To reach this proficiency, BA students start small. Addison Sagat, Level B, guides students at the start of the journey. “Our students build numbers with their hands,” she says. Before beginning the Singapore Math curriculum, they snap cubes apart and back together. “Watching students realize that the number 5 can be 2 and 3, and also 4 and 1, is when conceptual understanding starts,” Ms. Sagat notes. Mathematics begins in this discovery: that the concrete can be represented and manipulated.

As students grow, mathematics changes, and so does their way of thinking. At BA, math is taught intentionally through a sequence that deepens over time. In first grade and throughout Lower School, students follow the Singapore Math program. Reasoning is made visual, operations are made clear, and students learn the reasoning behind the algorithms. “We foster critical thinking and an understanding of the why behind each concept,” explains Tanya Schwartz, Head of Lower School. Techniques such as left-to-right addition and multiplication, “I have, I owe” in subtraction, and the stacking method of division deepen understanding. Reasoning, precision, and clarity become habits as students learn to justify ideas, not merely produce them.

In Middle School, the work begins to change as students transition to algebra. “Singapore Math has developed clear habits in students. If you ask them about a solution, you can ‘hear’ their thought process—how they first understand and then plan,” explains Michelle Sullivan, Head of Middle School. Dan Geu, a Middle School math teacher, builds on this foundation: “Students arrive with a strong, methodical approach. As they progress, they recognize patterns and find multiple ways to solve problems.” Students grow in confidence, develop disciplined and precise thinking, and, as Mr. Geu says, discover that “math can be pretty cool!” It is here that students move more fully from concrete understanding to symbolic and abstract reasoning.

Students grow into mathematical thinkers over time, guided by their teachers. The tiny Level B scholar manipulating blocks becomes the BA graduate entering college programs in mathematics, science, and engineering. The Upper School program is carefully designed to build on earlier foundations. “Upper School math, while still developing skills, becomes increasingly abstract and emphasizes mathematical theory,” Mr. Reiner explains. Students move at different speeds while developing the same core habits of thinking. Some accelerate; others deepen their understanding at a different pace, within a shared framework of rigorous study. The goal throughout is growth, and students follow different pathways toward that goal.

Seen as a whole, the journey reveals something remarkable: the child who once discovered that five could be made from two and three becomes a student capable of abstract reasoning, approaching complex problems with confidence and clarity. The path is carefully prepared, but it is the growth of the student along that path that defines the experience.