April 30, 2015

One of the main building blocks for children as they learn to understand math is grasping “number sense.” Number sense is how people conceptualize numbers and mathematics, including the relationships of numbers to one another, the ascending or descending value system inherent in their order, and understanding what makes the results of basic arithmetic reasonable. The National Council of Teachers identified five components that characterize number sense:

- Number meaning
- Number relationships
- Number magnitude
- Operations involving numbers and referents for number
- Referents for numbers and quantities

“Referents” are things in the real world that children and adults understand through numbers. When you see you three dogs, and know that you’re looking at more than two dogs and less than four, and also that if two more dogs join the group there are now five, you’re employing referents (the dogs) for the numbers.

Developing number sense is the first step for children to feeling comfortable with math and everyday calculation, and also the path to “making friends with the numbers.” When children learn the names of numbers, what composes them, what they mean, how to use them, and how to apply them to real-world referents, it makes the children feel comfortable and confident and both eager and able to engage with math.

Children can begin to develop their number sense as young as two, but it’s also easy for their development to stagnate if they aren’t exposed to notions of number sense frequently enough. As we noted in our last post, many children from low income families struggle to master the concept of cardinality—the principle of how many numbers a set contains, and an aspect of number sense—because they aren’t less often asked or told about numbers vis-à-vis referents.

How can you practice number sense with children? Well, it’s hard to make a friend without an introduction! Introducing number talk to children, especially in terms of every-day referents, is the best way of helping them gain a solid number sense. How can instructors help solidify number sense in children? Here are a few ways.

**1.)** Beginning with movable blocks or toys is a great way of introducing number sense because the objects can be manipulated easily into many different formations in a way that will capture their motor memory. If children are asked to “make five” from a pile of blocks, and then “make two and three” from their five, they will remember the physical experience of moving the blocks and tie it closely with the abstract meaning.

**2.)** When you present groups of referents to children, make sure you don’t present the referents in the same formation every time. For example, if you show six dots on a flashcard in two rows of three, children will probably recognize it easily as six because they’re familiar with the pattern. If you show them instead a flashcard with a line of four and a line of two, or even five and one, or three lines of two, it will help them realize that six can be made up of many different subgroups.

**3.)** Use numbers in conversation as much as possible—even when it seems obvious to adults, it’s important real-world learning for children. When they’re lining up to go to lunch or recess, count the students aloud, and have them count with you, and have them determine how many people are missing versus how many there should be. Talking them through numbers and asking them questions about referents will go a long ways!

For great games that teach kids number sense, check out our Mango Math crates!