If you are an early years teacher or parent, there are four milestones that you should be eagerly waiting for:
|Counting rotely||The ability to recite an ordered number list, and not necessarily with any understanding! (See here for more: Learning to count…baby steps.)|
|One to one correspondence||The ability to pair an object in a set with a number. (See here for more: (Making Math Meaningful with Manipulatives!)|
|Cardinality||The ability to understand how many are in a set (1, 2, 3, 4 so there are 4 objects in the set).|
|Abstraction of number||The realization that a number could apply to different sets, for example 3 could mean 3 cookies or 3 of something else.|
These milestones aren’t steps, in that children don’t progress from one to the other. Each milestone is interrelated and depends on the development of the others. For example, a child can’t demonstrate cardinality (#3) unless they have the proper vocabulary to back it up (#1). A child can’t show 1:1 correspondence (#2) unless they understand that everything can be counted (#4).
Usually these four milestones are achieved to some extent before a child enters kindergarten, although the difficulty level should be steadily increasing from year to year. For example, a 2 year old should be able to count to 2, subitize a group of 2, and show 1:1 correspondence for two things. A three year old should be able to do more.
By the time a child is ready for kindergarten, they should be able to rote count to 10 with no errors, show 1:1 correspondence for 10 objects, show cardinality for up to 5 objects (not necessarily subitize them though) and have a solid understanding that numbers can be used to count different sets and that the meaning of quantity remains the same regardless.
If your child isn’t able to do these things by the end of their 5th year, this could be due to a lack of exposure or a sign of a larger problem. Oliver (my baby!) is about to go for his kindergarten orientation! Let’s see if he has developed a solid foundation in number sense, by checking if he has mastered these four milestones!
Bottom line: number sense is the most important strand of mathematics. Without it, students can’t access higher math concepts, solve problems, or meet with success on basic number operations. We want our children to think flexibly and fluently about numbers and we can build that foundation in pre-school.
But why start so young? Research has shown:
“Preschool children’s knowledge of mathematics predicts their later school success into elementary and even high school” (Clements & Sarama, 2011).
Other research has shown that pre-school children can do math, so we need to take advantage of this fact, and as Nike would say: just do it!
So what can you do to help build this fluency?
- Children need repeated practice; sometimes termed ‘overlearning’, the goal is to produce ‘automaticity’. To do this – have your child practice number lists and counting often, correct errors as needed.
- Mathematize the situation: take situations and problems from the world around them and pose the situation in mathematical terms. To do this, count everything! How many cars in the drive-way? How many cups at the table? How many flowers in the garden? How many pieces of toilet-paper should you take to wipe your bottom?!
- Extending the numbers: have they mastered cardinality of 3 objects? Now try 4. To do this – start with movable objects so children can move them while counting.
- Build a better vocabulary. Current research on cardinality shows that it is very linked to a child’s language development. You can further its development by finding books, songs, stories, or videos that have to do with number and quantity.
The most effective place to develop a solid foundation of number sense is at home. Mathematizing situations is the best way to show children that numbers are everywhere, everything can be counted, and we can see numbers in different ways. Do it everyday!
At school, you need to make the learning explicit; don’t just hope children will pick it up. Although informal activities should provide many opportunities for exploring numbers, you should also intentionally direct the learning with guided lessons so children are exposed to numbers in a purposeful way.
THE WHERE TO GO NEXT:
The exciting thing, is once a child masters these four things, they are ready to start adding and subtracting! I checked to see whether Oliver was ready to learn to add, but as you saw in the video, adding one more meant recounting the set each time. That is okay though, and the perfect place to start the understanding of one more or one less. Next time, I would work with a smaller number set and see if he can master one more or one less without recounting.
Are you still stuck on where to start? Click here for some activities that will help you encourage your child to learn to count. Have more suggestions? Leave them in the comment section below!