October 6, 2025
The stress students feel in math class is so common that the experience has its own name: math anxiety. With national reports sounding the alarm on declining math scores, the need to make math classrooms more supportive is urgent.
WestEd’s Math Pathways & Pitfalls (MPP) helps address this need with a K–8 curriculum (grades K–1, 2–3, 4–6, and 6–8) and professional learning model that helps students turn common mistakes—pitfalls—into pathways for growth and achievement. The curriculum, now in its second and updated edition, can be used as an intervention, as part of core instruction, or in after-school settings. By addressing common misconceptions and providing clear pathways to understanding, it empowers educators with essential tools to improve student achievement while making the learning experience more supportive.
In this Q&A, experts José Franco and Bob Rosenfeld discuss the program, exploring how it works, what its impact is, and more.
José Franco: MPP encourages every student to explicitly examine and explain their mathematics thinking and processes. The program strives to engage all students in math discussions; agreeing, disagreeing, questioning, and valuing each other’s ideas in a respectful manner; addressing important content standards; and tackling misunderstandings they might have about the mathematics.
Each lesson takes the unique approach of confronting misconceptions head-on by asking students to analyze both correct and incorrect ways of solving a problem (“pathways” and “pitfalls”). The goal isn’t for students to guess which one is right but rather to build a sound conceptual understanding by discussing why the correct answer works and why the reasoning behind the incorrect answer doesn’t make sense.
The program helps create a safe classroom environment for students to make mistakes or to have respectful disagreements. Students are not embarrassed to make mistakes in front of their peers. In fact, they feel safe to test their thinking with a partner. It’s also OK to disagree with somebody so students can work through the problems together. MPP gives students opportunities and space to struggle productively and practice their communication skills.
Bob Rosenfeld: Building on the original work, the new edition of the curriculum identifies five Foundational Principles:
- Building Mathematical Discussions
- Making Sense
- Confronting Pitfalls
- Visualizing and Connecting
- Capturing Key Ideas
Each of these principles highlights valuable instructional practices and compelling benefits for students. For example, if an instructional coach or site administrator were to observe a teacher modeling the Making Sense principle, the observer would look for any of the following three teaching practices:
- Have students describe the meaning of the problem in their own words.
- Involve students in generating, analyzing, and discussing solutions.
- Have students justify why a mathematical idea or solution makes sense.
The benefits that students may experience include an improved ability to understand and solve contextual and symbolic problems and a deeper understanding of mathematical ideas and solution strategies.
Rosenfeld: To help teachers lead rigorous academic conversations in math classrooms, MPP provides sentence starters to help students use academic language to reason about, explain, and justify their mathematical thinking. In turn, these ideas foster a deeper understanding and capacity to make mathematical arguments.
The sentence starters are displayed on three sets of posters, each for different grade level spans (K–1, 2–3, 4–8). The posters have proven to be powerful scaffolding tools to promote and encourage student discussions. Over the past decade, we have heard from countless teachers asking for more tools to address the needs of their multilingual speakers. For the second edition of our books, we translated the sentence starters to give Spanish-speaking students additional entry points to participate in classroom discussions.
Franco: Most teachers have used MPP as an intervention program to address student learning gaps of mathematical concepts. When the material is used this way, teachers can differentiate the needs of students in small groups and afford each student more opportunities to demonstrate their thinking through visual representation, concrete representation, symbolic representation, verbal representation, or contextual representation.
Teachers can also use the MPP lessons in a preventative fashion. Using this approach, teachers choose a particular MPP lesson to provide students with a solid foundation as they launch into a unit in their district-adopted books so that students are prepared for the content to come. Essentially, it gives students a “jump start” on the learning ahead.
Teachers who use the lessons as an intervention along with their curriculum or teacher-created lessons have seen academic growth throughout the year.
To support teachers in selecting the most appropriate lessons for their students’ needs, WestEd staff have aligned MPP lessons with the Common Core State Standards, the California Common Core State Standards, and the Arizona College and Career Ready Standards for Mathematics. These alignment documents help educators
- find MPP lessons that match specific content standards, which is useful for targeting particular topics or skills, and
- see which standards each MPP lesson addresses, which helps students connect current learning to past and future concepts.
Rosenfeld: A trend that we are all seeing is the increased language demands of math assessments. This can be particularly challenging for Multilingual Learners. One of the things I love about MPP is that the overall exploratory approach of the lessons supports language development alongside math instruction, helping students gain the skills to express both simple and complex mathematical ideas.
Our program’s focus on language also supports the ongoing trend toward deeper conceptual understanding rather than a focus solely on rote memorization. By emphasizing discussions about mathematical concepts and actively tackling common misconceptions head-on, MPP allows students to build a solid foundation—and confidence—in mathematics.
Also, we have found that the program supports the increasing focus on tailoring instruction to meet the individual needs of students. When teachers listen carefully to their students’ thinking during the lessons and take notes on each student’s strengths and areas for growth, this sparks ideas for differentiated instruction during the school’s core math program and helps teachers make connections to individualized education program (IEP) goals.
Franco: I’ve seen and heard some powerful stories from teachers and students.
Numerous teachers comment that the program provides invaluable tools for conducting academic discourse where students take ownership of their learning and recognize and value each other’s strengths. At the start of the year, one 6th grader remained silent—avoiding both math lessons and class discussions. But when the teacher introduced MPP lessons and used Discussion Builders, everything changed. He began actively engaging in math conversations, confidently sharing his ideas, and offering help to classmates who were stuck. His peers came to value his insights, and over the year he grew into a confident student who had truly found his voice.
Teachers have also witnessed remarkable transformations in students with disabilities. Many who once stayed silent during math discussions gradually find their voice—with time, encouragement, and support—and begin to shine as brightly as their peers.
Teachers have experienced growth in their own practice as well. One shared that she became more comfortable letting go of full control, creating space for students to lead rich mathematical conversations. The classroom atmosphere transformed into a community of listening, discussing, accepting, and growing together as “mathematicians.”
Another teacher shared that the structure and practices of MPP lessons helped ease her own math anxiety. The “Mathematical Insights & Teaching Tips” at the start of each lesson equipped her with deeper content knowledge and insights into student thinking. The targeted questions for both the “OK” solution and the “Pitfall” guided her in probing students’ reasoning and deepening their understanding. Witnessing her students’ academic gains and confidence convinced her even more of MPP’s transformative power.
One teacher shared that mathematical comprehension and success was a yearly struggle to get certain students at grade level and above grade. The stress of teaching math was growing not only for the teachers but also for the students. MPP made the mathematics content being taught accessible to all students.
Rosenfeld: MPP is about exploring mathematical thinking and problem solving along with your students. Don’t worry about doing it exactly according to the script. Follow your students’ thinking instead. Take note of how your students are talking, what vocabulary they are using, how they are growing and where they continue to struggle.
Also, MPP is intended to be used as a complement to other programs. So, make connections to everything else going on in your classroom. For example, do you engage your students in small groups? If so, that’s a great opportunity to continue to explore any interesting discussions begun during an MPP lesson.
The bottom line is to embrace it as a philosophy and an approach to thinking and talking about math—and your students will shine.
About Our Experts
José Franco is Director of Math Pathways & Pitfalls. He has decades of experience in K–12 mathematics pedagogy and creates an environment for teachers to reflect on their practices, beliefs in students, and application of theory into practice. Franco helps teachers plan lessons that teach the content and academic language development in tandem.
Robert Rosenfeld, Senior Engagement Manager with WestEd’s Quality Schools and Districts team, has decades of experience supporting schools in creating systems that enhance leadership, strengthen teaching, and increase student learning. He leads projects that support the review and implementation of curricula, assessments, and innovative teaching practices.
Work With Us
Math Pathways & Pitfalls Institutes, customized professional learning opportunities, and coaching help educators boost mathematics teaching and learning, engagement, reasoning, and achievement for students in grades K–8. Our goal is to help you implement research-based principles and practices using both evidence-based, award-winning MPP lessons and your classroom resources. Learn more about Math Pathways & Pitfalls Institutes.
WestEd’s Discussion Builders Workshop will prepare you to facilitate evidence-based instructional practices that foster academic conversations and build communication and reasoning skills in mathematics classrooms. The one-day workshop is ideal for K–8 teachers interested in helping students from various academic, linguistic, and cultural backgrounds learn from discussion-based lessons. Learn more about Discussion Builders Workshops.
Contact José Franco or Bob Rosenfeld to partner with us to support improved math teaching and learning.
Math Pathways & Pitfalls Curriculum
- Math Pathways & Pitfalls: Early and Whole Number Concepts With Algebra Readiness—Lessons and Teaching Manual, Grades K–1 (Second Edition)
- Math Pathways & Pitfalls: Place Value and Whole Number Operations With Algebra Readiness—Lessons and Teaching Manual, Grades 2–3 (Second Edition)
- Math Pathways & Pitfalls: Fractions and Decimals With Algebra Readiness—Lessons and Teaching Manual, Grades 4–6 (Second Edition)
- Math Pathways & Pitfalls: Percents, Ratios, and Proportions With Algebra Readiness—Lessons and Teaching Manual, Grades 6–8 (Second Edition)
Discussion Builders Posters
English-language versions
- Discussion Builders Poster, Grades K-1
- Discussion Builders Poster, Grades 2-3
- Discussion Builders Poster, Grades 4-8
- Discussion Builders Posters Set: Grades K-1, 2-3, and 4-8
Spanish-language versions
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