Tall, Dark, and Mysterious

1/28/2005

Why invest in the children when you can invest in Texas Instruments?

File under: Sound And Fury, Those Who Can't, Queen of Sciences. Posted by Moebius Stripper at 8:57 pm.

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.

31 Comments

  1. I believe that the triumph of Texas Instruments in the school calculator market is a tribute to their business skills. When Hewlett-Packard introduced the HP-35 in 1972, it was the perfect tool (and toy!) for engineers and science geeks. I saw my first one in the Caltech bookstore, where the $395 device was locked in a heavy security cradle. We didn’t blink at the Reverse Polish Notation, which was clearly the One True Calculator Logic. No stupid “equal” key!

    Of course, we couldn’t afford it. I finally got the next-generation HP-45 when my grandparents gave it to me as a graduation present when I earned my master’s degree in math. These were not devices for the masses. Hewlett-Packard neglected the opportunity to button up the calculator market (in much the same way that Apple failed to take advantage of the Macintosh). By maintaining high profit margins and selling only to a sophisticated niche market, HP sat by for years as Texas Instruments flooded the school markets with low-cost devices that used more intuitive (but less efficient) algebraic command entry in lieu of good old RPN. Students snapped them up.

    Texas Instruments also formed alliances with publishers and education researchers, supporting projects to use TI calculators in new calculator-based curricula. As teachers found that more and more of their students were able to afford calculators, they increasingly found it helpful when textbooks began to carry advice to students on calculator usage. Naturally, this created pressure to anoint an “official” calculator because it was too difficult to give instructions for HP, TI, Sharp, Casio, etc. (One calculus text tried to support four different calculators with specific keystroke directions; too bad the calculators had been superseded by new models by the time the text hit print.) TI had prepared the ground well to become the dominant hand-held calculator. The 80 series of graphing calculators (TI-80, TI-81, TI-82, …, you get the idea) hold down the high end of the school market while the 30 series (particularly the TI-36 these days) dominate the non-graphing lower end. HP finally began to produce some lower-cost non-RPN devices (anathema!), but it was much too late. TI won the calculator wars. Not that it was much of a contest.

    - TonyB — 1/28/2005 @ 10:01 pm

  2. “evaluate antiderivatives of algebraic and transcendental functions (with all of the intermediate steps helpfully displayed),”

    Are you sure??? I don’t think this can be done on a TI-83+. It can iteratively find definite integrals, but it can’t symbolically find antiderivatives, at least not with the included software… and symbolically finding antiderivatives is surely too complex for anything which can run on a Z80, the TI-83+’s pathetic CPU.

    Graphics calculators are wasted on 95% of the students that have them… they can certainly be useful, if only for the fact that you get a proper work space inside your calculator rather than just a single memory slot, but many of the people I know who have them just use them to play games and cheat on exams. However, you can directly program in assembly on them, which makes them a good tool for anyone studying low-level programming languages. The ability to plug in environmental sensors etc and get data directly into the calculator is nice for science students, too… in fact, I’d say the TI-83+ is great for just about all students except those who are studying mathematics and have little willpower.

    Why don’t you disallow calculators in exams? That’s what my differential equations lecturer did last year. Admittedly, when he informed the class, there were gasps and someone let out an alarmed “What the hell did he just say???”, and the reaction in your classroom would probably be several orders of magnitude worse, and you probably want at least one of your students to pass, but hey, maybe they will learn a lesson? (well, there’s no harm in being optimistic, is there?)

    - rohan — 1/28/2005 @ 11:02 pm

  3. Another conspiracy in [math] education : textbook version changes. I taught an intro stats class for students planning on never taking another math credit… and the textbook was in its 12th edition. I compared to the first edition, and lo and behold! the text was identical up to permutation of problems and improved fonts. Oh, yeah, and a bundle CD-ROM that had all of the example data entered as comma delimited files, so you could import it into any statistics software and do whatever with it [one short example per chapter].

    The book was over $100, and went into a 13th edition immediately after I taught the course.

    My course didn’t even cover a third of the textbook. I felt horrible for my students and their highly wasted money.

    - Sam — 1/28/2005 @ 11:07 pm

  4. It actually makes sense for a text to contain more material than any individual instructor would want to cover in a single course. By a good selection of topics, a publisher can issue a text that appeals to a wider audience of text adopters. A book that exactly matches your needs won’t appeal to anyone who wants some additional topic that you don’t care to do. Within reason, one should expect texts to contain more than they absolutely have to.

    As to new editions, however, the truth is not pretty. The main reason for new editions is to kill the used-book market. As Sam noted, exercises may get permuted and a few minor (very minor) enhancements may be introduced, but the prevailing rule is that new editions are trivial modifications of their predecessors. It’s embarrassing.

    - TonyB — 1/28/2005 @ 11:34 pm

  5. The version change scam is becoming a well-known phenomenon in math textbooks. Even professors are starting to take notice. I’ve had two classes now where the professor assigned problems from the book according to more than one edition: “If you bought the new 5th edition, the problems are in this order on this page, but if you got a 4th edition second-hand, the problems are on in that order on that page.”

    - Geoff — 1/29/2005 @ 12:01 am

  6. rohan - I must have been thinking of another calculator; I know there’s one that displays all of the intermediate steps in evaluating antiderivatives. That calculator was the straw that broke my grad school’s math department’s back - they went straight from “you can use any calculator you want” to “no calculators”.

    I allow limited calculators in precalculus, and most of the time they aren’t even that useful. I deliberately give questions of the form “interpret this graph” as opposed to “graph this”, for instance. But in statistics, calculators are actually a valuable tool: if I don’t allow them, then students can’t compute standard deviations, for instance, unless they’re really artificially constructed (ie, they result in having to take the square root of a perfect square) and don’t involve many data points. Which defeats one of the purposes of the class.

    Re: textbooks - yup, problems are permuted, a big price tag slapped on the new edition, and that’s it. (Not just math, though, from what I hear.) But I do think that texts should contain a proper superset of one course’s worth of materials - otherwise, the instructor needs to follow the text to the letter, rather than work from/with it, choosing material and examples suitable to the course.

    - Moebius Stripper — 1/29/2005 @ 12:14 am

  7. Extra Credit Assignment: Great Reading…
    As always, the EduSphere offers some excellent reading that is to be had from a variety of sites and writers. We are pleased to present the weekend…

    - The Education Wonks — 1/29/2005 @ 12:14 am

  8. Do you have the option of forbidding graphing calculators and forcing the students to buy the $15 scientific calculator? I think that was the policy when I took community college chemistry.

    - Alison — 1/29/2005 @ 12:32 am

  9. At my grad school, I was teaching one of over a dozen sections, and I had to do what the other instructors and the course coordinator had chosen, and they’d chosen to allow any calculator, up until they decided not to allow any. Where I am now, I can do what I want. In statistics, I’m fine with the students using the fancy $150 calculator, which doesn’t give them any unfair advantages. (Sometimes I’ll specify “compute this by hand and show your work” just to make sure that they actually know, say, the formula for standard deviation, but that’s all it takes.)

    In precalculus, I tell my students upfront that starting halfway through the term, they won’t be allowed to use graphing calculators on tests. There’s a section of the course about graphing functions, fercryingoutloud. But I don’t insist on any particular brand of calculator. A math prof friend of mine had a good idea: limit students to calculators that have a display panel of, say, 2cm or less. Sounds like a good, and succinct, restriction, one that’s easy enough to follow and describes suitable calculators.

    - Moebius Stripper — 1/29/2005 @ 12:49 am

  10. You know what I have to say about calculators in math class.

    Off topic, during a 3-hour impromptu debriefing session at work, one guy brought up Matlab (which surprised me… we mainly use Excel for everything) and I explained Maple and Mathematica. What’s funny is I had to explain why generally it’s best to code your own optimizer for a particular problem, rather than use Excel, Maple, or Matlab… I guess they never had a job so large that they realized how slow Excel was.

    (I think I created a job for myself during that debriefing, and will actually be using stuff I know from nonlinear optimization. Woo. Go me.)

    - meep — 1/29/2005 @ 2:38 am

  11. Regarding the usefullness of graphing calculators … I do lots of math (mostly calculus and some differential equations) to crunch ungodly amounts of data as a graduate student studying the human visual system, yet I never use a graphing calculator, nor do I really have any use for one. I often *do* need to graph functions — for example, I’ll need to superimpose the graph of a function called for by a certain theory of the visual system onto data from actual human test subjects, to compare the two — but I turn to MatLab for that. Anyway, just a roundabout way of saying I totally agree with on on the essential worthlessness of graphing calculators for most people.

    And here’s something else. Way back in the dark ages, in 1994, I had to get a first-generation TI-81 for this math class I was taking. Thing cost $70 bucks, a lot of money even back then. Never used it since that class.

    - wes — 1/29/2005 @ 2:57 am

  12. My uni has a strict calculator policy - at the beginning of the year, every first-year gets a sheet listing the models of (strictly non-graphics) calculators they may use, and in order to use a calculator in an exam, it must have an “approved” sticker on it. My basic maths skills drastically improved compared to how they were at the end of highschool, though it was a bit of a pain having the expensive graphics calculator from upper highschool maths made redundant.

    (ps: this is kinda related, and also kinda scary…)

    - zoe — 1/29/2005 @ 2:58 am

  13. We are all going to need strict calculator policies in the future, something along the lines that Zoe describes, or big trouble is coming. Some of my students already want to use the calculator functions that are built into their cell phones or PDAs. Of course, I tell them “no” because I don’t want to create the opportunity for them to be text messaging (or should that be “txt msgng”?) during exams and quizzes. As these devices continue to morph into each other, students are increasingly going to be carrying things that look like hand-held calculators but include wireless communications. Oy!

    The “approved” list is going to be essential.

    - TonyB — 1/29/2005 @ 10:55 am

  14. “I know there‚Äôs one that displays all of the intermediate steps in evaluating antiderivatives.”

    I believe that’s the TI-89. It was very helpful in getting me through an upper-level stats class without having to brush up on my calculus. Throughout most of the rest of my engineering classes, I used the Windows calculator.

    - Amanda — 1/29/2005 @ 1:40 pm

  15. What’s truly amazing to me is how many of my students own expensive TI-89 and TI-92 calculators and can’t use them to evaluate derivatives or integrals.

    - Brian Borchers — 1/30/2005 @ 4:28 pm

  16. I’m not sure how much control each individual instructor gets over the way a class is taught at big universities, (maybe it would screw up entering calc 3 students if the calc 2 teacher messed with the curriculum too much) but at my school the policy is 0 calculators what-so-ever in any class prefixed by MATH. In Statistics we do use Excel spreadsheets to map/format data and so it does provide the utilities necessary to take standard deviation. (as well as map a mean chart/graph) As for calculus I-III, Diff. Equations, Discrete Math, etc? Sqrt(2) is a perfectly reasonable answer, why would you need a calculator for that?

    - Arima — 1/30/2005 @ 6:07 pm

  17. TonyB - I warn my students upfront, in the syllabus, that if I even so much as see a cell phone during a test (nevermind hear one), then I confiscate the test paper and assign the student a zero on the test, for the very reasons you give. (And also because I just plain don’t like cell phones and find the notion that my students need to be accessible 24/7 to be fundamentally objectionable.)

    Arima, I had no control over the way my classes were taught when I was back at Large Urban Grad School, but here at IslandU, I can do as I please provided I cover the relevant sections of the textbook. That said, some of the courses I teach lead into later courses (precalc -> calc, for instance) so I can’t completely forbid calculators if the next class doesn’t. That said, I do give plenty of precalc quizzes/tests in which calculators are not allowed, and plenty more in which calculators don’t help. And I never allow graphing calculators. (And I openly mock students who ask me if they’re allowed to use graphing calculators on the test that covers the section on graphing functions.)

    - Moebius Stripper — 1/30/2005 @ 7:10 pm

  18. Ahh, the good old calculators in math discussion.
    I went through high school with a HP 20s (programmable, but not very, and non-graphing) (since upgraded to a HP 48S, with real RPN and a bunch of features I still haven’t learned how to use). One physics teacher assumed his students would have calculators that could do polar vector addition (and told them how to do it on a TI-8x), so for that term my calculator’s memory had a polar vector addition program (which was about the only time I ever had anything useful in the memory at all). That’s about the only time something more would’ve been at all useful.
    Funny, though, when they pulled out the class set of TI-92s (full QWERTY keyboard and symbolic calculus software, yay!), I still managed to figure out what I was doing and get the assigned work done before the people who were used to using their graphing calculators for everything.

    - dave — 1/30/2005 @ 10:29 pm

  19. This peculiar focus is not limited to calculators.

    A certain math software company with which I am acquainted has as one of the central tenets of marketing the “focus on the concepts, not tedious mathematical notation” arguments similar to the ones you’ve cited here. You know, something like: “In the past, students have been bogged down by details of algebraic manipulation. With Package Foo, available as an add-on for only $50 per seat, with a free T-shirt for the instructor, students can explore concepts without becoming frustrated and discouraged by the algebra.”

    Mind you, the idea is not so much to escape from math syntax as much as the syntax specific to this software, which is more understandable.

    But the idea of making a pretty user interface with some buttons, in to which you can simply type a few numbers and click “Solve”, is very much present. And I fear it will only get worse with time.

    And I’m not kidding about the free T-shirts given to instructors. This has probably sold more copies of the software than any number of glossy brochures or glowing testimonials.

    - saforrest — 1/31/2005 @ 1:56 pm

  20. Pretty interfaces with ’solve’ buttons are fine as long as the user could solve equations if they wanted to, but just don’t want to.

    That said - free t-shirt?? I take back everything I said in this post. Hook me up!

    - Moebius Stripper — 1/31/2005 @ 6:51 pm

  21. Typical conversation with my dad (have had this more than once!):

    Dad: Hey, Beck, do you need a calculator?
    Me: I have a calculator. I have a class set of calculators.
    Dad: But those are scientific calculators.
    Me: And solar, too!
    Dad: I have an extra TI-9999999!!*+. Do you want it?
    Me: No.
    Dad: Don’t you need one? What about if you need to graph something in class?
    Me: The most difficult functions my classes see are lines with integer coefficients. I can graph those faster by hand.

    - Rudbeckia Hirta — 2/1/2005 @ 5:34 am

  22. Oh, forgot to say: TI has this pyramid scheme that my dad keeps trying to get me hooked up with. They run seminars about how to run a seminar on how to become a calculator-trainer. Once you take their seminar, you can run them for schools. And if the students in a class save the proof-of-purchase from their calculator, the teacher can get free stuff.

    - Rudbeckia Hirta — 2/1/2005 @ 5:35 am

  23. TI also offers goodies to math departments that mention their calculators in course syllabi. You can get projection screens and other useful classroom stuff (useful if you’re making calculators an important part of your courses). I’m not sure how TI decides how much largesse to bestow upon you, but I seem to recall that they like to get head counts of the students enrolled in the sections whose syllabi encourage TI calculator use. (”And now a word from our sponsor…”)

    - TonyB — 2/1/2005 @ 7:35 pm

  24. […] ousand trig integrals, and didn’t mediate every concept through a Maple program or a TI83+. In other words - […]

  25. […] 2 am.

    A few weeks ago, I wrote about the wholly indefensible ubiquity of the TI-83+ graphing calculator […]

  26. […] anent Link: “> I had been putting off writing about this until I found this post. I have yet to read […]

    - eon » Blog Archive » — 3/24/2005 @ 9:17 pm

  27. I agree that graphing calculators are inappropriate in almost all classes at the high school level– certainly anyone who claims to know calculus should be able to take derivatives and integrals by hand, and anyone who claims to know algebra should be able to solve systems of equations by hand.

    But graphing calculators have real uses:
    - in my circuits class, we had to solve systems involving up to dozens of variables; why would you *want* to do that by hand? The students without graphing calculators quickly corrected their folly.

    - in electromagnetics courses, there are a lot of weird integrals to evaluate, all of them doable by hand. I enjoyed doing them by hand to get the practice, but it’s nice to know that you can check your results versus a graphing calculator’s.

    - in the systems course where we did a lot of Laplace transforms on circuits, we had to do change large rational functions into sums of proper fractions. Graphing calculators were basically required, certainly to find the roots of the functions, and they also made finding the appropriate expansion go much quickly.

    I think the same can be said for any field of engineering.

    Personally, I think that once the student has completed the classes which involve the theories the calculators use to do what they do— algebra, trig, calculus, maybe linear algebra— that it should be up to them whether or not to use the calculator to avoid hand calculations.

    - Alex Gittens — 4/1/2005 @ 7:20 am

  28. Alex, I don’t think this conversation was saying that engineering students who know how to factor, add, divide, and what not should not be able to use graphing calculators. Introducing them to early can make students calculator depended which is not the ideal.

    Btw, TI-89 can not only solve for improper integrals, but they can also communicate with each other.

    If a student was really handy with any graphing calculator, they could program the calculator to use input values to solve equations for them - but students don’t read the manuals that come with the calculators.

    Most students don’t understand how a calculator does what it does, but they use it anyways.

    I, for one, am not against technology, but I never understood why professors let students use calculators on exams when, if you know what you are doing, it makes it easier for them to cheat (think about it, you don’t even have to program it but leave notes for yourself where there’s supposed to be a program). Let alone why students can use calculators on the AP exam, where if they’ve been paying attention in class they have a definite advantage.

    - V.

    - Vanes63 — 6/17/2005 @ 7:42 pm

  29. This comment thread is old, but I have an amusing related story. When I took Algebra I in university, the prof told us the only calculator we were allowed on the final was an abacus. :-) My friend and I actually went out and found ourselves an abacus each, just because we could…

    - parodie — 7/17/2005 @ 4:13 pm

  30. Hey - I used a sliderule… not just because I could (and this was in 1989, so no smart remarks about age), but because my sisters kept stealing my calculators. They never took the sliderule, which was our dad’s.

    I wonder where I put it. I still have the instruction book for the sliderule.

    - meep — 7/18/2005 @ 11:20 am

  31. I teach a high-school Calculus class (non-AP) in New York City and we used TI-83’s the first year I taught it, though it became apparent rather quickly that too many of the students would turn to punching numbers into the calculator to see if an answer may magically appear before making the slightest attempt at thinking through the problem on their own. One student never quite got past using a series of decimals to find limits (e.g. finding f(0.1), f(0.01), f(0.001) and so on to find lim f(x) as x –> 0) and never grasped finding derivatives by the limit process.

    Starting with the second year I taught the class, I’ve banned calculators outright for tests and quizzes, with the added suggestion that they not use them unless absolutely necessary on homework. They complain a lot (”Hey, how come we can’t use calculators when the class is called calculus?”), but I think they’ve learned a fair bit more as a result.

    - misunderstruck — 7/26/2005 @ 1:04 pm

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