Developing Number Concepts by Kathy Richardson 

Understanding numbers goes beyond simple counting or memorization. According to educator and researcher Kathy Richardson, developing number concepts involves helping children build a deep, flexible understanding of how numbers work. Her approach emphasizes hands-on learning, meaningful experiences, and a progression of skills that guide children toward number sense mastery.

What Is Number Sense?

Number sense is a child’s ability to understand numbers, their relationships, and how they can be manipulated. It’s not just about knowing how to count but also about recognizing quantities, comparing numbers, understanding part-whole relationships, and making reasonable estimates.

Richardson’s research highlights that true mathematical understanding develops gradually as children explore numbers in a variety of ways.

Key Ideas in Developing Number Concepts

1. Counting with Understanding

Children often begin their math journey by rote counting—reciting numbers in order. However, Richardson emphasizes that children must understand what numbers represent before they can truly grasp mathematical concepts. Activities like counting objects, grouping sets, and comparing quantities help build this foundation.

💡 Try This: Instead of just having students count aloud, ask them to show numbers using objects, tally marks, or fingers.

2. One-to-One Correspondence

Before children can grasp addition or subtraction, they need to understand that each number corresponds to a specific quantity. This skill is crucial in helping them accurately count and compare sets of objects.

💡 Try This: Have children match objects one by one (e.g., setting a table with one plate per person) to strengthen their understanding.

3. Understanding Relationships Between Numbers

Number relationships involve concepts such as more/less, before/after, and part-whole understanding. Richardson stresses the importance of helping children recognize patterns and relationships rather than relying on memorization.

💡 Try This: Use number lines, dot patterns, and ten frames to encourage students to see number relationships instead of just counting one by one.

4. Building Flexibility with Numbers

Rather than teaching rigid algorithms, Richardson promotes flexible thinking—the ability to decompose and recompose numbers in various ways. This skill helps children with mental math and problem-solving.

💡 Try This: Give students a number like 10 and ask them to show different ways to make it (e.g., 5+5, 6+4, 7+3).

5. Using Hands-On Materials

Manipulatives such as counters, base-ten blocks, and number tiles provide concrete experiences that allow children to visualize number relationships. Richardson’s work highlights the importance of using real objects before moving to abstract symbols.

💡 Try This: Use cubes, counters, or beads to model math problems before introducing written equations.

Why Richardson’s Approach Matters

Many students struggle with math because they never develop a strong foundation in number concepts. Richardson’s approach ensures that children don’t just learn procedures—they understand the "why" behind the math. By prioritizing number sense over memorization, teachers and parents can help children become confident, flexible thinkers who enjoy math.

Final Thoughts

Developing number concepts takes time, exploration, and meaningful experiences. By incorporating Richardson’s strategies—such as hands-on learning, number relationships, and flexibility—educators can help children develop a deep, lasting understanding of numbers that sets them up for success in higher-level math.

💬 What strategies have worked for you in building number sense with children? Share your thoughts in the comments!