Teacher Spotlight: Mr. Bill Carey

by Sheryl Blunt, AFA Parent and Freelance Writer

It isn’t unusual to find Bill Carey and his students outside, acting out logical arguments in a game of charades, or huddled around a lawn mower engine discussing chemistry and gas laws. Nor is it unusual to find them using a soldering iron to build a computer on a Wednesday afternoon, or solving challenging math problems without the use of formulas.

Bill Carey Students Acting Out Math

That is because Carey, who teaches Formal Logic, Pre-Algebra, Pre-Calculus, and Chemistry at Ad Fontes Academy, believes that the classical approach to learning applies just as much to mathematics and science as it does to other liberal arts subjects and the humanities.

“We believe that there is a profound unity in truth,” said Carey. “We believe that math, science and history–all of the subjects–are unified and can build on one another. What we’re trying to do is reconnect the way we teach math with the way we teach other subjects.”

Carey, who has worked in the private sector as a geospatial engineer, wants students to understand the real-world interconnection of the STEM disciplines through hands-on, problem-based learning. (STEM is the acronym for Science, Technology, Engineering, and Math education.)

“At AFA, [History teacher Mr. David] Mathwin isn’t just teaching students history,” said Carey. “He’s teaching them to think like historians. I want to teach students to approach the world like mathematicians, and the classical model is an awesome way to do it.”

STEM and the Liberal Arts

On April 7th Mr. Carey will demonstrate to parents and prospective AFA families his approach to classical mathematics at an event entitled, “Liberal Arts: Making STEM Work Possible.

“I think that if we want to communicate a vision for what classical mathematics education looks like we need to do that classically, meaning our interactions with parents need to look like what happens in the classroom,” said Carey. “In the classroom we don’t talk about math, we do math.”

At the event, which will be held at Centreville Presbyterian Church at 7 p.m., participants will encounter math in much the same way Carey’s students do.

“Today’s standard method for teaching math is the teacher explains and the students compute,” said Carey. “In the classical model, we all compute so the students can explain. What we all work on together is how to solve the problem. I don’t just give them the formula and tell them how to do it.”
Carey said that when students learn how to figure out problems on their own, it teaches them how to generalize and hone skills that help inform their arguments in other areas.

“It teaches you that what’s valuable in math is being able to reason and to work your way from what you don’t know, rather than simply memorizing the formulas,” he said.

Using Math to Map Haiti

After graduating from the University of Virginia with a major in Classics and an emphasis on Latin, Carey taught a wide range of classes at AFA including Latin, Calculus, Formal Logic and Physics. Desiring to better understand how adults were using mathematics in the workplace, he then took a job with the defense contractor SAIC. It was during this time that Carey came to a vital realization about mathematics education.

“I learned that how grownups think about and do math in the workplace has no overlap with how I learned math in high school,” he said. “You don’t work on things in isolation, for example. You work as a community.” Additionally, “you might work on a single problem that takes weeks, or even months to solve.”

One problem Carey had was to teach a computer to map all of the roads in Haiti on a model of the country. “It’s actually a medium-to-high level math problem,” he said.

“With the trivium model in most high school math, in general all we do is the grammar [stage], and the problems just keep getting harder, ” he said. “But we also need logic and rhetoric in math.

Image by

Photo credit: zaveqna on Flickr licensed under CC BY-NC-SA 2.0

Jumping Armadillos

Carey is convinced that traditional math education often fails to answer these questions. “There is a disconnect of math from the rest of our intellectual life, and that is very dangerous,” he said. “When we connect it poorly, the result can be hilarious.”

Once Carey said he found a problem in a math book that asked students to calculate how high an armadillo could jump. “The answer to the problem was 12 feet,” said Carey. “I double-checked the back of the book just to be sure. However, it got me to thinking. I did some research and guess what? Armadillos don’t jump at all. So what does that question teach a child? It teaches them that the result we get from math has no bearing on actual things. Of course, math does have bearing on actual things, but the way we’ve asked our question obscures that.”

Carey wants his students to not only understand practical applications of mathematics, but also learn to effectively communicate their findings through persuasion, the way professionals in STEM fields are often required to do. This is where the art of rhetoric comes into play.

Math and the Art of Persuasion

Carey wants to see classical education–which is based on the Grammar, Logic and Rhetoric stages–applied to math at all levels.

“With the trivium model in most high school math, in general all we do is the grammar [stage], and the problems just keep getting harder, ” he said. “But we also need logic and rhetoric in math. We need to be about effectively convincing others that our approach and solution is correct. It’s not enough to know the answer. I want you to be able to convince someone of the answer. The end result of a math problem for most adults is a number,” said Carey. “For us, it’s an explanation.”

Carey hopes those attending the April 7th event will come away with a better understanding of classical mathematics and how “math can be worked into the intellectual fabric of our students’ lives.”

“My aim in the presentation is to get parents to do math the way we do math in the classroom at the rhetoric level,” he said. “We’re going to have fun, and by the end, we will have done an interesting chunk of math.”

Bio: Sheryl Blunt is an AFA parent and freelance writer.