# enVision® Mathematics – Counting and Cardinality

Discover the foundations of the five principles for cardinality and counting and why they are essential for students to understand mathematics.

By Dr. Juanita Copley

enVision® Mathematics author Dr. Juanita Copley discusses Counting and Cardinality. Learn how projects are an excellent way to connect students’ interests with high-quality mathematics curriculum and real-world events.

The students in my kindergarten class were completing “I Can” books near the end of the school year. Five-year-old, Eli, wrote this beautiful entry expressing his excitement at being able to count to 30. As his teacher, I admit that I was equally excited about his progress because it was the result of many practice sessions. Indeed, he could count to 30 accurately without missing one word or object.

As these short examples illustrate, projects are an excellent way to connect students’ interests with high-quality mathematics curriculum and real-world events. If appropriately implemented, projects provide opportunities for the application of mathematics knowledge and skills.

No one questions that counting is an essential component of mathematical understanding. For example, Counting and Cardinality is a major domain for kindergartners as described by many state standards. In addition, counting objects or verbally saying the counting numbers has historically been foundational to early math learning. Both prekindergarten and kindergarten teachers name counting as one of three math ideas or procedures that children need to learn to “be ready” for first grade. For a young child, counting is not a simple process. Counting involves complex concepts, procedures that are modeled frequently, and the necessary practice to count successfully.

In this paper, we will examine five principles in counting and cardinality. While we will talk about each of these ideas separately, they are actually all connected to each other and are necessary for mathematical tasks. The five principles are: (1) cardinality (including subitizing), (2) object counting, (3) the verbal number word list, (4) reading and writing numbers, and (5) cardinal counting.