Development of Number Sense

Development of Number Sense

Number Sense starts in living beings as an ability to "perceive" small quantities without the need to count.

Starting from this, number sense develops, in humans into a sophisticated ability to look at numbers, properties and relations in various flexible ways.

We can call each of them a Number Sense Strategy, in the sense that each strategy can be different. This contrasts with the algorithm which is a single standardised procedure.

It is a set of conceptual abilities which ultimately have to be "caught" by the learner, as a result of exploring numbers, visualizing them in a variety of situations and relating them in ways which are not limited by traditional algorithms.

The teacher facilitates this process by providing a number of examples and discussing the various perspectives in which the example can be viewed.

Four Aspects of Number Sense

John Van de Walle’s book “Teaching Student Centered Mathematics K-3” gives four perspectives which can develop number sense. They build a spider’s web of interconnections in the brain so that “remembering & retrieving” becomes automatic.

1. Spatial Relationships – having a visual idea of quantity.

   1. A visual understanding of numbers as patterns. Like 4 as a square, 3 as a triangle etc

   2. Visual understanding of how number patterns are related. Like 6 can be seen as 3 & 3 or 2 & 2 & 2 etc

2. One and Two More, One and Two Less – this is not the ability to count on two or count back two, but instead knowing which numbers are one and two less or more than any given number.

   1. Knowledge of 1 more/ less than a number

   2. An intuitive/ visual understanding of a number and the numbers which are one/ two more/ less than it.

3. Benchmarks of 5 and 10 – ten plays such an important role in our number system (and two fives make up 10), children must know how numbers relate to 5 and 10.

   1. Understanding of number bonds of 5 & 10

   2. Having 10 in a computation makes it easy. Ex. 6 + 5 = 6 + 4 + 1 = 10 + 1 = 11

   3. A visual/ intuitive understanding of how a number relates to 5 & 10. Like 7 is 5 + 2 and also 10 -3.

   4. This skill ultimately leads to a Part-Part-Whole understanding

4. Part-Part-Whole – seeing a number as being made up of two or more parts.

   1. 6 can be partitioned as 5 & 1. 9 can be seen as 10 less 1. This again leads to the above strategy.

   2. Partitioning & combining numbers in such a way that computations become simpler & can be done mentally

   3. Like seeing 7 + 5 as 7 + 3 + 2 -> 10 + 2 -> 12 OR 18 X 5 as 18 X 10 /2 -> 180/2 -> 90

These four relationships need to be built around all types of numbers (whole numbers, fractions, decimals, etc.).'

It is important that children develop a strong understanding of numbers and their relationships before we ask them to compute.

These will not develop unless students have time to explore or if the focus is on speed.