# Numbers, sensibly

Teaching new skills and concepts depends on understanding what the student already knows. This applies to adults as well as children. When kids enter school and learn to read they need to know their alphabet and have an inkling that letters correspond to sounds. Most kids learn the alphabet by singing the ABC song as well as seeing letters in books, on signs, on television, etc.

Math is the same way. Before kids learn 1+1=2, they need to know what numbers are and what they represent. They must develop number sense, which is the understanding that numbers relate to the real world. Young children have number sense when they know that three people can fit in their family car, but 30 could not.

A study by David Geary at the University of Missouri confirms scientifically what parents and teachers know: that number sense is as essential to learning math as the alphabet is to learning reading. The study followed 177 elementary school kids for five years to track the differences in progress amongst the group of elementary school aged kids.

press release about the study reports, “A long-term psychology study indicates that beginning first graders that understand numbers, the quantities those numbers represent and low-level arithmetic will have better success in learning mathematics through the end of fifth grade, and other studies suggest throughout the rest of their lives.”

Number sense is part of the standards as set by the Arizona Department of Education for first grade but number sense is part of a youngster’s life when parents count things and play games with quantities.

When I taught third, fourth and fifth graders, I still taught number sense, though with a more advanced perspective than one would for a preschool student. When teaching multiplication, I needed to make sure my students understood that multiplying two numbers in the hundreds would necessarily be in the tens of thousands or in the millions — not just thousands. Number sense bolsters estimation skills also.

From the National Council for the Teaching of Mathematics: “Researchers note that number sense develops gradually, and varies as a result of exploring numbers, visualizing them in a variety of contexts and relating them in ways that are not limited by traditional algorithms (Howden, 1989).”

Hmmm. That’s a complicated way of saying kids should know that the five pieces of broccoli they don’t want to eat is four pieces of broccoli after they manage to choke down one piece of broccoli. 5-1=4 means very little to children without number sense, even though they may be able to count on their fingers and get the answer right on a worksheet. Kids understand math when they have number sense.

Before you rush out to find a cool number sense smartphone app, remember, number sense is a real-world, three dimension experience, not the flat screen of a smart phone or computer. Numbers count things. With your child, count the number of Cheerios that fit on a spoon or in a cereal bowl, or discover what 100 Cheerios looks like. Or count all the socks that have no mates. In the car count the number of orange cars compared to the number of white cars.

“Cognitive Predictors of Achievement Growth in Mathematics: A Five Year Longitudinal Study,” will be published in the journal Developmental Psychology. But really, you don’t need to read it. — Dan Friedman