Computers and Calculators in Schools

Photo: iStockphoto

Neal Koblitz, professor of mathematics at the University of Washington, begins his critique of computers in K-13 mathematics education as follows:

In Peru, as in many Third World countries, the system of public education is in crisis. Teachers’ pay — traditionally low — is falling rapidly because of inflation. The schools are dilapidated, and there is no money for basic supplies. …

Yet President Fujimori has said that he wants to get computers into the schools as soon as possible. The government’s priority is to “modernize” the economy and the educational system, and computerized learning is supposedly one way to do this.

Change Peru to New York City, and Fujimori to the city’s Department of Education, and we reproduce the current news of New York City’s half-a-billion-dollars-and-change effort to shove more technology into the classroom while eliminating 6,100 teaching positions (4,600 of those through layoffs).

In my last entry, I criticized high-stakes tests as the most damaging item in public education. But miseducation is a very competitive field, and I had momentarily forgotten about calculators and computers (whose baleful effects extend to the private schools). It’s hard to think of a better way to ensure that students not be able to reason or think for themselves.

Here is a small illustration of the problem. As I was finishing graduate school, I was helping to pack up the computer lab and ship it across the country. I went down to the IT desk and asked the price of one DAT tape for backing up all the files. I was told $6.50. Then I realized that we would need several, so I asked the price of the box of 10. The sales clerk whipped out his calculator and fiercely punched away. Perhaps he was figuring the different-in-every-county California sales tax — was it 7.25 percent or maybe 8.375 percent? Just as I had thought up that explanation, he announced the results of all the calculation: “That’ll be sixty-five dollars.”

It happened almost 13 years ago, and I remember it as if it were yesterday. The situation today is even worse thanks to graphing calculators, which have done for students’ understanding of algebra and functions what the regular calculators have done to their understanding of the number system.


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  1. YX says:

    I wouldn’t think computer itself is the problem, is how to use it. Also it makes economic sense since computer / calculator is more efficient at handling calculation and humans are better at logic and reasoning.

    I also not sure the guy at the IT desk had the benefit of calculator (certainly not computer) during his school, which suggests that some people will be ignorant no matter what tools school choose to give or not give them, as long as themselves chose so.

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  2. karen says:

    Embarrassingly, after gradating from undergrad and gleaning insights from complex statistical operations performed by fancy software, I had to re-learn my times tables for the GMAT.

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  3. jan says:

    That is a fair point, that people should be able to do basic math without the aid of technology. But for someone like me, a graphing calculator was what enabled me to pass the classes I needed to pass in order to get into medical school. To put it simply, numbers and I don’t get along–we never have, and as hard as I try, abstract reasoning with numbers just doesn’t make sense to me. Now, when we attach numbers to reality (as in 10 DAT tapes at $6.50 apiece), I function perfectly well. I calculate sale prices in stores and tip amounts in restaurants in my head, usually faster than my husband (who had sailed through two college calculus courses before his senior year of high school). But in trigonometry and calculus, at least the way they were taught in my classes, there was no reality to attach to the numbers–it was entirely abstract reasoning. Which meant that, for years, I was doing the mental equivalent of wading through hip-deep mud, trying to understand what in the world these numbers were doing. My graphing calculator at least helped me get the answers so that I could keep up with the pace of the class, pass the required standardized exams, and pass my classes. The way that our education system is structured, with a heavy emphasis on “get X amount of content covered” rather than “make sure things making sense”, and with the number of students at all ability levels and with all learning styles, sometimes there simply isn’t a way for a student to get through without the crutch of a graphing calculator. And, in my mind, that’s okay.

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  4. Dan Auns says:

    (Link to: TEDTalk, Conrad Wolfram)

    I think you should give this a watch, and possibly rethink your take.

    Computers, and calculators in classrooms is not the problem Sanjoy. Proper learning the application of mathematics in everyday life, is.

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    • Michael says:

      I was thinking of posting the exact same thing. We don’t teach high schoolers to write by copying text out of a dictionary or teach art students to paint by tracing. Why do the same thing with math? My math book in high school had all the answers in the back, to double check you work. When does that ever happen in life?

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  5. Diego Venancio says:

    Is this post just this? An old men’s cry and a simple example? Where’s the data to support the theory? At least a larger example that can represent how education have worsened? Not even the example proves anything.

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  6. Jeff says:

    At my University, we are not allowed to use calculators in any of the core math classes. From Calculus 1 to Differential Equations, I didn’t use my TI-89 a single time. As much of a pain as it was, I think it really forced me to learn the concepts and understand mathematical relationships.

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  7. Eric M. Jones says:

    Anything that reduces drudgery is a great idea. So much that passes for education is simply rote effort and pointless memorization. Stalagmite…Stalactite…give me a break. There are only three classes of ____small, medium and BIG. And my math lesson on fractions–There ARE no fractions. It’s easy.

    Bring on the calculators.

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  8. Donnie says:

    Isn’t this the ultimate in specialization? Not everyone needs to know how to grow their own food anymore. We have a small subset of the population using technology to provide food for everyone. Math could be similar. Let the computers do the math, and allow the humans to think creatively. It is what we are both best at.

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  9. Oldtaku says:

    Here’s another fun one. If you get a look at the cashier side of many (most?) cash registers these days they will show you exactly what change to give (2 quarters, 1 dime, 1 nickel, 3 pennies…) or at least have a button you can hit to do so if it’s not automatic.

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  10. Vergil Den says:

    I suspect even if the bloke didn’t have a calculator – he would have used chisanbop. A crutch is a crutch – regardless of how well dressed in technology..

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  11. Andrew says:

    My 15 year old son lost his graphing calculator a month ago and persevered without it (not wanting to tell me) for a couple of weeks. His geometry grade went up. It was a revelation to him that by having to write things out and do much of the math by hand, it slowed him down and he made fewer errors.

    What I take from this single observation is that calculators can become a crutch that artificially speeds students along and takes away the somatic learning experience of writing things out. By constantly using calculators, schools are bypassing some learning methods that benefit some students.

    My son realized that he was moving too fast, and that writing things out and doing things a bit more slowly helps him, both in understanding and in mistake avoidance. He is now using that lesson (after we worked out a joint plan on how he will participate in the cost of replacing the graphing calculator).

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  12. David Henderson says:

    Like others have pointed out, it depends very much on how the technology is used and not the actual allowance of use. I struggle thru mathematics exams as in it takes me longer to do the work and so I rarely have time to verify my answer by plugging it back in to the original equation. But on those exams where I have been permitted to use my trusty TI-89, I can check my answers quickly and move on to the next problem. What makes this a viable technique? There is no credit for a correct answer without showing how one arrived at that answer.

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  13. Joshua Northey says:

    Hehe, I spend a 1/3 of each day in excel and I still make sure to do some portion of everything by hand or in my head to keep my mind sharp and my intuitions on target. I have seen too many people who don’t even notice if answers are off by orders of magnitude. No Timmy 50 trips at $145 a trip is not $725…

    A large part of the problem here is money tied to specific uses. The government loves to do this, but on the receiving end it often seems insane. I remember at the University being part of a CoLA governance group in charge of determining how we were going to spend a $300,000 technology award. We really wanted to spend the money on more faculty, or nicer classrooms, or any number of other things. Instead we needed to spend it on IT equipment for the CoLA even though we all had our own personal computers and the University had already spent a ton of money updating the public ones. Eventually the conversion of a storage area into a specific “composition lab” for the psychology department (i.e. computer lab #600 on campus) was settled on, but even the psychology students felt this was a needless waste of money.

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  14. Uthor says:

    Seem to me that the clerk understood algebra just fine (you have to multiply to arrive at the answer) and just offloaded the tedious arithmetic to the calculator.

    Granted, in this case it would have been faster to do it in your head, but it’s hardly a convincing argument for calculators ruining math.

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  15. Sally says:

    Sanjoy, the sales clerk was mocking you. It was probably deserved.

    As a educator and computer scientist, I can tell you that nothing teaches linear algebra (matrix manipulation) like showing how to use it when manipulating 3d graphics.

    There are infinite examples like this, but apparently one example is the gold standard.

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  16. Mike says:

    At least give the clerk credit for getting the right answer. Which is the most important thing in math taking place outside the classroom.

    The real danger that (I think) most of the commenters here are identifying is that the clerk would get $650 on the calculator and not have the slightest clue he’d gotten the wrong answer.

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  17. Robin Jeffries says:

    This behavior has nothing to do with computers. Maybe someday we will have universal numeracy, but I gave up on that dream 40 years ago on a visit to Japan. At that time most (all?) Japanese store clerks used abaci to tally up purchases. They were lightning fast on them, and initially I was very impressed. But we had several instances where it was clear that they had no understanding of the numbers they were handling. One example was that we went into a small convenience store to buy film. The film was something like 395 yen per roll and we got 5 rolls. My husband handed them 2000 yen and expected to get some small change back (I’m sure he hadn’t done the math to know what to expect — just “small change”). The clerk pantomimed that we owed her more money. Given the language barrier, it took us a long time to convince her to recalculate the number (the abacus is never wrong, we learned repeatedly), and give us our change.

    You are beginning to sound like those folks who decried how written books would cause memorization to fall into disrepute. I think we have managed to survive as a society with kids and adults who haven’t memorized anything more important than an advertising jingle or a lady gaga song.

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  18. Emily says:

    It’s a popular human pastime to declare that technology is ruining everything. I read an essay in advanced composition that complained telegrams were destroying the English language. One of the transcendentalists–maybe Emerson–swore rushing around in trains going 35 miles per hour would make everyone forget about nature. It’s just not true, and technology marches on.

    Just like every new tech tool, calculators and computers have their pros and cons. But I think it’s silly to assume that critical thinking skills are being destroyed in all students because of a single incident with a person who probably reached for the calculator without even thinking.

    After my AP Calculus class I could look at almost any graphed function and write out the equation for it. There is no way I could have learned that if I hadn’t been able to practice by comparing graphs instantly on my calculator (and I’m not a “math person”–I’m a Spanish major). There will always people who will use technology blindly, but they would have been doing the same thing 50, 100, or 1000 years ago. The tools aren’t the problem. Knowing how to use them effectively is.

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  19. Andy in NC says:

    did anybody notice that the article was of 15 years ago?

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  20. crquack says:

    Surely Sanjay’s point was not that computers or calculators are bad but that they are bad *if used to replace good teachers* in classrooms.

    I do not think his example is all that atypical. Try giving a store clerk exact change and watch him struggle to work out how much a nickel, two dimes and a quarter amount to.

    I for one do not believe that “creative thinking” is likely to be productive in presence of ignorance of basics.

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  21. Shaun says:

    you sound curmudgeonly, sanjay. I am 29 and am great at doing arithmetic in my head and visuallizing functions, but i came up with a graphing calculator and computers. You can’t let your experience with one moron 13 years ago color your perception of an entire generation.

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  22. gpo says:

    I am definitely in the camp that students should not use calculators in school until around the 10th grade. Kids have to know certain math facts in their head. Using the calculator just slows the memorization of those facts.

    As I see my daughter progress through school I get disgusted in the ways they teach math these days.

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  23. Lance says:

    Ah, L fighting K. If these were machinists complaining about automation technologies being favored as opposed to additional hours/workers/other benefits, we’d call them Luddites. But, since they’re teachers, they are merely concerned about the educational prospects of the beleaguered student.

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  24. HartmanMath says:

    As a junior high Algebra teacher I agree 100%. I only use calculators for multiplying decimals or more complicated tasks such as factoring. My students tend to complain about this policy.

    Calculator use is emphasized by most elementary teachers and the NCTM. For this reason alone I will never join.

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  25. Duncan Miller says:

    I wouldn’t hold it against our generation (generation Y) as I know for a fact that the older generations have just as much trouble as we do with simple mathematics. I by no means think of myself to be a mathematician (in fact I hardly got by my first year university linear algebra course last semester) though I often find myself having to do the mental calculations for business, economics, and even my math professors. With that said I’ve never seen one of them have trouble with a simple 6.5×10, though I have watched them strain over equations in which they simply have to divide by fractions or easy decimals when I have had the answer figured out almost instantly.

    I agree heavily with the first comment posted regarding the use of calculators being the issue rather than the presence of them as I know a large number of kids who can easily out calculate their elders who have not had the priveledge of growing up in a culture with such a high level of computing convenience.

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  26. clive moss says:

    Arithmetic is the mechanical ability to add, subtract, multiply and divide taught and learned in the lower grades. Mathematics is abstract and conceptual and studied at higher grades. Remembering facts about numbers (9×6=54, or whatever) is not the same as understanding how to do algebra, or reason geometrically.
    The confusion between the two lead to the disastrous “New Math”.
    Mathematicians are sometimes arithmetically challenged. By calling the memory tricks of the the multiplication table mathematics we are potentially scaring off students from a mathematics career.

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  27. Chris says:

    I can one-up your anecdote…as a grad student teaching intro statistics, I had a nursing student come in for help, and in front of me, she actually multiplied a number rather large number by one on her calculator. I will never forget that as long as I live. Calculators can be a blessing…and a curse.

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  28. Anon says:

    I think this is somewhat inevitable today due to the level of our knowledge. These types of situations are probably MORE likely to happen among the “highly” educated (engineers, computer programmers, etc.). When we deal with the complex it’s sometimes easy to lose sight of the basics as those tasks tend to be taken up by other people or automated by technology.

    Its true what they say about how you lose what you don’t use. I aced all my advanced math courses in university but could not remember how to do long division. Now I didn’t forget the concept of what division was, just the method to do it on paper. This on its own to me is not an indicator of over reliance on technology. While it is acceptable to forget say the long division method or formulas, it is unacceptable if an individual forgets the concept or idea so much that even when brought up it seems alien to them. The unfortunate fact of having an education system which spans an entire country the size of America or Canada (where I was educated) is that good teaching cannot be standardized, and comparability between a student on the west coast and one on the east coast is more important in the eyes of policy makers and politicians (who decide how and where funding goes). A standardized curriculum, standardized teaching methods, standardized testing requirements are all detrimental to individual students but the decision makers are unwilling or unable to do anything about it.

    Education reform is something which everyone knows is needed, but no one seems to have a concrete plan which can feasibly work. Ultimately it is up to the individual (both student and their parents) to make sure they’re on the right track. That’s not to say the system does not have responsibility, just that they should not bear the sole responsibility.

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