Mike Croucher raises an important point for teachers: Are graphical calculators pointless? I think they are. I resented having to buy my daughter an expensive calculator when I could have bought her a netbook for not much more money.
Calculators are obsolete. I can’t remember the last time I used one. On the other hand, it could be valuable to have students use something really obsolete: a slide rule. Not for long, maybe just for a week or two.
- Slide rules are basically strips of log-scale paper. If you play with a slide rule long enough, you might get a tangible feel for logarithms.
- Slide rules make you concentrate on orders of magnitude. A slide rule will give you the significant digits, but you have to know what power of ten to use.
- Slide rules give you a tangible sense of significant figures. You can’t report more than three significant figures because you can’t see more than three significant figures. Maybe some experience with a slide rule would break students of the habit of reporting ever decimal that comes out of their calculators.
I’m not saying that being able to use a slide rule is a valuable skill. It’s not anymore. But the process of using a slide rule for a little while might teach some skills that are valuable. It would be fine if they forgot how to use a slide rule but retained an intuition for logarithms, orders of magnitude, and significant digits.
I’d recommend using a slide rule in high school for the same reason as using an abacus in elementary school: because it’s tangible, not because it’s practical.
Interesting. I did almost exactly what you recommend: use a slide rule for about a week. To be fair, this was in high school, which was starting to be a long time ago now. On the other hand, I still use my calculator almost daily. (A TI-92+, purchased shortly after the slide rule experience.) There’s just something about it that I love – I know how to use a computer to find the answers to most of the problems that I want, but using that calculator is fast – I know where every button is, I know what the various function names are, and I don’t have to leave the window that I’m working on with the computer.
I’m sure that familiarity is part of the problem. That calculator is powerful and I can make it do whatever I want in a heartbeat, so why use something else? The other part of the problem may be that I don’t have any software that I like using for these problems. I’m partial to MATLAB, but let’s be honest, it’s cheaper to by a calculator, especially if I want any toolboxes. MATLAB also spoiled me with it’s GUI – Octave is very similar (and free) but I just haven’t been able to find a GUI that I think is worth the effort (XOctave is the best I’ve found.) I’ve always wished that I had the time to learn Mathematica – but if you thought that MATLAB was expensive . . .
So I guess I have a question for all of you out there: what software do you use for serious math work? What should I be stacking up against my trusty TI?
-Ben
Ben: as far as software for serious math, I use a combination of Python, Mathematica, C++, and C#. For quick calculations I’d use Python. For simulations I’d use C++ for maximum speed or C# if I need to interface with .NET software. I mostly use Mathematica for symbolic computations and plotting.
I bought one when I was in college. I played around with it a little bit, but it’s decoration now.
Sorry, I didn’t specify: that comment could refer to a slide rule and a graphing calculator, though I bought my calculator in high school.
@Ben — Pondering your question, I reliazed that it has been a donkey’s age since I used any mathematical sofware that costs money, unless you count Excel. They don’t buy mathematical software at work and I can’t justify the expense for personal use.
In addition to everything else, check out:
http://www.wolframalpha.com/
If you have not played with it you will be shocked at what all it can do, and for free. I’m guessing that it does 99% of what people use Mathematica for, although I have never used Mathematica myself. I especially like the symbolic manipulation and series expansions. The automatic graphing is nice, too. Just type in Joe Random Expression and hit the button. For you iOS junkies out there, “There’s an app for that!” Cheap, too.
When teaching is hard to beat a physical tool to explain abstractions, so I agree with the use of a slide rule. For quick calculations and understanding concepts I use R: I can build toy examples and see what is going on in each matrix.
I use Python (or R) to call external functions (either in C or Fortran) for simulation purposes. Pen and paper for symbolic stuff, but I hardly do that anymore.
I keep a Pickett slide rule (larger than the one in the illustration) on my desk. I use it regularly and demonstrate it to students if they even hint at the slightest interest.
In addition to orders of magnitude, slide rules force one to think through a calculation and choose a better order.
Pickett sliderules went to the Moon.
Thanks for the reminder of my youth. I bought my first electronic calculator in 1974, when I was in high school, but for a couple of years before that I used a slide rule.
I completely agree that it’s a useful teaching tool, for the reasons you give, so I’ll have to find a place where I can buy one. (Alas, I lost mine way back then, which is part of the reason I bought my first calculator.)
There’s an app that emulates an HP48 for android phones, making standalone scientific calculators completely useless for me.
Personally, if I were to teach I would prefer to use the simplest equipment such as slide rules and graph paper, as much as possible, and jumping from there to python or mathematica. The purpose of education is to get students to learn, not to churn through material at varying levels as quickly as possible, I feel simpler methods facilitate that better.
Ben: ¿Serious Math?, I use (since 1976) Fortran, now Fortran 2003-2008, (gfortran is free). It´s far easy than C, C++, C#, and Python is OK, but I’m used to play Fortran. By the way, I had never used Mathematica, Matlab, Octave and the like, because I don´t need them, they are worthless. Excel is a social need, all the people in my area use it, so…
But I must to say that the important is the knowledge of problem solving. I’d passed almost all my examinations at the university with a slide rule, you had to be capable to solve a three level concrete building in three hours, with simplified methods, and design columns, slabs, beams and foundations (one of each) to pass the concret II assignature. Today you cant do that without a program, nither you can do one, and solve the problem in that time. My favorite Slide Rule was the pocket Faber & Castell with double W scales, now it costs $189. USD! (Santo D’Agostino: http://www.sphere.bc.ca/test/pocket.html) (sorry for my english, It´s my second lenguage ;) ).
I second the comment about WolframAlpha. Forget the Netbook, a phone is all you need these days! Android and iOS have WolframAlpha apps, which can do pretty much anything Mathematica can, for only a few bucks. It beats the pants off my TI-89 for anything I ever used it for. Not to mention that it does a much better job of teaching you WHY the answer is what it is and showing you additional information (like expansions for integrals). I imagine that over time, a collection of apps will replace all the functionality of any graphing calculator at much improved graphics and speed. I’d also be willing to bet that WolframAlpha alone includes more information than a single person could ever know or calculate in a lifetime.
Are typos (like in the first sentence of the article) part of the learning curve too. I get so distracted sometimes by foolish things. I still have a few trig tables (sin, cos, etc) that I like to look at. They give you a sense of what the values really are.
I agree with you. Graphing calculators are too expensive with no apparent reason. A netbook is a much better purchase because there are so many graphers available online! Wolfram alpha is a great one as @John V. mentioned before. Check out http://www.onlinefunctiongrapher.com if you want an interactive interface which is great for educational purposes. Some friends and I have written it so people won’t have to buy graphing calculators. Love to hear want you think guys.
I have had a succession of calculators since the mid ’70s; all have eventually died (buttons dropped off / can’t get replacement bateries etc); but my British Thornton slide rule that I got in the early ’70s is still fully functional (I had to replace the movable cursor after a somewhat ham-fisted individual used it). It has scales for e^0.01x, e^01.x, e^x, x^2, 1/x, x^3, sin x, sin tan x, tan x and (of course), two x scales.
The only scientific calculator that I use today is an HTML one that I wrote in the late ’90s. Its advantage is that it is quicker to fire up the web page than to delve into the desk and extract the slide rule from its plastic sheath.
The slide rule taught me the relevance of significant digits, the importance of knowing what you were doing with a calculation and the reality of log scales. Which is something that neither a computer or a graphing calculator does well. A circular slide rule also helped immensely in chemistry as it made proportions simple.
A slide rule is actually a form of analog computer. I started using one in High school. That made me a nerd as I was one of very few who had one or could use one. Then in college – mid 1960s they were required. I still have several tucked away in boxes somewhere. As for daily use, I have an old four function calculator that sits beside my computer and is used daily. It is quicker to use the calculator for simple math (arithmetic) than to call up the calculator function on the computer. Of course, for more complex math the computer is the best thing – yet.
Calculators obsolete? I use one several times a week at work. Outside of work, not too often.
Here is a link to a great on line slide rule simulator.
http://www.antiquark.com/sliderule/sim/n909es/virtual-n909-es.html
Excellent blog, and I found myself agreeing with most points. One thing, though, I noticed that slide rules didn’t really help understand significant decimal places. Even when folks lost all but two at the high end of the scale, they again squinted for three (that they really didn’t have anymore) at the low end of the scale. Whereas using a calculator, the decimal places are handed to you without effort, and its easier to teach good students to ignore what should be ignored. It seemed to be harder to give up hard-won decimal places obtianed by squinting than easy-come-easy-go decimal places given by a calculator.
Of course, this was only my own observation in EE classes during the mid-1070s when slide rules were the norm but scientific calculators such as the TI Programmer and venerable HP 35 (which just said Hewlett Packard and didn’t mention the model number until the HP 45 came out) appeared and came into wide use.
But that’s a small issue; your points are well-made and brought back a lot of memories!
I used a slide rule from third grade through my sophomore year of college. The thing I still use my slide rule for is ratios. When I set the ratio I need, the pairs of numbers to make that ratio pop out all along the scale. Gives a good feel for them.
Pilots still carry the E6B. It is essentially a circular slide rule, with printed scales that help calculate fuel burn, wind correction, time en route, ground speed, etc. The majority of flight schools still require that the students learn how to use it.
our brains, like our bodies, are being degraded by technology. like what we are seeing in our world economy the extreme rich and extreme poor. we will have the extreme smart and extreme stupid with nothing in between. the brain, like our bodies needs to be exercised and requires us to do what was once considered mentally back-breaking on a consistent basis to maintain our mental health – therefore, i would argue the slide rule, math tables, interpolation, and reading real books with depth and substance like the classics and even fiction should be part of our culture and lifestyle forever. otherwise, we will have a society and world that will be torn apart forever.
John,
Hate to hijack your blog here. In regards to those who use software for math, I’d like to point to a free program I started using after being introduced to MATHCAD, MATLAB, Mathematica, and Maple. I was raised on a TI-83, later switched to TI-89, and in college discovered the power of those aforementioned programs. Only 10 years later did I discover Maxima (!), a free cousin of Maple that has a GUI and many plugins. It is free, and just as powerful as the commercial titles. It’s worth a look if you’re a student, ans especially if you’re a teacher.
This is a really good idea. Students need to learn the hows and whys of math for it to be of any practical use to them. At least using a slide rule for two or three weeks would get them to actually think about what they are doing, rather than simply parroting the numbers churned out by a calculator.
For anyone interested in buying a slide rule, Thinkgeek has one:
http://www.thinkgeek.com/gadgets/tools/be12/
You can get better ones on ebay, although they’re mostly 20+ years old now.
I’m totally on-board with the author’s take on teaching the slide rule. I intend to do just that with my grandkids at the appropriate time. As for me, my trusty HP32S sits on my desk, always at the ready, more convenient than digging my iPhone out of my pocket, and the batteries last years, if not decades. Ditto my HP15C on my workbench at home.
XKCD had a great comment on (TI) graphing calulators:-
http://xkcd.com/768/
I think students should graph by hand. It gives a better feel of what the function is doing.
If you are running on a MicroSoft OS I would highly recommend MicroSoft Mathematics 4.0 Download here. It’s free and quite well done.
Interesting idea. I have never used a slide rule, in fact I don’t think I’ve ever been close to one (I don’t know why, maybe they’re not so common here in Spain?), but the tangibleness of it could be really useful as you explain in this post. As for using a calculator… I do have one old, expensive HP… that I never use. When I need to calculate something, I open up a terminal window and start gp/pari (my calculator of choice, I also do some programming when I need high precision arithmetic). Occasionally I use my Ben Nanonote with either pari or yacas as a kind of “pocket calculator”.
Cheers,
Ruben
Yay, slide rules! I still have both of mine, tho’ I have to say I haven’t used them since physical chem Some Time Ago. But I think there’s a good idea in here about exposure to the physicality of maths.
That said, good graphing calculators take up a hell of a lot less space on a lab bench than a netbook and therefore are not obsolete to my mind. And I write code on mine, so it mostly is a netbook – just smaller and with weeks to months of battery life. What’s not to love?
I forgot to bring my calculator to an organic chemistry exam once. Luckily, I had a slide rule in my backpack (mostly for sentimental reasons — it was my dad’s when he was in college). Since most of the math in organic chem is doing things with pH, the ability of the slide rule to do logs was a great help.
It also came in handy for some quick math aboard a boat, where I would not have wanted to take an expensive calculator that could get wet and ruined.
I have no idea how to use a slide rule. Nor an abacus. I kind of wish I knew. But I did learn a lot about the basics of programming via a TI-86.
No they are not, for several reasons:
1 – Graphical calculators are not for log plotting only. If you don’t know, research about the endless possibilities for calculations on a very productive and pocket device. As an engineer, it’s been handy forever.
2 – In college professors don’t usually allow you to take the exams with a laptop/netbook over the desk.
3 – They are specialized on their tasks. Plotting functions are just the tip of the iceberg. So they are useful for what they are made for. If you’re just doing simple math though, of course it’s a waste of resources.
I agree that the slide rule and abacus can both teach a lot about mathematical concepts and they should be part of a required high school curriculum. On the other hand, finger math is another form of abacus calculations where you always have the abacus with you.
I remember my Junior year and first year at a university. I’m taking required courses for my Mechanical Engineering degree.
Mom, Dad, OK, the HP 35 just came out last year and has dropped $100, so it’s only $300, and the HP 45 has just come out and is $400. TIs are substantially cheaper, but I need to survive this semester. It’s ridiculous to buy a $400 HP45, but it is the only tool that does this one calculation that I have to do, closed book, in a timed test.
To give you an idea how expensive that was, 2 years later, I was told to keep my mouth shut about my $12,500/yr salary because it was so much higher than the rest of the people around me were making. That HP cost about 150-200 hours of cannery work the summer before I bought it. Almost a month of the 3 months a year I could work.
Someone made a good point discussing this post on Reddit. rhlewis says
I worked for a concrete/gravel company in the late 90s and slide rules were still in wide use for calculating material usage for planning pours. I’m no longer in the industry but I googled a bit and it appears that they are still in use. Much like an abacus they were incredibly fast in the hands of a skilled user and provided tangible feedback on the calculation.
Calculators are obsolete ? Yeah, right.
Show me a computer that can COMPLETELY boot up the OS of choice in the same fraction of second that takes ANY calculator to be ready after you press the “ON” button and I will throw mine away as fast as I can.
Oh, by the way, not having to find the right icon ( or menu entry ) and watching some HD led flashing ( not to mention the hourglass or whatever ) would be a must to.
Not having to find wherever the calculator window went because you started something else ( or minimized it, or forgot that you had more calculations to do and closed it, or some program opened a pop-up or an “always on top” message box, or some other computer annoyance I forgot )
would also be sweet.
And last but not least, a computer that can run years on a power cell the size of my thumbnail or some AAA battery wouldn’t be bad …
THAT is what I call tangible AND practical.
Agreed with the slide rule thing thought. My only remark is that can take a bit more than two weeks to develop any intuition, especially for the non math-savvy.
I’ve occasionally amused myself by making a slide rule (integer ruled only) out of strips of notebook paper — you start out by picking an interval for log(2), and then interpolate. At some point I might try figuring out a more reliable procedure for getting the intermediate values right. With the right background, it could be a nice classroom activity to teach logarithms, too.
Such memories! I remember the last year I used a slide rule — I was a freshman in college (1978) and everyone made fun of me for being the last guy to get a calculator. Actually I had a calculator, but the slide rule was often better and easier. For example, in physics lab, calculations often involved multiplying a lot of numbers by the same constant. I simply put the constant on the slide rule and read off all the products. It took much longer for everyone else to punch in number after number. I definitely agree with your point, John, that slide rules give a good feel for digit significance, much better than rules about counting digits which aren’t always accurate.
As for the abacus, I teach that to my kids around 2nd grade. It gives them a wonderful understanding of how multi-digit addition and subtraction works, much better than paper and pencil algorithms. They’re a lot more fun for the kids too!
Many moons ago when I was in high school, we had a slide-rule quiz every day in physics class. I don’t think I’ve used it since – would have to re-learn it. It does seem pretty much pointless now, but it would offer people a look into the past and what ‘technologies’ we had at our disposal. Maybe not take what they have now so much for granted.
I’m doing my thesis on the difference in using a sliderule versus an electronic calculator in freshmen high school science classes. I’d be interested in any studies anyone has done before on this or just your anecdotal impressions.
In the mid 70’s I had an electronics teacher that I still appreciate for making us use slide rules. That is when I really learned how the reactances of various electronic components interact. Before that I was just putting numbers into memorized formulas and didn’t need to know how it worked. After his class I could understand how a circuit worked. I probably would have had my epiphany without the slide rule, but I feel it helped to bring me to it.