Friday, August 09, 2013

Calculator Dependence

There are plenty of people--math teachers among them--who think that calculators are so ubiquitous that we should teach students only minimal computation abilities and focus instead on helping them gain some "deeper understanding" of how to solve a particular problem.  It's "critical thinking" dogma for math.

Those of us who believe that students should use calculators only after understanding the calculations themselves have to fight that well-worn battle of "let the calculator do the drudgery, teach the kids to interpret what the calculator is telling them."  There are many levels of rebuttal to that silliness, the weakest being, "What do you do when the batteries die/the power goes out?"  No one, not even the person raising that argument, really thinks it's a good one.  There are plenty, though, for whom the concept of the necessity of "numeracy" is so clear and obvious that they've never thought through a clear and obvious rebuttal to the siren song of universal calculator usage.

I'm currently skimming through my personally-annotated copy of Sherman Stein's amazing book Strength In Numbers and came upon this beautifully-worded, succinct reasoning:
There is also the risk that a computer may play the role of the autocratic teacher who says, "Don't ask why.  Just do it the way I say."  It is then a mysterious black box, and using it places the pupils in a position of dependency.  This circumstance is most unfortunate in mathematics, where pupils should develop self-confidence and accept nothing on faith.  Several teachers have told me that "the capacity to reason seems to get lost when you start pressing keys too early."
I refer to calculators in class as "devil boxes", and I talk to my students about "black box numbers".  It seems I'd absorbed Stein's lessons well, even though I'd forgotten this particular passage from a book I last read several years ago.

By the by, I've met Professor Stein.  He's signed two books for me (Strength In Numbers and How The Other Half Thinks) and gave me an algebra book he co-authored in 1969.  His "popular audience" books are extremely interesting and well written, and the algebra book is among the best I've ever seen, certainly better than any book adopted in California in the sixteen years I've been teaching.

I used to recommend John Allen Paulos' book Innumeracy to people who ask me to recommend one "popular audience" math book; now, if I can recommend only one it's Strength In Numbers.


Elaine said...

I tell my students that calculators are the spawn of the devil... And ban them from my classroom until they start doing trig in geometry. (And even then, half the time I make them use the tables.)

I always liken it to texting and typing... How often do they have typos? Then I point out that they need an internal error checker, and they don't get that without doing the math themselves a LOT.

It helps that I'm the only algebra and geometry teacher at my school... And that almost all the kids get me for at least one year... And many for two years!

Auntie Ann said...

Don't trust computers!

Xerox scanner transposes 6's into 8's.

Raymond Matson said...

haha I noticed the higher up in math I get the more I use my calculator for the REALLY simple stuff. like 11x12 and then I'll work out the difficult parts on paper

Mrs. Bluebird said...

I find that my seventh graders have very little number sense because they're so used to getting their number from the "devil box". They learn their multiplication tables then promptly forget them when someone hands them a calculator. Honestly, I had a kid who couldn't tell me how many quarters were in a dollar. They have no clue if the number the get is right or wrong and no way of finding out. And they're so addicted to the calculator that if you take it away from them, like the state of Tennessee does on the science portion of their TCAP test (which has math on it), they panic. Out and out panic. Fortunately, we're haring rumors that the state may ban calculators up to a certain grade level. I hope so.

maxutils said...

I agree ... if you know your basic math skills, you don't need the devil box. The understanding is the most important.