On creating number sense among school beginners

Providing experiences for number sense at an early-childhood stage through objects is essential, otherwise innumeracy becomes a habit and learning of math mechanical. In our country, pre-schools and primary schools often do not quite meet this challenge.

Often, right from beginning, most primary teachers start with numerals or number symbols as drills and through rote learning without creating the number sense. Thus, a good majority of children learn mathematics without understanding and total absence of logical thinking.

In his write-up published in the journal of Commonwealth Association of Science, Mathematics and Technology Educators (CASTME), mathematics educator M. Wadhawa says that the language plays an important role in acquiring number sense among the beginners at the school level.

With introducing the pre-number concepts with a proper use of language and manipulative experiences with the objects can lead to acquisition of the number sense which is an abstract idea.

Wadhawa has advises in his write up a four step use of language for introducing the number sense, but a fifth step has been added by me based on my experience as a teacher. For example, while showing a pencil, the teacher must proceed as follows: This is one pencil…One pencil…This pencil is one…This is one…How many is this? One.

Similarly, while showing two pencils, the teacher must proceed as follows: These are two pencils…Two pencils…These pencils are two…These are two…How many are these? Two. And, so on.

This can be done with three or four different objects like chalk sticks, erasers, leaves, books etc. This kind of language along with objects can lead to acquisition of number sense followed by their symbolic representation.

I too feel that for constructing number sense, exploring relationships is a natural occurrence among elementary school students and such experiences should be deliberately planned in early grades as situated conceptual concrete experiences to develop a number sense prior to introducing the concepts of counting and numeric symbols.

If this is not happening in a good majority of schools, it reflects poorly on the teacher preparation and training institutes of the country.

Pre-number concepts build the critical foundation for future mathematics by transitioning children from rote memorisation to logical reasoning. Skills like matching and one-to-one correspondence directly enable meaningful counting and arithmetic. Meanwhile, sorting and patterning foster the algebraic thinking, data organization, and geometric spatial awareness required to comprehend complex place value systems, measurement scales, and advanced problem-solving structures.

The main pre-number concepts are: Classification (Sorting); Matching; Comparing; Seriation (sequencing, Ordering); Patterning; One-to-One Correspondence; Spatial Awareness (big-small etc, first-inbetween-last etc.; onservation

At least 30-house module should be transacted to consolidate the pre-numger concepts as foundational numeracy for school entrants

An acrostic on ALGEBRA

A: Arithmetical expression transformed into

L; Letter symbols or literals for

G: Generalisation or

E: Elaboration of relationship

B: Between variables or

R: Relationships seen in the

A: Advancing patterns of numbers, shapes and figures.