**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.

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.

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..

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).

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.

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.

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.

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.

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.