Building number sense in the brain: More than just counting to ten
Last week I wrote that for kids, thinking of the brain as a muscle empowers them to strengthen their brains through effort. This week, for parents I introduce the idea of the brain as an orchestra, and I give some tips on how parents can help kids develop an understanding of numbers supported by an orchestra of brain areas.
In the brain, instead of hiring a master conductor, we coordinate different sections by bringing them together literally, growing physical links between different brain regions as we develop and learn. The strength of our brains’ billions of neural connections correlates with cognitive abilities like reading and math, spatial memory, and musical expertise. For example, colleagues and I at Stanford found that adolescents who are better at mental arithmetic have stronger connections between the front of the brain and the side of the brain. The frontal region helps with language, while the side region supports our knowledge of quantity. The connections between the two regions let them operate together, and the stronger we can make those connections grow, the better we are at mental arithmetic.
For basic number knowledge, like the kind you may want to teach your preschooler at home, the key idea is that a mastery of numbers extends way beyond the ability to recite the numbers 1–20. It involves several different pieces of number knowledge coming together into a unified whole. A complete understanding of, say, the number three includes knowing that it stands for three items, that it comes after two in the counting sequence, and that it is one more than two and one less than four in quantity.
More advanced math like arithmetic incorporates even more pieces of knowledge, including a general sense of quantity, knowledge of arithmetic procedures, and memorization of arithmetic facts. Neuroscientists, by studying adult patients with brain damage in specific areas, have found that these functions are supported by different parts of the brain. One patient reportedly couldn’t answer arithmetic problems correctly, but he always made good estimates (He might say 4 + 5 = 10, but he would never say 4 + 5 = 30). A different patient could not estimate at all, but could calculate arithmetic problems perfectly. These patients had damage in different brain areas, showing that a sense of number is housed in a different part of the brain than knowledge of math facts and arithmetic procedures. You need both together for fluent math ability.
So, how do you give preschoolers this complete number knowledge we’re talking about? Research shows that one way is to get kids to think about the different aspects of number meaning concurrently. For example, in the program Number Worlds, currently developed by Sharon Griffin at Clark University, children’s math skill was boosted by playing a series of games in which they concurrently (1) counted, (2) associated the numbers with several representations of quantity (a cluster of items, a distance, and a number of movements), and (3) thought about “more” and “less.”
Here are some tips on encouraging your child to piece together a complete meaning of number:
- Practice counting items, not just reciting numbers as a “song.”
- Introduce vocabulary like more and less, closer and farther, bigger and smaller.
- While counting objects, point to them one by one, but then count them again using a different pointing order (backward, clustered, etc).
- Count many types of things: Objects, movements, sounds, etc.
- Use phrases like “one more” and “one less” (e.g., “Give me one more block. Now how many are there?”). This helps establish that counting up or down corresponds to adding or taking away one item. You may notice that children count the items over again each time they add or take away one. Don’t worry; that’s the usual starting step for addition. Soon they’ll be able to count up or down from the original number rather than counting from the beginning all over again.
Back to the orchestra analogy, just like the string, woodwind, and percussion sections play together to produce a piece of music, so do the parts of the brain work together to produce math abilities. And just like how orchestra members learn to work together by practicing together, so do different brain areas and different pieces of number knowledge. Neuroscientists have a saying, “fire together, wire together,” meaning when two neurons are active at the same time, the connection between them strengthens. It turns out this idea is a good way to think about teaching number concepts: The more we can get kids to think about different aspects of number concurrently, the stronger their connections and the more complete the knowledge.