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?

Yes. I'm a physics teacher and I find that one of the greatest barriers with my A level students (age 16-18) is that they get so caught up in the numbers (fucking around on their calculators) that they miss the physics! I've actually banned them from using calculators in some lessons and made them estimate answers using pencil and paper!

I'm not so sure about using slide rules (I don't know how to use one myself! ), but kids from a young age need to do more of the brute number crunching by hand so that when they get older they can just 'see' numbers and get the answers.

There is no reason to believe, as far as I am aware of, that today's generation in question suffers from ability to think, analyze, or imagine in comparison to "old school" generation.

There was a thread about creativity crisis in the USA raising similar concerns/questions, but my opinion is that inter-generation conflicts are usual, the old dog and new tricks saying has some merit, and nostalgia is part of memories.

Does it irk me? Maybe, sometimes, though I am not sure it is all that important to know how to use a ruler when having a laser. Time and energy is not usually infinite. Then again, as someone without personal experience in question I am willing to change my mind if I see some data.

When I was in elementary school, the abacus was introduced to teach the decimal system, and simple addition and subtraction, but it was quickly abandoned. I discovered a couple years later that it could be used for multiplication and division, built myself one, and learned how to do it.

Likewise, basic slide rule use was introduced in middle school when the concept of a logarithm came up, but nothing further was done. I found my father's old slide rule and manual and taught myself how to use it.

tuco wrote:There is no reason to believe, as far as I am aware of, that today's generation in question suffers from ability to think, analyze, or imagine in comparison to "old school" generation.

There was a thread about creativity crisis in the USA raising similar concerns/questions, but my opinion is that inter-generation conflicts are usual, the old dog and new tricks saying has some merit, and nostalgia is part of memories.

Does it irk me? Maybe, sometimes, though I am not sure it is all that important to know how to use a ruler when having a laser. Time and energy is not usually infinite. Then again, as someone without personal experience in question I am willing to change my mind if I see some data.

In my experience, today's generation don't suffer from a lack of the abilities you mention.

What I have found, though, is that many of my physics students are being hampered because they spend too much time on basic arithmetic and don't have that 'feel' for number. For example, I find the kids wasting their time getting their calculators out to do simple sums, say for example 4x28 (this calculation came up in today's lesson! I think it was a moments type problem), whereas for me (and my generation ) we do the sum in our head in a fraction of the time. This lack of fluidity with number means that when they are attacking a problem it all becomes very stop/ start because of the time it takes to do the calculations and thus the train of thought is easily disturbed.

I'm afraid I don't have any data to back this up, only anecdotal evidence (I'll see if I can dig up some at the weekend). I'll get to see my A level kids again next Tuesday. I might try them out on a few times tables...

Actually, I imagine it is fun to test pen and paper, it does provide data. That is not a task for me, but for educators. So, worry not and carry on :)

How to compute 24,50 x 4?

25 x 4 for instant 100 - 2? This kind of AI?

campermon wrote:

tuco wrote:There is no reason to believe, as far as I am aware of, that today's generation in question suffers from ability to think, analyze, or imagine in comparison to "old school" generation.

There was a thread about creativity crisis in the USA raising similar concerns/questions, but my opinion is that inter-generation conflicts are usual, the old dog and new tricks saying has some merit, and nostalgia is part of memories.

Does it irk me? Maybe, sometimes, though I am not sure it is all that important to know how to use a ruler when having a laser. Time and energy is not usually infinite. Then again, as someone without personal experience in question I am willing to change my mind if I see some data.

In my experience, today's generation don't suffer from a lack of the abilities you mention.

What I have found, though, is that many of my physics students are being hampered because they spend too much time on basic arithmetic and don't have that 'feel' for number. For example, I find the kids wasting their time getting their calculators out to do simple sums, say for example 4x28 (this calculation came up in today's lesson! I think it was a moments type problem), whereas for me (and my generation ) we do the sum in our head in a fraction of the time. This lack of fluidity with number means that when they are attacking a problem it all becomes very stop/ start because of the time it takes to do the calculations and thus the train of thought is easily disturbed.

I'm afraid I don't have any data to back this up, only anecdotal evidence (I'll see if I can dig up some at the weekend). I'll get to see my A level kids again next Tuesday. I might try them out on a few times tables...

Speaking as someone who had to use log tables and the old guessing stick at school and Uni, the thing I notice since I have some dealings in retail is that a lot of people trust the answer the calculator(till) gives them without even realising that the answer may not be in right ballpark let alone correct.

The old methods of pen and paper or mental arthmetic gives you a feeling for the calculation.

An interesting point about times tables, is Campermon, that one of the simple diagnostic tests for dyslexia (The Bangor Dyslexia Test) uses as part of its testing criteria the ability to recite certain times tables (can't remember which ones as my copy is at work). I use it on occasion as it some times backs up a reply to a teacher.

We had one physics teacher in high school who insisted that any number crunching done with a calculator also be checked with a basic mental number crunch, where all numbers get rounded to powers of ten and then the calculator answer is checked against this. It surprised us all how often this method would catch calculator errors.

When traveling in the truck on the way to the store to get materials for my next construction job I will often do the mental arithmetic out loud for the benefit of (and with the help of) my nine year old.

Onyx8 wrote:We had one physics teacher in high school who insisted that any number crunching done with a calculator also be checked with a basic mental number crunch, where all numbers get rounded to powers of ten and then the calculator answer is checked against this. It surprised us all how often this method would catch calculator errors.

When traveling in the truck on the way to the store to get materials for my next construction job I will often do the mental arithmetic out loud for the benefit of (and with the help of) my nine year old.

When working example problems in front of my students, I'd have them toss out example numbers when we got to a point to do a calculation. I offered any of them who could beat my mental math to 2 sig figs precision a free quiz score. Only paid out once.

I think the answer you have is right, OP, but the question may be wrong. I think the tools you recommend would help with gaining number sense, but I would suggest that perhaps all elementary learning be centered around the history of ideas. Basic knowledge, as it is today, is important, but I don't think the focus at the beginning should be to get people up to speed on it in the quickest direct way. If children learned instead to think at progressively later stages of human thought, I think they'd end up pretty solid--most of them--by the age of 18. I think they would definitely also have a much lower chance of being non-critical in their thinking.

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.

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.

You can find inexpensive sorobans (japanese abaci for base-10) on eBay.

sweitzen wrote:
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?

Hi, new old guy here.

I managed to finish all my formal education (community college, 4 year industrial electrician apprenticeship) just before the time that calculators began to appear in classrooms.

In elementary school, all calculations were done with paper and pencil. Never saw an abacus, and would need to be taught to use one.

As I recall, I was introduced to algebra in middle school. Around 11th or 12th grade, basic slide rules were introduced in Trig and Advanced Geometry classes, at about the time that learning logarithmic functions became part of the math.

I needed to improve my math to qualify for an apprenticeship, so took many math and electronic classes in community college. We used the slide rule there quite extensively.

When I was accepted to the apprentice program, our math, physics, and electrical theory/circuitry instructor was a former toolmaker. I suspect his training gave him a fetish for accuracy in calculation. He thought that a slide rule was fine for an estimate, but all our homework problems had to be solved to 5 decimal places. I carried around a dog-eared paperback book of 7 place logarithmic tables for 3 years. Those will make you blind, and I sure don't recommend that we go back to using them.

I agree that my use of the slide rule probably gives me a better insight to quick math calculations than the kid at the local gas station that punches the wrong keys and gives me back $22.00 change when I handed him a $10.00 bill.

I can see a couple of problems with training kids with slide rules, though. Like someone mentioned up thread, the time you have to teach students is kind of limited, and has problems as well.

With either the calculator or the slide rule, what is needed is the ability to do quick mental calculations, and be able to tell if your answer is in the ball park. Not sure if it matters which instrument you are using.

The calculator places the decimal point for you automatically, but it is no help if you enter too many of too few places in your entries. The rules for placing the decimal point with the slide rule are complicated, and require a lot of rote memorization.

Another small problem, are you even able to buy slide rules anymore? Within 5 years after calculators that could do advanced trig and logs appeared, every company that made slide rules was out of the business.

Only place I can find them is on eBay, and I had to stop hanging around there some time ago. The couple hundred that I bought over there are probably not that good of an investment.

tuco wrote:There is no reason to believe, as far as I am aware of, that today's generation in question suffers from ability to think, analyze, or imagine in comparison to "old school" generation.

Yeah but this generation's music is shit !

The_Metatron wrote:


I've got a collection of fifteen or so different rules, but I still need to build some sort of display case for them. I've also got a few virtual slide rules up on my web site, but the resolution isn't very good on most of them.

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

QFT!

I have one of those in the bookcase here beside my computer.

My slide rule collection has been growing lately, too.

I have a soroban sitting its a box on the shelf above my desk. I use it from time to time, but I never learned to use it well enough to use it on a regular basis. I'd ike to learn eventualy, though.

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.

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....