5 ms·

I'd have to say the absurdity of the whole thing is that calculators are allowed on math tests at all, thus fueling an entire market of crippleware calculators.

by hy3lxs 17y ago

I'd have to say the absurdity of the whole thing is that calculators are allowed on math tests at all, thus fueling an entire market of crippleware calculators. (1) If you're trying to teach mathematical _concepts_ then make your problems come out to whole numbers that are easily done with pencil and paper. (2) If (1) was true then maybe we'd see some real innovation in the calculator space, especially if the single-purpose electronic device costing $100 from TI had to compete with iphone apps costing $1. Or Google Calculator. Or Wolfram Alpha. (3) I've anecdotally heard from my math-tutoring friends that there is a growing pandemic of high school kids in America that can't multiply single-digit numbers anymore. O_o

icefox 17y ago
My high school physics teacher did #1. The math was pretty simple if you knew the concept and the first week he showed us stuff like finding a square root on paper.
- rbanffy 17y ago
  "finding a square root on paper." That's painful!
  - RiderOfGiraffes 17y ago
    Actually it's pretty easy. It also follows from the basics of long division, which underpins how CRC algorithms work.
- dhimes 17y ago
  I did exactly the same thing when teaching physics in college for many years. I made the numbers easy, but made people memorize formulas. No calculators or "cheat sheets" allowed, but you could leave an answer as pi/sqrt(2). I would tell the students: "The numbers should come out easy. If you get something weird, then one of us made a mistake!" This simple change made a huge improvement in comprehension in the class. It wasn't about "number jamming" any more, but about learning.
yequalsx 17y ago
I teach mathematics at a college. Doing (1) for every type of problem is not feasible. In college algebra courses we now give problems that involve using the best linear, quadratic, or exponential fit. We definitely do not do these problems by hand. The calculator is a black box that spits out the correct approximation and the student is asked to answer questions based on what the calculator spits out for the correct fit. Part of our jobs is to prepare students to use mathematics in engineering, physics, chemistry, etc. We don't want to always give problems where the numbers are nice. Is (3) a problem? How many people can find interpolating polynomials? Very few. Interpolating polynomials are no longer needed by most students of mathematics because computing power is cheap and ubiquitous. The skill set for mastering mathematics has changed given this reality. Think of it this way. Very few people can start fire without matches or flint. This used to be common knowledge years ago but is no longer needed. Fire making devices are cheap and plentiful.
- RiderOfGiraffes 17y ago
  Do you want your doctor to look at your symptoms and start leafing through reference books, or looking on Google to decide what you have? It doesn't matter how clever you are, or how good at reasoning, you have to have basic knowledge to use as the base. AI researchers came to this conclusion a long time ago. Reasoning or experience is not enough - you must have codified, accessable knowledge on which to work. Not knowing basic arithmetic cripples you when you need to work on the next stage. Not knowing that 7*8 is 56 means you can't work out the expansion of (x+1)^8. Working simple cases like that makes it clear what's happening when you differentiate, and gives insight that you can't obtain without doing the work. The maxim from medicine is "See one, do one, teach one." The middle step is crucial. If you get the computer to do everything, you never gain the experience, and rarely have the insights. And, personally, I can interpolate polynomials. It's an interesting example, because recently it allowed us to implement a new feature in our system. No one else to work out how to do it, and were amazed when I did. In your terms, I can make fire in a world where most people can't. It just earned us real money.
  - yequalsx 17y ago
    Interpolating polynomials used to be taught in high schools. I learned it in high school and today almost no high school graduate knows how to do this. Is this a bad thing? I don't think so. With new technology and the advancement of ideas and knowledge the basic skill set that is necessary changes. The division of labor has rendered many once necessary skills the province of specialists. This is a good thing. Is arithmetic one of those things? I begin to believe so. The expansion of (x+1)^8 does not require the ability to do 7*8. One can do the expansion using Pascal's Triangle. Besides, the real question is ought one do the expansion of (x+1)^8 by hand? The answer is no. The expansion is a purely mechanical process. A computer does it faster and more accurately. In such a long problem I am likely to make a mistake and this mistake does not mean that I don't know what I am doing. I do want my doctor to thumb through reference books particularly if my condition is rare. In such a case it is unlikely that the doctor will have encountered my condition and I want her to gain from the shared experience and collective wisdom of experts. That's what a reference book is for and it's a good thing. I want my doctor to be able to read and understand the book. That is what her training is for. One can get insights into algebra using a computer. It's just that the insights are different than what one could get without a computer. Instead of teaching interpolating polynomials in high schools they are teaching basic statistics and in this present age the latter is much more beneficial than the former.
sokoloff 17y ago
It's not just that. I've interviewed senior candidates who can't do basic arithmetic in their head. I had one project management candidate, who was doing fairly well up until that point on the interview loop, who literally couldn't multiply 600 by 3 in their head, nor on the whiteboard.

by hy3lxs 17y ago

icefox 17y ago

My high school physics teacher did #1. The math was pretty simple if you knew the concept and the first week he showed us stuff like finding a square root on paper.

rbanffy 17y ago
"finding a square root on paper." That's painful!
- RiderOfGiraffes 17y ago
  Actually it's pretty easy. It also follows from the basics of long division, which underpins how CRC algorithms work.
dhimes 17y ago
I did exactly the same thing when teaching physics in college for many years. I made the numbers easy, but made people memorize formulas. No calculators or "cheat sheets" allowed, but you could leave an answer as pi/sqrt(2). I would tell the students: "The numbers should come out easy. If you get something weird, then one of us made a mistake!" This simple change made a huge improvement in comprehension in the class. It wasn't about "number jamming" any more, but about learning.

yequalsx 17y ago

I teach mathematics at a college. Doing (1) for every type of problem is not feasible. In college algebra courses we now give problems that involve using the best linear, quadratic, or exponential fit. We definitely do not do these problems by hand. The calculator is a black box that spits out the correct approximation and the student is asked to answer questions based on what the calculator spits out for the correct fit. Part of our jobs is to prepare students to use mathematics in engineering, physics, chemistry, etc. We don't want to always give problems where the numbers are nice. Is (3) a problem? How many people can find interpolating polynomials? Very few. Interpolating polynomials are no longer needed by most students of mathematics because computing power is cheap and ubiquitous. The skill set for mastering mathematics has changed given this reality. Think of it this way. Very few people can start fire without matches or flint. This used to be common knowledge years ago but is no longer needed. Fire making devices are cheap and plentiful.

RiderOfGiraffes 17y ago
Do you want your doctor to look at your symptoms and start leafing through reference books, or looking on Google to decide what you have? It doesn't matter how clever you are, or how good at reasoning, you have to have basic knowledge to use as the base. AI researchers came to this conclusion a long time ago. Reasoning or experience is not enough - you must have codified, accessable knowledge on which to work. Not knowing basic arithmetic cripples you when you need to work on the next stage. Not knowing that 7*8 is 56 means you can't work out the expansion of (x+1)^8. Working simple cases like that makes it clear what's happening when you differentiate, and gives insight that you can't obtain without doing the work. The maxim from medicine is "See one, do one, teach one." The middle step is crucial. If you get the computer to do everything, you never gain the experience, and rarely have the insights. And, personally, I can interpolate polynomials. It's an interesting example, because recently it allowed us to implement a new feature in our system. No one else to work out how to do it, and were amazed when I did. In your terms, I can make fire in a world where most people can't. It just earned us real money.
- yequalsx 17y ago
  Interpolating polynomials used to be taught in high schools. I learned it in high school and today almost no high school graduate knows how to do this. Is this a bad thing? I don't think so. With new technology and the advancement of ideas and knowledge the basic skill set that is necessary changes. The division of labor has rendered many once necessary skills the province of specialists. This is a good thing. Is arithmetic one of those things? I begin to believe so. The expansion of (x+1)^8 does not require the ability to do 7*8. One can do the expansion using Pascal's Triangle. Besides, the real question is ought one do the expansion of (x+1)^8 by hand? The answer is no. The expansion is a purely mechanical process. A computer does it faster and more accurately. In such a long problem I am likely to make a mistake and this mistake does not mean that I don't know what I am doing. I do want my doctor to thumb through reference books particularly if my condition is rare. In such a case it is unlikely that the doctor will have encountered my condition and I want her to gain from the shared experience and collective wisdom of experts. That's what a reference book is for and it's a good thing. I want my doctor to be able to read and understand the book. That is what her training is for. One can get insights into algebra using a computer. It's just that the insights are different than what one could get without a computer. Instead of teaching interpolating polynomials in high schools they are teaching basic statistics and in this present age the latter is much more beneficial than the former.

sokoloff 17y ago

It's not just that. I've interviewed senior candidates who can't do basic arithmetic in their head. I had one project management candidate, who was doing fairly well up until that point on the interview loop, who literally couldn't multiply 600 by 3 in their head, nor on the whiteboard.