## “Number System Knowledge”: It’s Not Just About Counting

**What children know about numbers as they begin first grade predicts how well they do everyday calculations later on, reports the Associated Press:**

“About 1 in 5 adults in the U.S. lacks the math competence expected of a middle-schooler, meaning they have trouble with ordinary math tasks and aren’t qualified for many of today’s jobs.

‘It’s not just: Can you do well in school? It’s how well can you do in your life,’ says Dr. Kathy Mann Koepke of the National Institutes of Health, which is funding new research into math cognition. ‘We are in the midst of math all the time.’

A new study shows trouble can start early.

University of Missouri researchers tested 180 seventh-graders. Those who lagged behind their peers in a test of core math skills needed to function as adults were the same kids who’d had the least number sense or fluency way back when they started first grade.

‘The gap they started with, they don’t close it,’ says Dr. David Geary, a cognitive psychologist who leads the study that is tracking children from kindergarten to high school in the Columbia, Mo., school system. ‘They’re not catching up’ to the kids who started ahead.

If first grade sounds pretty young to be predicting math ability, well, no one expects tots to be scribbling sums. But this number sense, or what Geary more precisely terms ‘number system knowledge,’ turns out to be a fundamental skill that students continually build on, much more than the simple ability to count.

What’s involved? Understanding that numbers represent different quantities—that three dots is the same as the numeral ‘3’ or the word “three.” Grasping magnitude—that 23 is bigger than 17. Getting the concept that numbers can be broken into parts — that 5 is the same as 2 and 3, or 4 and 1. Showing on a number line that the difference between 10 and 12 is the same as the difference between 20 and 22.

Factors such as IQ and attention span didn’t explain why some first-graders did better than others. Now Geary is studying if something that youngsters learn in preschool offers an advantage.” (Read more here.)

**That last point bears repeating: IQ did not explain why some first-graders did better than others. Instead, it seems to be something about what and how kids learn. NIH’s Kathy Mann Koepke offers some tips for parents:**

• Don’t teach your toddler to count solely by reciting numbers. Attach numbers to a noun – “Here are five crayons: One crayon, two crayons…” or say “I need to buy two yogurts” as you pick them from the store shelf – so they’ll absorb the quantity concept.

• Talk about distance: How many steps to your ball? The swing is farther away; it takes more steps.

• Describe shapes: The ellipse is round like a circle but flatter.

• As they grow, show children how math is part of daily life, as you make change, or measure ingredients, or decide how soon to leave for a destination 10 miles away,

• “We should be talking to our children about magnitude, numbers, distance, shapes as soon as they’re born,” she contends. “More than likely, this is a positive influence on their brain function.”

Learning is a conversation between friends.

Kathy Koepke can predict later math skills from the number concepts when starting school. Same thing in reading; we can predict later reading failure in detail by grade 2.The cause is a mismatch between teaching method and development. Some infants, particularly males, have delayed capacity to process whole words. If you teach Whole Language strategies they will fail. However most of these children would have succeeded with a systemnatic phonic approach that doesn’t rely on whole word processing. It ain’t rocket science.

Lovely article. It reminds me of the book: “The Myth of Ability: Nurturing Mathematical Talent In Every Child,” by John Mighton.

With deep respect Byron, maybe this invisible gap problem is unrelated to teaching methods. What if it’s a level-up thing? Maybe level one skills can’t easily be learned at level two (or beyond). Perhaps there is also a stigma, in self-perception and socially, associated with trying to learn “remedial” things. Maybe many teaching methods would work, if only a child’s gaps were level-set and the stigma was displaced.

What is missing here is the recognition that ‘number-sense’ is not related to number-counting. These two process happen in different parts of the brain,but counting is dependent on the older ‘number-sense’ area.

Dyscalculia is a description of those who have weak number-sense. This is both the ability to ‘know’ how many there are without counting and also the ability to know which pile is larger, stick longer, mug fuller etc.

The exercises needed to develop these do not involve counting – indeed early introduction of counting/sums can suppress the development of number-sense.