Is right answer important in math?
I want to discuss this topic because of a possible confusion. Recently in a blogpost I linked to the article Math anxiety, which mentions this math-related myth:
MYTH #4: IN MATH, WHAT'S IMPORTANT IS GETTING THE RIGHT ANSWER.
Then, in another recent post I linked to an article Things not to learn in school where the author strongly convinces us that getting 70% in a test is not enough since in real life you need to get it 100% right.
So is it important to get the right answer when doing a mathematics problem?
Well, yes but it depends. This is not a simple cut-and-dried question.
It IS important if you're drilling multiplication facts.
But many times it's not your focus. For example, when a student is learning to do long division or multiplying 4-digit numbers, the emphasis should be in learning the procedure and why it works. Calculation mistakes might yield a wrong answer, but if the way the division was done is right, then some credit should be given.
And obviously all children need encouragement while they're learning - they need partial credit or acknowledgment of things they did do right, even if the final answer was wrong.
Often times, you can use a wrong answer as a springboard and delve into the WHY the calculation went wrong. There's lots of learning one can do from wrong answers.
See, in my mind kids should be taught from early on to check their answer, always be CRITICAL of their answer, "suspicion" it until they themselves can "prove" to themselves that their answer is indeed right.
They need to learn to think twice before they do things in life. Well, in mathematics we can teach them to do something similar: when the problem is done, go back and check. Think it thru again. Does the answer make sense? Can you check it? If you estimate, is your final answer in agreement with your estimation?
So a wrong answer just means your student hasn't yet perfected this "checking and criticizing your own work" process - you know, learning to think critically about your own thought processes.
Encourage your students to point it out in their exam paper, if they know they got a wrong answer but can't find their mistake. You should give more credit to that answer than to the same wrong answer without that explanation (though not full credit of course).
Categories: philosophy
MYTH #4: IN MATH, WHAT'S IMPORTANT IS GETTING THE RIGHT ANSWER.
Then, in another recent post I linked to an article Things not to learn in school where the author strongly convinces us that getting 70% in a test is not enough since in real life you need to get it 100% right.
So is it important to get the right answer when doing a mathematics problem?
Well, yes but it depends. This is not a simple cut-and-dried question.
It IS important if you're drilling multiplication facts.
But many times it's not your focus. For example, when a student is learning to do long division or multiplying 4-digit numbers, the emphasis should be in learning the procedure and why it works. Calculation mistakes might yield a wrong answer, but if the way the division was done is right, then some credit should be given.
And obviously all children need encouragement while they're learning - they need partial credit or acknowledgment of things they did do right, even if the final answer was wrong.
Often times, you can use a wrong answer as a springboard and delve into the WHY the calculation went wrong. There's lots of learning one can do from wrong answers.
See, in my mind kids should be taught from early on to check their answer, always be CRITICAL of their answer, "suspicion" it until they themselves can "prove" to themselves that their answer is indeed right.
They need to learn to think twice before they do things in life. Well, in mathematics we can teach them to do something similar: when the problem is done, go back and check. Think it thru again. Does the answer make sense? Can you check it? If you estimate, is your final answer in agreement with your estimation?
So a wrong answer just means your student hasn't yet perfected this "checking and criticizing your own work" process - you know, learning to think critically about your own thought processes.
Encourage your students to point it out in their exam paper, if they know they got a wrong answer but can't find their mistake. You should give more credit to that answer than to the same wrong answer without that explanation (though not full credit of course).
Categories: philosophy
Comments
A lot of the confusion about what some of us believe is caused by misunderstanding of this issue. This isn't, in my opinion, a matter of so-called "self-esteem" or "feel-good math," but rather understanding what's really important in a given context. As you've suggested, getting the right answer in a single-digit multiplication problem is mostly what it's all about. However, for younger students just encountering the concept of multiplication, having the right idea about how to conceptualize what multiplication is may be more important than getting the exact answer. Context and who is doing the problem are far more important than we are generally led to believe.
I don't think it's that "It's okay you didn't get the right answer" as much as it is that "It's okay that you made an error." Does that sound like a distinction without a difference? If so, think about it a bit. We learn from making mistakes. Understanding why we got something wrong is probably more helpful than simply being told, "Oh, you goofed. Well, you'll do better next time." Mistakes are great tools for learning, if we take advantage of them as teachers and learners. If it's just a "simple" computational error (we knew how to do it and made a slip) that's fine, and probably isn't all that instructive. What can I tell the student? Be more careful next time? Sure thing, teach!
But a misconception about what's going on that is revealed through an error should be a powerful opportunity for correcting the misconception if the teacher understands that and knows how to help the student learn from the error. If we made getting the right answer the be all and end all, then why would we bother to try to analyze errors? They're "bad," aren't they? Aren't all wrong answers equally "wrong," and hence lacking in value? Obviously, I don't feel that way at all.
My main concern is that teachers and students learn to look carefully at errors (and, by the way, at the wrong answers on multiple choice standardized tests, to understand why they were put there and why they are wrong). Wrong answers are GREAT, in that regard). So that when someone says, "Reform math teaches kids that the right answer doesn't matter," those of us who know that isn't the point at all will be able to explain what that means.