The Common High-School Tool That’s Banned In College
By William Pang
Step inside any high-school math class in the United States, and chances are youll find students gazing down at their Texas Instrument calculators, nimbly typing commands into those $100 pocket computers. Calculators are so commonplace in modern American education that a TI-8 4 or -8 9 can be found stashed away in many homes, mementos from taking the SAT or calculating integrals on the Advanced Placement calculus exam.
Still, college professors remain divided on the use of calculators in their class. When I took my freshman math courses at McGill University in Montreal last school year, I had to revert back to pencil and paper, clumsily lining up columns to do addition and long-multiplication problems at my profs request. This isnt an unusual predicament: According to a 2010 national survey by the Mathematical Association of America, nearly half of Calculus 1 college teachers proscribe students from employing graphing calculators on exams.
The debate over the use of calculators in math classrooms has ensued for more than four decades nearly as long as the contemporary calculator has been around. Although the abacus has been in use since the time of the Sumerians and Ancient Egyptians, it wasnt until 1958 when the Texas Instrument technologist Jack Kilby devised the integrated circuit, which paved the way for the inexpensive and compact computer chips used in most electronic devices today.( Kilby afterwards won the Nobel Prize in physics .) A decade afterward, calculators would no longer be stored in gigantic cabinets with a price tag of over $700,000; they would substantially diminish in size and gradually was increasingly affordable. Today, prices for graphing calculators hover around $80.
The debate over the use of calculators in math classrooms has ensued for more than four decades nearly as long as the contemporary calculator has been around.
By the mid 1970 s, 11 percent of Americans owned a calculator. Four-function calculators those that merely perform addition, subtraction, multiplication, and division gradually entered the classrooms, dividing educators and mothers alike. Debates over the role of calculators in the classroom quickly emerged, and arguments for and against their employ have hardly changed since then. Proponents of the calculator argued that machines could help students make sense of abstract mathematical notations through real-life problems, stimulating math fun and interesting. Foes worried that students would become over-dependent on calculators, losing the ability to do simple arithmetic operations and exercise a solid sense of numbers.
In 1986, Connecticut became the first nation to mandate the use of calculators on country exams, signaling the beginning of a calculator-dependent generation. But the most consequential move arrived three years later from the National Council of Teachers of Mathematics( NCTM ), which advocated for the use of calculators from kindergarten through grade 12. The guidelines set by the NCTM were soon adopted into many local and country syllabu. In 1994, the College Board constructed substantial changes to the SATs math section to allow the use of calculators. The 1995 Advanced Placement calculus exams were the first to require the use of graphing calculators, a powerful electronic assistance that is still used in most high-school math class today.
For W. Stephen Wilson, a math and education prof at Johns Hopkins University, using a calculator is akin to relying on a crutch when one doesnt have a bad leg. I have not yet encountered a mathematics conception that required technology to either teach it or assess it. The conceptions and abilities we teach are so fundamental that technology is not needed to either elucidate them or enhance them. There might be teachers who can figure out a route to enhance learn with the use to new technologies, but its absolutely unnecessary, Wilson wrote in the periodical Education Study in Mathematics .
Proponents of using technology in classrooms argue that graphing calculators, particularly those equipped with programs that they are able calculate algebraic emblems, would reduce the need for students to memorize formulas and perform time-consuming computations. But Wilson fears that students who depend on technology will fail to understand the importance of mathematical algorithms.
Yes, a calculator could effortlessly churn out the derivative of an equation, but would students understand how to find the answer use the fundamental theorem of calculus or the definition of the derivative? The notion, Wilson says, is not to have students mindlessly perform mechanical operations, but for students at all levels to apply linear supposing in understanding the beauty of efficient algorithms. If a student cant master long division, how can she grasp derivatives and integrals?
Wilson says he has some evidence for his claims. He gave his Calculus 3 college student a 10 -question calculator-free arithmetic test( can you multiply 5.78 by 0.39 without pulling out your smartphone ?) and divided the them into two groups: the individuals who scored an eight or above on the test and those who didnt. By the end of the course, Wilson compared the two groups with their performance on the final exam. Most students who scored in the top 25 th percentile on the final also received an eight or above on the arithmetic exam. Students at the bottom 25 th percentile were twice as likely to score less than eight points on the arithmetic test, demonstrating much weaker computation abilities when compared to other quartiles.
Its worth noting that calculators are also more likely to be barred in math quizs at research universities than at two-year colleges and regional public universities. Out of the 50 national universities ranked at the top by U.S. News and World Report, only four schools had policies letting electronic devices on Calculus 1 exams. One explanation is that selective organizations are less likely to offer remedial math courses and generally accept those individuals who possess a strong math background.
Why arent high school taking their cue from math professors at Harvard and MIT? Because most college student wont major in STEM topics and wont want advanced math knowledge for much of the performance of their duties. Dan Kennedy, a high-school teacher at Baylor School, argues that to set a reasonable expectation for all students, calculators should be used because many real-world problems cannot be solved without technology. Students, he says, would be better served by learning likelihood, statistics, computer literacy, financial maths, and matrix algebrathe kind of math that requires the use of graphing calculatorsnot the kind of theoretical math that dominates math competitions.
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David Bressoud, a math professor at Macalester College in Minnesota, has a different hypothesi: He thinks that large research universities typically ban calculators because the devices are essentially obsolete there. The larger universities are typically had computer-lab resources,[ and now] it is easier to expect that all students have access to a computer, Bressoud said. Computers, Bressoud says, are a much better tool for teaching calculus because they are more flexible and faster than calculators.
At Macalester, first-year calculus is known as Applied Multivariable Calculus 1. Computers are heavily encouraged in class, and profs arent slowly chalking away proof and theorems on the blackboard. Unlike those at traditional college math class, Macalester professors take the word applied seriously: A lecture on functions, for example, is demonstrated employing the Body Mass Index, a function of height and weight used to determine whether a person is obese. Students in their first year of calculus also learn differential equations, a topic that is generally covered only when students have three semesters worth of calculus under their belts. The intent is that, by introducing differential equations early on, students understand how mathematical models are produced. Why? Because these models are used in many fields, including, but not limited to, economics, environmental science, psychology, and medicine.
The calculator debate also plays into a larger discussion of whether colleges should be less theoretical and more practical. For technology proponents, an increased emphasis on technology is often seen as a route to prepare students for the real world. Calculator adversaries tend to see it differently. The goal of university education, they contend, is for students to get a good grasp of the theoretical foundation of a subject , not to master calculators or computers. After all, todays technology might become drastically different 20 years from now, but a good foundation will always last.
Even Socrates once quipped that a reliance on writing would lead to the deterioration of memory. And many of the best practises in pedagogy teach that memorization does have its merits when it comes to education, despite the invention of the internet and search engines. Describing the line between the use of and prohibit of calculators could prove difficult, says Jon Star, an education prof at Harvard University. That line is also moving as time goes on, at different levels. There might be students who bring different skills who put the line in different places, Star noted. Im very wary of anyone who tells it should be at one extreme or the other.
Many schools opt for the middle way. While calculators might not be allowed on tests and exams, colleges know that tech-savvy students will utilize programs such as Wolfram Alpha, a powerful web-based computational tool, to assistance with calculus assignments. Homework problems often involve calculator utilize, asking for solutions that involve cumbersome values or algebraic symbols that are too tedious to calculate by hand. Will future professors who were born in a generation of smartphones and tablets change the course of this discussion? Only hour will tell.
This story originally appeared on TheAtlantic.com.
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