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Yeah, Wolframalpha is a disruptive technology. Is it still relevant to learn algebraic manipulations? I don't know. There are compelling arguments for both p

Yeah, Wolframalpha is a disruptive technology. Is it still relevant to learn algebraic manipulations? I don't know. There are compelling arguments for both points of view. When you say problem solving do you really mean so called practical applications? If so then I disagree. If you mean solving problems to understand the essence of mathematical ideas then I agree. For instance, linear equations are the easiest equations to solve. All of them can be manipulated to yield the solution (or be reduced to showing all numbers are solutions or have no solutions). Linear equations are really 1st degree polynomials. What about second degree polynomials? After a clever bit of insight and some work we get that all 2nd degree polynomials can be solved. The quadratic equation is a solution to a problem in mathematics. It's useful as it leads to a greater understanding of mathematics. I believe that this is what mathematics courses ought to focus on. Not on problems that involve throwing a ball in the air and predicting how long it takes to hit the ground.

jimbokun 17y ago
"Yeah, Wolframalpha is a disruptive technology. Is it still relevant to learn algebraic manipulations?" We've had calculators for decades now, and my kids are still learning how to do arithmetic.
- yequalsx 17y ago
  But is it worthwhile or important?
  - jimbokun 17y ago
    I think it is. If you can't perform the algorithms yourself, I don't think you really understand what the symbols on the machine really mean. When I worked at a bank, I remember complaints about an employee whose job involved running certain calculations in a spreadsheet. Sometimes the numbers would be off orders of magnitude due to some error somewhere, but the employee would just carry on as normal. If you have some clue as to what the calculations are supposed to be doing, there should be some alarms going off if the numbers are not at least reasonable. Or what if you just wrote a program that includes some arithmetic calculations, and need to verify that you are getting the right answers for your test data? I remember another time at that same bank, where a developer did not know that multiplication had precedence over addition, which led to errors in a financial calculation. I'm sure you could easily think up many more examples like this.
    - yequalsx 17y ago
      There was a time when it was important to know how to use interpolating polynomials. Rationalizing the denominator was only useful before calculator became ubiquitous. Being able to make fire was without use of matches or flint used to be essential. There are plenty of ways to teach algorithms without using arithmetic. Maybe a knowledge of doing basic arithmetic by hand is essential to understanding higher math. I don't know. It's worth exploring though.

jimbokun 17y ago

"Yeah, Wolframalpha is a disruptive technology. Is it still relevant to learn algebraic manipulations?" We've had calculators for decades now, and my kids are still learning how to do arithmetic.

yequalsx 17y ago
But is it worthwhile or important?
- jimbokun 17y ago
  I think it is. If you can't perform the algorithms yourself, I don't think you really understand what the symbols on the machine really mean. When I worked at a bank, I remember complaints about an employee whose job involved running certain calculations in a spreadsheet. Sometimes the numbers would be off orders of magnitude due to some error somewhere, but the employee would just carry on as normal. If you have some clue as to what the calculations are supposed to be doing, there should be some alarms going off if the numbers are not at least reasonable. Or what if you just wrote a program that includes some arithmetic calculations, and need to verify that you are getting the right answers for your test data? I remember another time at that same bank, where a developer did not know that multiplication had precedence over addition, which led to errors in a financial calculation. I'm sure you could easily think up many more examples like this.
  - yequalsx 17y ago
    There was a time when it was important to know how to use interpolating polynomials. Rationalizing the denominator was only useful before calculator became ubiquitous. Being able to make fire was without use of matches or flint used to be essential. There are plenty of ways to teach algorithms without using arithmetic. Maybe a knowledge of doing basic arithmetic by hand is essential to understanding higher math. I don't know. It's worth exploring though.