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Program Foundations
Built on the latest academic research and best pedagogical practices, Reveal Math provides every student with a strong foundation in mathematics and conceptual skills that go beyond the math classroom. With robust differentiation instruction and opportunities for student agency baked into the instructional design, the program empowers every student to build a math mindset and master critical standards.
Pedagogy
K–8 Instructional Design
Reveal Math leverages leading expertise and contemporary research to ensure instruction is standards-driven, routine-based, and taught using the most effective teaching practices.
Reveal Math breaks down the standards into a coherent scope and sequence that emphasizes and reinforces each grade level’s major content areas to develop a strong foundation. Major, supporting, and additional standards are labeled at point-of-use within the Teacher Edition along with the rigor, focus, and depth of knowledge of practice and assessment items where appropriate.
Reveal Math not only addresses the Standards for Mathematical Practice within its instructional design, but it also defines and models the math practices for students. Within the "Math Is…" unit, the first unit of every grade level, students learn how to use mathematical practices while problem-solving. Integrating mathematical practices into the math classroom becomes a daily expectation and is reinforced by "Math Is..." labeling within the Teacher and Student Edition.
The Reveal Math instructional design integrates NCTM’s eight Effective Teaching Practices to ensure an environment that promotes rich learning, deep and meaningful understanding, and mathematical success for all. Embedded supports help teachers facilitate rich discourse and productive struggle with effective questioning techniques and guidance.
ETP labeling throughout each lesson allows teachers to know where specific teaching practices are being implemented for all eight practices:
- Establish mathematical goals to focus learning.
- Implement tasks that promote reasoning and problem-solving.
- Use and connect mathematical representations.
- Facilitate meaningful mathematical discourse.
- Pose purposeful questions.
- Build procedural fluency from conceptual understanding.
- Support productive struggle in learning mathematics.
- Elicit and use evidence of student thinking.
Instructional routines are vital to a productive classroom, providing structure and dedicated time to help students strengthen their understanding. Embedded within every Reveal Math lesson are three types of routines:
- Number Routines support the development of number sense—the ability to think flexibly with numbers. Number sense is an important mathematical foundation and a precursor to higher-level mathematics achievement that requires daily focus. Written by John SanGiovanni, M.Ed., these number routines are found throughout each grade level so that students can develop and refine them as they move from grade to grade.
- Math Language Routines promote mathematical language use and development as part of math instruction—important for all students, especially multilingual learners. Eight routines support the four design principles: Support Sense-Making, Optimize Output, Cultivate Conversation, and Maximize Linguistic and Cognitive Meta-Awareness.
- Sense-Making Routines build sense-making as a foundation for problem-solving and mathematical modeling. Students must make sense of problems first before moving on to solving them. Sense-making routines set the stage for a safe learning environment focused on thinking and strategies rather than just the answer. Instructional moments like Be Curious, Notice and Wonder (created by Annie Fetter), Which Doesn’t Belong?, and Is It Always True? are just a few of the sense-making routines found within Reveal Math.
K–8 Student Agency
Reveal Math engages students in learning by prioritizing student agency—encouraging them to explore at their own pace and discover how math skills transcend the classroom and apply to the real world.
Reveal Math is designed around the belief that all students can be doers of mathematics! That’s why the first unit of each course, the "Math Is..." unit, is dedicated to building a growth mindset while learning math.
Daily "Math Is... Mindset" prompts in each unit and lesson of the Student Edition and Teacher Edition remind students to persist with a growth mindset throughout the course and beyond.
Ignite! activities at the beginning of every unit also promote a growth mindset. These interesting problems and puzzles spark student interest, providing only enough information to spark their thinking—motivating them to persevere through challenges in problem-solving.
Math is all around us in our daily lives. Observing real-world mathematical situations and exploring ideas with curiosity helps to generate excitement and drive student agency. Reveal Math emphasizes this curiosity and sense-making as the foundation to problem solving and mathematical modeling.
- In each Unit Opener, an Ignite! activity works to spark engagement and mathematical curiosity. These collaborative activities designed by Reveal Math contributing author, Raj Shah, Ph.D., are focused on an interesting problem or puzzle, providing limited information and interesting questions to get students thinking and motivated to persevere.
- Ignite! activities support productive struggle and facilitate student discourse in problem solving. For Grades 6–8, the activities follow the STEM-focused theme for the unit and connect to the Mathematical Modeling tasks at the close of the unit
- In each Lesson Opener, a Be Curious activity encourages student curiosity and ideas while considering a problem or phenomena. These low-floor, high-ceiling activities are an opportunity for all students to share and respect each other’s ideas about what they notice and wonder about what they do not understand. Notice and Wonder—developed by Reveal Math author Annie Fetter—is one of four sense-making routines in the program used to build conceptual understanding and make sense of the lesson’s math.
Mathematics is not just a series of operations, but a way of communicating through thinking, listening, speaking, reading, and writing. Reveal Math was developed around this belief and embeds language supports to help students build a shared, universal language that transcends borders and drives mutual understanding.
Reveal Math abounds with mathematical language and specialized terms that may be new to students. Built-in academic language and text features help them grow their mathematical vocabulary and master key terms they are expected to know.
In every lesson, Reveal Math includes a language objective, Language of Math vocabulary and activities with teacher guidance, Multilingual Learner Scaffolds, Math Language Development mini-lessons, and Math Language Routines. Students have access to a Multilingual Glossary as well as read aloud functionality within the Interactive Student Edition and digital assessment features.
K–8 Differentiation
Differentiation is the cornerstone of effective teaching—and the instructional design of Reveal Math. Our program tailors classroom activities to each student’s specific needs with rich multimodal differentiation, ensuring that every student is appropriately challenged as they uncover their inner mathematician.
Purposeful Learning Driven by Data
Research & Thought Leadership
We developed Reveal Math in collaboration with leading scholars, researchers, and educators. Our research-based approach to educational equity, student agency, social and emotional learning, and more ensure that students learn in ways that work for them.
Modern classrooms should be served by proven teaching strategies. Check out our Medium blog to bridge the distance between academic research and instructional practice.
K–12 Academic Research
K–8 Research Foundations
A Research Summary of Program Focused Outcomes
Guided Math in Action: Six Components to Making It Work
Promoting a Math-Positive Classroom: A Guide for K–12 Educators
Talking About Math: How K–12 Classroom Discourse Can Develop Mathematical Thinkers and Problem-Solvers
Using the Mathematical Practices Effectively in the Classroom
Four Ways to Encourage Sense-Making in Math
Math Workstations: Purposeful Practice
Identifying Student Misconceptions with Formative Assessment Math Probess
K–12 Academic Research
K–8 Research Foundations
A Research Summary of Program Focused Outcomes
Guided Math in Action: Six Components to Making It Work
Promoting a Math-Positive Classroom: A Guide for K–12 Educators
Talking About Math: How K–12 Classroom Discourse Can Develop Mathematical Thinkers and Problem-Solvers
Using the Mathematical Practices Effectively in the Classroom
Four Ways to Encourage Sense-Making in Math
Math Workstations: Purposeful Practice
Identifying Student Misconceptions with Formative Assessment Math Probes
Reveal Math Authors
Sarah Bush, Ph.D.
- Professor of K–12 STEM Education at the University of Central Florida
- NCTM Board of Directors, 2019–2022
- Program Coordinator, Mathematics Education Track of the Ph.D. in Education at the University of Central Florida
Ralph Connelly, Ph.D.
- Professor and Professor Emeritus, Faculty of Education, Brock University, 1977–present
- NCTM Mathematics Education Trust Board, 2016–present
- NCSM Board of Directors, 1994–1996 and 2006–2008
- President, Ontario Association for Mathematics Education (OAME), 1987–1988, 1998–1999
Annie Fetter
- Math Education Specialist at the 21st Century Partnership for STEM Education, present
- Founding Member, The Math Forum, 1992–2017
- Workshop Leader and Developer for Key Curriculum Press, 1995–2013
- Administrative Assistant for the Visual Geometry Project, the NSF-funded project that developed the first version of the Geometer’s Sketchpad software, 1988–1992
Linda Gojak, M.Ed.
- Director, Center for Mathematics and Science Education, Teaching, and Technology at John Carroll University, Ohio, 1999–2016
- President, National Council of Teachers of Mathematics (NCTM), 2012–2014
- President, National Council of Supervisors of Mathematics (NCSM), 2005–2007
- NCTM Board of Directors, 1996–1999
- Elementary Mathematics Specialist, Hawken School, Cleveland, Ohio, 1978–1999
Christa Jackson, Ph.D.
- Professor of Mathematics, Science, and STEM Education, Saint Louis University
- Founder and Director, Institute for STEM Collaboration, Outreach, Research, and Education (iSCORE)
- NCTM Representative, U.S. National Commission on Mathematics Instruction (USNC/MI)
Susie Katt, M.Ed.
- K–2 Mathematics Coordinator, Lincoln Public Schools, Lincoln, Nebraska
- Special Appointment Lecturer, University of Nebraska–Lincoln
- Robert Noyce National Science Foundation Master Teaching Fellowship, University of Nebraska–Lincoln, 2012–2016
- R.L. Fredstrom Leadership Award, Lincoln Public Schools, 2008
Ruth Harbin Miles, Ed.S.
- Mary Baldwin University Adjunct Instructor, Staunton, Virginia, 2006–2018
- K–12 Mathematics Coordinator, Olathe District Schools, Olathe, Kansas, 1980–2006
- NCTM Board of Directors, 2013–2016
- NCSM Board of Directors, 2005–2008 and Conference Chair, 2018–2020
Nevels Nevels, Ph.D.
- PreK–12 Mathematics Curriculum Coordinator for Hazelwood School District in Saint Louis, Missouri
Nicki Newton, Ed.D.
- Educational Consultant and Speaker in districts across the U.S. and Canada
- Former Bilingual Elementary and Middle School Teacher
- Former Graduate Instructor, Columbia, CUNY, MCNY, Mercy College, Cambridge College
- Founder and Developer of Math Online PD Academy
Georgina Rivera, M.Ed.
- NCSM Vice President, 2021–2023
- NCSM Professional Learning Director, 1999–present
- EdReports Math Advisory Board, 2021
- Elementary STEM Supervisor, District Math Coach and Administrator, Bristol Public School, 2014–present
George Roy, Ph.D.
- Expert in integrating technology into middle school instruction
- Associate Professor, University of South Carolina
- Former Middle School Math Teacher (eight years)
John SanGiovanni, M.Ed.
- Coordinator of Elementary Mathematics, Howard County, Maryland
- President, Maryland Council of Supervisor of Mathematics
- Graduate Program Coordinator, Elementary Mathematics Instructional Leader program, McDaniel College, Maryland
- NCTM Board of Directors, 2015–2018
Walter Secada, Ph.D.
- Acting Dean of the School of Education and Human Development, University of Miami
- Director of "Language in Mathematics," a research and development project focused on improving the teaching of mathematics to middle-school English language learners
- Former Director of the U.S. Department of Education’s Hispanic Dropout Project
Cathy Seeley, Ed.D.
- Former Senior Fellow at the Charles A. Dana Center at The University of Texas at Austin
- Past President of NCTM
- Former Director of K–12 Mathematics for the state of Texas
Raj Shah, Ph.D.
- Founder, Math Plus Academy, an after-school STEM enrichment program for students, ages 5 to 14
- Founding Member, The Global Math Project
- R&D Engineering and Management, Intel Corporation, 1999–2008
- Affiliate, Math Teacher Circles and the Julia Robinson Math Festival
Jeffery Shih, Ph.D.
- Instructor and Professor, University of Nevada, Las Vegas Mathematics Education, 1999–present
- Co-Director, Center for Mathematics, Science and Engineering Education, 2013–present
- NCTM Board of Directors, 2018–present
- Recipient, University of Nevada, Distinguished Teaching, Service, Math Education Awards, 2005, 2006, 2010, 2013, 2014, 2016
Cheryl Tobey, M.Ed.
- Mathematics Program Director, Mathematics and Science Alliance, Augusta, Maine 2001–2008, 2019–present
- State Elementary Mathematics Specialist, Department of Education, Augusta, Maine 2016–2019
- Professional Development Specialist, Education Development Center, Waltham, Massachusetts, 2008–2016
- Co-Principal Investigator and Projector Director on NSF, IES, and State MSP grants 2001–2016
- Classroom Educator, 10 years, 1991–2001
Dinah Zike, M.Ed.
- Founder of Dinah Zike Academy, an accredited professional development center for K–12 teachers
- Inventor of Foldables® and other multi-sensory graphic organizers
- Educational Publisher, Dinah.com and Dinah-Might Activities, LP
- Author of numerous award-winning books and educational materials