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Should colleges drop calculators in math class?

U. PITTSBURGH (US) — Math instructors promoting calculator usage in college classrooms may want to rethink their teaching strategies.

That’s according to Samuel King, postdoctoral student in the University of Pittsburgh’s Learning Research and Development Center, who has proposed the need for further research regarding calculators’ role in the classroom. King has conducted a limited study with undergraduate engineering students published in the British Journal of Educational Technology.

“We really can’t assume that calculators are helping students,” says King. “The goal is to understand the core concepts during the lecture. What we found is that use of calculators isn’t necessarily helping in that regard.”

Together with Carol Robinson, coauthor and director of the Mathematics Education Centre at Loughborough University in England, King examined whether the inherent characteristics of the mathematics questions presented to students facilitated a deep or surface approach to learning.

Using a limited sample size, they interviewed 10 second-year undergraduate students enrolled in a competitive engineering program. The students were given a number of mathematical questions related to sine waves—a mathematical function that describes a smooth repetitive oscillation—and were allowed to use calculators to answer them. More than half of the students adopted the option of using the calculators to solve the problem.

“Instead of being able to accurately represent or visualize a sine wave, these students adopted a trial-and-error method by entering values into a calculator to determine which of the four answers provided was correct,” says King. “It was apparent that the students who adopted this approach had limited understanding of the concept, as none of them attempted to sketch the sine wave after they worked out one or two values.”

After completing the problems, the students were interviewed about their process. A student who had used a calculator noted that she struggled with the answer because she couldn’t remember the “rules” regarding sine and it was “easier” to use a calculator.

In contrast, a student who did not use a calculator was asked why someone might have a problem answering this question. The student said he didn’t see a reason for a problem. However, he notes that one may have trouble visualizing a sine wave if he/she is told not to use a calculator.

“The limited evidence we collected about the largely procedural use of calculators as a substitute for the mathematical thinking presented indicates that there might be a need to rethink how and when calculators may be used in classes—especially at the undergraduate level,” says King. “Are these tools really helping to prepare students or are the students using the tools as a way to bypass information that is difficult to understand? Our evidence suggests the latter, and we encourage more research be done in this area.”

King also suggests that relevant research should be done investigating the correlation between how and why students use calculators to evaluate the types of learning approaches that students adopt toward problem solving in mathematics.

Source: University of Pittsburgh

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7 Comments

  1. Truthspew

    It is my opinion that if they’re smart enough to program the formula into the phone and just setup a program to solve it, they understand the problem well enough.

    Fourier Transforms – they generally suck but are relatively easy to implement in a programmable calculator.

  2. R.Will

    Some students will be stronger with abstraction, and with pure math; other students will tend toward concreteness and applied math. Suggesting that one is superior to the other, a priori and with no sense of student capabilities or context, is a bit like favoring nature over nurture or vice versa as a theory of development. The fact of the matter is that each student will probably evince some linear combination of pure/applied aptitude and the trick is to shore up the weak side of the equation. Recent research (below quote) is the underpinning of my above argument. Punching buttons in robot mode is not the answer, nor is teaching pure abstractions the way to go. As “we” move forward, we probably need MOOC to get folks pointed in some direction, but the long run future of education is probably best rooted in 100% customization which will match curriculum to BOTH strengths and weaknesses of the student.

    “A new study by researchers at UT Dallas’ Center for Vital Longevity, Duke University, and the University of Michigan has found that the strength of communication between the left and right hemispheres of the brain predicts performance on basic arithmetic problems. The findings shed light on the neural basis of human math abilities and suggest a possible route to aiding those who suffer from dyscalculia– an inability to understand and manipulate numbers.

    It has been known for some time that the parietal cortex, the top/middle region of the brain, plays a central role in so-called numerical cognition–our ability to process numerical information. Previous brain imaging studies have shown that the right parietal region is primarily involved in basic quantity processing (like gauging relative amounts of fruit in baskets), while the left parietal region is involved in more precise numerical operations like addition and subtraction. What has not been known is whether the two hemispheres can work together to improve math performance. The new study demonstrates that they can. The findings were recently published online in Cerebral Cortex.”

  3. Steve O.

    I think the two previous commenters are missing the point–these students are not programming anything into the calculator, and neither are they not dyscalculic. They’re in college, and they’re simply not putting forth the effort to actually understand the concepts being taught in class.

    Nothing worthwhile is easy. That’s why learning is hard. Stop trying to make it easy, and you will find it much more worthwhile.

  4. R.Will

    “I think the two previous commenters are missing the point”
    Maybe so.

    “–these students are not programming anything into the calculator”
    If “trial and error”=”calculate”, the above comment directly contradicts the article. So, modulus a linguistic equivalence, the commentator is probably incorrect in that he contradicts the article, but it is not clear that he has a researched foundation to do so and is not just offering a fact-free assertion without support.

    “, and neither are they not dyscalculic.”
    not-not-dyscalculic= “dyscalculic”…is the commentator using litotes to make a point, agreeing that they are suffering from dyscalculia; or is he saying they do not…it is not clear from the double negative. It is also not clear how the commentator has access to facts not otherwise in evidence: whether or not the students in the sample do or do not suffer from that syndrome?

    “They’re in college, and they’re simply not putting forth the effort to actually understand the concepts being taught in class.”
    This appears to be another bald assertion: where is the evidence as to effort in the article. How is the level of effort known to the commentator?

    There is a studied behavior is the Western world: parents praise success of a child to the child by talking about the child’s intelligence. There is a similar but parallel Eastern behavior where effort is praised. Both approaches are “normative” but it is not clear that they form tested components of success. The commentator seems to follow the Eastern mode, but with no discernable foundation. Nor has that foundation been tested, that I know of.

  5. Jill

    Understanding how to use a calculator is a different skill than understanding math. Not that both aren’t valid skills – but they are different.

  6. Bill James

    There is an alternative of course to this decades old argument. Develop calculators so that they help at all times, not hinder progress.

    The brand new alternative – only out this year and my definite find of the year – is the QAMA Calculator http://www.qamacalculator.com. This calculator requires users to enter a reasonable estimate first, before it delivers the right answer. In the case of something like 7×8 or 3.54 x 1000, the only acceptable estimate is the correct answer, so the calculator acts as a check and gives immediate non-judgemental feedback. The need to be able to estimate Trig is key, and there is advice on how to do these estimations.

    There is so much fuss about i-pads and such like transforming education. I think QAMA COULD transform math and end for once and for all this, what should be, phoney argument.

    Those who want to ban calculators will see a calculator aid the skills that are lost – such as estimation, and also knowing about fractions rather than using the most pernicious ‘fractions function’ found on most calculators. (You can even find specific ‘fractions calculator’ apps now – what a complete and utter waste of time and money on something that deskills our children.)

    Those who want to allow full calculator use can use the QAMA wherever and whenever. And on the way, improve their pupils arithmetic skills whilst increasing their mathematical skills.

    and if you need to, you can always switch the estimation mode off for speed – with a few provisos of course.

  7. Donkeyrash Hubcousin

    They can pry my TI-89 from my cold dead hands. Seriously, my calculator has helped me understand the transformation of families of functions, how to visualize multivariate calculus, and help me catch my own mistakes.

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