CMI: Improving Students’ Understanding of Mathematics

Comprehensive Mathematics Instruction is helping students think like mathematicians (and improving their test scores as well).

Many school districts struggle to achieve proficient math standardized-test scores; however, three teacher education professors and their public school partners have found a way for teachers to improve these scores—by helping students understand mathematics thinking and reasoning, not merely parrot algorithms.

The results are striking. The Comprehensive Mathematics Instruction (CMI) developed by BYU professors and K-12 educators has helped to increase standardized-testing scores by as much as 16.5 percent. One elementary school increased its district rank from thirteenth to first­ in fewer than four years. Teachers report that their students are learning the hows and whys of mathematics—and enjoying it. McKay School professor Sterling Hilton, chair of the committee that developed CMI, says, “It’s not a fad or a pendulum swing.”

In 2000 the National Council for Teachers of Mathematics (NCTM) released mathematics teaching standards for the nation, which stressed teaching students mathematical principles and thinking. However, BYU research found many teachers did not understand how to meet these standards. The Governing Board of the BYU-Public School Partnership (BYU-PSP) understood the need to rethink teaching mathematics; they developed a math initiative committee of 16 school and university personnel, who later selected Hilton to lead the committee.

The committee engaged in multiple research studies as they developed CMI as the framework to improve math instruction. The CMI model has directly affected teaching and learning of mathematics on all elementary grade levels. CMI professional development is introduced to schools through the Center for the Improvement of Teacher Education and Schooling (CITES), the facilitating unit for the BYU-PSP.

CMI is a teaching process. Teachers select a learning goal and then plan lessons and activities to achieve that goal. Instructors design teaching plans which emphasize students’ reactions to certain tasks and engage them in discussions.

The effective spread of the program is due to the goals and supporting structure of the BYU-PSP: simultaneous renewal of teacher education and public schooling. For the past four years, the CMI framework has been infused into the McKay School of Education’s teaching of mathematics methods classes. BYU students learn CMI in their classes and practice it during their practicum work in the schools, thus sharing it with school districts’ mentor teachers and students. “The simultaneous renewal allows everyone to learn, so the children are being blessed by powerful math instruction that is well documented and effective,” Damon Bahr, professor in the Department of Teacher Education, explained.

The McKay School of Education students take two content math classes, followed by a math methods class to learn the CMI framework. Later as the teacher candidates student teach or intern, they are supported by a district liaison who presents monthly seminars to ensure that CMI is properly taught. Clinical faculty associates at BYU and master-mentor teachers in the schools offer additional guidance and support.

CMI has been extremely effective in a number of schools. Now the challenge is to expand its use. “Our next step is expanding CMI to secondary schools by investigating how to sustain and scale-up the change CMI makes,” Hilton said. “We’ve found CMI works in individual schools, but now we want to impact more students and sustain the change.” Hilton encourages teachers and administrators to contact their districts to implement this change in their own schools.