The Great Conversation: Math in the Liberal Arts

By Katie Maslow, Assistant Head of the Upper School

If a liberal arts school sees education as not purely utilitarian, but as a way of helping students become more fully human, more fully awake and alive to the world, the study of mathematics presents us with a unique challenge. 

The main reason for this challenge is that math has deep and broad utility in our lives. We need to calculate tips, consider sales prices, and do our taxes. The modern world is flooded with data, studies, and statistics that are easy to misinterpret. We need calculus to do physics and engineering. These important skills and goods are often what animate discussion about the importance of math education. 

And in the context of liberal arts education, we can acknowledge and appreciate mathematics’ deep utility. Part of the wonder of math is how “unreasonably effective”¹  it is at helping us understand and describe the world we live in. Students become more fully awake to the world when they can understand and delight in this. However, we should be careful not to miss something more fundamental: beyond its utility, the practice of mathematics is deeply human. 

Mathematics is a fundamental part of human experience. We love patterns, are fascinated by numbers, and think about shape. We count and sort, decide that things are alike and unalike. We naturally try to abstract or generalize our concrete observations and put rules to what we see around us. As Melissa Nussbaum said in her commencement address at MacLaren Graduation in 2022, one only needs to watch small children playing to know that counting, sorting, measuring, comparing, and pattern making are some of the most natural human activities. The language of mathematics is a direct result of human observation, curiosity, and imagination. 

If we want our students to be more fully human, more fully awake to the world, then they deserve a rich education in mathematics that engages with and develops these natural human instincts.
 
What does this look like in the classroom? Rather than starting by telling students a new rule or formula and then just having them practice, we ask them to participate in the process of building the mathematics they will use. We want to give them a new problem or scenario to consider and have them try things, make observations, notice connections, and identify the pattern or rule themselves. This is a process that needs to be guided by the teacher, and there will still need to be plenty of time allotted to practice and master skills, but from the basics of arithmetic to calculus and beyond, the starting point in the classroom should always be one of questions and exploration. 

Want to try this yourself? The three problems below require you to make observations, look for patterns, and generalize. They all require very little background math knowledge, so even if it has been a long time since you have taken a math class, give them a try!