How old am I? I remember when there weren’t any electronic calculators. I remember when the mathematical shortcut of choice was the slide rule (I still have two of them available should a massive EMP wipe out all electronic access). Then came the late-mid 70s. My dad brought home one of the first electronic calculators, an HP model that required reverse-polish-notation (RPN) to enter calculations (instead of entering “4″ then “+” then “3″ and finally “=”, you entered “4″ then “3″ then “+” then “enter”). It was heavy and bulky by today’s standards, and it sported an eight-character LED readout. But it was most certainly WOW-licious. This four-function beauty with (I think) one memory cost *only* $350 (in 1970s dollars).
It didn’t take long before affordable models became available. My first calculators were the original Texas Instruments TI-30 (under $100!). They came at just the right time, too… my last two years in high school math consisted of Math Analysis and Calculus. Though there was some initial resistance, it was soon apparent that the calculators would allow us to learn more higher math because we weren’t wasting time doing tedious arithmetic calculations by hand. Thank heavens for the calculator. It made those classes so much more enjoyable.
This isn’t to say that I didn’t revisit hand calculations in college. No, not in the regular math classes, but in my boolean logic and microcode computer classes. We had to be able to convert to/from binary, octal, hexadecimal, and decimal number systems and do math with all of them. Calculators, even the ones capable of doing programmer math like this (though none to the precision needed), were verboten. How tedious was this multi-number-base math? Well, I finished our final, scheduled for two hours, in three hours and ten minutes…and I was the second one done by just a minute or two…talk about your tedious.
It may surprise some to find that I think that calculators should be banned from math learning until students start doing trigonometry. Is it just because I didn’t have that resource? No. Actually, it’s because I think there are some basic skills that as a productive citizen you need to learn. Arithmetic is one of those skills. You need to learn how to add, subtract, multiply, and divide (yes, even long division) by the same old methods used for millennia. It’s simply a basic skill the same as learning to read via the phonics method is a basic skill. In order to be functionally numerate, you need to be able to do arithmetic.
Nowadays, kids are allowed calculators even as early as kindergarten, and I think that’s simply wrong. The argument goes that it allows the math-challenged to learn higher math concepts without having to endure the tedium of basic calculations (with their inevitable errors). Poppycock. I use as an example, my checkbook. Because I use calculators and computers so much now, I’ve gotten lazy and balance my checkbook with electronic aids even though it’s just simple addition and subtraction. Do you hear me, ADDITION and SUBSTRACTION, people. Thing is, when I don’t have a calculator available, I still have the ability to break out of my laziness and do the calculations. Or when I’m at a hardware big box store and need to figure out how much carpet (say) I need to get and how much it will cost, I can do a fairly accurate rough calculation in my head simply because I carry the tools with me (yes, I could use the calculator function on my cell phone, but the interface is clunky enough that I don’t want to unless I need to be very accurate).
I’ve have the skills available to me to continue on even if every calculator and computer disappeared. I’m pretty sure that a lot of the children and young adults who have never not had a calculator will be in a more desperate state.
And while I’m here, let me put in one more push to insist that ALL mentally-able US youngsters be required to be numerate through basic trigonometry. I will agree that any math beyond that is either going to be for task-specific purposes or showing off. Despite the scary words of “algebra” and “trigonometry”, these are basic useful mathematics skills. While I can’t remember the last time I really needed to handle imaginary numbers or to calculate an integral for a real-world purpose, I have had to use trig.
Most recently, I wanted to calculate the amount of paint I needed to buy to paint my house. Not wanting to climb up to the peak of my roof to measure it, I instead used a stick and a protractor to calculate the heights I needed. With those angles, combined with the ground measurements, I was able to accurately calculate the outside paintable area of my house in just a few minutes without ever having to leave the ground. (Yes, I did use a calculator to speed things up, but I could have just as easily used the trig tables in the back of one of the math books I still have).
I used to hate hate hate all those silly word problems in my math books for calculating the height of a flagpole based on nothing but the length of its shadow and the angle of the sun. In the real world, that doesn’t seem so silly anymore. Yes, you could climb the flagpole, or I could have taken a ladder up to my roof’s peak, but things aren’t always so accessible. Sometimes you need to figure stuff out on paper without the ability to measure hands-on. Most people just don’t bother. Me, I have the trigonometry tool in my toolbox, and I can use it whenever the need arises.
So kids, stop fighting math. It really isn’t very difficult if you don’t make it difficult. You learned to read (well, most…er, many of you learned to read), and that’s so much harder. Learn how to add and subtract. Memorize (yes…there’s no better way to do it) your multiplication and division tables up through the twelves. Once you have those, the calculator becomes a tool to make your life easier instead of a crutch you have to have because there is no other choice. I know it’s hard to believe, but once you have this skill in your brain, math actually becomes kind of fun… as most things are when you are no longer scared of them.
But what of the calculator? I say once you have the basics down, use them for all they are worth. Learn as many functions as it has to be able to do the stuff you need to do. Simple four-function calculators can get you by most problems, and are so inexpensive they are essentially disposable. While the fancy graphing calculators are nifty, honestly, for day-to-day stuff, you really don’t need one. Sticking with an inexpensive calculator with trig functions will see you through just about any problem you’re likely to come across. What do I use? Well, since I still do number-base math and stuff, I had to seek out multi-function calculators that allow me to also work in binary and hexadecimal. Back when computers were new, in the 80s, they were easy to find. Now, I think I have examples of the only two models still in production (plus my PDA with conversion software, of course).
To Texas Instruments, I raise my metaphorical class to you in toasting what is arguably one of the most useful tools available to mankind… even more generally useful than the personal computer. Y’all done good, and I thank you.