September 2023

Knowing Truth through Math

One benefit of MacLaren's K-12 campus is that its curriculum and instructional approach is truly cumulative. Even MacLaren's youngest students learn math in a way that builds in each grade level and finds natural culmination by senior year.

Katie Maslow, Upper School Assistant Head of School, brings leadership and passion to mathematics instruction at MacLaren. She explains, "We don't view math as just a practical skill to acquire for performance on a standardized test or a future job. Instead, we view math as one strand of the human experience of the world. Our students deserve as much exposure as we can give them."

Math lessons are designed to develop student skills for computational competency while recognizing the beauty in mathematical concepts and growing the ability to apply those concepts.

Maslow explains, "We train students to ask interesting questions and explore ways to solve problems, not by copying steps or a formula from a book, but by thinking like mathematicians." This approach produces many 'ah ha' moments as students uncover mathematical truth.

MacLaren students in kindergarten through eighth grade are taught using Singapore Math, a curriculum that teaches math first concretely, then pictorially, then abstractly. It's an approach that honors the natural development of children. Maslow explains, "Children love to count things, organize things, and put things in order. The mathematical organization of the world is deeply natural."

In Mrs. Baxter's first grade class, students are learning to think and work like mathematicians. Baxter engages the entire class as she explains that number bonds have two parts. Students must bring the two parts together to find the whole.

Using pictures of crayons, erasers, and scissors as concrete examples, Baxter leads her class through the lesson. Students work independently at their white boards, expressing the problem as a number bond, then progressing to express it as an equation.

Her students are engaged throughout. She asks, "Who would like to come to the board and explain? Can you be the teacher?" Hands shoot up in the air, as students are eager to take a turn at the board as the 'teacher.' In this exercise, Baxter reminds her students, "You have to explain where you got the numbers from and explain how you combined the numbers." More than just inviting students to model their work on the board, Baxter gives students opportunities to explain what they are doing and why they are doing it.

Though the problems presented are more complex, students in Ms. Los's fourth grade class and Ms. Hall's fifth grade class similarly start their mathematical discovery with a question and use manipulatives to explore visual and concrete solutions. Hall presents her fifth-grade class with an example that requires both multiplication and division steps. Her students work independently at their desks before discussing with their classmates their answers and process to arrive at those answers. They then move to expressing the example as numerical equations.

Instead of primarily memorizing formulas or copying steps from examples in a textbook, students continue building their collection of mathematical concepts, approaching problems with an ever-growing well of knowledge to draw upon.

Mrs. Templin leads her seventh grade Pre-Algebra students through an equation, asking them to recall the order of operations. Several students volunteer to solve problems at the white board. After arriving at answers, Templin similarly invites students to discuss the equation: how they solved it, why they took that approach, and to explain why it worked.

This style of learning is not always easy. Instead of spoon-feeding answers or steps, students are challenged to wrestle with the material. Some who would have preferred a formula to copy will later express appreciation for the process. Maslow recounts a certain student who expressed, "Thank you for not giving me what I was asking for. I can see the value now. I'm excited to better understand."

MacLaren's unique approach to mathematical instruction is seen in the Upper School. Maslow explains, "Every junior is going to take calculus. That's really very unusual. Calculus has unlocked for scientists and mathematicians much about how the world works. Every student deserves to be exposed to that."

In her 2022 valedictory address, Sydney Randall brings into focus the ways this approach grows and develops students. Reflecting on the Advanced Math Topics class taken senior year, she describes the challenge of considering infinite sets of numbers. Of this exercise she says, “These proofs were difficult, time-consuming, and extremely confusing to think about . . . and yet, at the same time, I was totally captivated. Infinity, even if it is just a thought experiment, is fascinating to imagine.” Recognizing that the effort likely did not have direct application to her future career, she concludes, “The work I put into thinking about them was still worthwhile, because as a human being, it is my nature to wonder about that which I do not understand. The questions that have fascinated me most have been some of the hardest to answer. And when I do answer a difficult question, it gives me a feeling of accomplishment like no other. This delight in discovery, this feeling of accomplishment, these are the fruits of learning for its own sake.”

MacLaren faculty model for their students a passion for mathematics and the commitment to ongoing learning. Mr. Skaggs, seen above teaching seventh grade boys, helps highlight for students out-of-school opportunities to enjoy the field of mathematics. As a past participant in the Soifer Mathematical Olympiad, held annually at UCCS, Skaggs invites his students to consider participating. Of this mathematics competition, drawing students in sixth through twelfth grades, Skaggs explains, "It is a very rewarding educational experience for anyone with an interest in creative mathematics and the persistence to give it their best shot."

Our Vision

We believe all students should be immersed in the best our tradition has to offer. We believe all students can be active and useful participants in the ongoing and enduring conversation that is a vibrant civilization. We believe all students can be formed in a habitual vision of greatness that makes lifelong learners of the doctor and the mechanic, the homemaker and the professor. Thomas MacLaren School strives to build a lasting community of learners in which each student is the agent of his or her education.



Our Mission

From the seminar to the science lab, from the music room to the playing field, we begin with the conviction that all human beings can know truth, create beauty and practice goodness. To that end, we expect students to develop basic tools of learning, ordered basic knowledge, moral seriousness, breadth and depth of imagination, artistic ability and sensitivity, and a sense of wonder.

We believe all students can be active and useful participants in the ongoing and enduring conversation that is a vibrant civilization. Jacques Maritain, the French philosopher, described education as a human awakening. The goal of Thomas MacLaren School is to develop young men and women who are fully human and fully awake to the world.