Multiplying Students' Mathematic Understanding

picture of hilton sterling

Are students in elementary schools simply being taught to pass math tests, or do they truly understand mathematical concepts? This question was the focus of a McKay School EIME seminar presented by Sterling Hilton, a professor in the Department of Educational Leadership and Foundations.

Hilton is a three-time BYU alumnus. He received a bachelor’s degree in economics in 1987 and two master’s degrees in 1990—one in political science and the other in statistics. He then went on to earn a PhD in biostatistics from Johns Hopkins University in 1996. During his presentation, Hilton focused on the work done by the Math Initiative Committee, formed at BYU in 2003 under the Center for the Improvement of Teacher Education and Schooling. Both Hilton and Richard Sudweeks, EIME director, sat on the original math committee set up by the Governing Board of the BYU-Public School Partnership, which included district curriculum directors, math curriculum specialists, principals from area school districts, and faculty from each McKay School department. “Our task was to investigate the best practices that would improve students’ understanding of mathematics,” Hilton explained.

The difference between teaching for math understanding versus promoting math achievement is found in the long-term results associated with each method. “They’re not unrelated, but they have distinct outcomes,” Hilton clarified. Understanding goes beyond simply memorizing facts and algorithms with an ultimate goal of passing the next test. Rather, true understanding is characterized by connection, competence, confidence, and appreciation, among other things. As Sudweeks put it, “There’s more to understanding than achievement.” Hilton called understanding a “multi-faceted construct,” with achievement being only one aspect.

The math committee determined that the key to increasing students’ understanding would be to work directly with the teachers. “Teachers themselves need to gain mathematical understanding,” Hilton expressed. “We needed to address teachers’ beliefs at a foundational level.” Instead of promoting a quick fix to mathematics deficits, the committee focused on stimulating a philosophical shift in mathematics instruction at the elementary school level. “Sustained and meaningful change is necessary in order to achieve our purpose,” Hilton stated.

The committee developed and implemented a pilot project in 2004 at Mapleton Elementary School in Mapleton, Utah. “It was a two-year pilot project,” Hilton said. “We learned a lot about what was good about our thinking and what wasn’t working.” In 2006, the committee was awarded a Math-Science Partnership grant from the Utah State Office of Education to extend their pilot to other schools. Now in its fifth year, the program currently runs at six additional elementary schools. Increased grant money was recently awarded for continuing expansion and refining of the program.

The program begins with a 15-hour summer workshop. Over the following two school years, the teachers attend 16 sessions of 2 to 3 hours. The committee conducts pre- and post-tests to collect data from the teachers, their students, and administrators. Thus far, the data have revealed statistically significant results in teachers’ math understanding and students’ math understanding, as well as a shift in classroom practice. “You rarely see this,” Hilton observed. “Teachers are actually shifting their practice.”

In addition, the committee has found that mathematical understanding continues to increase as teachers and students spend more time in the program. When the first group of first graders was initially tested in 2004, they had a passing rate of 75 percent for their math curriculum. By the time these students were in fifth grade, that rate had increased to 94 percent. When surveyed about their favorite aspects of their school experience, 70 percent of students included math as a favorite subject. “It’s pretty powerful stuff,” Hilton remarked on the findings. “With all modesty aside, this is innovative. It has meaning for all teaching, not just mathematics.”

3 June 2009