Subitizing in the preschool classroom: seeing how many there are, without counting

As preschool children’s mathematical development is already in progress, high-quality early childhood education should involve math activities. We share with you a very popular blog post by teacher trainer Astrid Cornelis (Thomas More), published earlier on the Flemish blog Kleutergewijs.

Subitizing is the ability to immediately see how many there are, without counting. In preschool, we tend to focus on counting. There is nothing wrong with counting, but in this blog post, I want to highlight the importance of subitizing. I recommend organizing more activities where children have to see how many there are, without counting. Subitizing is a basic component of understanding numbers and math skills (Le Corre et al., 2006), so it is important to practice this regularly. In their “Learning Trajectories Approach”, Clements and Sarama (2014) describe the growth line of subitizing and provide practical ideas from toddlers to elementary school.

Perceptual subitizing: start with the youngest toddlers

Perceptual subitizing means recognizing small amounts by sight, without counting (Clements, 1999). With the toddlers, start with quantities one and two, and if controlled, you can switch to three and four. Children can learn to subitize to 4 without prior knowledge of counting (Charlesworth & Lind, 2013). You can stimulate this by appointing small amounts throughout the day. You have 2 pieces of apple. How many acorns do you have on your plate? Try putting one potato in the pan. Further on, you will find more games.

Conceptual subitizing: challenge older preschoolers

Conceptual subitizing allows the child to divide a quantity into smaller parts within a whole (Clements, 1999). For example, the child recognizes “6” as two rows of three. Here you can play with the spatial arrangement to make the task more difficult: children usually find setups in a rectangle (in rows) the easiest, followed by setups in a line, in a circle, and the most difficult randomly mixed together (Clements, 1999). In the subitizing tasks, you only move on to the next quantity – with one more – when the child masters the previous one (four to five times correctly recognized).

Why is subitizing so important?

Subitizing is a basic component of understanding numbers and math skills (Le Corre et al., 2006).

o  Subitizing saves time. When one immediately sees how many there are, one does not have to count (Reys et al., 2012). This comes in handy when learning more complex numbers and operations such as addition or subtraction. After all, they recognize smaller groups within a larger whole, which is useful for example with 2 + 4 = 6 or 6-2 = 4.

o  Subitizing is a precursor to more complex numerical skills. Children who subitize well understand better that 4> 3 and that 2 is one less than 3.

o  Subitizing supports counting: If you already see a first group of 4 with 7 objects, you can continue counting “5, 6, 7. There are 7.” Subitizing also allows you to count by jumps later on. When we see groups of 2, we can count “2,4,6,8,10. There are 10. ”

Go for sober materials

When subitizing, you best go for simplicity in the choice of materials (Clements & Sarama, 2014). Use similar objects, with similar shapes and colors. If you work with images, “less is more” also applies there. Simple dots or other sober representations are best. That way there is as little chance of distraction as possible. Subitizing is exciting enough in itself, so you don’t have to add “extra decorations” to it.

Games

Flip the Flash: Flip the Flash can see in a flash how many there are and challenges the children to try it too. You explain that you will show a dot map or a number of objects very briefly (2s or less) and that you will ask to show with fingers how many they saw. You invite the children to look carefully and calmly (Teaching and learning with learning trajectories, 2021). How many have you seen? You can tell that you take a “picture in your head” in a flash. You can also ask the question: How did you know it was 5? How did you see 5? This way you let the children articulate their strategy and you get an insight into how they make groups. To check whether they are correct, the children can count whether it is correct. Over tasks, you not only vary the quantities, but also the spatial arrangement. You can find inspiration for spatial arrangements here. You can, for example, work with:

• loose objects on a tray under a cloth
• flashcards (some examples: five structure 0-5 and 6-10, varied arrangements)
• dominoes
• dice
• a flash book as in this video: https://youtu.be/5gYEjBnKIj8
• a quantity of building blocks under a cardboard box that is briefly lifted
• card with a number of holes on the overhead projector (Clements, 1999). One child puts a hole card on the projector and another child takes the card off. Can the classmates see how many holes there are on the map in this short time?

Squeak under the jar: Together with the children, you hide small numbers under two or three jars. You can start with only numbers one and two. Now shuffle the jars. Who can find the “tricky two”? They choose a jar and turn it over. How many do you see? Is that the “tricky two”? Whoever finds the “tricky two” is won, but if it is not the “tricky two” and you see how many there are, then that is worth a star. When the children do this correctly 4 to 5 times, you can move on to larger numbers. Who finds the “thrilling three”, the “foxy four”, the “fantastic five”? You can also do something similar with boxes where you put small numbers in. The children open a box each time and see whether it is, for example, the “cool two” (Learning and teaching with learning trajectories, 2021).

How Much Under the Tile?: Two players each have a card like this (up to 5), with each square covered by a tile. One player briefly lifts a tile and the other has to look and say how many dots he saw. If it is correct, he wins the tile (Bolin et al., 2021).

Ten Black Dots (Donald Crews, 1995): How many dots do you see? What can these 1, 2, 3, 4,… 10 black dots all be? How do you see that there are 8 of them?

Laying tiles: You invite the children to, for example, take 5 tiles and arrange them freely. Does everyone have 5? Did everyone put them in the same way? Or you can lay 5 tiles yourself and ask the children to put 5 as well but in a different way. Through this activity, children learn that they can put the whole together in 5 different ways.

Sources:

• Bolin E., Rooks T. , Werner S. &Wu S (2021). What is subitizing?  Geraadpleegd via https://subitizing.weebly.com/pedagogy-curriculum-links-teaching-points–resources.html
• Clements, D. H. (1999). Subitizing: What Is It? Why Teach It? Teaching Children Mathematics, 5(7), 400-405.
• Clements, D., & Sarama, J. (2014). Quantity, Number, and Subitising. In Learning and Teaching Early Math: The Learning Trajectories Approach (2nd ed., pp. 9-20). New York: Oxford: Routledge.
• Le Corre M, Van de Walle GA, Brannon E, Carey S. Re-visiting the performance/competence debate in the acquisition of counting as a representation of the positive integers. Cognitive Psychology. 2006;52(2):130–169.
• Learning and Teaching with Learning Trajectories (2021). Geraadpleegd via https://learningtrajectories.org/index.php/learning_trajectories
• Reys, R.E., Lindquist, M.M., Lambdin, D.V., Smith, N.L., Rogers, A., Falle, J., Frid, S., & Bennett, S. (2012). Helping children learn mathematics. (1stAustralian Ed.). Milton, Qld: John Wiley & Sons, Australia.