Like many parents, Tracy Solomon spends quite a bit of time counting with her son Xavier.
“First, we learned to recognize numbers: speed signs on the road or pointing out people with numbers on their sports jerseys,” she recalls of his preschool days. Next came counting sets of objects. “I tried to count things he was into, like cars and airplanes.”
Parents teaching their kids basic math before school is nothing new. What is different is we now know how incredibly important it is.
“A child's level of math skills on their first day in kindergarten predicts their mathematical ability in grade five,” says Solomon, who, in addition to being Xavier’s mother, is a developmental psychologist and research scientist at The Hospital for Sick Children (SickKids) in Toronto. “The literature shows a kid’s incoming number knowledge is a forecast for how well they will be doing in math as much as seven years down the road.”
The good news is Solomon’s ‘number talk’ with Xavier during the preschool years works. Research shows parents can easily increase their child’s math knowledge before school begins and set them up for success in the future.
What is ‘number talk’?
“Number talk is any talk about numbers,” says Susan Levine, professor of psychology at the University of Chicago, who studies the relation between how much number talk goes on in the house and how well kids do in math on the first day of school. “We told the parents to do what they ordinarily do with their kids, recorded it, then went back to count how much number talk was going on. Parents who do this more have kids who score better in math.”
But Levine and her colleagues also found that some types of number talk proved to be better indicators for future understanding than others. “Kids can rattle off their numbers early, often from 1 to 10, and parents are surprised and impressed. But it’s a list with no meaning. When you say ‘give me 3 fish’ they give you a handful.” Gradually, kids figure out the meaning when objects counted are labeled by the parents. In essence, pointing to the objects while counting them and noting how many there are when the counting is done. “If you count 4 trucks, they are all 4 but it’s the fourth truck that carries the meaning.”
The key to understanding why some types of number talk might be more effective than others lies in understanding how children learn to count.
How kids learn to count
Before children have any counting ability, they have an innate understanding of quantity. Six-month-old babies can tell the difference between ‘more’ and ‘less’. So can many animals. It is easy to imagine how this could develop through evolution: going for the big pile of food is better for survival than the smaller pile of food. ‘Numerosity’, or the ability to recognize groupings, becomes sharper over time. Babies can tell the difference between a pile of 6 things and 12 things, but recognizing the difference between a pile of 3 things and 4 things takes longer to develop.
Actual counting is a process of mastering and accumulating separate skills. To understand counting, a child must understand five processes, each one building on the next:
- Stable order. The child learns number words have an order. For example 1, 2, 3 is correct. 1, 2, 4 is not.
- One-to-one correspondence. The child learns each number can only correspond to one object in a set of things counted. For example, when counting, each truck has its own number: the child can’t skip a truck or count the same truck twice.
- Cardinality. The child learns the last number used when counting a set of things is the number of things in that set. For example, when counting 4 trucks, when they label the last truck as number 4 that is how many trucks there are in the set.
- Abstraction. The child learns anything can be counted, even things that are not the same. For example, 2 trucks and 2 cars is 4 things in the set of things counted.
- Order irrelevance. The child learns that things can be counted in any order. For example, a set of trucks can be arranged in a circle and then in a line and there will still be the same number.
One last skill worth noting here involves knowing a number of objects just by looking. If you show a toddler 3 things and say ‘how many?’ they can recognize 3 without counting. Levine believes this ability, called subitizing, provides another clue as to why some types of number talk are more effective at prepping kids for future math skills than others.
“Most parents use low numbers when counting with their kids, but when kids see 3 bears they don’t have to count to understand. They can say ’3’,” says Levine. But the ability to subitize quickly diminishes with larger numbers of objects. “When parents extend the number talk beyond 3 up to 10, their kids have a better understanding of cardinality. We think this is because the somewhat higher numbers provide the opportunity to make the link and understand ‘this is why I’m counting’”.
Getting kids to make these links need not be a chore. “Parents can do fun, simple things around the house,” says Levine. “You don’t have to drill them.” In fact, by putting in a fun effort early, parents may be avoiding more unpleasant efforts down the road helping their kids catch up in math, which can be very difficult.
Simple ideas to teach math to preschoolers
At the request of AboutKidsHealth, both Levine and Solomon have provided some suggestions on how to help preschoolers learn the five steps to counting. The general advice is to simply incorporate these activities and others like them in to daily life around the house.
- Encourage your child to the list off numbers 1 to 10 in the right order. While not necessarily counting, it helps them become familiar with number sequence.
- Count objects that are in front of the child and label the set size: “Let's count your dolls. 1, 2, 3, 4. You have 4 dolls.” Point at each object as it is counted and encourage the child to do the same. Counting something is better than just counting.
- Vary what you count: count objects, but also steps, stairs, and sounds.
- Numbers can also be talked about in the context of reading stories to young children. There are often objects in pictures that can be counted and then the set size should be labeled. After counting something, labeling at the end is just saying “so there are 3 bears”
- Line up two sets of things: 3 trucks and 2 cars. Then count each set while pointing to each member of the corresponding pair: “1” (point to a car and a truck that are side by side); “2” (point to a car and a truck that are side by side); "there are 2 cars”; and “3” (pointing to the one extra truck that is not paired with a car); “there are 3 trucks. There are 2 cars and 3 trucks.” This helps kids learn one-to-one correspondence.
- Parents should find contexts in their daily routines when they can talk about numbers with their children. For example, “tonight there will be five people at home, so we need to put five plates on the table. Let's count them: 1-2-3-4-5. We have 5 plates.” This lets kids know people do math all the time.
- When you are walking in the neighbourhood, count the number of red cars you see, “1 red car, 2 red cars, 3 red cars -- today we saw 3 red cars.” This helps give kids a clue to the fact that things can be categorized, and therefore counted, in different ways.
- Counting can come up when you need to share. “We have 4 cookies and 2 children -- let's give 1 to you, and 1 to your friend, another 1 to you and another 1 to your friend. Let's count how many each of you have -- 1, 2 -- you have 2. 1, 2 -- you have 2. Each of you has 2 cookies!” This gives kids a clue to the fact that the same items can be counted in different ways.
- Introduce basic calculation. “You have 2 trucks. If I give you 1 more, you will have...?” (Wait for child to answer, or supply an answer if the child doesn't know: "Now you have 3 trucks.”) Subtraction: “You have 3 trucks -- if you give one to me you will have...?" (wait or supply an answer).
Where is all this heading? Fractions!
Learning to count is just the first step. Solomon suggests keeping an eye on where this knowledge is heading, which has to do with fractions, arguably the biggest math hurdle kids face.
Typically, the objects parents count with a preschooler are considered ‘whole entities’: trucks, oranges, coins, and blocks. But the reality is these objects are all potentially made up of smaller units or could be part of larger units.
“The basic idea behind fractions is that quantity is continuous and that a ‘unit’ can be just about any size,” says Solomon. “Imagine a ruler. It’s not the marks on a ruler that represent the number 1, 2 and so on. It’s the space between the marks that represent the quantity.”
The idea is not to try to get your child to fully understand this concept, but rather to insert little clues into your child’s head about the concept which may make the “ah ha” moment about fractions down the road easier to achieve. Solomon suggests counting objects that are more easily variable in terms of their unit size.
For example, stand with the child in the centre of a room and ask the child to guess how many steps it would take to walk to the window. The child guesses then tries it out counting the steps – say 4. Then ask the child to guess how many steps it will take the parent to get to the window. It only takes 2. Why is it different? Because mummy takes bigger steps.
Another way to demonstrate this concept is with a big pile of something small like buttons. If there are 100 buttons, a number much too large for the toddler to count, they could be counted in terms of scoops. A child can learn that there are five scoops of buttons in the pile. Solomon says the exercise can be done with water or sand and that the scoop size can also be varied.
“Don’t invest a lot of time trying to explain the concept. Just getting used to the idea is enough for a preschooler,” says Solomon, whose son Xavier is now seven years old and doing well in math using number lines -- essentially, paper rulers that help teach the concepts behind fractions. "Once you have prepared them for the first day of school, your work is not done. Parents should be helping their child learn math all through their childhood. I just wish I'd done more of it when he was younger.”