Numerically Challenged? 4 Ways to Meet the Early Maths Challenge
As a parent, I admit that I am a little technologically challenged. My son never misses a chance to call me that whenever I fumble with my new mobile or I get horribly entangled in the workings of a new gizmo. But this is only one among the many challenges that I have faced. Long before I was called technologically challenged, I realized that I was numerically challenged (my taxonomy) as well. While my fellow first graders added up a given sum like a breeze, I struggled to keep up. So, what made my other fellow first graders tick? It turns out there is this thing called ‘number sense’ that was not quite prewired into me. But the good news is that the challenge can be met by intervention and support. In other words, once numerically challenged does not mean always challenged likewise.
So, what is number sense? A definition given by Kalchman, Moss and Case says:
“The characteristics of good number sense include: a) fluency in estimating and judging magnitude, b) ability to recognize unreasonable results, c) flexibility when mentally computing, [and] d) ability to move among different representations and to use the most appropriate representation.”
Still, gobble-de-gook to you? It was a little foggy to me as well till I chanced upon the key components that make up number sense. Let us discuss this a little.
Strategic Counting
Counting efficiently happens to be an important ingredient of number sense. Pundits say that efficiency in counting is strongly related to knowledge of counting principles.
A Tip to Develop Strategic Counting Skills: One of the counting principles is to adopt ‘minimum strategy’. Once a child possesses this minimum strategy, if asked “what is 8 more than 3,” she will automatically know that it is much more efficient to reverse the problem to 3 more than 8, and simply “count on” from 8. Of course minimum strategy is not rocket science for us adults but for the young ones this is like Archimedes’ Eureka. She has to know the commutative principle of addition. (And for the uninitiated, commutative principle of addition simply means, 8 + 3 is equivalent to 3 + 8.)
Magnitude Comparison
As children develop keener understanding of number and quantity, they are able to make more complex judgment of magnitude, albeit with different proficiency levels. For example, when I was in grade one I possibly knew that 8 mangoes are more than 3 mangoes but my son when he was in the same grade knew that 8 mangoes are 5 mangoes more than 3 mangoes. If you ask five kindergartners that if there is only one pizza in the kitchen and all of you race to get it, would all of them get one? They would probably give you the right answer and this will be their gross magnitude judgment. However, if you ask how many of them will not get one pizza they would probably get stumped by the question. The ability to make finite magnitude comparison is critical to the ability to calculate.
Retrieval of Arithmetic Facts
A good indicator of sound number sense is smooth transition from counting on fingers to mental calculation. When I reflect back to my early days in school, I recollect that my transition was a little painful. Indeed as the complexity of the additions increased, I wished at times that I had more fingers than ten to count with. This deficiency suggests underlying problems which experts call semantic memory.. (OK, semantic memory is an easy one. It is the ability to store and retrieve abstract information efficiently). This ability appears to be critical for students to succeed in mathematics and, ultimately, to understand mathematics
Numerical Recognition
Children begin to learn about the written symbol system for numerals before they enter school. At least, our house address and our telephone number were drilled into me again and again. The idea was, that God forbid, if I ever got lost I could blurt out ’123, Lost Valley’ efficiently and as if on reflex. This was eons before spotting lost kids through GPS became fashionable. However, this method was associated with description of our house. Things became tougher in the school settings. Here numbers are used in abstract computations. For example, working out how to solve a simple addition problem depends on a student’s recognizing the number symbols and then using other facets of his mathematical understanding, including the concepts of magnitude comparison, and counting. Here ones numerical recognition prowess was needed to be developed.
Now that I have introduced you to ‘number sense’, you have probably realized that the ideas given out here are not intuitive; some may have it some may not. It is as if ‘number sense’ is ones sixth sense. The trick obviously is to spot the deficit of the ingredients in a child and intervene with methods to make up the deficit. We have given an example how to bolster a child’s strategic counting skills by adoption of the minimum strategy method. You can similarly find ways to perk up your child’s number sense.