Multiplication - Do you I have to show the work?
View PDF (printable) versionTeachers have uttered the mantra of "you must show the work!" since any of us can remember. But is there any good reason for it?
The only reason that would make sense is to find out if the child understood the problem.
But if a child can consistently get the right answers to multiplication, or other math equations, what good reason would there be for him or her having to show work? Does the teacher think the child doesn't know how to do the problem? That would be crazy, because the child clearly just did the problem!
In English class, when they ask a pupil to read a paragraph, and s/he does it well, do they say, "Okay, now write an essay on how you knew how to read that?"
How nuts would it be to ask a kid in gym class how they ran that mile, or else the running wouldn't count?
What if, in history or social-studies class, students were required not only tell you who won the Battle at Gettysburg, but prove it, with archeological facts. It might be a nice exercise once, but for every question?
"Hey, Picasso, put down that brush and write a 300 word essay about why you put two eyes on the same side of that woman's head. If you can't, I'm afraid we'll just have to rip it up and do it again right, won't we?"
No wonder Einstein said, "Education is what remains after one has forgotten everything he learned in school."
All too often, the wonderful experience that should be school is turned into a learner's nightmare because of ill-thought-out pedagogical dogma.
Schools seldom take into account that different students have different learning styles. Misguided efforts like the "No Child Left Behind" act (what a cynically sinister misnomer!) would have you believe that there's one thing to learn, one way to learn it, and one way to test it. (Maybe more than the name is sinister!)
People who do not understand people who are "different" have a hard time reaching them. The loss is on both sides.
If you'd like some insights to the problem and some possible solutions, you might find them at http://mathmojo.com/chronicles/2009/04/16/why-do-we-have-to-show-the-work/
About the Author
| mathmojo
If you or someone you know (your child or student, maybe?) hasn't totally mastered the "multiplication tables," you'll be happy to know that there is a fool-proof, easy way to teach or learn the basic times-tables in minutes. If you are serious about teaching multiplication, you owe it to your child or your students to Learn to Multiply at http://Learn2multiply.com, now.
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Telling the student to show work actually helps the teacher. If the student shows their work and gets the problem wrong then the teacher could see what mistakes the student is making. Just say the student is solving (1/2) x 3 wrong. The student could be making the simple mistake of multiply the three by the two to get (1/6). With the student showing their work, the teacher can tell if the strudent is doing it wrong and can correct them. If the student didn\'t show work even for bigger problems, it would become complicated for the teacher to find out how the student got the wrong answer.
Also there are some problems that you can solve many ways to get the same answer but the logic to the problem might not be correct for every probelm. For example, Don says that (16/17) > (11/12) because 16>11 and 17>12. Even though he is correct that (16/17) is greater than (11/12) is logic and reasoning to how he found the answer is not because if you take (3/12) and (1/4), Don would say (3/12) is bigger because 3>1 and 12>4 but we know those equations are the same if you reduce (3/12).
It is not just to help the student see what they are doing but it is to help the teacher see if the students are making a mistake.