4 ms·

> given the choice in examinations between log-tables, slide-rule, or calculator, we all made the same choice Students would benefit greatly if given a slide r

> given the choice in examinations between log-tables, slide-rule, or calculator, we all made the same choice Students would benefit greatly if given a slide rule instead of an electronic calculator for their exams. The former is an effective teacher which viscerally reveals crucial insights, while the latter is pedagogically almost useless; using an electronic calculator to solve problems consists of nothing beyond punching keys and looking at the result, given as a disembodied string of digits entirely out of any context. The slide rule probably even ends up slightly more efficient for the type of problems students typically see in high school, after a bit of practice. Precision is more than sufficient. Any assigned problem which needs a calculator would be more effective if the calculator were removed and the numbers involved were simplified to the point students could manage them mentally or with a trivial amount of scratch work. Where electronic computers really shine is in their programmability, and for that students should be working with a full programming language and a real keyboard.

willyt 6y ago
When I did my A-levels, we were taught to give answers as surds the exams usually asked for this when we were doing trig and it was generally accepted to give answers as fractions so I think I ended up using my expensive graphic calculator once or twice in 6 hours of maths exams.
- pacaro 6y ago
  This matches my recollection too. I had a calculator, I used it almost exclusively for "wasting" time programming in class, I don't believe I ever used it in an exam. While the graphing calculators were available we weren't told we needed them so, being on a tight family budget, I didn't have one. My sister, a few years later was told that she had to have a graphing calculator, which she claims she never used
acqq 6y ago
What I liked is the awareness of the inexactness which is inherent in everything but which slide rules made more obvious. The joke from these times was "ask an engineer what is 2 times 3 and he'll take out his slide rule and say between 5.9 and 6.1" Whoever thought that up maybe wanted to show how the engineers just use tools and don't think, but I've seen the opposite: it was some with just a theoretical mathematical training who blindly believed in every digit of the result they saw or produced, even when it was really meaningless or where it was obvious to me that the process resulted in an error.
- segfaultbuserr 6y ago
  The Art of Electronics warns the reader in the first chapter: > There is a tendency among beginners to want to compute resistor values and other circuit component values to many significant places, and the availability of inexpensive calculators has only made matters worse. There are two reasons you should try to avoid falling into this habit: (a) the components themselves are of finite precision (typical resistors are 5%; the parameters that characterize transistors, say, frequently are known only to a factor of two); (b) one mark of a good circuit design is insensitivity of the finished circuit to precise values of the components (there are exceptions, of course). You'll also learn circuit intuition more quickly if you get into the habit of doing approximate calculations in your head, rather than watching meaningless numbers pop up on a calculator display.
  - jet_32951 6y ago
    There's a small book called "Errors of Observation and Their Treatment", ISBN 978-94-011-6928-8, which seemed dull in class but it emphasized being able to express and defend a numerical result as x +/- y . I did that thereafter and it made a lot of difference in my understanding of the result. It isn't done by many engineers any more, and I always look with suspicion on results claiming absurd precision. There isn't so much understanding there and people who engage in it are much more likely to submit work with multiple order-of-magnitude errors. They do not -know- the answer, they accept the line on the screen un-critically.
    - acqq 6y ago
      Those interested in this thread should also consider the posts by the user "anonytrary" while commenting this article in this context.
throwaway2245 6y ago
This seems to imagine that the only thing being taught/worth teaching on the mathematics curriculum is number sense. Firstly, that's not the case. If you want students to answer a problem with any practical application (e.g. money/finance, statistics), or more complex problems where the point is to follow the logic, being able to use the calculator in your pocket is great. A perfectly reasonable assigned problem might be: add the 7.1% sales tax to this ticket price, do you have enough cash? And secondly, number sense is easier to teach without depending on particular algorithms. This is the same complaint as people grumbling about "common core" math, or saying we should go back to the basics of just rote learning times tables and long division. Students are learning about number sense by different routes now - routes that don't end up with most students blindly trying to follow a particular algorithm with no sense of what is actually happening.
- lopmotr 6y ago
  I once taught in a physics curriculum that went a step beyond calculators. Students never had to do numerical calculations in the exams. For example, a question asking you to find a force, could have an answer like "F=ma where m=3 kg and a=2m/s". There were higher grades for showing insight into the physics that you could get by looking at the form of the symbolic equations you'd derived but would have trouble noticing if you'd substituted numbers early on. I wish I had learned times tables properly as a kid though. I struggle with things like 6*7 on a near daily basis for my work and general life. Not really for number sense but for not having to shift my attention to a basic math problem while I'm working on something else.
- jacobolus 6y ago
  I think you are misunderstanding me / underestimating students. The slide rule teaches in a very direct physical way how logarithms work and how they can be used. This is something that most people never learn, but is extremely valuable. > This seems to imagine that the only thing being taught/worth teaching on the mathematics curriculum is number sense First of all, number sense is extremely important. Probably the most important thing taught in primary/secondary math courses. But it is certainly not the only important thing. Students can learn to use an electronic calculator in very little time. A person of average intelligence who understands the relevant math should be able to learn to use their calculator pretty much independently, and become fluent at it with a tiny bit of practice over a short time. There are very quickly diminishing returns to teaching “calculator skills”, because those are extremely shallow. > And secondly, number sense is easier to teach without depending on particular algorithms. I really have no idea which ‘particular algorithms’ you are talking about. Have you ever used a slide rule? It is a very flexible general-purpose tool. > This is the same complaint as people grumbling about "common core" math, or saying we should go back to the basics of just rote learning times tables and long division. No, it is precisely the opposite recommendation to those. > A perfectly reasonable assigned problem might be: add the 7.1% sales tax to this ticket price, do you have enough cash? This is a reasonable problem to teach students about for like 1 week at age ~10. If they learn how to do it using pen and paper, or a soroban, or mental arithmetic, or a slide rule, or a pile of loose pebbles, they’ll have no trouble accomplishing the same with a calculator. It is not a reasonable problem to spend 5 more years on. We are talking about exams for 15-year-olds.
HeyLaughingBoy 6y ago
As I mentioned in a comment upthread, I was trained in navigation as a Merchant Marine officer and we were not allowed to use electronic calculators during exams. The reason given was "what if you're in the middle of the ocean and your batteries die?" or something stupid like that. But the real reason was that our instructor wanted us to think about what we were doing. Celestial navigation involves a lot of steps and errors compound. Forcing you to think clearly about the intermediate results means that you're more likely to realize you pulled the wrong number out of a table, or your star sight was just plain wrong and you're not off the coast of Madagascar, but somewhere near the Azores instead.

willyt 6y ago

When I did my A-levels, we were taught to give answers as surds the exams usually asked for this when we were doing trig and it was generally accepted to give answers as fractions so I think I ended up using my expensive graphic calculator once or twice in 6 hours of maths exams.

pacaro 6y ago
This matches my recollection too. I had a calculator, I used it almost exclusively for "wasting" time programming in class, I don't believe I ever used it in an exam. While the graphing calculators were available we weren't told we needed them so, being on a tight family budget, I didn't have one. My sister, a few years later was told that she had to have a graphing calculator, which she claims she never used

acqq 6y ago

What I liked is the awareness of the inexactness which is inherent in everything but which slide rules made more obvious. The joke from these times was "ask an engineer what is 2 times 3 and he'll take out his slide rule and say between 5.9 and 6.1" Whoever thought that up maybe wanted to show how the engineers just use tools and don't think, but I've seen the opposite: it was some with just a theoretical mathematical training who blindly believed in every digit of the result they saw or produced, even when it was really meaningless or where it was obvious to me that the process resulted in an error.

segfaultbuserr 6y ago
The Art of Electronics warns the reader in the first chapter: > There is a tendency among beginners to want to compute resistor values and other circuit component values to many significant places, and the availability of inexpensive calculators has only made matters worse. There are two reasons you should try to avoid falling into this habit: (a) the components themselves are of finite precision (typical resistors are 5%; the parameters that characterize transistors, say, frequently are known only to a factor of two); (b) one mark of a good circuit design is insensitivity of the finished circuit to precise values of the components (there are exceptions, of course). You'll also learn circuit intuition more quickly if you get into the habit of doing approximate calculations in your head, rather than watching meaningless numbers pop up on a calculator display.
- jet_32951 6y ago
  There's a small book called "Errors of Observation and Their Treatment", ISBN 978-94-011-6928-8, which seemed dull in class but it emphasized being able to express and defend a numerical result as x +/- y . I did that thereafter and it made a lot of difference in my understanding of the result. It isn't done by many engineers any more, and I always look with suspicion on results claiming absurd precision. There isn't so much understanding there and people who engage in it are much more likely to submit work with multiple order-of-magnitude errors. They do not -know- the answer, they accept the line on the screen un-critically.
  - acqq 6y ago
    Those interested in this thread should also consider the posts by the user "anonytrary" while commenting this article in this context.

throwaway2245 6y ago

This seems to imagine that the only thing being taught/worth teaching on the mathematics curriculum is number sense. Firstly, that's not the case. If you want students to answer a problem with any practical application (e.g. money/finance, statistics), or more complex problems where the point is to follow the logic, being able to use the calculator in your pocket is great. A perfectly reasonable assigned problem might be: add the 7.1% sales tax to this ticket price, do you have enough cash? And secondly, number sense is easier to teach without depending on particular algorithms. This is the same complaint as people grumbling about "common core" math, or saying we should go back to the basics of just rote learning times tables and long division. Students are learning about number sense by different routes now - routes that don't end up with most students blindly trying to follow a particular algorithm with no sense of what is actually happening.

lopmotr 6y ago
I once taught in a physics curriculum that went a step beyond calculators. Students never had to do numerical calculations in the exams. For example, a question asking you to find a force, could have an answer like "F=ma where m=3 kg and a=2m/s". There were higher grades for showing insight into the physics that you could get by looking at the form of the symbolic equations you'd derived but would have trouble noticing if you'd substituted numbers early on. I wish I had learned times tables properly as a kid though. I struggle with things like 6*7 on a near daily basis for my work and general life. Not really for number sense but for not having to shift my attention to a basic math problem while I'm working on something else.
jacobolus 6y ago
I think you are misunderstanding me / underestimating students. The slide rule teaches in a very direct physical way how logarithms work and how they can be used. This is something that most people never learn, but is extremely valuable. > This seems to imagine that the only thing being taught/worth teaching on the mathematics curriculum is number sense First of all, number sense is extremely important. Probably the most important thing taught in primary/secondary math courses. But it is certainly not the only important thing. Students can learn to use an electronic calculator in very little time. A person of average intelligence who understands the relevant math should be able to learn to use their calculator pretty much independently, and become fluent at it with a tiny bit of practice over a short time. There are very quickly diminishing returns to teaching “calculator skills”, because those are extremely shallow. > And secondly, number sense is easier to teach without depending on particular algorithms. I really have no idea which ‘particular algorithms’ you are talking about. Have you ever used a slide rule? It is a very flexible general-purpose tool. > This is the same complaint as people grumbling about "common core" math, or saying we should go back to the basics of just rote learning times tables and long division. No, it is precisely the opposite recommendation to those. > A perfectly reasonable assigned problem might be: add the 7.1% sales tax to this ticket price, do you have enough cash? This is a reasonable problem to teach students about for like 1 week at age ~10. If they learn how to do it using pen and paper, or a soroban, or mental arithmetic, or a slide rule, or a pile of loose pebbles, they’ll have no trouble accomplishing the same with a calculator. It is not a reasonable problem to spend 5 more years on. We are talking about exams for 15-year-olds.

HeyLaughingBoy 6y ago

As I mentioned in a comment upthread, I was trained in navigation as a Merchant Marine officer and we were not allowed to use electronic calculators during exams. The reason given was "what if you're in the middle of the ocean and your batteries die?" or something stupid like that. But the real reason was that our instructor wanted us to think about what we were doing. Celestial navigation involves a lot of steps and errors compound. Forcing you to think clearly about the intermediate results means that you're more likely to realize you pulled the wrong number out of a table, or your star sight was just plain wrong and you're not off the coast of Madagascar, but somewhere near the Azores instead.