Culver Academies’ math department teaches more than the right answers

Sept. 15, 2023

Mathematics at Culver Academies is much more than finding the right answers. Teachers also encourage students to ask the right questions and try different strategies to find the most efficient ways to solve problems.

The goal is to inspire and challenge students to investigate and discover math fundamentals in a collaborative, student-based classroom experience so students can realize their full potential. Teachers foster a deep understanding of math concepts with real-world applications by encouraging students to become mathematical thinkers.

It’s about taking the mystery out of math so students can work confidently to find solutions. Strong math skills are essential for students as they prepare to enter a rapidly changing world.

“We want students to be doing the mathematical thinking, not just memorizing what the teacher has shown them without any sort of understanding of the concepts,” said Dustin Smith, chair of the mathematics department at Culver Academies. “We do that by having teachers ask a lot of questions of students, to have them think about the process. We have them think a lot about why something is true.”

That goal of making students mathematical thinkers fits perfectly into Culver’s aim of leading the world in whole-person education.

Students at the boarding school in northern Indiana are expected to be active participants in class discussions, asking pertinent questions and offering insights and solutions that help classmates understand. Teachers give students room to roam through the possibilities.

“Too often in mathematics we jump very quickly to the efficient solution and we miss, or don't talk about, all of the wandering you could do on a math problem before you get there, all the trial and error that could happen,” Smith said.  “We spend a lot of time processing. What are the possibilities for how we could tackle this? What are the strengths or weaknesses of this approach? Is this approach legal or not. Is it efficient or not?”

At Culver, students frequently work in groups to try to find answers because they often learn better through collaboration. Look in on any class at the Academies and students are working in groups of two to four people. It gives students the opportunity to see how others approach a problem to find the answer.

“One of the most effective ways to understand mathematics is to have to explain to somebody who is asking good questions,” Smith said. “Sometimes mathematics isn’t straightforward. So, processing it with other people and having people see a different perspective is helpful. My advice to students is: If you have a question, talk about it in your group. If your group has a question, that’s when you go to the teacher.”

Smith said students are sometimes assigned various roles when working in groups.

“One student’s role would be to make sure that nobody has a question. Their job is to say, ‘Did you understand that? Do you have a question?’  Somebody else's role might be to check everybody's work, to make sure everyone is all on the same page. Somebody else’s role might be to get my attention and ask questions for the whole group.”

Smith said great teaching moments occur when different groups use different paths to reach a solution.

“That leads to some fruitful compare-and-contrast moments. That's how we can talk about efficiency, for instance, (by having) multiple paths to a solution,” he said. “That’s ideal for us, if we can find interesting questions for students to dive into that can generate those multiple approaches or questions about how one idea connects to another.”

While students often are at different math levels, teachers at Culver set aside time for students to work on areas where they need to focus.

“That's a time when students can be working on or practicing whatever they need to practice on,” Smith said. “In those cases, students can be working at various levels.”

While English and social studies teachers are struggling with how to deal with ChatGPT and other forms of artificial intelligence, Smith said math teachers have been dealing with this problem for several years. Apps like PhotoMath and Wolfram Alpha not only give students the answer to a problem, the apps also give students the step-by-step process that shows the work of how to reach the solution.

Smith said students using those apps are working counter to what teachers are trying to develop: the thinking to solve the problem.

“Students are going to just suffer the consequences of that. Because we're going to ask them in class to do the thinking. And if they aren't practicing thinking because they are letting technology do the thinking, they're going to struggle in class,” he said.

Smith said most students at Culver Academies want to become mathematical thinkers.

Students at Culver Academies are required to take seven credits in math, including introductory algebra, geometry, intermediate algebra, pre-calculus and statistics. A pre-algebra class is available for students who need it.

Some students choose to take more advanced classes, such as calculus, business calculus, AP calculus AB, AP BC calculus, multivariable calculus, AP statistics, and honors seminar mathematics. This year the department added two one-term classes that are previews of college classes: modelling with differential equations and modelling with linear algebra.

Smith said the goal is to get most students to take a calculus class.

“The whole reason of taking algebra and precalculus is to do calculus. The first place where mathematics gets really interesting and really applicable to situations is calculus,” Smith said. “It’s a little annoying conceptually that students might spend all their math career doing algebra and some precalculus and end there because it's getting too hard. But they never got the payoff of all that algebra.  Calculus should be accessible to everybody.”

He said most Culver students take calculus. He said he’s received notes from past Culver students saying that the calculus they took at Culver helped them be better prepared for college classes than many of their classmates.

The two new courses being offered this year are for those students who have taken at least one of the calculus classes.

“Those classes are meant to touch on some of the major ideas that would be discussed in a college-level class. In the linear algebra class we’ll take a look at how we can use matrices to do some animations of figures on a plane,” Smith said. “We can use matrices to rotate, stretch, shrink and move around different figures.”

Students can go as deep into that as they want, Smith said.

“If they really want to dig into some college level math, we give that to them,” he said. “Not every boarding school can offer those classes. It’s rare to have those level courses.”

Culver Academies also has sponsored some outstanding math students taking only courses at Stanford University and other students have taken independent studies in areas of math.

“I think we also do a good job on the other end, helping students who arrive at Culver struggling at math to grow where they can do some of this higher-level math by the time they leave us,” Smith said.

So whether it is basic math or advanced studies, Culver Academies has classes to help students become better mathematical thinkers. When it comes to math, Culver Academies is the right answer.