## Thursday, April 12, 2012

### Is number sense common sense?

First off, what is number sense?  My understanding of number sense is the awareness of the value of a number.  For example, which is larger 2x13 or 3x12?  My number sense tells me that 3x12 is larger because 3x10 is larger than 2x10.  So it seems like number sense is intuitive, but I've had a lot of computational experience.  I know number sense can be learned, but it seems like students nowadays have weak number sense.  I was horrified to see high school students still counting with their fingers.  I think a strong number sense is tied to a good foundation of multiplication tables.  I'm not a fan of rote learning, but knowing these multiplication facts helped me compute faster and guesstimate values.  For example, the square root of 5 is some irrational number between 2 and 3 because the square root of 4 is 2 and the square root of 9 is 3.  I would also recommend students play around with the real number line.  A student should attempt arrange the following numbers on a number line with appropriate spacing: 1/5, 0.45, -3/7, -1/2, 10, 10^2, 10^5, 10^-3, and 0.  It's funny to think about guesstimating in Mathematics when there is a strong emphasis of finding the precise answer using arithmetic.  Guesstimating is a valuable tool because it gives a sense of where our solution is located amongst all the real numbers.  As students progress in Mathematics, a strong number sense plays such an important role because students will deal with very large or very small quantities.  With practice, people can have a sense of the value of a number and will improve their overall mathematical skill.  Here's a neat article about number sense as well :)