"The right answer isn't important. It's knowing what you're doing."No matter how you parse this, it's ridiculous. The right answer is the whole point of doing the problem ... has always been, is now, and will always be. The "knowing what you are doing part" leads to the right answer. If it doesn't, then you don't know what you are doing.
Variations on this include: "It's the concept that matters" and "We're putting the emphasis on the method." It shows up as sarcastic responses from Institute Professionals and college professors, too:
@MathCurmudgeon Good thing math is only about answer-getting, then! Phew!What we should be saying is "The right answer is vitally important ... so important that we also want students to explain the method and how we all know the answer is correct; they must be able to detect an error if it occurs and describe how to fix it so that the solution IS correct."
— xxxx (@xxxx)
If you go to the trouble of having the students communicate, verbally or in writing, how they solved a problem, then you are focused on the right answer ... there would be no need to explain anything, or fix errors, if you didn't care about it. You'd take any randomly achieved answer as long as it was correct, and move on.
Just cancel the 6s.
Does anyone ... ANYONE ... seriously think that the right answer doesn't matter here? I don't consider this a "right answer" even though it looks like it.
|I'm going with "No."|
Just cancel the x² from numerator and denominator.
One hallmark of mathematical understanding is the ability to justify, in a way appropriate to the student’s mathematical maturity, why a particular mathematical statement is true or where a mathematical rule comes from. There is a world of difference between a student who can summon a mnemonic device to expand a product such as (a + b)(x + y) and a student who can explain where the mnemonic comes from.That is a far cry from " The right answer isn't important."
For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge.You can't detect errors unless you know the right answer, or at least have a sense of what that right answer should be.
Even the infamous "Letter to Jack" assumed that the kid could get the right answer, then could find the error made by the other kid ... the assignment took this two steps beyond the right answer: explain the error to the other kid and help him fix it.
JD2718 banned FOIL, Dan Meyer used immediate feedback, countless teachers rearrange PEMDAS (as BEDMSA) to avo
We need them to explain what and why.
I often "let them in on a secret" and share the mnemonics after they get the understanding ... especially if the mnemonics speed up computation so we can get on with what we are actually doing, but every teacher worth his salt knows that you have to periodically make sure that random, blind luck isn't at play.
The last reason that we need to stop saying "The right answer isn't as important as knowing what you're doing" is that too often we teachers are speaking to people who don't know that it is merely step 1, namely school boards, administrators and parents.
I watched a young teacher from another school give a presentation to her school board. Among other weird things, she came out with this statement ... immediately, board members latched onto it.
"What do you mean? Of course the right answer matters."
"I've been in business for forty years; every time, the right answer matters."
She doubled down ... "No, they need to know HOW they are solving the problem." No one was buying it, nor should they have. Whether she didn't understand their concerns herself or honestly didn't believe that the right answer was so vital, she certainly couldn't communicate her stance to the Board.
A blind acceptance and repetition of poorly-understood Twitter broadsides and mindless slogans is the rhetorical equivalent of canceling the sixes.
That makes us all look bad and we're gonna need you to stop saying it.