How to Teach Math Effectively

When many students think of math, they think of a lonely and frustrating struggle to understand material or solve a problem. 

Some of the most effective math programs available try to reduce the “lonely” part of that struggle and emphasize cooperative learning, says a recent summary of two research reviews conducted by The Johns Hopkins University's Center for Research and Reform in Education.  

The reviews examined the evidence on the effectiveness of 22 elementary math programs and 24 middle and secondary school math programs. These math programs were the focus of studies that met the criteria for inclusion in the review.

“Cooperative learning can significantly enhance mathematics learning in the classroom,” says the summary of review of evidence supporting elementary, middle and high school math programs. “In cooperative learning, students work in pairs or small groups to help each other.  Learning increases if the groups have a common goal that they can only achieve if all group members do well on independent learning.  In other words, students have to teach each other, because their own success depends on it.”

What the Research Says

In general, the research found that there is no evidence that different curricula improve achievement and limited evidence that technology is effective.  However,  programs based on instructional processes did demonstrate evidence of effectiveness.

The Johns Hopkins research center found the following 5 elementary math programs had strong evidence of effectiveness:

Classwide Peer Tutoring—pair learning in which children take turns as teacher and learner
Missouri Mathematics Program—focuses on active teaching, classroom management and motivation

Peer Assisted Learning Strategies (PALS)—structured pair learning strategy in which children take turns as teacher and learner

PowerTeaching: Mathematics (formerly Student Teams-Achievement Divisions)—Structured cooperative learning program in which students work in 4-member teams

TAI Math—Cooperative learning program in which students work on individualized materials in 4-member teams

Only two middle and high school math programs showed strong evidence of effectiveness in studies:

IMPROVE—Combines cooperative learning, metacognitive instruction, and mastery learning and is designed to accommodate student diversity

PowerTeaching: Mathematics (formerly Student Teams-Achievement Divisions)—Cooperative learning program in which students work in 4-member heterogeneous groups to help each other master academic content

At the elementary school level,  programs that focused on classroom management and motivation also had strong evidence of effectiveness.

The researchers reviewed  189 studies on the effectiveness of math programs that met the inclusion criteria. The summary of these 2 reviews, “Educator's Guide What Works in Teaching Math?”, is posted on the website of the Johns Hopkins University  Center for Research and Reform in Education.  www.bestevidence.org/word/math_Jan_05_2010_guide.pdf)   The website also lists math programs for which there is moderate and little evidence of effectiveness.

Research Findings on Math Teaching Techniques

The reviews of elementary math programs and of middle and high school math programs examined studies of math programs that could be grouped into the following 3 categories:
• mathematics curricula
• computer-assisted instruction (CAI)
• instructional process programs

“Programs designed to change daily teaching practices—particularly through the use of cooperative learning, classroom management, and motivation programs—have larger impacts on student achievement than programs that emphasize textbooks or technology alone,” the summary says.

At the elementary level, CAI is typically used as a supplement to classroom teaching and is often used only a few times a week. Many studies on computer-assisted instruction dat the elementary level reported positive effects, but outcomes were stronger for computation than for concepts or problem solving, the research found.

In middle and high schools, technology is typically used in 3 ways:
• supplemental programs, used to fill gaps  in children's knowledge
• core programs, where the computer largely replaces the teacher
• computer-managed learning systems

In the 40 qualifying studies that looked at CAI programs for middle school and high school, researchers found little evidence of effectiveness.

One limitation of  both reviews is that technology is changing rapidly and many of the studies looked at programs that are no longer available, the summary says.

“Findings suggest that educators, as well as researchers, might do well to focus more on how the classroom is organized to maximize student engagement and motivation, rather than expecting that choosing one or another textbook by itself will move students forward.”

“Educator's Guide What Works in Teaching Math?” by Robert E. Slavin et al., January 2010, The Best Evidence Encyclopedia, www.bestevidence.org/word/math_Jan_05_2010_guide.pdf