about the project

Math Pathways and Pitfalls (MPP) provides professional development for teachers, which is coordinated with 10 to 12 lessons for students at each grade level, K-7 (view a sample lesson). Together they address the need for improving instruction of key mathematical standards and learning pitfalls, regardless of the core instructional materials being used. The topics for grades K-3 focus on developing whole number concepts and operations, while the topics in grades 4-7 focus on developing rational number concepts. Professional development offerings include:

• Discussion Builders Workshop (K-8, any subject area)
• Institute for Teachers (K-7, math focus)
• Institute for Leaders (K-7, 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.

MPP was developed and field-tested with grants from the Stuart Foundation and the National Science Foundation (NSF). A randomized experimental study, conducted as part of the NSF grant, demonstrated a measurable impact on the mathematics test scores for ethnically and geographically diverse students in all grades involved in the study. A randomized field trial funded by the U.S. Department of Education is studying the impact of MPP on mathematics learning, as well as academic language development, with special interest in learning more about the effects for Latino students and 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.

2003-04 Research Outcomes
In a randomized controlled experiment, complete data were collected for 1,971 diverse second, fourth, and sixth grade students on pre and post math tests. Hierarchical linear modeling showed that across districts, at every grade, the difference between adjusted posttest scores of students in the Math Pathways and Pitfalls (project) group and those of the control group were significant, with the project group having higher mean adjusted posttest scores. Also, posttest scores of the project group were significantly higher for English learners at the fourth grade.

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 a sample lesson).

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:

1. Topic-based units, one each for grades K-7 (in English and Spanish), each with 10 core lessons and follow-up mini lessons for students (view a sample lesson).
2. Teaching guides for each lesson, including each mini lesson.
3. Videos, including professional development for teachers and videos for students that model how to present and discuss mathematical ideas.
4. Discussion Builders posters for grades K-1, 2-3, and 4-8.