Your Math Support System, Right When You Need it!

The Concrete–Representational–Abstract (CRA) model, developed by Jerome Bruner, along with Richard Lesh’s Translation Model, has influenced nearly every aspect of the work we do at Meaningful Math. Bruner’s CRA model emphasizes that students build the strongest understanding of mathematical concepts when they move through three stages of learning: using concrete materials, transitioning to visual representations, and finally working with abstract symbols. Similarly, Lesh’s Translation Model highlights the importance of helping students make connections across different representations of mathematical thinking; such as manipulatives, drawings, number sentences, and real-world situations. Together, these models guide how we create teaching resources, blog posts, podcast episodes, printable materials, professional articles, and professional development workshops. They remind us that learning is not linear and that true understanding comes from helping students bridge ideas across multiple forms and experiences.

The work of Douglas Clements and Julie Sarama on learning trajectories has deeply shaped the way we think about teaching and learning mathematics at Meaningful Math. Their framework breaks down mathematical ideas into developmental progressions, showing how understanding builds over time, and offering practical guidance for supporting students at each stage. You’ll see this influence in how we develop resources that align with these progressions, as well as in our progression videos which visually map how understanding unfolds over time. Their research continues to guide us as we help teachers make math instruction more responsive, intentional, and grounded in how children learn.

Kathy Richardson’s book How Children Learn Number Concepts: A Guide to the Critical Learning Phases has been foundational in shaping our understanding of how math concepts develop over time. Her research outlines the specific stages children move through as they build number sense and emphasizes that math learning is developmental; not something that can be rushed or skipped. At Meaningful Math, this work directly informed the creation of our progression videos. These 3–6 minute animated videos trace how math understanding grows from the earliest concepts to more complex ideas, showing how everything is connected. They’re designed to help educators see how critical each phase of learning is, and how gaps in early understanding can create stumbling blocks down the road. Richardson’s framework helps us show teachers what it really means to build math from the ground up.

At the heart of Children’s Mathematics: Cognitively Guided Instruction is a simple but transformative idea: students’ mathematical thinking should drive instruction. Authors Thomas P. Carpenter, Elizabeth Fennema, Susan B Empson, Megan Loef Franke & Linda Levi show that children enter our classrooms with informal strategies and intuitive understandings that, when recognized and built upon, can lead to powerful learning. You’ll see its influence in our resources that focus on student strategy use and problem-solving development, as well as in our workshops, podcasts, and blog posts that explore what it means to teach responsively. CGI reminds us that meaningful math instruction begins with understanding how students make sense of problems, and using that as the foundation for our next steps.

Clear, intentional teaching starts with understanding how students learn. That’s the focus of Helping Children Learn Mathematics by Robert Reys, Mary Lindquist, Diana Lambdin, and Nancy Smith. Their work emphasizes the importance of building conceptual understanding, fostering mathematical reasoning, and supporting problem-solving from the earliest grades. The book outlines the content knowledge teachers need, along with the instructional practices they must understand and apply to help young learners think deeply and flexibly about mathematics. Their examples of effective questioning techniques, developmentally appropriate strategies, and student work samples have reinforced key principles we carry into our resource development. You’ll also see this influence in the language we use throughout our blog posts, podcasts, and workshops. Their work continues to inspire our commitment to helping teachers teach math in meaningful, student-centered ways.

Marilyn Burns' book, About Teaching Mathematics, is crucial to our work at Meaningful Math. Her work emphasizes that math instruction should be rooted in reasoning, communication, and meaningful problem-solving. Burns advocates for asking open-ended questions, encouraging student thinking, and creating space for mistakes as vital parts of the learning process. Her belief that students need time to explore ideas, discuss their reasoning, and construct their own understanding has influenced many of our podcast topics, teaching resources, and professional development workshops. Her emphasis on listening to student thinking continues to shape how we talk about effective math instruction and helps guide teachers in seeing math through the eyes of their students.

The book Teaching Student-Centered Mathematics by John A. Van de Walle, Karen S. Karp, LouAnn H. Lovin, and Jennifer M. Bay-Williams has had a strong influence on many of the instructional resources we’ve developed at Meaningful Math. Their research emphasizes that students learn best when they are actively engaged in constructing their own mathematical understanding, rather than only being shown procedures to memorize. The authors advocate for an “upside-down” approach to math instruction, where students explore, reason, and make sense of problems before being introduced to mathematical symbols and formal algorithms. Their work highlights the importance of using open-ended tasks, math talk, and representations to support deep understanding. This approach has guided the design of our hands-on activities and inspired many of the topics we explore in our podcast episodes.

At Meaningful Math, so much of our work is grounded in both constructivist and sociocultural theories of learning. The Constructivist theory, rooted in the work of Jean Piaget, emphasizes that children build their understanding of mathematics through active exploration and internal sense-making. This guides us to design teaching resources that prioritize hands-on and exploratory-based learning experiences over rote instruction. Sociocultural theory, based on the work of Lev Vygotsky, reminds us that learning is deeply social. It happens through interaction, discourse, and collaboration within a meaningful context. This influences our emphasis on number talks, math talks, and the importance of classroom discourse. Together these theories shape our belief that children learn best when they are active participants in their learning, rather than passive recipients of information.

At Meaningful Math, we equip teachers with everything they need to become confident teachers of math, including: • Resource Library: This ever-growing library includes hands-on resources designed to build math concepts with manipulatives. These resources are currently available for grades 1-3, with K resources coming in only a few short weeks! • Concept Video Library: You’ll find bite-sized PD videos that break down the progression of math concepts to strengthen your understanding of HOW students learn math. • On-Demand Workshops: Our growing library of professional development workshops offers you professional development right from your couch! Look forward to regular releases of new workshops to always give you new ideas to inspire your teaching! • Bonus Resources: Access additional bonus content such as Number Talk Slides, Curriculum Maps, Math Talk Prompts, Math Word Walls, Math Manipulative Guides, and more! • Exclusive Online Community: Ask questions, celebrate wins, and share challenges with a group of like-minded educators who love talking and sharing about all things math!

At Meaningful Math, we believe our tools and resources provide teachers with everything they need to feel successful and confident in the classroom, but it’s important to us that you love your experience, too. After your purchase, you have 48 hours to preview the content and decide if Meaningful Math is right for you. If for any reason you decide to cancel, just reach out to us within that 48-hour window and we will provide a full refund.

Our goal at Meaningful Math is to deepen your understanding of the content you are going to be teaching in your classroom, and give you the resources to teach it more effectively. Meaningful Math is not a curriculum but rather content and resources designed to support the learning that is already happening in your classroom.

Meaningful Math focuses all content and resources on kindergarten, first, second, and third grade math concepts. While we wish we could support teachers at all grade levels, you will likely not find the content specific enough to meet your needs unless you work directly with these grade levels.

Meaningful Math is a living and growing library of resources, workshops, and articles that will expand each month. Immediately after purchase, you will have access to all previously released videos, workshops, resources, and bonus content.

We are here for you! You can always contact support@meaningfulmathco.com and a team member will get back to you as soon as possible.

You will have access to everything Meaningful Math offers (resources, workshops, videos, and community support) for as long as you are a member. If you should cancel your membership, you will no longer have access to the resources, videos, workshops, and community inside Meaningful Math.