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"...and proving how I got that answer..." That's the part that counts, and is largely missing today.

nl 12y ago
I'm not at all convinced that has changed. I've read the Common Core (and the Australian equivalent) and they certainly require proving how answers were obtained.
goodcanadian 12y ago
I am not so sure you are talking about about the same thing as the article. Usually, when "proving your answer," I found there was still an expected procedure for you to follow, and you would lose points for deviating from that procedure even if what you did was mathematically correct. What the article talks about is learning how to reason about a problem even if your reasoning is questionable and even if you don't arrive at an answer.
- sanxiyn 12y ago
  That is unbelievably terrible. You would lose points for a mathematically sound justification?!?! For example, when solving quadratic equations, I often used trial substitutions and the fact quadratic equations have at most two solutions to justify answers, instead of using quadratic formula. Why wouldn't this get the full mark? (I would actually argue this is a better procedure if you are looking for integer-only solutions, for example.)
  - fredophile 12y ago
    What do you mean by "trial solutions"? Were you just substituting numbers for x and seeing if they worked out? If that is what you mean I can't see why it would be a better procedure than using the quadratic formula.
    - sanxiyn 12y ago
      Yes, I meant substituting numbers for x and seeing if they worked out. To get integer solutions, it's enough to try divisors of the constant term. Try it yourself. It's faster.
      - fredophile 12y ago
        Yes, it is faster for small integer values. Most numbers aren't small integer values. Test questions are usually designed to give nice clean answers but the real world isn't like that. They were trying to test your ability to solve quadratic equations in the general case. Your approach doesn't demonstrate that ability.

nl 12y ago

I'm not at all convinced that has changed. I've read the Common Core (and the Australian equivalent) and they certainly require proving how answers were obtained.

goodcanadian 12y ago

I am not so sure you are talking about about the same thing as the article. Usually, when "proving your answer," I found there was still an expected procedure for you to follow, and you would lose points for deviating from that procedure even if what you did was mathematically correct. What the article talks about is learning how to reason about a problem even if your reasoning is questionable and even if you don't arrive at an answer.

sanxiyn 12y ago
That is unbelievably terrible. You would lose points for a mathematically sound justification?!?! For example, when solving quadratic equations, I often used trial substitutions and the fact quadratic equations have at most two solutions to justify answers, instead of using quadratic formula. Why wouldn't this get the full mark? (I would actually argue this is a better procedure if you are looking for integer-only solutions, for example.)
- fredophile 12y ago
  What do you mean by "trial solutions"? Were you just substituting numbers for x and seeing if they worked out? If that is what you mean I can't see why it would be a better procedure than using the quadratic formula.
  - sanxiyn 12y ago
    Yes, I meant substituting numbers for x and seeing if they worked out. To get integer solutions, it's enough to try divisors of the constant term. Try it yourself. It's faster.
    - fredophile 12y ago
      Yes, it is faster for small integer values. Most numbers aren't small integer values. Test questions are usually designed to give nice clean answers but the real world isn't like that. They were trying to test your ability to solve quadratic equations in the general case. Your approach doesn't demonstrate that ability.