I am old enough that, as a kid, I did not have access to a calculator. My mother, a teacher, had an electronic calculator that you had to plug in the wall. She would use it to crunch in the grades at the end of each term. It felt fantastically modern.
In any case, one night, when my mother was away, I decided to slide into my mother’s bedroom, plug the calculator and use it to do my math. homework. I was in third grade. This was, let us be clear, cheating.
What happened? I got a terrible grade. Turns out that using a calculator does not guarantee the correct results.
I lived through a similar experience when I got to college. After learning algebra by hand for years, I soon realized that computers could do algebra too! I had discovered computer algebra systems. Wow! So mathematics would be easy from now on. But as I would soon learn, these systems allowed evil professors to ask even harder problems…
In 2009, for the proof of a result, I had a computer algebra system (in this case Maxima) run a long script to check many possible cases. This intensive search would have taken days or weeks to do by hand. Yet I was able to do this work with the help of my computer precisely because I have some degree of mathematical sophistication… A naive user would not have known what to ask of the computer. The better at mathematics you are, the more you can get out of computer algebra systems…
The Guardian recently reported that some expect that within 25 years, we will get instant language translation. Contrast this with the fact that Richard Stallman, one of the world’s leading hacker and free software advocate, is fluent enough in French to give talks. In fact, I find that Stallman sounds more dignified and polite in French, but maybe it is just me.
Is learning a foreign language a waste of time given that computers can translate?
Let me consider programming languages as an analogy. Most programming languages today are Turing complete. And all Turing complete programming languages are mathematically equivalent. So you only ever need to learn one programming language… they are all equivalent! But this is abstract nonsense as any programmer will tell you. And it is just as much nonsense to claim that computer translation makes learning a foreign language obsolete.
As an aside, reputed AI experts in the 70s and 80s were discouraging people from learning to program. They expected that very high level languages would make programmers obsolete by 2000 or 2010. I do not think they could have been more wrong. Who benefited most from software technology? People who learned to program.
Or consider spelling. Should I give up teaching my boys to spell flawlessly given that we all have spelling autocorrection? I would say that spelling and grammar checkers have, if anything, raised the bar. Kids today need to master more thoroughly the grammar, and they need to spend more time studying the nuances of spelling.
The problem is the same whether we use calculators, computer algebra systems and language translation… You need to be smart to use technology effectively. As we acquire more and more technology, we need to get smarter.
It is true that as technology evolves, we should learn things differently. For example, there is little need to train students in very technical algebra. Much of the standard curriculum today is antiquated. Last night, I was doing a word problem with one of my boys and he got discouraged because he had to compute 70% of 280. I told him that I would never expect him to do this by hand… what mattered to me is that he was smart enough to realize that the answer was 0.7 times 280. Similarly, when learning a foreign language, you should probably focus more on how the languages differ, than on vocabulary and spelling. But one thing is certain: with increased technology comes higher intellectual requirements.