HEADLINES with James Nelligan
Recently I spoke with a parent about the importance of Number Sense. Number sense is a big idea often poorly explained, and a huge predictor of one's success in mathematics. Because it is poorly explained, it is often poorly understood, and is thus a casualty in our rush to memorize concepts and apply algorithms (formulas used to solve problems).
Number sense is part of a larger idea, Numeracy--the ability to reason and apply numerical concepts. We are all hard-wired with some degree of numerical cognition, regardless of our culture or education. Even animals have at least a basic numerical cognition, which, from observation, allows them to make approximations of quantity (few or many) and magnitude (big or small). These mental "calculations" reinforce responses like fight or flight. In humans, our innate awareness of quantity and scale is only the beginning of our understanding of numbers. We are gifted with spectacular brains capable of deducing and comprehending a wide-range of increasingly complex associations. This is where number sense comes in.
Number sense is the ability to ascribe meaning to numbers. It is the ability to determine relationships between numbers, to understand symbolic relationships like variables, to perform mental calculations, and to apply these approaches and understandings to novel situations and problems. Number sense allows us to rank and order, to compare, to measure, to round, and to estimate. Number sense is a critical attribute of numerical fluency, and ultimately numeracy.
For example, with minimal effort I can intuit the difference between one or a few or many. With a little training, I can determine rudimentary relationships, such as 11 is close to 10, farther from 15, without having to do much thinking. With a little more learning and practice, I can determine fractional relationships without much thought; e.g. 9 is fairly close to 10, and therefore roughly half way to or from 20. I might rewrite a problem, like 19 + 7, into a simpler problem, like 20 + 6. My times tables taught me that 6 x 9 is 54. I can memorize my tables, and probably recall this math fact with little difficulty. With number sense, I might approach this problem differently, say 6 tens is 60. I can easily subtract one 6, and arrive at 54. Eventually, ideally, I can make nearly automatic associations thru simple mental calculations. For example, I know that five 20s are equal to 100. It stands to reason that since 18 is close to 20, five 18s is also close to 100. 18 is 2 less than 20, so five 18s must be 10 less than 100, or 90. If I can do this in my head with little effort, I have fairly strong number sense. If I understand that all mathematics is fundamentally addition, I can really run with numbers, and solve increasingly complex problems.
Developing number sense is no small thing. A lack of number sense can have real impact, such as when miscalculations led to significant error, causing the Hubble telescope to miss its intended field of study. Math facts, while important, are actually a small part of mathematics; number sense is far more significant. As a matter of fact, a student with poorer memorization skills can still be quite successful in mathematics if they have strong number sense; the inverse is not true, especially in advanced mathematics. Students tend to solve problems in one of two ways: memorization (of math facts or algorithms) or number strategies. Interestingly, research has shown that memorization and number strategies use very distinct neural pathways. A best case scenario would have the learner memorize important facts and algorithms and develop diverse number strategies for basic problem solving and transference.
There are many on-line educational sites and applications that help to develop number sense in elementary age children. The more their number sense is developed at an early age, the farther your child will go in mathematics.
See you around campus!