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Improving Calculus by Focusing on Foundations

Some BYU freshmen who enter the university with Advanced Placement (AP) math credits struggle in BYU mathematics classes. Most of them wonder why these college preparation courses don’t help them more during their first year at college. Calculus is a required course for many majors, but even students who take AP calculus in high school find it far from easy.

Dr. Dawn Teuscher and other faculty in the Department of Mathematics Education discovered that by testing students’ foundational calculus skills, they can discover who could excel in the class. Teuscher has found that whether or not the content of high school math courses focuses on the basics makes a big difference between these varying levels of success.

Her study showed that students who have not learned specific foundational concepts will not perform as well in a college calculus class. “The curriculum makes a difference because if teachers have that [foundation], then they know what the students need . . . instead of just teaching what [educators] know,” Dr. Teuscher said. “To me, the driver is curriculum.”

Teuscher and her colleagues studied two groups of AP calculus students: those who used a traditional pre-calculus textbook and those who used a new pre-calculus curriculum called Pathways.

Both groups of students took the Pre-Calculus Concept Assessment (PCA) at the beginning and end of the school year to test five foundational concepts. Teuscher found those students who score higher on the PCA have a better chance of passing AP calculus, which is equivalent to BYU’s introductory calculus course, Math 112.

Dr. Teuscher explained that the Pathways curriculum is unique. “It focuses on the foundational concepts of calculus based on [educational] research,” she said. “Most students look at a math problem and create a picture in their head instead of a mathematical relationship, even though the picture is just a visual image of what’s happening.”

The Pathways curriculum helps students learn how to translate vague, visual images into more precise mathematical concepts. The curriculum also acknowledges that initial misconceptions are common in the learning process, so it discusses them in the classroom instead of attempting to prevent them.

“Students are talking a lot more in the Pathways classroom rather than just listening to a lecture,” Teuscher said. “They are working together, and then there’s discussion at the end . . . . So it’s not the typical [classroom] setup.”

Teuscher previously taught AP calculus at Lone Peak High School in Alpine, and she attributes her dissertation and research in AP calculus to her experiences there.

By Alysa Kleinman Posted on