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A fascinating theory has been gaining traction: the idea that an effective way to teach counting might be by not counting at all. This seemingly paradoxical concept is at the heart of “subitizing,” a practice derived from the Latin word “subito,” meaning “suddenly.” Subitizing involves instantly recognizing the quantity of a group of objects without explicitly counting them, similar to how you instantly see four dots on a die without counting “one, two, three, four.”
What is Subitizing?
Subitizing is becoming a common practice in pre-K classrooms across the country. For instance, in Milwaukee, district math coach Danielle Robinson has observed an increase in subitizing exercises in the city’s pre-K classrooms over the past two years. A typical subitizing exercise might involve a teacher flashing a picture of three dots on a screen and asking students how many dots they see without counting. The students then discuss how they arrived at their answers.
The Growing Popularity of Subitizing
At first glance, asking children to recognize quantities without counting might seem counterproductive. However, this method is gaining popularity in elementary schools nationwide. Prominent researchers in early childhood math education have been advocating for subitizing for over 25 years, suggesting it helps build number sense. According to their theory, subitizing complements explicit counting instruction, providing a meaningful understanding of quantity. Without subitizing skills, children may struggle to grasp the true meaning of the numbers they are counting.
The Importance of Subitizing
Art Baroody, professor emeritus at the University of Illinois at Urbana-Champaign, has dedicated his career to studying the best ways to teach counting and arithmetic concepts to young children. He emphasizes that subitizing helps children construct a foundational understanding of numbers. Without this understanding, children might find it challenging to progress in their mathematical education. As children grow older, subitizing becomes more sophisticated and aids in comprehending advanced math concepts. For example, recognizing a cluster of seven dots might involve seeing subgroups within the larger group, which helps in learning addition and subtraction.
Practical Applications of Subitizing
Doug Clements and Julie Sarama, researchers at the University of Denver, describe this advanced form of subitizing as “conceptual subitizing.” This skill helps children compose and decompose numbers, which is crucial for learning addition and subtraction. For instance, understanding that 7 + 5 can be broken down into two groups of 5 (making 10) plus 2 more to arrive at 12 is more meaningful and easier to remember than simply memorizing the sum.
The Broader Impact of Subitizing
Subitizing is not limited to simple math problems. It also helps with understanding multiplication and fractions. For example, recognizing groups of smaller numbers within a larger set can aid in understanding the concept of multiplication. Researchers have found that children who can subitize tend to have a more sophisticated understanding of mathematical concepts and perform better in math overall.
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Long-Term Benefits and Recommendations
Clements and Sarama recommend incorporating subitizing exercises throughout elementary school to reinforce these skills. They argue that subitizing is a fundamental skill that should be developed in parallel with other math skills. This recommendation aligns with findings that even infants as young as five or six months can subitize small numbers, indicating an innate ability that can be nurtured from a young age.
Empirical Evidence and Current Practices
While empirical evidence supporting the benefits of subitizing is still emerging, initial studies show promising results. For example, a study of over 3,600 kindergarteners found that those with stronger subitizing skills performed better in first-grade arithmetic. Another study of young children demonstrated that those who could subitize up to four items had a better understanding of quantity.
Despite the need for more extensive studies, many elementary school teachers have been incorporating subitizing into their classrooms for years. This practice is gaining momentum, with curriculum publishers including subitizing exercises in their materials and some states explicitly including subitizing in their math standards.
Teaching Subitizing Correctly
Teaching subitizing effectively involves ensuring that students do not count the dots, as counting can undermine the development of mental images of sets. The key is to display the dots briefly, encouraging students to visualize the quantities quickly. According to researchers, these exercises can be completed in just a few minutes each day, building memory for quantities through repeated exposures.
Encouraging Subitizing at Home
Parents can also help their children develop subitizing skills at home. This practice does not require fancy materials; everyday activities can provide opportunities for subitizing. For example, talking about quantities while folding laundry or during meals can help children develop their number sense without explicit counting.
Conclusion
Subitizing offers a unique and effective approach to teaching young children about numbers and arithmetic. By fostering an understanding of quantities without counting, you can help build a strong foundation for future mathematical learning. While more research is needed to fully understand the benefits of subitizing, the existing evidence and growing popularity of this practice suggest it is a valuable tool in early childhood education. As you explore different learning methods and study tips, consider incorporating subitizing into your educational toolkit to enhance your child’s number sense and overall mathematical abilities.
