At Pierrepont, students see the poetry of mathematics. To solve mathematical problems, we take fragments of apparently unrelated thoughts and connect them in imaginative and surprising ways. This element of pure fantasy, linking mathematics and poetry, is something Pierrepont students are encouraged to appreciate. In a poem, a word is a door to a universe of possibilities, a universe of feelings. When we introduce our students to prime numbers, we want them to see more than the mere definition of a positive integer that has no positive integer divisors other than 1 and itself. They are led to a universe of relations, of possible paths, of conjectures. How many primes are there? Can we map them? Can we know them? What does knowing primes mean? Is there a pattern in the occurrence of primes? These large questions belong to research mathematics; but they also belong to our mathematics classes from the earliest years.
Through imagination, Pierrepont mathematics students learn how to make sense of their surroundings. With mathematics, they find simple coordinates to understand and map a world that is otherwise difficult to approach. But this exploration is not by imagination alone: students achieve a complex understanding of the rigorous language of mathematics. This allows students to extend their learning beyond mere skill acquisition. Third graders, for instance, when studying natural numbers and addition, may spend an entire class period or more exploring a deceptively simple question: How many ways are there to write a positive integer n as a sum of positive integers? Students find in mathematics not a list of facts to be memorized but a universe of facts to be discovered, created, put into doubt or proved.
Mathematics is a fundamental part of the human endeavor. We strongly believe in the ancient tradition that connects mathematics to the humanities. The historical and philosophical aspects of mathematics are present in all our classes. When studying square roots, students rediscover irrational numbers, walking the path of the ancient Greeks. Geometry students carefully explore proofs and constructions from Euclid’s Elements.
We strongly believe in respecting the individuality of our students as learners. Learning is an individual path to self-knowledge. To respect our students for who they are, we focus on two fundamental elements: we tailor our teaching as much as possible to the individual students and we do not espouse a model of teaching that sees the teacher as the source of all knowledge. To achieve this, the math department as a whole carefully discusses and selects the proper class for each student. We want students to feel they are where they need to be. Our teachers accompany students in a path of discovery.