idea.
We also make an effort to incorporate some mathematics into the field trips that kids go on for other subjects. Visiting an aquarium, for example, can involve estimation difficulties regarding the size of a certain pool, the amount of money earned by the aquarium each day in ticket sales, and the ratios between (linear) dimensions of distinct creatures. A visit to an art museum provides an opportunity to challenge students to identify and name 2D and 3D figures in various parts of the building and paintings, as well as to calculate surface areas and volumes, among other things.
COMBINING MATH WITH OTHER CONTENT AREAS
Another very important way for students at my school to make mathematical connections to other content is to set aside time each year for them to focus on a particular topic and draw connections between various subjects, drawing on the resources available to them at the school and in the surrounding area, as well as their imaginations. These days, experiences that are designed to increase students’ comprehension of a topic are often driven by the language arts or social studies curriculum; they are open-ended and can be extremely interdisciplinary.
Although not all schools set out time for this type of collaboration, you may be able to collaborate with a teacher or a group of teachers from other topics to provide students with an interdisciplinary perspective on a subject. In this type of inquiry-based, integrative work, students may first listen to a speaker, watch a video, or go on a field trip to frame the essential question, and then, working in groups, they may go through a series of rotations that approach the issue from various perspectives to address the issue.
The duration of each rotation at our school is one class period (50 to 60 minutes), but the lengths of the lessons outlined here can be customised to fit the needs of your school and team. Because these are mostly topics in discrete mathematics, the mathematical content of these lessons is extremely rich and not typically covered in the regular curriculum. As a result, you can create and use conceptual material and activities, as well as adjust your goals to fit the time constraints of the lesson.
When we plan these multidisciplinary events at my school, we make certain that there is always a rotation that is concentrated on mathematics. In one day of civil rights studies, for example, we discussed different voting systems and how they functioned. There are several, and none of them is ideal, as demonstrated by Arrow’s impossibility theorem, which piqued the interest of students. Students participated in the Redistricting Game during the same class, which explored how changes to electoral maps can have an impact on the outcomes of elections.
An interdisciplinary exercise on indigenous Central and South American civilizations included studying the Mayan and Aztec numerical systems to gain a better understanding of the Hindu-Arabic number system that we use today and then looking at the binary system used in computers as part of a computer-based exercise.
On a day devoted to the Golden Age of Islam, we learnt how quadratic equations were addressed historically, and how Arab mathematicians solved them by generalising the completing-the-square method, which was developed by the Arabs in the seventh century. Our investigation into how the quadratic formula came to be was successful after illustrating the process analytically and geometrically. This provided the students with a much better understanding of the subject.
The documentary Promises will serve as the basis for our next interdisciplinary activity, which will take place when the students are studying the Middle East; the film is about the Israeli-Palestinian conflict. The subjects of community construction, land distribution, dispute resolution, biases, and segregation will be emphasised by the history teachers in their lessons. When the math team suggested that students spend part of their rotation playing the Parable of the Polygons, one of the social studies teachers agreed. The Parable of the Polygons is a simple online game that demonstrates how seemingly harmless choices made by individuals can lead to institutional bias.
Because the game is based on the work of Nobel Prize-winning game theorist Thomas Schelling, the math team will offer a lesson on Schelling and John Nash, the subject of the film A Beautiful Mind, and their work on game theory, the Prisoner’s Dilemma, and the evolution of human trust.
The promise is a documentary that documents the intertwined lives of Israeli and Palestinian children, and a social studies teacher and a math teacher will collaborate on another rotation to discuss fair division, a topic of discrete mathematics that is rarely taught in the regular school curriculum even though it is extremely useful in real-world situations.
In this approach, multidisciplinary exercises demonstrate to pupils in a tangible way that mathematics is a tool that they can use to statistically understand the world around them.