What is Number Sense?

Number Sense – A New Interpretation

Until now we have been using the term “number sense” in a general sense of getting a sense or idea of what numbers are; about quantities & their sequence. We can call it as a layman’s idea of a number.

With the understanding of properties of numbers, relations between them and different operations that can be performed on them, the term has been recently invested with a specific mathematical meaning, by math educators & psychologists.

It encompasses all the older meanings in which we have been using the term while at the same time expanding its scope.

This new interpretation of “number sense” was voted as the most important topic for understanding abstract concepts in math in a recent poll of math educators, mathematicians & learning psychologists.

But the new meaning has not reached most teachers in schools, who only have the layman’s understanding. For example, the Indian school math curriculum does not touch upon this new meaning.

From now on we will be using the term Number Sense in this new mathematical perspective.

What is Number Sense?

Number Sense is defined in various ways. Some of them are given below. 1. It is an intuitive understanding of numbers, their magnitude, relationships, and how they are affected by operations.

It develops gradually 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.

It is the ability to see 9 + 7 as 9 + 1 + 6 as 10 + 6 as 16.

2. It is an ability to work outside of the traditionally taught algorithms, e.g., “a well-organized conceptual framework of number information that enables a person to understand numbers and number.”

It is the ability to use number properties & relations to restructure numerical expressions so that they become easy to compute mentally

It is the ability to add 43 & 58 as 43 + 50 =93; 93 + 7 = 100; 100 + 1 = 101 (splitting 58 into 50 + 7 + 1)

3. Number sense refers to a person’s fluidity and flexibility with numbers, the sense of what numbers mean and an ability to perform mental mathematics and to look at the world through the prism of numbers.

It is the ability to realise that 18% of 25 is the same as 25% of 18 which is 4.5.

4. It is an important aspect of “problem solving” in math.

Number Sense in math is "in a limited way" the equivalent of phonemic awareness in language.

Though number sense starts with understanding small whole numbers, it is equally applicable to bigger numbers and all types of numbers.

The great mathematician Littlewood, who knew Ramanujan, said that “all the natural numbers are Ramanujan’s personal friends.” It was like he knew each personality of each number. That was a tribute to his Number Sense.

You are aware of the story of 1729, which Prof Hardy found uninteresting but Ramanujan pointed out that it was the smallest number that can be expressed as the sum of two cubes in two different ways!

Perceptual Numbers – The Starting Point for Number Sense

The ability to “subitize” or recognize quantities as numbers by “perceiving”, lays the foundation for building a strong Number Sense.

As children proceed to higher classes, the variety of numbers they encounter& the processes associated with them also become more complex. Hence in higher classes also teachers need to ensure that the number sense of the students, about the numbers they are studying, is continuously deepened and strengthened.

Discovery of Number Sense

In a sense we can say that research into the causes of Dyscalculia led to brain-research into how the human mind understands math.

This led to the proposal of a “numerosity module” in the brain which figures out answers to “how many”

Number Sense in Animals

Research is proving that even other living beings like birds, insects, animals and fish have at least a rudimentary number sense. In that sense number sense is not unique to humans.

Bees seem to have an understanding that the hexagonal shape provides the maximum area with a minimum perimeter! Hexagon also gives sufficient strength to the hive to support honey which is a very dense liquid. According to one study, bees can also grasp the concept of zero.

Some fish draw extraordinarily symmetric & complex diagrams on the ocean floor to attract mates. Dolphins seem to understand the concept of "less".

Birds seem to be able to identify numbers up to 4 or 5. When an egg is removed from its nest, from a collection of 4 or 5 eggs, the bird gets agitated. But when the collection of eggs in the nest is more than 6 or 7, the birds do not seem to be aware of the missing egg. So, their ability to subitize does not seem to extend beyond 5 or 6.

Pigeons can be trained to peck a certain number of times on a board.

Spider webs seem to be designed with geometrical principles which give them the needed strength.

Recently a pair of whales have been photographed blowing bubbles to form a Fibonacci spiral of bubbles to trap fish.

It is only recently that scientists have started researching intelligence in animals. The research is likely to reveal the variety of intelligences animals have. Logico-mathematical intelligence would surely be a major aspect of animal intelligence. Their number sense is just the tip of the iceberg.

There is a recent research (Institute of Neurobiology at the University of Tubingen - May 2024) which seems to indicate that crows are capable of counting much the same way humans count - using number names!

Logical Thinking in Animals

Discovery of number sense in animals indicates rudimentary logical thinking in them.

Recent research is proving that some animals can also teach complex behaviors to their peers. This also proves the capability for deeper thinking.