The Case Against Computers in K-13 Math Education (1996) (opens in new tab)

I don't know about general purpose computers, but my life would be completely different if my high school hadn't required the use of computers that masqueraded as calculators.

My school required us to use either a TI-81 or TI-85 and my friends and I quickly discovered the power of TI-Basic. We started with small games to amuse ourselves, since this was an era before mobile phones. But I quickly realized that I could write programs to solve the kinds of problems I expected to see on my math tests. And I was amazed when I asked my teachers whether I was allowed to do that and they said yes...it felt like cheating. Suddenly studying became an altogether different experience where cramming and hoping I'd learned enough was replaced by writing small scripts that gave me full confidence I'd ace the tests. It was so much more efficient. The funny part was, I never actually used my programs during the tests...the act of programming, I realized, forced me to understand the material in a way that cramming never did.

From that experience, and a Doom-like game I built on my calculator, that spurred me to take a computer programming class the summer before college and eventually major in CS and go into tech. And none of that would have happened if my math teachers hadn't been so open minded about allowing us to use what was essentially a computer in class and on tests. So I hope they're not advocating removing all computers from class, because I'd be sad if the path I took into tech was closed to today's students.

> We already saw an extreme example of misallocated resources in Peru. But even in a ``wealthy'' country one has to be concerned about this problem. Many educators in North America share the feeling of betrayal of the teacher who said, They can give us the axe, but they can spend thousands on computers. We have to fire our music coordinator, we have to fire our music teachers, we have shitty libraries. (Lynn, a Canadian schoolteacher, quoted in [14, p. 41])

I’ve seen this happen in the relatively wealthy schools my kids are in. They spend many thousands on smartboards and iPads, and they’ve gotten rid of the “non-essential” arts and music teachers. Parents are personally funding some arts educators on a part time basis a couple of days a week. I think it’s an egregious misuse of funds, wasteful and ultimately damaging to the kids.

What’s worse, the tech is not being used effectively. The teachers don’t have enough training to incorporate the smartboards and iPads, and they don’t have the budget for tech training because they spent it on the iPads. Kids play games on them that they have access to at home, but they’re not being taught about the technology or being taught to use it to do things they can’t do on paper.

I don’t mind computers in the classroom, as long as the arts are funded and the teachers are paid enough. What I’d really love to see more of is using computers to integrate math and arts together... digital arts with an emphasis on both rigorous math and rigorous art. Give the mathy students some aesthetics training, and make sure the art students are capable with computation.

Some declarations of the limits of computers jump out to me as dated:

"The inability to develop good translation software has been one of the most embarrassing failures of Artificial Intelligence. If the best computers in the world are unable to translate from French into English..."

"in the calculus final exams at my university we usually ask for exact (not decimal) answers. For example, sin(60°)=\sqrt{3}/2, not 0.866; the circumference of a circle is 2 pi r, not 6.283r"

Also, the comparison of computers to automobiles in order to dismiss them is odd, as driver's education was part of school when I attended in the 90s. And so was auto repair, which I regretted not taking in later years.

A computer from 1996 seems, in today's context, rather ironically like "simple, unstructured play material like clay, sand, blocks, rag dolls, and finger-painting sets".

One of the keys to learning is making students engage in the material and to fix their mistakes. Computers are uniquely able to give individual, rapid feedback.

Even at the advanced level it would be really cool for students to have access to and use proof software. I wish I could have had the opportunity to work out proofs for myself, guided by software, instead of just being given them.

Asking whether "computers" belong to education is like asking whether "books" belong to education. I can imagine a book that does. I can also imagine a book that does not. Same for computer programs.

We should debate specific applications, whether they help the education, or are just shiny toys. Then we should make the cheapest computer which runs exactly these applications and nothing more, and use that in schools.

If teachers don't know how to use a computer, these two things could fix that easily: set up the educational computer so that it can only run those selected educational applications; and write a book about how to use each of those applications in education.

A debate on the level of "Computers good! No, computers bad! Good! Bad! Good! Bad!" is not helping anyone.

An example of a useful application in math education could be e.g. something that shows you how a graph of a function changes when you change the equation. For example, you could have a quadratic equation, where you can use the mouse to change each coefficient. When the time is right, bring the computers and let the kids experiment with this. On other days, do not bring the computers to the math lesson.

Collect some applications like this, make a Linux DVD which can be installed or run live, write teachers' manual for each application and put it on the DVD and online as a PDF file, and that's it. (I suppose someone already did something like this, although probably without the PDFs.)

The question is not whether to use the computers or not, but how to use them.

The purpose of education should be learning how to think and to apply one's thoughts. The most important tools in the class are the brains of the teachers and pupils. Those are really the only tools that are needed. My youngest son had to have a laptop for the final three years of school (Norwegian videregående). It was justified on very flimsy grounds. One of the programs was a geometry program; what he learnt from that could have been taught by Pythagoras with a sharp stick in the dust on the ground.

The #1 important need in math education is repetition. Repetition with understanding. If you don't internalize all the simple rules, you can't do it for yourself when you need to.

Which side of the division line do you put each quantity on? How do you use unit math to verify your problem statement? Multiplication table, and simple addition/subtraction. Probability and statistics. Repeat, repeat, repeat.

I've long held that, if we want computers in the classroom at all, we should steer well clear of any modern gee-whiz gadgets. A modern Commodore 64 clone would teach vastly more about computers than an iPad and would cost maybe $50 total. Modern computers are designed so people don't have to understand them, which is exactly backwards for a student.

If I were a professor, I wouldn't allow open laptops or phones. I would imagine it's a huge distraction and students are there to listen to the lecture and learn, not goof off with their devices. I'm old and crotchety though. We had laptops when I went to school, but no one (that I noticed) used them in non-computer class.

Pardon my ignorance but can somebody educate me on what K-13 means? I know about K-12 and have seen K-14,-16, ... as well but I've never seen K-13 in an international context.

At my local school in Germany the final year was called K-13 but it's probably not what's meant in the article.

The short argument is make is that learning happens in the brain, when it thinks about stuff. It doesn't happen in the computer. We can create a faster pace by having more individualized education, but that's about it.