Scot Dutchy wrote:It was log books for me. Four figures normal maths and six figures for physics. Never did like slide rules. They were not accurate enough.

Do you mean accurate or precise?

Accuracy would be a matter of poor slide rule construction, warpage, or sloppy use, whereas precision is the number of sig figs you can obtain -- they were precise enough to get us to the Moon and to build the atomic bomb. (I wonder if that's the origin of the phrase, "Close enough for government work"?)

I once found an exhibition in the science museum about slide rules, abacus', big wheels that work out trig functions and similar stuff like that. I was under the impression those who used slide rules had died decades ago.
For those who are worried about finding slide rules, you can probably find a computer program, perhaps even an online one, that does the same thing.

I don't think I had much number sense before I did the first year of my physics undergraduate course. There was a module where they taught us 'back of the envelope' thinking. So nobody uses the calculator and they ask you to work out the escape velocity from Venus, the mass of the Earth or the impulse exerted by a single raindrop. Its quite fun and I'm fairly sure I have a good number sense now.

Numeracy has been defined as the ability to use a four-function calculator intelligently. The operative word being intelligently.
I was part of a CAN curriculum task force headed by the late Hilary Shuard some /many years ago. CAN being Calculator Aware Numeracy and one skill we emphasised was having some idea of the answer before you used the calculator and not just blind unthinking acceptance of the answer. After all have you asked the right question of the calculator. For instance I have asked an audience of adults, including primary school teachers just what they would key into a calculator to find the cost of 0.87 kg of beef at 2.83 gbp per kilo. Amazing how many thought that because it was less than a full kilo you had to divide to get a smaller answer. I was also told ' I don't do kilograms.'
I now live in the Philippines where motorcycle trikes are the taxis and all have a four digit identification number. I exercise my numerical skills by calculating the remainders of those numbers when divided by 9. Also look for interesting numers like 1881 which is palindromic and has lovely reflective symmetry too with no remainder. I was doing this one day and wondered what the odds were of the next trike to pass me would have the number 0001. 9999 to 1 I reckoned . I nearly fell off the back of the motor bike I was passenger on when that very number passed us. I can be a bit boring when as a trike passes us I cant help making comments like 'sqaure root of 2' or 'e' or ' my birthday' etc

Jakov wrote:
I don't think I had much number sense before I did the first year of my physics undergraduate course. There was a module where they taught us 'back of the envelope' thinking. So nobody uses the calculator and they ask you to work out the escape velocity from Venus, the mass of the Earth or the impulse exerted by a single raindrop. Its quite fun and I'm fairly sure I have a good number sense now.

You mean Fermi questions?

I read that in your blog (which I finally only got around to a couple of days ago), Amergin. Cool, huh?

sweitzen wrote:

Jakov wrote:
I don't think I had much number sense before I did the first year of my physics undergraduate course. There was a module where they taught us 'back of the envelope' thinking. So nobody uses the calculator and they ask you to work out the escape velocity from Venus, the mass of the Earth or the impulse exerted by a single raindrop. Its quite fun and I'm fairly sure I have a good number sense now.

You mean Fermi questions?

Ah so that's what they're called.

twistor59 wrote:

Scot Dutchy wrote:It was log books for me. Four figures normal maths and six figures for physics. Never did like slide rules. They were not accurate enough.

Yeah I had a British Thornton (double sided), but I preferred logs too (you could take your log table book into exams), so if you wrote out some formulas in the book REALLY lightly in pencil, no one would notice....

You did that as well

sweitzen wrote:It's a pity we don't make more use of these in elementary school and high school math education.

I taught physics for 10 years, and my students generally had absolutely no number sense, and couldn't do any kind of mental arithmetic, reaching for their calculators to add two 2-digit numbers and multiply a 2-digit number by a 1-digit number.

Many can't even recall the multiplication tables without effort.

Don't get me wrong, I love my TI-83 graphical calculator, Excel, and Mathematica/MatLab. These, and the like, should absolutely be the tools professionals use today.

However, for LEARNING math, for gaining basic number sense and numerical reasoning skills, they are anathema. They rob the student of grasping basic numerical skills.

I feel that the basic operations (addition/subtraction and multiplication/division) should be taught first on the abacus, and this should be the primary mechanism of arithmetic calculation used in elementary schools. Beginning in middle school, the slide rule should be introduced for multiplication/division, and then expanded to more complex operations through high school.

Contrary opinion, anybody?

Yeah.

Start with pencil and paper. And stay there.

Why allow non-electronic calculators and forbid electric ones? What difference does it make if they reach for a calculator or a slide-rule (other than the uber-cool geek cred of actually being able to use a slide rule)?

Kazaman wrote:Hmm ... I've been wondering how I might improve my mental arithmetic. I hadn't thought of those tools. No high school student really does anymore. I may just have to buy myself an abacus and practice a bit.

Also, just do math. When I'm driving, I'll often multiply the numbers on license plates...then multiply them in a different order to check my result.

That, and playing a lot of RPGs when I was younger (ok, I still play them when I get the chance...). And not computer RPGs. Start figuring out thac0s, skill tests, etc. and it gives some good math practice..and you're having fun while doing so.

The_Metatron wrote:Slide rules are the thing, man. I get worked up just thinking about them.

I have one that you would probably love. It is a "teacher's model"...for lack of a better term.

It's about 5 feet long.

Re Mental Maths. I was an advisory teacher of Maths in the Primary sector and was visiting a school . I walked around a class that was head down with their tasks and passed one boy who was doing his page of 'multiplying by 7'. I checked his work quietly from behind and without disturbing him. All correct. I told him he certainly knew his seven times tables. He threw a quick glance at his teacher and said he didn't know his seven times at all, but not to tell his teacher. But they are all correct I commented . How did he get them right. He said he used his 5 times and two times tables. I looked at him and asked him to explain 7 times 8. He said,'5 8's are 40 and 2 8's are 16, 40 and 16 are 56'. Who had shewn him that way I asked. 'I figured it out' he said. Why did he not want his teacher to know. Because his teacher had marked him down on the class list as knowing his 7 times. The lad had worked out the distributive law all by himself. Apart from his ability it demonstrated that kids do think about their mathematics sometimes. I told him I would say nothing but asked him to keep thinking like that.

MrFungus420 wrote:

The_Metatron wrote:Slide rules are the thing, man. I get worked up just thinking about them.

I have one that you would probably love. It is a "teacher's model"...for lack of a better term.

It's about 5 feet long.

*wibble*

im not gd at mental arithmatic, im very slow at it, make mistakes and my mind grinds to a halt trying to do it

but i have a feel for numbers and for calculations im doing, i can tell if my calc is giving me an answer that doesnt seem right

I just got a new addition to my collection. A nice little Mannheim rule from eBay for twelve bucks. I had to repair the end of the case top piece and glue a split in one end of the body, but aside from that, it's good to go.





Coolness.

I was also able to make a perfect repair on a Keuffel and Esser DeciLon rule I snagged for twenty bucks. The end of the bottom part of the body was cracked where someone really cranked down the two screws holding it into the end frames. While cleaning the crack with acetone under my stereoscope, I noticed immediately that the acetone was attacking the plastic. Result! Instead of using epoxy resin, I was able to use plastic cement, active ingredient butyl acetate. The repaired crack, while visible, is a perfect match. I can't even feel it with my fingernail. These particular rules are fetching several hundred dollars from collectors now. But that's not my motivation. I wanted one to use as a utility rule, and perhaps one each for my boys when they are older.

whoa whoa man, hang on there... There were calculations before calculators?

In all seriousness, I agree with Joe09, mental maths just takes a lot more time for us post-calculator people.. I suppose a brain gets better at what it does more often, thus if you do more mental maths you get faster at it.

I've found a surprising result of knowing some of the more mathsy parts of music theory is learning to approximate logarithms.

When measuring intervals, the standard interval is the cent. The cent is a hundredth of a semitone. Or a 1200th octave. 1 c = 2^(1/1200). Now, certain intervals are rather relevant in western music: 3/2 (the fifth), ~702.0 c (but flattened normally to 700 for various reasons), the fourth ~4/3 (498.0 c, but likewise changed to 500), the major third 5/4, ~386.3 c (but sharpened to 400 for convenience), the minor third, 6/5 (the distance between 5/4 and 3/2), at ~315.6 (but likewise flattened to 300) - their inversions (multiplied by two, so 6/5 -> 5/3, 5/4 -> 8/5) are obtained by taking 1200 - their measured number of cents. Then there's a few interesting intervals mostly absent from western music but which do sound quite stable in harmonies:, the subminor third at 7/6 (~267), the supermajor second at 8/7 (~231), the eleventh harmonic at 11/8, (551 c), the 9/7 supermajor (~435), the undecimal third 11/9, (at ~347), etc.

Basically, though, all you'd need to learn is high enough accuracy for every prime number up to some x, (possibly taken down to the right 'octave' by dividing it by powers of two), and you could obtain quite an accurate approximation of all non-primes that factorize to a subset of those primes simply by addition and subtraction - e.g. if you want to know what 12/11 is, you take the number you've learned for 4/3 (~498.0 c) minus the number you've learned for 11/9 (~347 c) and you obtain something along the line of 151 c (which you divide by 1200 to obtain the 2-log of it, so ~= 15/120 = 3/24 = 1/8, and it turns out (12/11)^8 is v. close to 2) (You could also get close enough to primes you haven't learned with some other methods.)

Surprisingly enough, this is something I've learned by osmosis in mathsy music theory rather than by exposure to such a method in school. I do find it unlikely I'd learn these numbers by heart in school anyway.

i think abacuses are good for kindergarden and up to the third grade or whenever the transition to multiplication and division starts. i think the slide rule is obsolite. basic arithmatic needs to be understood for next level computations to be comprehended.

I take it you don't know how to use one?

i do not know how to use one, but after seeing one and reading about in on wikipedia i see how the need for a sense of magnitude is over used. it takes away from the amount of calculations that can be processed.

There are quite a few operations that are considerably quicker to do on a slide rule. I presume you realize the importance of understanding the concepts behind mathematical operaions in contrast to simply keystroking an electronic calculator and transcribing the results.

My boys will learn how to use them as soon as I get them to understand logarithms.