An important feature of an early childhood math curriculum that parents may not know about is something called subitizing, which is a large word for a very simple phenomena: the ability to recognize the number of objects simply by looking at their arrangement. If you have every rolled a pair of dice and recognized 12 pips by seeing two sets of boxcars, then you know what it feels like to subitize.
Subitizing helps us count objects quickly using familiar patterns: the first set of dots directly above is completely disorganized, so the brain cannot discern a pattern. The second card shows the dots organized, but not in a way that the brain can count easily. The third card enables us to actually carry out subitizing by seeing two distinct groups of five.
While subitizing is something that occurs in newborns, as well as primates, dolphins, birds and even amphibians, it is a fertile area to explore numerical reasoning with young children. In the Manhattan Country School Lower School math program, we do a series of three tasks that develops and explores this important concept.
The first exercise is to look at small groups of dots arranged in different patterns and instruct students to photograph and develop pictures of dots. A dot pattern is shown for a very brief amount of time, students shut their eyes to record what they’ve just seen, and then reproduce the remembered pattern using magnetic dots on a board.
This exercise stimulates provocative discussions about how we recognize quantities. Some children visualize numbers as shapes, while others see them as patterns, and these patterns take on different interpretations. A set of four dots can be seen as a square of four dots, or two sets of two vertical or horizontal dots. A group of 10 dots arranged in a triangle can be remembered as an ascending pattern of one, two, three and four dots.
In the second exercise, students are shown a number and asked to arrange the dots in patterns or shapes that can be remembered easily. Students will arrange dots as two rows of three, three rows of two, or as two sets of three dots arranged in a triangle. By putting dots into groups like this, they are exploring concepts like multiplication (in that the dots can be skip counted by two), or addition (3 + 3 = 6 dots.)
In the final exercise, students use their understanding of subitizing to play the game Compare, where they take a set of dot cards, split them into two piles and then flip them over one at a time and call “mine” if the set of dots on their card is larger than their opponent’s. The idea here is to further refine their estimation and numerical reasoning skills by comparing two sets of dots and deciding which has more. Students are discouraged from counting the dots one by one, because the activity emphasizes numerical perception, which is an important component of developing number sense.
If you’d like to know more about subitizing and it’s importance in early childhood mathematics, you could do no better than perusing Douglas Clement’s article, “Subitizing: What Is It? Why Teach It?” If you want to practice subitizing with your child at home, you need look no further than a set of dominoes or playing a board game that uses dice.