### Free Resources

#### KENS Math Assessment Test

Read the full text of Douglas H. Clement’s “Subitizing: What is it? Why teach it?”

## Subitizing – A Building Block of Successful Mathematics

Subitizing is the ability to quickly identify the number of items in a small set without counting. Researchers have demonstrated a strong relationship between subitizing skill and math achievement including a recent study with over 500 kindergarten students.

Subitizing skill has also been shown to be a reliable predictor of later math achievement. Educator Douglas H. Clement addressed a key question related to subitizing in his article, “Subitizing: What is it? Why teach it?”. Clement concluded that subitizing can play an important role in the development of basic math skills including addition and subtraction skills.

## Perceptual Subitizing vs. Conceptual Subitizing

In his article, Clement distinguishes between the perceptual subitizing common in very young children and conceptual subitizing. When a child quickly perceives that three dots are more than two dots, and names the total number of dots, the child is using perceptual subitizing. Because we are biologically limited to quickly subitize no more than four or five dots, it would require a conceptual understanding of number to know that four dots and two more dots make six dots.

Conceptual subitizing is similar to the ability to combine small sets of numbers or number combinations. This can be accomplished in several ways. One way is to memorize a specific pattern of numbers. When a child learns that two columns of three on a die make six, the child is memorizing a pattern for six. With explicit training, however, students can combine numbers non-verbally to determine the sum of two sets of numbers.

As Clement suggests, the arrangement of dots or items in a set can make knowing “how many” difficult or easy. Dots that are too tightly arranged or placed in a circle are more difficult to subitize than dots that are placed in a line or in a rectangle. In KENS Math, the arrangement of dots is purposefully created to provide a measured degree of challenge. In most cases, a linear arrangement is used, because it models a number line.

Additional research studies have documented the success of teaching older students to subitize. In one study, students were trained to recognize sets of numbers presented on a computer screen for a fraction of a second. With practice, these students developed the ability to subitize. These students also demonstrated increased arithmetic

skill without explicit training!

In KENS Math, the placement of dots, the gradual increase in challenge, and the intentional training of subitizing and number combinations is designed to take advantage of these key research findings to further support each student’s number sense development.