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Technology use in education?

  1. Jan 7, 2017 #21
    I know I could do a bunch of integrations correctly long before I could visually inspect slope functions and reconstruct the actual functions with just eye and a sketch.

    The latter is way more important I think in analysing problems than following a set of calculations that give the correct answer with no intuitive insight.
     
  2. Jan 7, 2017 #22

    Mark44

    Staff: Mentor

    I agree, to a point. One should be able to set up an integral correctly, but it's also important to be able to complete the calculation and arrive at the right answer, including at times, without the use of technology.
     
  3. Jan 7, 2017 #23
    OTOH few calculations, if any, in the real world would ever be trusted in human hands in terms of a manual calculation.

    That cuts both ways, the local radiotherapy unit here requires by law that all treatment plans simulated on a computer must be eye-balled by a human with a few point calculations done.

    The computer can optimise the plan but also fry a spinal cord in the process leaving the patient a paraplegic.
     
  4. Jan 7, 2017 #24

    Mark44

    Staff: Mentor

    Right, but we're talking about tech use in education, not the "real world." As someone said earlier in this thread, students should know how to do relatively simple problems by hand (i.e., paper and pencil) first, and once they are proficient, then they should be allowed to use the available technology.
    One example that comes to mind was the division bug in the first Intel Pentium chips, discovered in 1994 (see https://en.wikipedia.org/wiki/Pentium_FDIV_bug). Certain division problems came out incorrect, but the error was not glaringly obvious, as it occurred out in the 6th or so decimal place, and only for certain pairs of numbers. Total reliance on computing devices can come with a cost. Recalling all the bad Pentium chips cost Intel close to $500,000,000.
     
  5. Jan 7, 2017 #25

    lurflurf

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    ^I love my defective Pentium, I am holding it right now. Yes, if you use a 24 year old processor and ignore a well known and easily avoided bug that is accounted for in all competent software to perform 360 billion divisions you will be wrong about forty times. This error will usually be in the ninth or tenth digit but once or twice it will be in the forth digit. I know when you need to do 360 billion divisions you do them by hand faster and more accurately than that 24 year old Pentium can. I am not that good so while I would probably use a newer processor or avoid the error with software, in a pinch I would take my chances with the Pentium.
     
    Last edited: Jan 8, 2017
  6. Jan 8, 2017 #26

    Mark44

    Staff: Mentor

    This is not an all or nothing choice. What I and others in this thread are saying is that while technology is useful after some basic concepts have been mastered, you have to be aware of its limitations. Being able to do 360 billion arithmetic operations per second is of no use if most of them are wrong. For a more modern example that doesn't rely on a bug in a particular 24-year-old CPU, consider this:
    Code (C):

    float sum = 0.0;
    for (int i = 0; i < 20; i++)
       sum = sum + .05;
    if (sum == 1.0) printf("Success\n");
    else printf("Failure\n");
     
    Here we are adding .05 to itself 20 times, so the result should be 1. After only 20 additions (orders of magnitudes fewer than 360 billion!), the output is "Failure" because sum is measurably larger than 1.0. On my Pentium i7 system running Visual Studio 2015, sum ends up at 1.00000012. The same code will produce similar incorrect results on other architectures and other compilers.
     
  7. Jan 8, 2017 #27

    lurflurf

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    ^
    It must have been your lucky day you were only off in the least significant bit.
    That is a perfect result let us rejoice at the power of technology.

    It takes me a long time to do 360 billion arithmetic operations. Computers only get most of them wrong in the unfair sense that they have limited precision. That is not really wrong. The Pentium misses the precision goal on 40 out of 360 billion divisions, even that is not so bad. If more accuracy and precision are needed by all means double check results that is how the error was found. Hand calculation is quite useless and a waste of time. I am moderate on the issue. Spend a thousand hours or so practicing your hand calculations if you like, you will not be able to beat a 20$ calculator much less a 200$ calculator/tablet or 2000$ computer.
     
  8. Jan 9, 2017 #28

    Andy Resnick

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    2016 Award

    Can you expand on this a bit? Specifically, why you consider education disjoint from the 'real world'.
     
  9. Jan 9, 2017 #29

    Mark44

    Staff: Mentor

    When students first learn some technique, such as finding the factors of a polynomial, or solving a differential equation, or calculating the trajectory of a thrown ball, there are assumptions usually made to make the calculations simpler. After the students attain some proficiency at the particular technique, some of the simplifying assumptions can be relaxed, so that the problems can at least approach those of the real world.
     
  10. Jan 9, 2017 #30

    Mark44

    Staff: Mentor

    You're repeating yourself. The argument here seems to be that quantity trumps quality. Either that or you're just trolling.
     
  11. Jan 9, 2017 #31

    Andy Resnick

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    2016 Award

    I hear what you are saying, I would reply that "when learning something new, try to deal with a simplified situation before dealing with the full mess" is a common and important real-world situation. In the context of STEM classroom technology, the processes of simplification and complexification can be clearly demonstrated.
     
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