Organized in our book *Big Ideas in Early Mathematics,* we’ve determined key topics that exist in early math. They are reflective of our own expertise on the important thinking that takes place in early childhood.

Within the Early Math Topics are 26 key mathematical concepts, or Big Ideas, that lay the foundation for lifelong learning and thinking. They are comprehensive, developmentally organized, and flexible.

Additionally, reflective of the real-world teaching that takes place in preschool and after, many resources have a Common Core Alignment that demonstrates their thinking in the context of the National Governors Association’s effort to define best practices in mathematics education.

# Counting

Counting is a part of young children’s daily life. They love to count everything from the stairs they climb to the crackers they eat. But what is counting? What is there to be understood about counting? What do most children know about counting? What more is there to be learned? Counting seems very simple; but it is really quite complex. By developing a sophisticated sense of what counting is and what kind of counting we ought to emphasize in teaching, parents and teachers can better assist children with the development of counting skills and mathematical thinking.

© Erikson Institute’s Early Math Collaborative. Reprinted from Big Ideas of Early Mathematics: What Teachers of Young Children Need to Know (2014), Pearson Education.

# Data Analysis

Data analysis can be very simple, like making a list of items and writing how many you have of each in parentheses, or creating and talking about a bar graph whose bars are higher for snowy than rainy days in the month of January. Whether the process involves specialized statistical software or markers and chart paper, what remains the same is that data analysis gathers information in a quantitative way (how many?), and then organizes it in some way that makes comparison and generalization possible.

© Erikson Institute’s Early Math Collaborative. Reprinted from Big Ideas of Early Mathematics: What Teachers of Young Children Need to Know (2014), Pearson Education.

# Measurement

Measurement is any process that produces a quantitative description of an attribute, such as length, circumference, weight, temperature, volume, or number. Measurement is an essentially mathematical procedure that we apply in many different contexts. In our daily life, we often wish to know how many beats per measure, how many more minutes until preschool is over, how hot it is today, or whether I am taller than my friend. In all these circumstances, we use some kind of comparison process to measure or to answer the question “how much?” or “how many?” Attributes like length and capacity are more readily apparent and meaningful to young children than less visible ideas like temperature and time.

© Erikson Institute’s Early Math Collaborative. Reprinted from Big Ideas of Early Mathematics: What Teachers of Young Children Need to Know (2014), Pearson Education.

# Number Operations

When children focus on what happens when we join two sets together or separate a set into parts, they learn about how quantities change. When they have lots of experience comparing amounts, they become familiar with thinking about differences between sets. And when they have opportunities to see how a single large set can be composed of two or more smaller sets, they get comfortable with the fact that larger numbers contain smaller numbers. These ways of mentally modeling real situations are what we mean by number operations.

# Number Sense

Number sense is the ability to understand the quantity of a set and the name associated with that quantity. Strong number sense developed in the early years is a key building block of learning arithmetic in the primary grades, as it connects counting to quantities, solidifies and refines the understanding of more and less, and helps children estimate quantities and measurements.

# Pattern

Pattern is less a topic of mathematics than a defining quality of mathematics itself. Mathematics “makes sense” because its patterns allow us to generalize our understanding from one situation to another. Children who expect mathematics to “make sense” look for patterns. Children need many opportunities to discover and talk about patterns in mathematics. These experiences help them form the attitude and confidence that mathematics should make sense, the crucial foundation all children need to become persistent and flexible problem solvers.

# Sets

Sets are basic to children’s thinking and learning. They are also basic to our number system. One of the most important jobs of each number is to describe “how many” there are in a set of things —be it one, seven, or three hundred and nineteen. Before we can figure out how many apples there are, we have to decide which things are apples, and which are not. Once we’ve created the set of things that are apples, perhaps by separating them from the oranges, then we can count them. Counting requires a set, and as a result, the properties of sets have a large influence on the number system, and on mathematics.

# Shape

Everything in the material world has shape. In mathematics, the focus is very much on regular shapes, such as the two-dimensional circle, triangle, and rectangle and the three-dimensional solids known as spheres and polyhedrons. In our everyday world, these solids commonly appear in objects we describe as boxes, pyramids, blocks, cylinders, and balls. A deeper knowledge about how two- and three-dimensional shapes are defined and relate to one another will help educators be aware of subtle distinctions and rules. Such an understanding allows educators to notice and highlight children’s key discoveries and to guide their experiences to make this knowledge explicit for them.

# Spatial Relationships

Children between the ages of 3 and 6 are more than ready to develop their skills at expressing directions from different locations and understanding relative positions. They are fundamentally interested in modeling their world, whether in the block corner or the housekeeping area, and spatial relationships are a large part of what they grapple with there. The more such experiences they have, particularly in the company of adults who help to mathematize them, the easier it will be to make their own representations of space mathematically precise when they get to geometry class.