The Book

In 2014 we authored the book Big Ideas in Early Mathematics: What Children of Young Children Need to Know. For teachers of children ages three through six, the book provides foundations for further mathematics learning and helps facilitate long-term mathematical understanding. It’s the perfect guide for those who want to focus their instruction on mathematics that is central, coherent, and rigorous.

The simple, concrete mapping of the sequence of how children develop math concepts and skills makes learning, understanding, and implementing the ideas an easy task. The visuals to help explain the concepts are essential as well.
– Connie Casha, Tennessee Department of Education

The Website

The Early Math online environment is full of ideas, all collected in our Idea Library. At the root of these ideas are the Early Math Collaborative’s Approach to Foundational Math and Approach to Teaching and Learning.

Our goal is to improve and provide resources for real-world teaching. This means not just accumulating and distributing knowledge about foundational mathematics, but providing resources that have practical implications for teaching, affecting attitudes and practices as well. Resources need to be relevant, easy-to-find, and assigned importance for classroom or training purposes. It is not enough just to provide an avenue for online learning math, but to provide context for the concepts presented whenever possible.

This website is designed with a focus on the Big Ideas. It aligns to the Common Core State Standards so that educators and trainers can find what they are looking for according to learning standards. But it also connects those standards to our own Foundational Math Concepts and Big Ideas, drilling down to the heart of what standards intend to do, which is communicate what central concepts children need to understand.

For researchers, we catalogue research publications and presentations from our ongoing, applied research to further advance the field of early mathematics education.


The resources we add to our website are part of a growing number of series. Some of the series are aimed at teachers and caregivers to provide ideas for mathematizing the world around us, like our Book Ideas, Early Math Lists, and Focus on Play series. Others are aimed at teacher educators or teachers who are learning to improve their practice, such as our Focus on Collaboration and Focus on the Child series. You can refer to the filter bar in our Idea Library to browse the different series we have available.

Age/Grade Ranges

Our resources are labeled with age and grade labels: 0-3, Pre-K, Kindergarten, 1st, 2nd, 3rd.

Counting and Cardinality

The domain of Counting and Cardinality is about understanding and using numbers. It begins with children knowing number names and the count sequence. Then children count to tell the number of objects in a set and compare sets of objects using numbers.

Big Ideas

Sets can be compared and ordered. More
Counting has rules that apply to any collection. More
Counting can be used to find out “how many” is in a collection. More

Operations and Algebraic Thinking

The domain of Operations and Algebraic Thinking deals with the basic operations—the kinds of quantitative relationships they model and consequently the kinds of problems they can be used to solve as well as their mathematical properties and relationships. At first, children focus on concrete uses and meanings of the basic operations (word problems).

Big Ideas

A quantity (whole) can be decomposed into equal or unequal parts; the parts can be composed to form the whole. More
Sets can be compared using the attribute of numerosity, and ordered by more than, less than and equal to. More
Sets can be changed by adding items (joining) or by taking some away (separating). More
Identifying the rule of a pattern brings predictability and allows one to make generalizations. More
Patterns are sequences (repeating or growing) governed by a rule; they exist both in the world and in mathematics. More

Number and Operations: Base Ten

Children develop an understanding of place value through their work on counting and cardinality, and with the meanings and properties of the basic operations. Children develop computational competencies such as fluency and estimation. Over time, they develop base-ten algorithms using place value and properties of operations.

Big Ideas

Counting has rules that apply to any collection. More
A quantity (whole) can be decomposed into equal or unequal parts; the parts can be composed to form the whole. More

Number and Operations: Fractions

Children gradually enlarge their concept of number beyond whole numbers, to include fractions. Initially, fraction concepts arise in measurement or geometric contexts. Later, children use their understanding of the four operations to extend arithmetic to fractions.
RELATED FOUNDATIONAL MATH CONCEPTS: Number Operations Measurement Shape

Big Ideas

A quantity (whole) can be decomposed into equal or unequal parts; the parts can be composed to form the whole. More
Quantifying a measurement helps us describe and compare more precisely. More
Shapes can be combined and separated (composed and decomposed) to make new shapes. More

Measurement and Data

The domain of Measurement and Data emphasizes the common nature of all measurement as iterating by a unit. Children focus first on linear measurement and build an understanding of the linear spacing of numbers on the number line. Later, children explore the geometric measures of area and volume. Measurement is an important and meaningful source of data for analysis.

Big Ideas

Quantifying a measurement helps us describe and compare more precisely. More
All measurement involves a “fair” comparison. More


As children explore the domain of Geometry, they gradually progress to increasingly precise definitions of shapes and shape categories. Children learn to reason spatially with shapes, leading to logical reasoning about transformations. Over time, they connect geometry to number, operations, and measurement through the concept of equal partitioning.

Big Ideas

Shapes can be combined and separated (composed and decomposed) to make new shapes. More
The flat faces of solid (three-dimensional) shapes are two-dimensional shapes. More
Shapes can be defined and classified according to their attributes. More
Spatial relationships can be visualized and manipulated mentally. More
Our own experiences of space and two-dimensional representations of space reflect a specific point of view. More
Relationships between objects and places can be represented with mathematical precision. More