### #1

Posted 24 February 2009 - 05:38 AM

I know all of the benefits of a calculator, but DH and I (who never took calculus) would like DS to learn the subject 'manually' as well as with a calculator (as it is required on the SAT subject test). Everything I've ever read from older engineers is that it is an invaluable skill, but I can't find any programs that still teach it.

Will I just have to find a tutor?

asta

### #2

Posted 24 February 2009 - 06:28 AM

I suspect the last group of people who learned mostly with a slide rule were the people who taught me.

The slide rule is essentially a calculator. You are not actually doing the calculation when you use a slide rule. And you don't actually need any calculation device to do and understand calculus. Neither a slide rule or a calculator will help you actually understand calculus better.

If this type of device is really a concern to you then you need to find a program that can be done without either a slide rule or calculator. I doubt that exists. Most texts contain complex problems which may be found "in real life". "Real life" usually isn't simulated in nice easy to manipulated whole numbers.

### #3

Posted 24 February 2009 - 06:38 AM

Laura

### #4

Posted 24 February 2009 - 07:15 AM

What you might want to do is purchase an older Calculus book that does not have any handy-dandy calculator applications.

As one who had to learn to interpolate values off trig charts, I truly appreciate calculators. But I think they have their place.

Best,

Jane

### #5

Posted 24 February 2009 - 07:42 AM

You'll also need something with instructions on the slide rule itself, because they weren't in the calculus book. Like this site:

http://www.sliderule.ca/

It even has a link to directions for

*making*one.

### #6

Posted 24 February 2009 - 08:02 AM

### #7

Posted 24 February 2009 - 08:31 AM

### #8

Posted 24 February 2009 - 09:59 AM

### #9

Posted 24 February 2009 - 10:08 AM

One exam, at Polytechnique (engineering college), the prof banned all calculators because the programmable ones were coming out, and he didn't want anyone to cheat. He said "too bad, you'll have to calculate by hand, and approximate".

Oh oh.. I can't count. I can't multiply ...

I showed up with a slide rule and an abacus. The prof was speechless. He stood in front of my desk all throughout the exam, and watched me use those 'antiquated' tools. LOL... The rest of the class were free to cheat. I have no idea if they did or not, I was too busy with the prof breathing down my neck.

At the end of the exam period, he told me he'd make me pass just for that. And he congratulated me on having learned what was necessary to me.

### #10

Posted 24 February 2009 - 11:41 AM

Hee hee hee. Thanks for the memories.

One exam, at Polytechnique (engineering college), the prof banned all calculators because the programmable ones were coming out, and he didn't want anyone to cheat. He said "too bad, you'll have to calculate by hand, and approximate".

Oh oh.. I can't count. I can't multiply ...

I showed up with a slide rule and an abacus. The prof was speechless. He stood in front of my desk all throughout the exam, and watched me use those 'antiquated' tools. LOL... The rest of the class were free to cheat. I have no idea if they did or not, I was too busy with the prof breathing down my neck.

At the end of the exam period, he told me he'd make me pass just for that. And he congratulated me on having learned what was necessary to me.

This is AWESOME!

We aren't survivalists by any means, but my little family is very concerned that people have forgotten how to do things without computers. And a battery/solar powered calculator is just that - a computer. We really like knowing how to do things in a manner that would still be possible if an EMP hit the earth.

Call us whack-jobs, but how many people out there (under 45-50 y.o.) could honestly build a building or a bridge w/o a calculator?

It's the little things... :: shrug ::

asta

*(thanks for the ideas about getting a pre-graphing calculator Calculus book. That shouldn't be too difficult)*

### #11

Posted 24 February 2009 - 03:09 PM

-Nan

### #12

Posted 24 February 2009 - 05:37 PM

My assumption is that when you get to calculus, you understand basic math and algebra. Using a simple calculator or slide rule can allow you to practice the calculus more, because you won't be spending as much time on the basic math. You want to practice the calculus problems a lot (at least I needed to). Using a calculator or slide rule allows you to spend more time on the actual calculus.

I'm curious. The OP said that neither she nor her dh had had calculus. Is her ds going to do this completely on his own, with no one to question. That would show real discipline I think.

### #13

Posted 24 February 2009 - 06:22 PM

### #14

Posted 25 February 2009 - 04:44 AM

The fact that neither of us ever took Calc is the whole reason I'm looking for a

*program*. I had horrific maths instruction growing up (I actually took college Algebra, but that was a long time ago, and much of what I did was strict memorization, not comprehension). As a result, I have found great programs for kiddo, and am doing work along with him so that we'll be at the same "level" by the time he gets to Calc.

It just seems so absurd to me that a calculator would be required for Trig or Calc. I understand that it is a tool, and that it could enable him to do certain calculations

*faster*, but I'm not concerned with speed, I'm concerned with comprehension. I remember doing trig functions on a calculator in high school, but I never learned WHAT I was doing. Pushing buttons doesn't teach a student what they are doing, it teaches them a tool.

Like the poster wrote above, I want (and I want him to know) what logs, cosines, sines etc. ARE. I really believe that the largest problem with the maths and sciences disconnect in this country is that so few people actually know what the "language of math" IS. I don't view it as any different than learning grammar: if you don't understand the construction, how can you be expected to write well? Well, if you don't understand how to "read" math, how can you honestly expect to ever utilize it well?

I really think it is sad that we have a couple of generations of people whose only knowledge of how to solve an equation is to punch it into a calculator.

/rant

asta

### #15

Posted 25 February 2009 - 07:25 AM

### #16

Posted 25 February 2009 - 07:30 AM

*faster*, but I'm not concerned with speed, I'm concerned with comprehension. I remember doing trig functions on a calculator in high school, but I never learned WHAT I was doing. Pushing buttons doesn't teach a student what they are doing, it teaches them a tool.

I would not recommend a calculator/slide rule before calculus and I would not recommend graphing calculators at all. Graphing calculators do the work for you. I think you are correct that a calculator is unnecessary in trig and it's too bad your class used them. I did not use a calculator before I took calculus my first year of college. At that point I certainly understood all the building blocks to calculus, so I just needed to focus on mastering the calculus.

Anyway, I don't have a calculus student yet. I'd start looking at current texts, but my guess is if you can get your hands on something published in the very early 80s that would work. That's when I took calculus. The book had all the tables in the back, I would assume they still do, but I haven't been shopping calculus lately.

### #17

Posted 25 February 2009 - 07:51 AM

How did you do trig when you were little? I had a calculator when we did trig, and so did most of the rest of my math class (most of our fathers were engineers for the same company). There were, however, a few of us who didn't, so we did all our trig both ways. As far as I can remember, most of our problems didn't require either a calculator or the tables, just like most algebra problems don't require a calculator. Most of them just dealt with manipulating the variables. Every once in a while we'd have a batch of problems with actual numbers associated, and we'd assign variables, manipulate the equations until we had our unknown by itself on one side, plug in the numbers, and THEN do the actual calculations. That is the point at which we'd use the tables to get an actual number for the sin or cos or tan of an angle. The rest of the time, we were manipulating the trig around without the numbers. I don't remember it mattering how we actually got the numbers in the end because that was a small part of the whole process, as you keep pointing out GRIN. And I haven't noticed that using a calculator stopped my son, even my non-mathy son, from understanding what he is doing. Granted, he only just got a graphing calculator (midway through pre-calc) and hasn't been able to rely on that. I'm only fuzzy on what they do. But he has used a regular calculator. We did Singapore math, which discouraged calculator use until quite late in the process, and I more or less forbid mine to use the fancier functions early on, also, only letting them do their mult. and div. on it. Mostly, they can do simpler calculations fast enough in their head that they aren't interested in using one. All that is trying to explain that I think it is possible to grow up using a calculator and a modern textbook and still understand the math. I think the lack of understanding is because of the lack of applied math problems (word problems) and a lack of having to say why something works, rather than a calculator problem. I think your hair would stand on end if you saw how math is taught in our public elementary school GRIN. It took me years to unravel the confusion in my middle son's brain, and my oldest is still suffering in college (not homeschooled).

I'm not trying to disuade you from using tables and a slide rule at all. I'm just trying to tell you that I don't think it matters as much as you think it does. If you have a little money to spare, look for an old copy of Eshbach. It is an engineering handbook with the most fantastic tables you've ever seen for all sorts of things, like the blackness of different materials and how much longer different metals get when you heat them. It has a great summary of math and all the math tables. It is such a cool collection of knowledge!

-Nan

### #18

Posted 25 February 2009 - 08:00 AM

I would not recommend a calculator/slide rule before calculus and I would not recommend graphing calculators at all. Graphing calculators do the work for you.

Having taught a variety of mathematics courses (primarily Precalc and courses in the Calculus sequence through Differential Equations), I'd like to chime in on the use of calculators and/or slide rules in mathematics.

Over the years, we have had many discussions on teaching mathematics on these boards. Purists would agree that calculators/slides rules are completely unnecessary in mathematics courses and not because they favor tables in the back in the text. Purists would tell you that mathematics is about

**proving things**not calculating things. Calculations are made when solving application problems.

That said, very few students embark on a course of Pure Mathematics instruction. (And if you want your student to go that way, search old posts by Charon and Myrtle for text advice like Gelfand.)

No calculator does mathematics for you, but students do use calculators as a crutch. Suppose a student is given a polynomial of 5th degree with a negative leading coefficient. I'd like a student to do a quick analysis along the lines of: "This function approaches positive infinity as x gets large and negative, whereas it approaches negative infinity as x is large and positive. It has five roots. I can use Descartes rule to determine possible number of postive and negative real roots. From there I can use the Rational Root Theorem to list the possibilities and the Intermediate Value Theorem to narrow the list."

The student who does this quick analysis understands the nature of polynomials.

Most students today plug the function into their graphing calculator to see what it looks like. They can approximate roots using the trace function of their calculator. For many students approximate answers are good enough (i.e. using 1.414 instead of sqrt(2)). Whether you get the 1.414 from a calculator, table or slide rule does not matter. It is still an approximation which is useful in engineering but not necessarily in mathematics. Students need to learn how to manipulate quantities like square roots, pi, e, etc. Calculators do not help them do this.

As I said in a previous post in this thread, I hated interpolation when I used tables in high school. It is a dreadful waste of time in my opinion and does not give any insight on the behavior of transcendental functions (like the trig functions). It is a matter of calculation not mathematics.

Learning trigonometry should never be about plugging a bunch of angles or radian measures into a calculator. Yes, I might give an application problem on a trig test for which a calculator can be useful. But properly taught trig will not require much button pushing--or pages of memorization for that matter. Trig is a system which requires students to make connections. No calculator or slide rule aids this.

No calculator or slide rule can prove the Fundamental Theorem of the Integral Calculus. There are some nifty software programs out there that can take a derivative symbolically, but it is meaningless unless students understand what a derivative is. For this reason, some college Calc courses do not permit calculators. The average graphing calculator does not have this software but there are some on the market that will "do the work" for you. Note the ban on certain calculators on standardized exams.

In my opinion, we all need to get away from teaching mathematics as a series of algorithms or tricks which are soon forgotten after the test. That will improve the quality of mathematics instruction. Calculators have their place, but should not become a crutch. Hence students should not have multiple choice tests in mathematics and should always, always, always show their work.

A lot to say before breakfast.

Jane

### #19

Posted 25 February 2009 - 08:02 AM

What you're really looking for (imo) is a book which emphasizes understanding and theory versus "Here is the formula, memorize it. Here are 500 practice problems, use the formula to solve them." A book of the second kind will give little understanding regardless of the computational tool used.

### #20

Posted 25 February 2009 - 08:08 AM

It is entirely possible for a student to use a slide rule and still have no comprehension of what's going on other than a rote knowledge of how to manipulate the slide rule to acquire the answer.

What you're really looking for (imo) is a book which emphasizes understanding and theory versus "Here is the formula, memorize it. Here are 500 practice problems, use the formula to solve them." A book of the second kind will give little understanding regardless of the computational tool used.

You win! You said much more succinctly what I wanted to say.

### #21

Posted 25 February 2009 - 08:08 AM

You just made my day!

teresa

### #22

Posted 25 February 2009 - 08:22 AM

It is entirely possible for a student to use a slide rule and still have no comprehension of what's going on other than a rote knowledge of how to manipulate the slide rule to acquire the answer.

What you're really looking for (imo) is a book which emphasizes understanding and theory versus "Here is the formula, memorize it. Here are 500 practice problems, use the formula to solve them." A book of the second kind will give little understanding regardless of the computational tool used.

There you go. His first homeschool math program was ALEKS (awful, awful, awful). Then we switched to Systematic Mathematics (wonderful, wonderful), but it doesn't have Geometry or Calc; it just goes to Algebra 2. He is doing MUS for Geometry and loving it (yes, it has some trig at the end, but he's not at the end).

He finished a year of Algebra one in less than a semester, and is whipping through his geometry because much of it is review (Systematic Mathematics actually has about 1/2 of a Geometry program, but they don't call it that, and it doesn't include proofs), so at this rate, he'll be done with Algebra 2 by fall and be done with Trig/Pre-Calc by Spring/Summer 2010. So... I really don't have a huge amount of time to find "the world's best calc program for a visual learner". Heh.

Thanks to everyone for their input - I'm going to look for that engineering text.

asta

### #23

Posted 25 February 2009 - 11:57 AM

### #24

Posted 26 February 2009 - 02:35 PM

Sometimes it's easy to make him happy ....

### #25

Posted 19 March 2012 - 04:46 PM

You win! You said much more succinctly what I wanted to say.

A big necro - but I found this discussion via google.

I would disagree with both of you and suggest that using a sliderule is better than a calculator for some of the reasons discussed here and here

http://www.johndcook.com/blog/2011/04/11/sliderules/

The Author argues that while using a slideruler might not be a practical skil learning how to use one teaches the student an understanding of logarithims, orders of magnitude and scientific notation. He suggests that everyone should spend a few weeks learning how to use one and then move back to calculators.

http://www.engcom.ne...ng/view/4982/1/

This Author goes further and states that sliderulers have modern practical applications viz. had the engineers (or at least one eng.) who designed the Mars Observer that crashed used sliderules they would have figured out that the different teams were using different measuring systems (metric/imperial).

In any event - the textbook the OP was looking for is probably something like Technical Mathematics, Rice & Knight (1957). The sliderulemuseum.com has a section from the book on its site.

Cheers

**Edited by tad10, 19 March 2012 - 04:59 PM.**

### #26

Posted 19 March 2012 - 07:58 PM

A big necro - but I found this discussion via google.

I would disagree with both of you and suggest that using a sliderule is better than a calculator for some of the reasons discussed here and here

http://www.johndcook.com/blog/2011/04/11/sliderules/

The Author argues that while using a slideruler might not be a practical skil learning how to use one teaches the student an understanding of logarithims, orders of magnitude and scientific notation. He suggests that everyone should spend a few weeks learning how to use one and then move back to calculators.

http://www.engcom.ne...ng/view/4982/1/

This Author goes further and states that sliderulers have modern practical applications viz. had the engineers (or at least one eng.) who designed the Mars Observer that crashed used sliderules they would have figured out that the different teams were using different measuring systems (metric/imperial).

In any event - the textbook the OP was looking for is probably something like Technical Mathematics, Rice & Knight (1957). The sliderulemuseum.com has a section from the book on its site.

Cheers

Wow--a forgotten thread! But a great opportunity to welcome a new poster who apparently joined the community to discuss slide rules. Welcome!

### #27

Posted 20 March 2012 - 03:03 PM

Adding an interesting, new-info.-to-me thread to my "math" folder...

### #28

Posted 20 March 2012 - 03:25 PM

The Feeling of Power, Isaac Asimov

http://www.math.umn....006/extra_1.pdf

### #29

Posted 20 March 2012 - 03:48 PM

### #30

Posted 20 March 2012 - 05:39 PM

### #31

Posted 12 July 2012 - 09:08 AM

A big necro - but I found this discussion via google.

I would disagree with both of you and suggest that using a sliderule is better than a calculator for some of the reasons discussed here and here

http://www.johndcook.com/blog/2011/04/11/sliderules/

The Author argues that while using a slideruler might not be a practical skil learning how to use one teaches the student an understanding of logarithims, orders of magnitude and scientific notation. He suggests that everyone should spend a few weeks learning how to use one and then move back to calculators.

http://www.engcom.ne...ng/view/4982/1/

This Author goes further and states that sliderulers have modern practical applications viz. had the engineers (or at least one eng.) who designed the Mars Observer that crashed used sliderules they would have figured out that the different teams were using different measuring systems (metric/imperial).

In any event - the textbook the OP was looking for is probably something like Technical Mathematics, Rice & Knight (1957). The sliderulemuseum.com has a section from the book on its site.

Cheers

Thank you so much for this. I downloaded the Versalog manual (that is the one we have), a great intro book for newbies by Asimov, and the Rice and Knight book.

asta

### #32

Posted 12 July 2012 - 10:31 AM

Really cool.

### #33

Posted 12 July 2012 - 10:33 AM

You can also find pdf versions of the original text, which is out of copyright.

### #34

Posted 12 July 2012 - 10:55 AM

NASA has three TOPS science manuals available as free downloads at the link below. One of them, "Far Out Math," has students build their own slide rules and then use them in various investigations. You need to scroll down to about mid page to find the links to the downloads:

http://www.nasa.gov/...n_outreach.html

Project Mathematics movies on sine and cosine:

http://math.buffalos...thematics!.html

Discovering Trigonometry (stick and shadow diagrams):

http://catcode.com/trig/index.html