Last week, I gave my stats students an assignment: to figure out how to use the statistical functions on their calculators. The distribution of times at which twenty or so of them came to my office for assistance with [above] was heavily skewed to the left, with five or so of my pupils asking for help before the quiz day, and around fifteen coming in between forty five minutes and three hours before they would be called upon to find the standard deviation of a month’s worth of daily snowfalls in Edmonton.
I am not a calculator expert, and took pride in my nonownership of one from the time I ditched my physics minor until the beginning of this term. But I have a decent intuition for these things – most of the time. Half of my students, God bless ‘em, had taken my advice and invested in $15 calculators; I was able, with little effort, to figure out how to finagle standard deviation computations from a variety of those. The other half carted in their TI-83 Pluses, which they’d been required to use in their high school math classes. Most of these students had left their manuals at home, though one girl brought in a slightly older version of the machine, along with the accompanying guidebook. Clearly I’m behind the times; back in my day, we used wee little scientific calculators with ten page instruction booklets and you never heard us complain; but a manual the size of the TI-83 Plus’s could fit, with room to spare, all of the directions that Moses himself would have needed to free his people, lead them through the desert for forty years, and compute the standard deviation of a month’s worth of daily snowfalls in Edmonton. In case you’re interested, it’s available online – all 3.7 MB of it.
For a mere $150, students who think that 5/2+5/2=10/4 can (in theory, anyway) multiply matrices, graph functions (in Cartesian, parametric, or polar form; no need to do any conversions by hand), evaluate antiderivatives of algebraic and transcendental functions (with all of the intermediate steps helpfully displayed) program directly in assembly (according to rohan), and find the covariance of two sets of data. They can also hook up their calculators to the internet and download games that they can play in class. (I’d hate to be the math teacher instructing her students to put that calculator away, right now, or leave the class.) When one girl brought hers to my office, I was tempted to check the menu to see if it could also vacuum my living room carpet and clean my bathtub.
The writer of the otherwise valuable stats text I use (Essentials of Statistics, 2e, by Mario Triola) refers to this beast in every chapter; ditto for the Precalculus book, while my calculus text only “recommends” that its users own graphing calculators, “such as the TI-83 Plus”. I have seen no evidence that the “all calculators, all the time” approach to elementary and high school mathematics education has been anything short of an unmitigated disaster, and I know of no math teachers who disagree with me on that front. I tend, in general, not to assume that my ideological opponents are motivated entirely by money, but I can’t think of any other explanation for this unholy alliance between a wide variety of math text books and this one brand of calculator.
One prof at my grad school once railed against the oft-cited explanation that students should use graphing calculators as a means of making their math classes “relevant to real life”: “When on earth does anyone have to use a graphing calculator in real life?” he demanded. “I certainly never do.” Nor am I convinced for even an instant that calculators “[liberate students] from ‘computational algorithms’” so that they may “pursue higher-order activities, like inventing personal methods of long division.”
To the contrary: never having become familiar with computational algorithms, many of my students cannot make connections between the nuts and bolts of math and the pictures and equations produced by their calculators. I have dealt with students – plural – who do not know that 3/5 means “3 divided by 5″. Their calculators, you see, have “fraction” buttons, not to be confused with the “division” buttons.
The market for such a powerful calculator should be limited to applied mathematics and physics graduate students and a handful of professionals – far from every single high school math student in British Columbia, and I can’t fathom a charitable motivation for requiring every high school student in British Columbia to possess one. Requiring those students’ parents to shell out such a huge sum of money in order to secure their children decent math marks (not to be confused with decent mathematics educations) makes me ill.
In the calculus and precalculus textbooks I’ve used, the graphing problems have been accompanied by suggestions that students check their work on their graphing calculators. “If you have a graphing calculator,” I tell my students, “it may be worthwhile to use it for this purpose. But don’t rush out to buy a graphing calculator for this class; it’s not worth it. And if you do use a graphing calculator,” I continued, “make sure that you know how to check your calculator’s work.”
“What do you mean?” said one guy in the back row. “We never learned how to do that.”
Sure enough, the ample manual omits those instructions.