“Although most children learn to subtize until age three or four before they go to kindergarten, some children simply don’t have the opportunity, and these children have very big problems in kindergarten,” she said. said Art Baroody, professor. emeritus at the University of Illinois at Urbana-Champaign, who has spent his career studying the best ways to teach counting, numbers and arithmetic concepts to young children. “The reason for this is that Subitization involves constructing an understanding of what one is, what two is, what three is, what four is, which is the conceptual basis of number sense. There are so many things that build on this understanding.
As children grow, Subitization may become more sophisticated and useful for understanding more advanced math concepts. Imagine a group of seven points like this:
Most people can’t sample that many dots, especially when they aren’t arranged in a familiar pattern, but they can detect subgroups. Some might see two groups of three plus an extra point. Others might see a group of four and a group of three. There are many possibilities.
Doug Clements and Julie Sarama, a research team at the University of Denver, call this rapid compartmentalization “conceptualization.” They say it helps kids compose and decompose numbers, which is helpful for learning addition and subtraction facts. For example, 7 + 5 can be a difficult sum to learn. But a child who knows how to objectify can quickly see that the 7 can be divided into 5 and 2. This makes it easier to put the two 5s together to make 10 plus 2 more to get to 12. “It makes sense and we don’t forget not that,” Clements said.
Of course, counting from 7 is another approach. But it can be mentally taxing to keep track of five more when a child is counting from 7 to 12. Children who know how to add only by counting quickly realize that they don’t have time to count when asked. presents a long addition worksheet. These children often resort to memorizing a series of meaningless numbers (5, 7, 12) which they quickly forget. “They skipped the step of making sense of it,” Clements said. “In first grade, teachers will say, ‘He knew that last week.’ Now he has forgotten it. Well, he never really knew.
Subitization seems to help with all sorts of math concepts, according to its proponents. In 2014, another group of researchers described how third graders, who were able to quickly group sets of small numbers, such as three groups of two, had a more sophisticated understanding of multiplication and could multiply more quickly. Some say that the ability to divide a number into smaller subitizable pieces helps one understand the relationship between a part and a whole and makes it easier to use fractions.
Clements and Sarama recommend using Subitization exercises until the end of elementary school. For example, a 24-point chart can support a conceptual understanding of multiplication in grades three through five.
“Suditization is not a baby thing that you walk away from,” Clements said. “You just continue to develop it alongside all the other skills you’re developing.”
Well, sometimes it’s baby stuff. Some researchers believe that infants as young as five or six months experience small numbers, like two and three. This belief is based on experiments in which infants held their gaze longer in response to changes in quantities. As children grow, they begin to associate number words with collections of objects, for example “two socks”, and by age 2, many children can objectify up to three items, and the Children aged 4 and 5 years old can undergo Subitization. up to five elements.
Researchers hypothesize that fostering this innate ability could help children develop their number sense. A case study of two students struggling in math, published in 2009, found that Subitization was helpful. Baroody, of the University of Illinois, promoted the teaching of perdition in a 2013 how-to guide titled “Teaching Mathematics to Young Children” for the Institute of Education Sciences, the research arm of the U.S. Department of Education.
Several studies have shown that children who have greater subconscious skills also tend to perform better in mathematics. For example, a 2022 study of more than 3,600 kindergartners in a southwest school district found that children who were better listeners also had significantly better arithmetic skills in first grade. A 2020 study of 80 young children, aged 2 to 5, found that children who could identify the number four and who had learned to count could generally answer the question “How many?” » But children who could only tolerate the number three demonstrated only a partial understanding of quantity.
Yet the strong correlation between Subitization and math ability does not prove that students will benefit from Subitizing teaching. It’s possible that stronger subtizers come from wealthier families who play more board games. These higher-income children also benefit from a range of other factors at home, from better nutrition to less stress, that could contribute to their math success.
Empirical evidence that it is worth investing classroom time in subtization is thin, at least so far. In a new but small study, 14 preschoolers aged 3 to 5 were randomly assigned to two different math interventions. Those who received more practice in Subitization performed better on a test of understanding quantity. This study, available online, is expected to be published in the December 2024 issue of the Journal of Mathematical Behavior. More and larger studies are needed.
Even without this evidence, many elementary school teachers have been incorporating aspects of Subitization, sometimes called “quick images,” into their classrooms for decades. But more systematic teaching of this practice appears to be growing in popularity, based on interviews I’ve had with teachers, researchers, and the National Council of Teachers of Mathematics, a professional organization. One motivation is the desire to close large achievement gaps between rich and poor children by building stronger mathematical foundations in the early years. Subitization is explicitly included in the Illinois math standards for kindergartners, while many other states suggest Subitization as an example of a way to teach numbers. Curriculum publishers are increasingly printing images of dots to be used in their materials.
Beth MacDonald, associate professor of early childhood mathematics education at Illinois State University, said Subitization was a hot topic at the International Congress on Mathematics Education earlier this summer. “People come in and say, ‘Oh, we want to look at this,'” said MacDonald, who wrote his thesis on submitization more than a decade ago and has authored several articles and studies on submitization that I read to write this article.
Despite the simplicity of Subitization, experts say they sometimes consider it poorly taught. A common mistake is to ask students to count points. Researchers say this undermines the child’s self-confidence and ability to develop mental images of settings.
Speed is essential. Often the dots are displayed for too long, long enough for children to count them. “That’s the biggest mistake,” said Sarama, Clement’s partner, who explained to me that brevity encourages children to visualize the image for themselves.
Sarama says each point exercise can be done in 10 seconds for a total of three minutes per day. According to researchers, the memory of quantities is built through brief but repeated exposures.
According to Robinson, a math teacher in Milwaukee, kids want to talk so much about the different ways they see points that it’s difficult for teachers to move on to the next activity. Children really like to amuse themselves.
And many children learn to suddenly at home. Researchers say this practice does not require sophisticated equipment and parents do not need to create dot cards. They advise parents to talk about quantities during daily activities. When folding laundry, talk about matching pairs of socks. Or, at the end of lunch, ask who will eat the three fries left on the plate. Sometimes you don’t need to count them!
