As one of our students pointed out, “My father says you can learn from your mistakes.” The pitfalls highlighted in Math Pathways & Pitfalls® lessons address some of the most common misconceptions cited in the research literature on student thinking and that are often used as distractors on state and national assessments. During each lesson, students contrast correct and incorrect ways to solve a problem. They talk explicitly about how a particular pitfall doesn’t make sense, how to avoid the pitfall, and how to think correctly about the mathematics in the problem.
Experimental studies by cognitive scientists Durkin and Rittle-Johnson (2009) suggest that comparing examples of common mathematical errors to examples that are correct may prevent such errors from being made in the future. They also report that the contrast between correct and incorrect examples prompts students to recognize correct concepts. Other research supports the idea that pitfalls serve as strong motivators for inquiry and sense making (Festinger, 1957; Borasi, 1994).
Findings From Studies
The Impact of Math Pathways & Pitfalls on Students’ Mathematics Achievement and Mathematical Language Development: A Study Conducted in Schools with High Concentrations of Latino/a Students and English Learners, 2005–2010
U.S. Department of Education’s Institute of Education Sciences Study
(R305K050050)
The purpose of this 5-year study was to evaluate the efficacy of Math Pathways & Pitfalls, a supplementary K–8 curriculum for students that includes professional development for teachers. With an overall goal of effective and equitable learning, this discussion-based curriculum has a dual focus on building mathematical concepts and developing mathematical language. The Math Pathways & Pitfalls intervention takes unique approaches in fostering correct ways to represent and reason about mathematical concepts but and in explicitly calling students’ attention to common pitfalls and misconceptions. Math Pathways & Pitfalls provides a model for teaching and learning mathematical concepts that can be applied to mathematics lessons in any adopted curriculum.
WestEd researchers used a cluster-randomized experimental design to investigate the efficacy of using these instructional materials and procedures in place of 15 hours of regular mathematics lessons during each of two academic years (from grade 4 through grade 5). Nearly 70 percent of the participating students were Latino/a, 55 percent were classified as multilingual learners, and 75 percent were eligible for free or reduced-price meals. This study examined the impact of Math Pathways & Pitfalls on mathematics achievement and mathematical language development, with special interest in the effects for Latino/a students and multilingual learners.
This research study, funded by the U.S. Department of Education’s Institute of Education Sciences, was conducted with 126 teachers and over 3,300 of their consenting students in Arizona, California, and Illinois.
Key Findings: Results from this efficacy study indicated that exposure to Math Pathways & Pitfalls over two years raised project-administered, scores as well as standardized mathematics test scores, for the full sample of students and for the subsamples of Latino/a students, English learners, and English-proficient students. When comparing two years of Math Pathways & Pitfalls experiences to one year, effect sizes were as high as .40 for English learners and .29 for Latinos on standardized mathematics tests. These findings suggest that Math Pathways & Pitfalls adds considerable value to the regular mathematics curriculum in promoting mathematics achievement.
The results of this research, combined with findings from an earlier efficacy study in grades 2, 4, and 6 (Heller, Curtis, Rabe-Hesketh, & Verboncoeur, 2007), funded by the National Science Foundation, confirm the positive effects of Math Pathways & Pitfalls. These studies provide considerable evidence that Math Pathways & Pitfalls increases mathematics learning for students with a variety of economic, geographic, ethnic, and language backgrounds.
“Math was a yearly struggle to get certain students to and above grade level, and the stress of teaching math was growing not only for the teachers but also for the students at times. Math Pathways & Pitfalls made the math being taught accessible to all students. Give Math Pathways & Pitfalls a chance. Find a way to use it in your classroom. The proof is in the research, and once you make it a version for your classroom, the explosion of learning begins.”
—Ellen, instructional math coach middle school