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#1 asta

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Posted 24 February 2009 - 05:38 AM

Has anyone ever run across a program that teaches Calculus with a slide-rule instead of a modern calculator?

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 betty

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Posted 24 February 2009 - 06:28 AM

The idea is totally frightening to me. I used to have my dad's slide rule, but I never used it. I ran out and bought a solar calculator the day my chemistry professor announced that if we came to him during a test and said our calculator's battery died he would lend us his slide rule. I still have the calculator--25 years later.

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 Laura Corin

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Posted 24 February 2009 - 06:38 AM

I had no idea what I was doing most of the time: it was just a rote action, no more meaningful than pushing a calculator's buttons, perhaps less. I love that scene in the Apollo film though where the stranded astronauts pull out their slide rules to calculate their re-entry. Unimaginable.

Laura

#4 Jane in NC

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Posted 24 February 2009 - 07:15 AM

Some of us on this board are old enough to have taken Calculus in the days when calculators were prohibitively expensive for most students. (My college library had calculators for use and, yes, I learned Fortran using binary tape.) Most of Calculus is abstract and does not require a calculator or a slide rule. Your old engineering friends were performing some calculators on a slide rule--not learning Calculus.

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 In The Great White North

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Posted 24 February 2009 - 07:42 AM

I have several older calculus books and they would all work. It doesn't have to be pre-calculator, just pre- graphing calculator.

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 forty-two

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Posted 24 February 2009 - 08:02 AM

Though part of the graphing calculator generation, I've always wanted to learn to use a slide rule. I don't think you need wait till calc, though. IIRC, slide rules use the properties of logarithms to simplify multiplications/divisions and taking square/cube/etc. roots. So you could learn to use it as soon as you learn logarithms (Alg 2 or Pre-Calc). Just reading about how it works increased my understanding of logs - for the first time, I really grasped log properties and how to use them. I can't fathom, though, how so many of the pp managed to work a slide rule by rote - if you didn't understand why it works, how in the world could you correctly use it? The instructions seemed like a bunch of gobbledygook until I figured out the underlying principles. But since it indeed seems possible, you will want to watch out for that when teaching your ds - it loses all its benefits if you don't know why it works.

#7 Jane in NC

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Posted 24 February 2009 - 08:31 AM

Library book sales often have books that teach how to use slide rules. My husband and I collect slide rules (:D--geeks that we are!) When a nephew finished engineering school, we "knighted" him with one.

#8 kiana

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Posted 24 February 2009 - 09:59 AM

I have both a slide-rule and a book on how to use it. It was actually helpful for understanding logarithms, IMO. But it's a computational tool, just as a calculator is. You don't need a textbook that teaches specifically with a slide rule so much as you need one that does *not* teach "This is the key sequence to solve the problem on your TI-93". Any textbook of sufficient age should work. Some of the modern ones would probably work as well, just not one that's a reform text.

#9 C_l_e_0..Q_c

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Posted 24 February 2009 - 10:08 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.

#10 asta

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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 Nan in Mass

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Posted 24 February 2009 - 03:09 PM

Maybe I'm wrong, but doesn't "manually" just consist in using the tables from a book of engineering tables like Eshbach, with a slide rule to approximate your long calculations? I'm not sure it is that big a deal? I remember my father showing me how to do calculations on a slide rule. I don't remember them being anything complicated, just arithmetic. My father and his workmates bought their children calculators when they were still very, very expensive. They thought they were cool and useful. I think you could do math using a calculator (a nice timesaver) but include a unit showing how to do things by hand if necessary. It is sort of like using spell-check or looking things up in the dictionary. Maybe I'm wrong, though.
-Nan

#12 betty

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Posted 24 February 2009 - 05:37 PM

I would think that the OPs son has been using the tables already having completed trigonometry. I don't like to see students using calculators until after trig/functions. I've never used a graphing calculator. If you locate an older text you could do the work without a calculator or slide rule (in my opinion a slide is essentially a calculator). Even with an older text, you will be using the tables. Since this student has had trig, he should know his way around the tables.

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 Nan in Mass

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Posted 24 February 2009 - 06:22 PM

As someone who spent 7th grade being retaught the long division I'd learned in 3rd because I didn't know my multiplicaiton and addition tables, and then spent 8th grade trying to deal with algebra without prealgebra, I LOVE this story! If only I had been as ingenious!

#14 asta

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Posted 25 February 2009 - 04:44 AM

Actually, kiddo is finishing Geometry. He then has his Alg 2 program. I still have to find a calc program, but I'm trying to look ahead.

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 MyThreeSons

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Posted 25 February 2009 - 07:25 AM

My Dad had one, and I played with it a little, but I never really learned to use one. I'd love to take one in to show my Physics students at co-op.

#16 betty

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Posted 25 February 2009 - 07:30 AM

[quote name='asta']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.


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 Nan in Mass

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Posted 25 February 2009 - 07:51 AM

Is he using the tables already?
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 Jane in NC

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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 kiana

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Posted 25 February 2009 - 08:02 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.

#20 Jane in NC

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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 tajott

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Posted 25 February 2009 - 08:08 AM

make sure you tell this to your kids MANY times.

You just made my day!

teresa

#22 asta

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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 Nan in Mass

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Posted 25 February 2009 - 11:57 AM

Phew! I've been waiting for you guys to chime in. I've been afraid I was remembering wrongly. Asta - It sounds like you want math texts from the 1960's. Ask Jane or someone to recommend them. They are the exact opposite of Aleks. No wonder you went looking for something else! Jane and others here can recommend some.

#24 C_l_e_0..Q_c

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Posted 26 February 2009 - 02:35 PM

Ok, DS is playing incessantly with his new slide rule..

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

#25 tad10

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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 Jane in NC

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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 Colleen in NS

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Posted 20 March 2012 - 03:03 PM

Welcome, tad10!

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

#28 Mommy Grommy

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Posted 20 March 2012 - 03:25 PM

I know this is an ancient thread, but I couldn't resist adding this short story from Isaac Asimov. I remember reading it in high school and thinking how right it was. It didn't stop me, however, from eventually earning a degree in computational chemistry where the equations are so complicated that they can only be approximated using computers. :D

The Feeling of Power, Isaac Asimov
http://www.math.umn....006/extra_1.pdf

#29 stripe

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Posted 20 March 2012 - 03:48 PM

My mom gave me a slide rule manual and a slide rule!

#30 Sebastian (a lady)

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Posted 20 March 2012 - 05:39 PM

Great story.

#31 asta

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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 Sebastian (a lady)

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Posted 12 July 2012 - 10:31 AM

When we were in Kyoto, we stopped into a tiny little abacus store. They had school versions, store sized versions and even some big ones as long as my arm (which I imagine were for demonstration).

Really cool.

#33 Sebastian (a lady)

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Posted 12 July 2012 - 10:33 AM

Martin Gardner has revised Calculus Made Easy by Silvanus Thompson. I've seen this at library sales and used book stores.

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

#34 Vida Winter

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Posted 12 July 2012 - 10:55 AM

Funny you should bring up this old thread because I can add some useful links I found somewhere around here, probably from Kathy in Richmond and other math moms...the videos are interesting and show the elegance and simplicity of trigonometry.

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



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