about the project

About the Project

Math Pathways and Pitfalls (MPP) provides professional development for teachers, and intervention lessons for students in grades K-8. Together they address the need for improving instruction of key mathematical standards and learning pitfalls, regardless of the core instructional materials being used. There are 4 books with 20 to 22 lessons per book. The books for students in grades K-3 focus on whole number concepts, place value, and operations, while books for students in grades 4-8 focus on fractions, decimals, ratios, proportions, and percents. Algebra readiness is integrated into the lessons for students in grades 1-8. View the booklet with a sample lesson and additional information about the program and research.

Professional development offerings include:

• Discussion Builders Workshop (K-8, any subject area)
• Institute for Teachers (K-8, math focus)

Even on straightforward items, students' understanding easily caves into pitfalls. Only about one quarter of the U.S. sixth graders correctly responded "60%" when asked to complete the number sentence: .6 = ___%. The most common incorrect response for this problem is the prevalent pitfall identified in research, "6%." MPP addresses the need for rigorous research-based instructional approaches and materials that help students develop mathematical concepts and the academic language needed to understand and reason about those concepts. This dual focus is important for all students, but may be especially important for English learners.

To support academic language development, MPP provides specific assistance for helping students learn how to use mathematical vocabulary and symbols; to present complete and coherent explanations orally and in writing; and to participate in mathematical discourse where they learn to present, expand, and prove or disprove mathematical ideas in paired, small group, and whole class settings. These academic language skills spread to other mathematical topics and subject areas as well.

The MPP lessons are particularly appropriate for students who are English learners because each lesson includes exercises and tools for building discipline-specific language skills. The English versions of the materials have shown promising results regardless of the students' language background. However, the lessons also have been printed in Spanish to provide greater access for the rapidly growing population of new students from Spanish-speaking countries.

MPP Research Findings

Two large-scale efficacy studies and several descriptive studies have been funded to document the impact of MPP and help explain why it is effective with diverse learners.

A cluster randomized experimental study conducted in 2003-04 as part of a National Science Foundation grant (ESI-9911374), found significant positive effects (ESS = 0.43 to 0.66) for Math Pathways and Pitfalls students in all grades as measured by a project-designed mathematics achievement test. Study participants included geographically and ethnically diverse students in grades 2, 4, and 6. When the data were disaggregated, significant positive effects were also found for both English learners and native English speakers in all three grades. A total of 99 teachers and 1,971 students participated in the study. This study demonstrated that teaching only seven (MPP) lessons in conjunction with the regular mathematics curriculum boosts the achievement of students in all grades during the course of one school year.

Another study is in progress, titled Math Pathways and Pitfalls: Improving Mathematics Achievement for English Language Learners. This cluster randomized trial study investigates the efficacy of Math Pathways and Pitfalls in school settings with a high ratio of students who are Latino (at least 50%) and English learners (EL). It is funded by the U.S. Department of Education’s Institute of Education Sciences and the final report for that study will be completed in the fall of 2009.

Lesson Overview

Each lesson uses a consistent, easy-to-follow format and includes sections that 1) introduce key words and symbols; 2) promote discussion about two excerpts of student dialogue, one that contains a correct example of student thinking and another that contains a pitfall in thinking; 3) provide teacher-guided and individual practice; and 4) reinforce each concept through follow-up mini lessons, one requiring responses to multiple choice questions and the other a written explanation of a mathematical idea. View the booklet with a sample lesson and additional information about the program and research.

MPP Components

MPP consists of a variety of professional development offerings for teachers and teacher leaders. The offerings are coordinated with video and print materials for teachers and students. These materials include:

• 4 topic-based books appropriate for grades K-8, each with 20-22 core lessons and follow-up mini lessons for students. View the booklet with a sample lesson and additional information about the program and research.
• Teaching guides for each lesson, including each mini lesson.
• Videos, including professional development for teachers and videos for students that model how to present and discuss mathematical ideas.
• Discussion Builders posters for grades K-1, 2-3, and 4-8.