A member of the Virginia legislature believes he has found a way to improve the mathematical abilities of students in his state. His plan was detailed in a recent article in the Washington Examiner:
“Students would be banned from using their calculators on the seventh- and eighth-grade Standards of Learning math exams under a bill introduced by a state lawmaker from Fairfax County…
“Del. Dave Albo, R-Springfield, said he was encouraged to introduce the bill by a ninth-grade math teacher who said his students couldn’t multiply or divide fractions on a pretest he gave his Algebra 1 students.
“’It’s making sure teachers are teaching basic math skills without calculators, like we used to do in the ’70s before we had calculators,’ Albo said.”
Should educators in Virginia really strive to recreate the math classrooms of the 1970s? Could a return to the Dewey Decimal System be far behind? Without going all Election 2012, Mr. Albo’s comments do bring back memories of “horses and bayonets”.
Number sense is important
The math teacher’s concerns that motivated Mr. Albo are not without merit. As a retired math teacher, I absolutely believe it is extremely advantageous to be able to manipulate numbers, including fractions, efficiently and effectively. Individuals who have a firm grasp of the fundamentals will find their everyday lives much easier. Equally important is the fact that those who are not fluent in basic math concepts are often handicapped in handling relatively mundane situations.
On a recent visit to a small store where there were no automated machines to aid the checker, I received my change of 76 cents in the form of seven dimes and six pennies. The cashier gave me a lame smile and said “Quarters and nickels are just too confusing.” A similar incident occurred at a store where the computers crashed and suddenly the employees had to determine what the difference was between a payment in the form of a ten-dollar bill and an eight dollar and forty-seven cent purchase. The checkout line came to a virtual standstill.
No one can argue that a society is better if it can add, subtract, multiply and divide. Being able to work with fractions, percentages and decimals are equally critical. However, throwing out calculators and longing for the math of forty years ago is misguided and counterproductive.
Good penmanship and memorizing the fifty state capitals were noble endeavors that were rewarded with high marks in schools during 1970. But in the world of 2012 the use of cursive is dying out and a Google search can provide the correct answer within a few seconds for virtually any question previously reserved for memorization. The ability to manipulate numbers is a wonderful talent to possess. But, for those whose skills are not at the highest levels, those same tasks can be accomplished by technology with stunning accuracy and speed. It is important to note that Mr. Albo is far from alone in his concerns about student dependence on machines. In the early years of calculators I would often be asked at Back-to-School Night about student dependence on hand-held devices. The most common concern was what would happen to their child “if the batteries on their calculators die?” The answer was simple, “That calculator will make your child a better math student. Buy them spare batteries.”
Calculators and math education
The graphing calculator has profoundly changed math education in a positive manner. When I first began teaching in the 1970s a typical study of logarithms would include about twelve days of instruction on how to create a log and five days of utilizing them in fundamental arithmetic calculations. Fast forward thirty years and everything has changed. A TI-83 can create a log with two keystrokes; two days of classroom instruction are required to explain the meaning of common logs and how they can be utilized in computations. The next fifteen class meetings are now free to journey through real world applications of logs. Students, with the aid of their calculators, can determine the time of death in murder case scenarios, find expected miles per gallon capabilities for automobiles, establish actuarial tables, discover the tipping point of world overpopulation and when the Russian city of Chernobyl would again be inhabitable. Students stopped “putting in the numbers and turning the crank” and became enthusiastic math problem solvers. For the first time math classes could replicate the “hands-on” laboratory experience of science. Formerly abstract data became concrete answers. Similar experiences could be found at every level of the math curriculum.
An additional fear of hand-held technology in math is that it will somehow work against the better students. There is an unfounded belief that the simple possession of a calculator makes all individuals equally adept at the subject. The reality is very different. The better someone is at math, the more advantage they will obtain from technology. For proof watch how different people navigate the internet for quality information. Whether working with a calculator or perusing the World Wide Web, the skill of the person using the technology will be predictive of their success.
The solution is addition not subtraction
Removing the calculator may lead to improvement in arithmetic skills but will slow the growth of mathematical problem solving. Greater focus on the fundamentals should be a priority in the elementary levels with instruction by teachers with strong math backgrounds. But then the study of math must move forcefully into the 21st century with the inclusion of every technology available. That is unless the goal of math education is to return to the 1970s.