David Wees, a mathematics edublogger, posted the following earlier this week. My comments to it follow below. In my opinion, math teachers must help student’s learn math, not erect barriers by insisting on manual manipulations when a calculator is more effective, and frankly, the way the world operates in the 21st century. Read David’s posting, too.
Stephen Shankland posted an interesting article on CNET today. Here is an exerpt from his article, which you should read in full. He says:
Clearly, children need some understanding on their own of math, and reliance on a computer has a lot of drawbacks. But computers can also aid those who otherwise would fall by the mathematical wayside, or let people with more advanced abilities bypass drudgery and move on to the challenging material. Graphing calculators can let many students explore curves and functions that realistically they’d more likely ignore if they had to plot them by hand.
I wholeheartedly agree, David. Students should take an exploratory set of courses in basic numeracy skills in primary school to develop familiarity with the fundamental operations of mathematics. However, once they have observed and experimented with the fundamentals, regardless of whether they mastered the more complex ones or not, they should be free to use technology resources such as calculators, even on standardized tests. Requiring students to continue manually manipulating fractions, performing long division, and pondering other foundational mathematical operations best left to calculators or computers is an archaic and ineffective use of time, talent, and treasure; we stopped using slide rules a while back for a reason.
In this country, we waste considerable amounts of scarce resources (time, young minds, and money) in a senseless devotion to the past. Due to a mathematics curricula imposed mostly by academics, rather than a mixture of academia and industry, we are crippling our nation’s intellectual capacity. It is time these outdated approaches are shown for what they are: loadstones around the neck of our nation.
For those that will lament not doing math the old-fashioned way, each of the procedures for manual mathematical manipulations can be taught in a history of math class, or as a dedicated segment of another class, to illustrate how our “ancestors” used less effective means to perform mathematical operations. Those “skills” are simply prerequisites for manipulating data, a means to an end. However, with their inclusion in today’s mathematics curricula and standardized tests as well the mandate by “old school” math teachers not to rely on technology, these manual operations serve more as a roadblock to students developing higher order mathematical thinking.
Most students get stuck procedurally, or make a minor math error transposing digits, dropping a negative sign or some other lower-order task, and equate that with a lack of mathematical expertise or capability. We have created tens of millions of mathphobic citizens with this approach. In spite of this, we continue to instill fear and loathing of math today in students of all ages. When will we wake up, let go of the past, and embrace our future? When will we push aside the gatekeepers who insist on outdated procedure over unleashing the creative potential of our youth? We do not have to remain on this tragic trajectory. Success is within our grasp, if we embrace in our educational system that which industry recognized over forty years ago: leverage technology to unleash efficiency, creativity, and innovation.
Technological efficiency exponentially improves effectiveness. We can overcome the results of our mistaken insistence on drudgery as the path to mathematical might if we embrace technology and strive for higher-order thinking rather than lower-order procedural prowess. Allow students to leverage their iPhone, iPod, calculator, home computer, or whatever other technology that is accessible to them; and for those without access, make it so. Let them start using technology to assist in problem solving as most in industry do. The time has come. We can no longer afford to constrain our national intellectual capacity due to a well-intentioned, but outdated insistence on doing things as they were before the Internet age.
The only real debate is whether to use a conventional or RPN calculator! Or for computers, which OS: Mac OS X, Windows, or Linux?