Math Pathways and Pitfalls

Director: Carne Clarke    (Director, Mathematics Pathways & Pitfalls) Director: Alma Ramirez    (Senior Research Associate, Math Pathways & Pitfalls) Contact: Carne Clarke Tel: 503.534.2646 Email: cbarnet@wested.org

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: 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). 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.

Who's involved with this Project? Carne Clarke (Director, Mathematics Pathways & Pitfalls) Alma Ramirez (Senior Research Associate, Math Pathways & Pitfalls)

What kind of Resources are available? Discussion Builders Poster, 2-3 By talking to learn, students who engage in successful classroom discussions can better express ideas, raise questions, develop keen listening skills, and expand on challenging subject matter. The grades 2-3 Discussion Builders poster and teaching guide are designed to cultivate a respectful community of learners where the goal is to develop shared understandings. Sentence stems on the poster provide students with a scaffold for voicing their ideas and questions, valuing others’ contributions, and thinking creatively. The poster is a powerful tool for helping students – including English language learners – present, expand, and reason about important ideas. A teaching guide includes tasks and blackline masters for introducing and sustaining the use of Discussion Builders in any subject area. This poster is one in a set of three: K-1, 2-3, and 4-8. As a set, the Discussion Builders posters and teaching guides scaffold progressively more sophisticated language and reasoning across the grades. Posters can be ordered individually, as a set, and at bulk discount rates. Discussion Builders Poster, 4-8 Classroom discussions promote academic success by building powerful communication and reasoning skills. This Discussion Builders poster for grades 4-8 helps students of all achievement levels build these crucial skills. Sentence stems on the poster provide students with a scaffold for voicing their ideas and questions and valuing others’ contributions. The poster is a powerful tool for helping students — including English language learners — present and expand on their ideas. The language in the grades 4-8 poster supports sophisticated thinking processes by prompting students to consider counter-examples and conjectures and to justify various options. A quick-guide for teachers explains how to get students talking — and thinking — more conceptually. The guide includes tasks and blackline masters for introducing and sustaining the use of Discussion Builders in any subject area. This poster for grades 4-8 is one in a set of three that also supports discussions in grades K-1 and 2-3. As a set, the posters and teaching guides scaffold progressively more sophisticated language and reasoning across the grades. Posters can be ordered individually, as a set, and at bulk discount rates. Discussion Builders Poster, K-1 Talking, thinking, and understanding go hand in hand. This colorful Discussion Builders poster helps students learn through active participation in classroom discussion. The K-1 poster and teaching guide are designed to nurture a community of learners with the goal of shared understanding. “I’d like to build on Juanita’s idea!” “I’m confused about Oscar’s idea.” Effective classroom discussions occur when students understand how to verbalize their ideas, integrate others’ notions, raise questions, and build on the topic at hand. Sentence stems on the poster provide students with a scaffold for voicing their ideas, questions, and thinking processes. The poster is a powerful tool for helping students – including English language learners – present, expand, and reflect on important ideas. The accompanying teaching guide includes tasks and blackline masters for introducing and sustaining the use of Discussion Builders in any subject area. This poster for grades K-1 is one in a set of three. Posters and teaching guides for grades 2-3 and grades 4-8 incorporate increasingly more sophisticated language and thinking across the grades. Posters can be ordered individually, as a set, and at bulk discount rates. Discussion Builders Posters Set: K-1, 2-3, and 4-8 By talking to learn, students also learn how to think. The sentence stems on these colorful posters provide students with a scaffold for voicing their ideas and questions, valuing others’ contributions, and incorporating increasingly sophisticated thinking strategies. Using Discussion Builders, students learn through active participation in classroom discussions. Accompanying quick-guides for teachers explain how to get students talking — and thinking — more conceptually, in any subject. Powerful for English language learners and students of all achievement levels. Posters and teaching guides scaffold progressively more complex reasoning across the grades. In K-1 the focus is on helping students present, expand, and reflect on important ideas. In grades 2-3, Discussion Builders prompt students to use these skills at more sophisticated levels. The 4-8 poster strengthens students’ complex reasoning, including their abilities to consider counter-examples and conjectures and to justify options. Order a set of all three posters for $38 (shopping cart above), or individually for $14.95 (links below): K-1, 2-3, or 4-8. Participate in our one-day Discussion Builders Workshop, which will further enhance your ability to lead effective discussions that boost collaborative and respectful critical thinking among your students. Math Case Methods Project: Materials for Students R&D Alert® Vol. 9, No. 1 Contents Making the Most of Mistakes: Math Pathways and Pitfalls Improves Student Learning Helping English Learners Acquire the Language of Mathematics Opening the Gateway: Interventions Aim for Algebra Success Formative Assessment: At the Center of Effective Science Instruction It All Adds Up: Strengthening Mathematics Teacher Leaders Means Better Teaching and Learning What's New & Useful: WestEd Products & Services Single copies are available free of charge. All current and past issues of R&D Alert are available online. Science and Mathematics Education Solutions: 2008 Products and Services Catalog Our Science and Mathematics Education Solutions catalog presents evidence-based products and professional development services, from language development to differentiated instruction, from data-driven decision-making to assessment and more. Order books and other products reflecting WestEd work and expertise. 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