You would think that I had been around long enough to know that when the government says that a particular change will either “save money” or be “revenue neutral”, it should really be taken with a grain of salt.
Even so, I was lulled into a sense of false hope when it was announced that we were phasing out the penny. Retailers, we were told, would adjust prices by “rounding” (up or down) and that the change (no pun intended) would be revenue neutral for them (cost neutral for us) and money saving for the government.
The first hint that I had that all might not be what it seemed happened the very next morning when my large cup of coffee at the local shop went from $2.07 to $2.10. Now, every good KGMS student knows that if you are properly “rounding”, $2.07 should become $2.05. Apparently basic mathematics does not apply in the “real” world!
The second revelation came just this week. I was picking up my wife and son at the airport. Fighting a nagging cold, I went to the newsstand to buy at packet of Hall’s.
“That will be $1.67”, the salesperson told me. I put down $1.65 and said that I had a couple of pennies in my wallet. “We no longer accept pennies.” I was told. “Well”, I asked, “will you accept $1.65?” “No, the price is $1.67.” “If I give you $1.70 will I get change?” “No, we no longer deal in pennies.” I was told.
“So”, I asked between coughs, “is the price actually $1.70?” “No”, I was corrected “if you would like to pay by credit card, the charge will only be $1.67”.
I thought of pointing out that when they factored in the 2% administration cost for using plastic then they would actually only receive $1.64 for the packet of Hall’s but the blank stare facing me from across the counter convinced me that further dialogue would be a waste of time. I paid my $1.70 and pocketed the cough drops.
Rounding should not be a particularly difficult concept. School children from my day to the present have completed exercise after exercise which ask them to round to the nearest 5 or 10 or hundred or thousand. Even in our calculator dependent age, everyone should understand that. Could it be that in our pendulum swinging between math “facts” and language-based math problem solving we have chosen mastery of mechanics over the understanding of concepts?
At KGMS we spend a great deal of our instructional time in mathematics using hands-on manipulatives or virtual manipulatives on the SmartBoard. The intent is to ensure that as more abstract concepts are introduced, they are based on a foundation of concrete, meaningful experiences from which the student can draw. By definition: A manipulative can be any object (cube, rod, disc, bead, etc.) that is designed so that a learner can demonstrate some mathematical concept by manipulating it, (hence its name). The use of manipulatives provides a way for our students to learn concepts in a developmentally appropriate, hands-on and experiential way. These mathematical manipulatives are used in the first step of teaching mathematical concepts, that of concrete representation. The second and third steps are representational and abstract, respectively. As the National Council of Teachers of Mathematics (NCTM) states: Multiple experiences with manipulatives provide children with the conceptual foundation to understand mathematics at a higher conceptual level.
So how do we reintroduce some of these basic hands-on concepts in our digital age? There would have been no point in me lining up seven pennies on the counter to try to demonstrate the concept of rounding. After all, “they no longer deal in pennies”.
There may be no easy solution, but I was pleased to hear of one victory for rounding brought on by customer pressure on the Chipotle Mexican Grill restaurants in the United States (see picture above). Their cash registers now automatically “round” the total according to the accepted rules of mathematics (lower half down, upper half up).
Maybe there is still a chance that I can get my cough drops for $1.65 without having to wait for full-scale educational reform! In the meantime, I will continue to fight the good fight and horde my pennies. At the very least we can use them as manipulatives in our math classes!