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# NUMBER SENSE STARTS WITH COUNTING!

Jan 5, 2023

Number Sense is the ultimate goal of Mathnasium teaching – because it is the foundation of mathematics! Larry Martinek, the creator of Mathnasium Method™, conceptualized the three pillars of Number Sense as Counting, Wholes and Parts, and Proportional Thinking. A student will face these three types of math problems in all grades, in all math lessons in their life from Kindergarten to Grade 12 and beyond.

Number sense isn’t inborn: it’s the result of interaction with specific concepts and skills, presented in a way that makes sense to the learner. It cannot be replaced by calculators or computers – it requires exercising “math muscles”!

Let’s start with Counting (next time we will discuss the other two important concepts).

What is Counting?

Number sense starts with Counting, i.e. the ability to count from any number, to any number, by any number.

Children learn to count the same way they learn to speak, through immersion in a sea of mathematical experience. Counting is generally the first experience, the one from which all other mathematical abilities grow.

In Kindergarten, a child starts learn basic counting by ones like 1, 2, 3, etc., then counting by twos, fives, tens, etc., including counting backwards. Starting mid elementary they’ll learn counting by common fractions and then by decimal fractions, at appropriate level.

Counting and Groups

As children become experienced at counting, they can be taught that numbers can be seen in groups:

• 5 fingers make 1 hand,
• 1 package of peanut butter cups contains 2 cups,
• 1 trio is made-up of 3 people.

Counting and “seeing” numbers in groups is the basis of virtually all mathematical operations and processes, because:

• Addition is counting “how many altogether.”
• Subtraction is counting “how much is left,” or counting “how far apart are the two numbers,” or counting “how many are missing.”
• Multiplication is counting “equal groups of things.”
• Division counting “how many of these are there inside of that.”
• Percent is counting “how many for each 100.”
• Area is counting “by squares.”
• Volume is counting “by cubes.”
• Probability is counting “the chances.”

Whole Numbers are the numbers that result from the repeated addition of 1 to itself:

1 = 1

2 = 1 + 1

3 = 1 + 1 + 1

7 = 1 + 1 + 1 + 1 + 1 + 1 + 1

Every whole number is a group of 1s, gathered together and expressed in a convenient, compact symbol. When we add “2” and “3,” we are using shortcuts for adding (1 + 1) + (1 + 1 + 1).

Starts Early

We have a kindergartener, who was able to count from 1 to 10 when she first came. But when asked “what comes after 8?” she couldn’t answer right away; she needed to count from 1 again to find out that it’s 9. After a week with us her fluency grew and she was able to count forward and backward from 1 to 10, and then was also able to do basic addition up to 10. She has been with us for over a month now, and has started to learn 10 plus a single digit number and decomposing single digit numbers.

As in other aspects of learning such as sports, language, music, etc. the earlier you learn a new skill, the stronger and the more fluent you are going to be. By having a good number sense, a third or fourth grader would be able to recall basic facts right away when asked what is 12 x 9 or 12 x 11. It is not just about getting good math grades, but having a solid math foundation will empower your child’s brain to think and reason. This is especially important in today’s world where data is everywhere and jobs require more analytical thinking than ever before!

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