Number Sense is Critical

Language aids Number Sense in Humans

Though animals have rudimentary number sense, it is only in humans that it can be developed into very sophisticated levels.

Our ability to invent languages seems to aid in learning math. Language also accelerates formation of abstract concepts.

There seems to be consensus among scientists, that only humans can mentally represent numbers precisely and with symbols, and that we need some kind of education to do so. Many higher math skills, including arithmetic, depend on the use of language—a symbols-based system—where quantity-based judgments are pre-verbal.

Indeed, arithmetic is difficult to do if one does not have the language for it.

Criticality of Number Sense

Scientists & educators confirm that a sound foundation of number sense is very essential for mastering complex mathematical concepts. It enables us master abstract concepts like numbers & their relationships to be stored & manipulated in the brain as visual images (both concrete and abstract). It provides for flexibility and fluency while thinking and working with numbers.

In his article “Number Sense: the most important mathematical concept in 21st Century K-12 education “mathematician Keith Devlin underlines the importance of number sense for mastering concepts of math and as a corollary for 21st century K-12 education. The article can be accessed here.

https://www.huffpost.com/entry/number-sense-the-most-important-mathematical-concept_b_58695887e4b068764965c2e0

It has been well demonstrated that children who do not acquire number sense early in their mathematics education struggle throughout their entire subsequent school and college years, and generally find themselves cut off from any career that requires some mathematical ability.

Number Sense is critical to the future of our children.

Reality in the Pre-School

Children acquire it over a period of time when they hear number words being used in contexts (Bring two plates, show 2 fingers) repeatedly. They also develop visual pictures or patterns of numbers. In homes where such interactions could be less, the development of number sense could take a longer time or may be less sophisticated.

Hence children come to school with varying degrees of understanding of a sense for numbers.

But in pre-school, teachers generally do not realise the difficulty children have in understanding the idea of numbers. This could be because of 2 reasons.

1. Most children have already acquired a rudimentary number sense at home and play before coming to school. Hence, they manage to make the connection between numerals, numbers & quantities over a period of time.

2. Preschool syllabus focuses more on rote-learning and memorising number shapes & words and not much on understanding what numbers mean. If we think about it, the numeral “3” does not look anything like the idea of “three” for a child who is just getting exposed to the idea.

The reality is that children come to school with varying degrees of number sense due to the unevenness of their number experiences at home. There are quite a few students without a robust sense of numbers. These children find math very difficult and start lagging behind in understanding math. Hence incomprehension of math starts from the early classes.

Hence teachers in pre-school need to find out the level of number sense among their students. They need to build on these rudimentary ideas and build a robust number sense by providing children many situations involving concrete objects & life experiences.

Number Sense and the Indian School Math Curriculum

But the reality in our schools is very depressing. The entire math curriculum has no mention of number sense. The teacher certification courses do not talk about number sense and the difficulty of understanding numbers. The math syllabus focuses more on rote-learning and memorizing number shapes & words and not much on understanding what numbers mean.

Hence incomprehension of math starts from the early classes.

As children proceed to higher classes, the variety of numbers they encounter& the processes associated with them also become more complex. Their incomprehension slowly develops into math avoidance, fear of math, math anxiety and math phobia.

Reality in the Modern World

Our world is changing very fast. Our children are going to live in a digital and information driven world which puts a premium on understanding and using math.

The discipline of math has been developed by a handful of highly intelligent mathematicians, very rapidly to very abstract levels, starting from the idea of “how many.” Ideas in math have gone far ahead of the “how many” ability of humans.

Systematic instruction is needed by children to master the ideas of math. This is the reason math and language are disciplines taught in schools right from preschool.