Four hundred years ago Galileo Galilei observed that "Mathematics is the language with which God has written the Universe." The "unreasonable effectiveness of mathematics," in the words of famous physicist Eugene Wigner, has been and continues to be incredibly successful in describing the world around us, from the movement of atoms to the Big Bang, from the spread of diseases to political election predictions. Mathematics is a universal language because it has no border: a formula or a proof is the same in any corner of the Earth and for anybody in the world whatever verbal tongue they use in their daily life. And because mathematics as we know it now has been created across centuries—and in fact millennia—of hard work and inspiration by cultures and scholars across the globe, it is truly a shared, common tool that is not owned by a single civilization. It belongs to all.
Adding a little history of the various mathematical ideas to classroom discussions whenever time permits is a way to cherish and celebrate mathematics' universal foundations. What child doesn't enjoy the story of the number zero, a most unusual number conceived in the Indian subcontinent and spread around the world by the Arab traders or the Al-Khwarizmi geometric proof of the "completing the square" method for solving quadratic equations, a method otherwise so dry and abstract? In addition, the history of mathematics, with its wealth of elegant concepts and proofs, colorful characters, and interesting stories, can inspire students' interest and enhance positive attitude towards learning math.
At the same time, we can leverage mathematics' global reach with relevant, authentic, real life examples from other parts of the world or cultural contexts. As we strive to graduate globally minded, competent problem solvers and citizens of the world, mathematics can provide plenty of opportunities to foster and reinforce the 21st century skills of creativity, critical and higher-order thinking, breadth of knowledge, interpersonal skills, and dependability (https://www.brookings.edu/research/skills-for-a-changing-world/, May 19, 2016). Today I would like to share some of the projects and resources I have used and look forward to hearing readers' ideas, suggestions, advice, and recommendations.
Many curricular and extra-curricular occasions at our school, such as Mini-mester and Out of the Box (OTB) Days, promote interdisciplinary and experiential learning opportunities that are enriched by, and encourage the development of, global competencies in math. During Latin America Day we concentrate on the Mayan numerical system to learn about different base numerical systems (including decimal and binary) and introduce the way computers communicate with each other. During the Golden Age of Islam OTB Day we explore the contributions of Arab mathematicians or we look at geometric patterns, tessellations, and transformations. For Africa Day we are planning a Market Day funded with microcredits and possibly connected with the online lending platform Kiva. We have been studying freshwater scarcity and walking for water in the Water Mini-mester and explored sustainability and cryptography in other Mini-mester courses, to name a few opportunities. All these topics and projects can be integrated in the regular math classroom any time the appropriate skills and concepts need to be studied or reinforced.
Technology can be useful for cultivating global mindedness. Tools like Google Earth and Google Maps can foster and exercise spatial thinking. "Students' skills in visualizing and reasoning about spatial relationships are fundamental in geometry" (NCTM Principles and Standards for School Mathematics, 2000, pg. 237); they are essential in many fields, and crucial in any STEM (science, technology, engineering and mathematics) discipline. And while there is evidence of a gender gap in this area (I teach in an all-girls school), there is also evidence that they can be improved with practice.
Incidentally, there are plenty of lesson plans available online, and Google provides a website for using its mapping tools in education that includes tutorials and lesson plans. The following are a few examples of how I have used Google Earth:
- Coordinates – Cartesian coordinates are just the beginning! It is fun for the students to find interesting places on Earth and record the coordinates and vice versa starting with coordinates and seeing where they land. (Scavenger hunts are a big hit and there are plenty of ready-made examples in the resources listed above.) Mathematically, a lesson like this opens the opportunity to talk about different types of coordinates, different ways to map a surface, and even different types of surfaces that need to be mapped.
- Measuring distances, calculating ratios, and making maps – The (Google) map of Chicago is extremely useful when drawing a map on scale for the book Divergent and the areas where the different factions live.
- Geometry of solids and polyhedra – Create a building tour of famous, interesting, original buildings around the world on Google Earth and deconstruct each complex shape as the composition of various simple solids.
Another tech tool that fosters a global outlook in the math class is Gapminder, a website provided by a non-profit foundation that promotes the achievement of the UN Millennium Development Goals through understanding of statistics about social, economic, and environmental development at local, national, and global levels. At the beginning of our small statistics unit, a look at what Hans Rosling does with statistics and how many layers of information his graphs display is a great reminder of the power of visualization and of current world knowledge.
Statistical literacy can be encouraged by reading articles in high quality magazines (like The Economist, NewScientist, and Scientific American) and newspapers (The New York Times (its Upshot section, in particular), The Washington Post, etc.). Online print and digital publishing software tools allowed my students to create a couple of STEM magazines out of their summaries. The students really enjoyed this project because the articles were appealing to them, they had the freedom to choose what they were most interested in, and they could be as creative as they wanted to be in formatting their article page.
For another project, each student in my classes interviewed a woman in mathematics/STEM and wrote an essay about her, which was later entered in a contest organized by the Association of Women in Mathematics. The women they talked about (and their stories) were inspirational for me as well as for the girls, and because of the diversity of our schools, they came from around the world: South Africa, China, Russia, Argentina, Thailand, Italy, USA, Bangladesh, India, etc. For easy sharing, I compiled their essays in two websites to give the students an idea of their collective achievement and allow them to enjoy each other's work and share it with their families.
Finally there is the entire field of social justice and equity, about which there are many great resources online including on the National Council of Teachers of Mathematics website. One of the most important ways to generate empathy is simply sharing correct information and letting it sink in, as ignorance and distorted information can be powerful bases of prejudice and bigotry. In particular, democracy is an important global issue and math is well-suited as a discussion item in this area. For example, students discover there are several ways of counting votes and that depending on the counting method the winner can be different.
The students are flabbergasted by this result, and realize the necessity to understand the set of counting rules in depth, to monitor them carefully, and to keep them stable for the duration of the election once the election has started. The students are even more surprised (and also have a great time) when they play the re-districting game and realize that a mapmaker can have an outsized effect on an election through redistricting. The game allows them to actually redraw the map of a voting district to accommodate the wishes of the chairman of a party if they are careful enough and follow some basic rules. There is a lot to learn to protect our democracy and democracy around the world. Or, as Sam Wang (professor of neuroscience at Princeton) puts it in his New York Times article, let math save our democracy!
I would like to end with a quick mention of Games for Change, a collection "of social impact games that serve as critical tools in humanitarian and educational efforts." The website, useful for interdisciplinary and STEM exploration, carries a great variety of games, all with a socially conscious, "gaming-for-good" bend—from trying to understand the global refugee experience to realizing how individual "harmless" preferences can create a harmful world or institution. Most of these games are free, and there is some research that shows that practicing positive behavior in a game setting pays real-life dividends.
As the Asia Society so cogently puts it, "math helps students make sense of the world;" it "enables them to make contributions to the global community … and to solve complex problems in a complex world …. The global era will demand these skills of its citizens—the education system should provide its students the wherewithal to be proficient in them."
Alessandra King is a mathematics teacher and middle school mathematics coordinator for Holton-Arms School, an independent school for girls in grades 3-12 in Bethesda, Maryland.
Published in AMLE Magazine
, Febuary 2018.