I have often heard students coming out of a class saying, "That stuff doesn't make sense!" This is because many students have not developed a good general sense of the mathematical subject matter that is presented at school. Students are not provided with enough context when they learn material in school. Context provides students with a suitable environment to integrate new ideas and information in a meaningful way. Unfortunately, rather than integrated learning, fragmented learning (learning without a sense of continuity) takes place in today's schools. To fill in the gap between fragmented and integrated learning, student's need to establish Number Sense.
So, Number Sense... what is it? Number Sense is the ability to appreciate the size and scale of numbers in the context of the question at hand. There are three elements that fall under Number Sense: counting, wholes and parts, and proportional thinking. Today we will focus on counting.
Counting, simply put, is the ability to count from any number, to any number, by any number, forward and backward. When I ask students to explain what counting is, they will usually respond by counting from 1 (1, 2, 3...). Although this is completely correct, kids need to grasp how to count from other arbitrary numbers, for instance, 28 (28, 29, 30...). How about when counting by 2s? Starting from 2 (2, 4, 6...) is easy to get down. Can our kids do the same when starting from 3 (3, 5, 7...)? After a good deal of practice, an experienced counter will know how to count to 250 by 1s forward and backward; to 300 by 2s, 5s, and 10s; and to 3,000 by 100s.
As children are learning to become experienced counters, they should also be learning how to group the numbers they count. Parents, ask your child questions like "A group of 10 take-away a group of 3 leaves how much?"
Another important idea at this stage is interval: the distance from one number to another-the space between two numbers. From 6 to 7 is 1, and from 7 to 8 is 1, making a total distance from 6 to 8 of 2. Another important aspect of counting is its connection with the basic math operations: addition (counting how much altogether), subtraction (counting how much is left), multiplication (counting in equal groups), and division (counting how many of these are in that). The basis of Number Sense begins with counting.
Remember, children don't hate math, they hate being confused, frustrated, and embarrassed by math. Once they understand math, the passion will follow naturally.