## Guest Post: Bring Back The Slide Rule!

*This is a guest post by Gary Cornell, a mathematician, writer, publisher, and recent founder of StemForums.*

I was was having a wonderful ramen lunch with the mathbabe and, as is all too common when two broad minded Ph.D.’s in math get together, we started talking about the horrible state math education is in for both advanced high school students and undergraduates.

One amusing thing we discovered pretty quickly is that we had independently come up with the same (radical) solution to at least part of the problem: throw out the traditional sequence which goes through first and second year calculus and replace it with a unified probability, statistics, calculus course where the calculus component was only for the smoothest of functions and moreover the applications of calculus are only to statistics and probability. Not only is everything much more practical and easier to motivate in such a course, students would hopefully learn a skill that is essential nowadays: how to separate out statistically good information from the large amount of statistical crap that is out there.

Of course, the downside is that the (interesting) subtleties that come from the proofs, the study of non-smooth functions and for that matter all the other stuff interesting to prospective physicists like DiffEQ’s would have to be reserved for different courses. (We also were in agreement that Gonick’s beyond wonderful*“Cartoon Guide To Statistics”* should be required reading for all the students in these courses, but I digress…)

The real point of this blog post is based on what happened next: but first you have to know I’m more or less one generation older than the mathbabe. This meant I was both able and willing to preface my next point with the words: “You know when I was young, in one way students were much better off because…” Now it is well known that using this phrase to preface a discussion often poisons the discussion but occasionally, as I hope in this case, some practices from days gone by ago can if brought back, help solve some of today’s educational problems.

By the way, and apropos of nothing, there is a cure for people prone to too frequent use of this phrase: go quickly to YouTube and repeatedly make them watch Monty Python’s Four Yorkshireman until cured:

Anyway, the point I made was that I am a member of the last generation of students who had to use slide rules. Another good reference is: here. Both these references are great and I recommend them. (The latter being more technical.) For those who have never heard of them, in a nutshell, a slide rule is an analog device that uses logarithms under the hood to do (sufficiently accurate in most cases) approximate multiplication, division, roots etc.

The key point is that using a slide rule *requires* the user to keep track of the “order of magnitude” of the answers— because slide rules *only* give you four or so significant digits. This meant students of my generation when taking science and math courses were continuously exposed to order of magnitude calculations and you just couldn’t escape from having to make order of magnitude calculations *all *the time—students nowadays, not so much. Calculators have made skill at doing order of magnitude calculations (or Fermi calculations as they are often lovingly called) an add-on rather than a base line skill and that is a really bad thing. (Actually my belief that bringing back slide rules would be a *good thing* goes back a ways: when that when I was a Program Director at the NSF in the 90’s, I actually tried to get someone to submit a proposal which would have been called “On the use of a hand held analog device to improve science and math education!” Didn’t have much luck.)

Anyway, if you want to try a slide rule out, alas, good vintage slide rules have become collectible and so expensive— because baby boomers like me are buying the ones we couldn’t afford when we were in high school – but the nice thing is there are lots of sites like this one which show you how to make your own.

Finally, while I don’t think they will ever be as much fun as using a slide rule, you could still allow calculators in classrooms.

Why? Because it would be trivial to have a mode in the TI calculator or the Casio calculator that all high school students seem to use, called “significant digits only.” With the right kind of problems this mode would *require* students to do order of magnitude calculations because they would never be able to enter trailing or leading zeroes and we could easily stick them with problems having a lot of them!

But calculators really bug me in classrooms and, so I can’t resist pointing out one last flaw in their omnipresence: it makes students believe in the possibility of ridiculously high precision results in the real world. After all, nothing they are likely to encounter in their work (and certainly not in their lives) will ever need (or even have) 14 digits of accuracy and, more to the point, when you see a high precision result in the real world, it is likely to be totally bogus when examined under the hood.

Oh, I agree *soooo much* with the whole calculus/prob/stat approach to high school math. Fascinating stuff for all students even the best, motivating stuff for the others, and real life applications for all. Maybe some day…

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For training future scientists and engineers, whose existence is fundamental for a prosperous society, it is essential to teach calculus and linear algebra as early as possible.

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I wasn’t advocating not teaching this stuff to them, students going into those fields could do the stat/probability sequence very quickly – many in high school. Then, they take the more traditional sequence afterwards-and probably it would be a better sequence as a result of the knowledge they gained in the unified prob/stat/calculus sequence. They still need to no about distribution shapes and statistical tests: everybody needs to understand that stuff and not all engineers do either. I have a PHD in math but I learned a fair amount of stuff in the statistics part of the business math course the first time I taught it.

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I do miss my old slide rule. Sadly, it did not survive a year in a box in the attic while I was on sabbatical.

And re absurd precision: I recently stayed in a hotel whose web page very sensibly gave the hotel’s coordinates in addition to other ways of explaining its location. The coordinates were given with an accuracy corresponding to 10 cm, which made me worry (1) that this would be such a small hotel, the rooms would be really cramped, and (2) equipped with a GPS receiver that is only accurate to within a couple of meters, would I have trouble finding the hotel? This problem is akin to the common pastime of geocaching, but you don’t expect an entire hotel to be geocached.

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So… I reserved this Opinion article from NYT: http://www.nytimes.com/2011/08/25/opinion/how-to-fix-our-math-education.html?module=Search&mabReward=relbias%3Ar

A quote: “Imagine replacing the sequence of algebra, geometry and calculus with a sequence of finance, data and basic engineering.” Hmmm. Wouldn’t that be fun?

Thanks for the post!

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Bring back the abacus! (Actually, sorobans are still around, and cheap. :)) And I do mean for elementary school. No more confusion about carrying the one.

Good point about order of magnitude calculations. 🙂 Kids can get a head start, also in elementary school, by learning to be good guessers. (Being a good guesser helps on standardized tests, too. ;))

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To be honest, I think you’re treating the symptoms and not the cause. Revising the topics covered in calculus courses is for me like pushing the chairs around the Titanic (to use an overused cliché). The core problem is how poorly math is taught, not just in the secondary schools but *in the universities*.

And, to be clear, this is not the fault of the secondary school teachers themselves. Without proper training and guidance, they have no choice but to teach math as best as they can based on the way they were taught themselves as well as the textbooks and curriculum they are forced to use. Even if the curriculum design is great, the execution by for-profit publishers is more often than not a travesty. Moreover, if the teachers aren’t properly guided or trained on how to teach the curriculum most effectively, how can we expect even good teachers (who might be skeptical or even resentful of what’s being imposed on them) to do it all well?

On the other hand, there are no such restrictions on university teachers (professors and contract faculty), but the teaching is no better (and maybe even worse). Here’s where new ideas and approaches for teaching calculus should be tried and developed. Unfortunately, math professors turn out to be just as good or better than anyone else in killing any kind of new initiatives to improve the situation.

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I too am of that age, and I vividly recall the day in Mr Bateman’s class when multiplying by adding logarithms via first Napier’s bones and then a proper slide rule suddenly clicked. Thanks for the post. Maybe I should try and find one, not that I have any use for it any more, other than to bamboozle the youngsters.

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“we discovered pretty quickly is that we had independently come up with the same (radical) solution to at least part of the problem:”

Interesting post. And, the solution offered here might indeed solve part of the problem.

Unfortunately, I believe at best it would solve only a very small part of the problem.

Because I believe the major part of the problem is the inability of most math teachers (from grade school through graduate school) to explain things clearly.

I like the way mathematician Gian-Carlo Rota expressed the idea in the book “Discrete Thoughts”:

“Gifted expositors of mathematics are rare, indeed rarer than successful researchers. It is unfortunate that they are not rewarded as they deserve, in our present idiotic pecking order.”

The ability to understand math and the ability to explain it are two completely different abilities. Out of approximately 25 brilliant professors I took courses from in graduate school at the University of Maryland, I encountered only two who had the ability to explain the concepts of their course. Yes, the others had the ability to state the facts, but that’s quite a bit different than giving one insight into the material. The situation in undergraduate school was about the same.

In high school the situation was about the same as far as the ability to explain was concerned. But, it was worse overall, because these teachers didn’t even understand the material that well. This, on top of not having the ability to explain, is the worst case scenario, and it is common.

As a retired actuary, I have spent 15 years tutoring high school students in math. Most of my students are bright mathematically, but encounter difficulties because their teachers are so bad.

So, until we somehow address this problem of basic teaching, the “horrible state” of math education is going to remain, with or without slide rules.

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Ouch. Please don’t make sweeping assumptions that all HS math teachers are “so bad.” Having been on the teacher side, the student side, and the parent side, teachers get a worse rap than most of them deserve. My children had the unfortunate experience of my working as a math coach in their elementary school… At home, there were times they asked for help with their math homework. SEVERAL TIMES, their defensive response was, “the teacher never taught me that.” Unfortunately, I knew that they HAD been taught that~ often times introduced in third grade, taught in fourth grade, extended contexts/skills in fifth grade (think fractions, for example)~ so even if they had a crummy math teacher in fifth (which none of them did), they had seen the material before.

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Just because kids may have seen something in a textbook does not mean that they had been taught it. How many elementary and middle school teachers are good at math? My guess is a smaller percentage than the general population, because those who are good at math do other things, on average. And that matters, even in elementary school.

In elementary school my girlfriend was asked to add 48 to some other number in front of the class. She added 50 and then subtracted 2. The teacher told her that she was doing it wrong. The teacher was doing her best, bless her heart, but she was not good at math. She was teaching what she had been taught, and what was in her teacher’s guide. (BTW, students who learn on the soroban are going to add 50 and subtract 2, as well. 🙂 Or maybe add 40 then add 10 then subtract 2.)

Now let’s talk about fractions. From what I have read, most adults do not understand fractions. That is true both cognitively and mathematically. If you give people a test with 50 questions and then ask them what percentage they got right, they will overestimate their score, on average. But if you ask them how many they got right, they will not overestimate their score. They are better at thinking about integers. Even many people who can do math with fractions do not understand them. When they talk about ratios they will tend to focus on he numerator and ignore the denominator. Mathematically, if you give the average 25 year old a middle school test on fractions, they will flunk.

To those of us who are good at math, that is incredible. After all, manipulating fractions is on the same order of difficulty as manipulating differences. So why don’t people learn fractions as well? Neither the textbooks, nor the teachers, who can certainly do the manipulations, seem to be doing a good job. When students say that their teacher never taught them , they are probably right.

When I was coming along, the math taught in elementary and middle school was cookbook math. Students were taught recipes to make dishes that most of them found indigestible.

Sorry for the rant, but let me continue. Early in my high school geometry course I approached the teacher before class and showed her a proof from our homework. I told her that my proof was flawed because I had been unable to prove that two specific points were on opposite sides of a certain line. Her response was, “Well of course they are.” Was she a bad teacher? No, she was an excellent teacher, for the other subjects that she taught. Was she bad at math? Well, I think that there was only one other teacher in our high school who was capable of teaching the geometry course. But again, my teacher taught to the textbook, and did not have much of a deeper understanding of geometry. My proof looked OK to her.

At the college level professors are chosen for their ability in their subject, not for their ability to teach it. The best math teachers may well be at the high school level. They are good teachers, and they know some math.

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The only reason for my initial response was this quote from the initial post: “Most of my students are bright mathematically, but encounter difficulties because their teachers are so bad.” Think about the narratives we tell ourselves about learning math in this country: Americans are bad at math; elementary school teachers are bad at math; teachers are bad at teaching math. If you contribute to those narratives based on a hunch or a guess you are doing school children and teachers a disservice.

In the elementary school where I was a math coach, out of 21 teachers, there were 3 that were “not good” at math. And, like Min suggested, they were superior at other things important for student development: character development and language arts, for example. Similarly, there were 7 of those 21 teachers who were masterful at teaching math: recognized more than one way to solve problems, encouraged student discourse, tied conceptual learning in with skill building. I learned a ton from them.

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Hi Katie

“Please don’t make sweeping assumptions that all HS math teachers are “so bad.”

I didn’t make that assumption. I specifically said:

“Because I believe the major part of the problem is the inability of *most* math teachers (from grade school through graduate school) to explain things clearly.”

I have met excellent math teachers at all levels of my math education. But, very few.

Based on my personal experience in all levels of math education, as well as the experience of most people I’ve ever talked to (including the hundreds of bright students I’ve tutored who report their experience to me) it is obvious that very few people have the ability to explain mathematics coherently.

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I’m off the age where calculators became ubiquitous in jr high and high school. Luckily, my dad still had a slide rule about… Although I never calculated anything more complex than a square root… It gave me exactly the intuition you describe for orders of magnitude. The short film Powers of Ten was also a good introduction.

Now you can download a free slide rule app for your phone… I have.

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I still have my Pinker slide rule. Those were the days, when nobody would mess with a geek packin’ a slide rule on his belt, the ambiguity of that tan suade case suggestive of a dagger. HaHA!

For younger folk, be sure to visit the International Slide Rule Museum: http://sliderulemuseum.com

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I still have my old Deci-Lon slide rule, and it works smoothly even after having been alternately frozen and baked in the attic for years. It has ten scales on one side and twelve scales on the other side. I’m pretty sure I still have the instruction book somewhere.

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In 1977, at the age of 16, I received my first calculator. I was saved, just in time, from having to learn how to use a slide rule. The sense of relief has stayed with me ever since:)

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As an engineering undergrad I had great math teachers. (In high school I used logarithms, but never a slide rule.) Don’t understand what the fuss is about..

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I’ve had engineering students punch numbers furiously on the calculator and conclude the moon is 20 mi away.

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I think I was the last to use a slide rule in college (in 75). The profs in engineering used to take points off for too many digits in the answers.

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I still take off points in trigonometry for incorrect significant digits. It’s important that they understand “good” numbers versus manufactured, bogus numbers.

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Can you please explain why it’s so significant to you? I remember that I was taught to write 1/4 in decimal notation as “.25,” without a leading zero. When I wrote “.25” as the answer to a question on a test in a foreign country, the teacher marked the answer as wrong, because he said the correct answer was “0.25,” with a leading zero. The net effect was that I lost all respect for him.

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It’s easier to read when there’s a leading zero.

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Yes, but the answer was still correct. Pedantic teachers are not always the best.

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Totally agreed.

On Wed, Sep 24, 2014 at 12:10 PM, mathbabe wrote:

>

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I’m pretty sure that I taught myself to use a slide rule outside of school. It ended up being

a useful skill when my calculator broke halfway through high school physics and I used

a slide rule for the rest of the semester. It didn’t seem to hurt my grade as I was still

at the top of the class. This was in the late 70s and calculators had already become “essential” in my high school.

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Reblogged this on YMXB.

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Yes, yes, yes! I’m older than phlogiston theory: almost as old as dirt. Back in the day, when I was an alchemy TA, I banned calculators in the physical alchemy lab and insisted on slide rules (we called them “Napier’s bones”), for exactly the reason that Gary Cornell stated. You don’t understand the physics unless you know roughly what the answer will be before you start to calculate it. And besides, the experiments were only accurate to only one or two decimal points anyway. (Titration is hard!) The students took it in good grace–HP-45s were still expensive back then, and everybody had learned how to use a slide rule in high school.

(Oh, note to GPE–slide rules at the belt were phallic, not daggers. Which, of course, shows how pathetic an alchemy TA’s life really was.)

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For multiple guess exams such as AP Chemistry, knowing the magnitude solves more than half of the problems. Knowing 0.301 and 0.477 solves the rest. Who needs a slide rule?

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I have some old school slide rule and ‘computer’ pictures here you might like: http://mikethemadbiologist.com/2014/04/11/how-many-hertz-do-these-computers-clock-in-at/

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How funny, I got to this blog by Googling “grant for teaching using slide rules”. I didn’t grow up with a slide rule, but my Dad did, and he tried to teach me how to use it. Teaching at a community college for 14 years has given me perspective on how many students really don’t have an intuitive, tactile feel for numbers. They’re just something that comes out of the calculator. My father still has a much more accurate feel for numbers than I do!

No hope for an NSF grant for teaching with slide rules, eh? I’ll wander over to the DOEd website and sniff around. Surely, surely, probably at elementary or secondary levels, someone has tried this. Excellent blog!

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