Anita's son is having a problem in math class. He does complex division problems correctly in his head but his teacher isn't looking for the answer, she's looking for long division. She wants to see the work between the question and the answer.
This is a touchy subject for me. I was exactly the same as her son with long division. I did it in my head lickety split and got the correct answer in a fraction of the time. My teacher enlisted my mother and forced me to go through long division, the very same situation that Anita and her son are in right now.
Why use long division?
The rote answer is "you need to know the process". Why? We use a process that works. We get the correct answer faster. We also get the correct answer more reliably. Long division is only a regressive loop of simple division problems. An error at any step yields a wrong answer. What is wrong with our process?
Absolutely nothing. It is superior to long division in efficiency and accuracy. The problem is that only a fraction of students can do division this way so it is not permitted in school. This is lowest-common-denominator instruction at its worst. Hold back the advanced students to the limits of the generic lesson plan. It is incredibly frustrating to somebody who is being thrashed with it.
I despised my math teacher after the long division debacle and my opinion of my mother went down several notches as well. My "math sense" went way down and I started hating math class, formerly my favorite subject. I got fed up to the point where I forcibly rejected long division. I spent months unlearning the method that had been hammered into my brain and relearning my method. Once I'd removed the taint and returned to my method the problems went away and I enjoyed math class again.
A few years later I was placed in an advanced self-paced math program. The guide/teacher not only acknowledged fragmented division (the name he gave to my particular method) but promoted it. Do a Google search for "long division in my head" and you'll see just how common this is.
My advice to Anita? Don't force your son to lose his process. Educate the educator. If she can't be brought around to the fact that there is more than one way to do division then you face a very tough choice. Maybe he can use his method to get the answer and then use long division to provide the proof. That will frustrate him too, but not as much as having to abandon his method.
When it all comes down to it though it's about education and not grades. He has the education part covered and it's superior to what the teacher is trying to impose. I'd rather have that and an "F" than to go through what I went through.
Both myself and, to a greater extent, my brother had the same problem. In British maths exams, you get say 3 or 4 marks for the working, but only 1 for the correct answer (lowest common denominator, again - they know the theory but can't actually plug the numbers into it - still only lose 1 mark). So we learnt very quickly that even if we could go through the paper and jot down the answers quickly, we would still have to go back through it and write down the working, even if we never actually used it.
What always confused our teachers was when we misread a number when we were copying out the working - so the answer from the working should have been different to the one we actually gave...
Whoa. I really didn't expect to see a response like this. It honestly never occurred to me that this could really be a way to do division in the long run with hard problems. I just assumed that it was easy for my son now, but that later it would become impossible.
You really have given me food for thought. I'm off to google "long division in my head" to see what I find.
I appreciate hearing from someone who has been through this.
This is why I hate math to this day. The process, no matter how difficult and incomprehensible, is more important than getting the right answers. Oddly enough, while I barely passed any math class after this, I always got excellent grades in Chemistry or Physics. Go figure!
That's an understandable concern. It's unneeded though - "short division" is just as scalable as long division.
Ok - so I googled "long division in my head" and I came across one of those hits you wouldn't normally read, then I had too...
http://www.wordriot.org/template.php?ID=449
Completely unrelated, yet somehow appropriate given Jim's normal subject matter. :-)
I had no idea people could seriously have such a problem. There is one guy here at work who is infamous for his stall usage (and subsequent on the seat pissage) and we always figured that he suffered from "infantile penile syndrome." Perhaps he just needs to do long division...
I had the same "problem" to an extent when I transferred schools one year (long story). Like Dafyd, I ran into problems when I "did" the work--right answer, wrong process.
I always did the "work" so the teacher wouldn't suspect me of cheating, and that might have something to do with the teacher's insistence on Anita's son doing the work. Jim, I'm sure you'll agree: sometimes you have to fight your battles and sometimes you just have to accede. This may be one of the times to choose the latter.
You do have to pick your battles but this is one I'd be willing to fight. It's incredibly rough on a kid to know that he's right and that he's being forced to do something poorly for no reason whatsoever. His skill and ability need to be celebrated and nurtured, not stomped on because of an inflexible lesson plan.
I went through the same crap in Germany.Right answer,wrong process,therefore an F on the test.You are correct but....
My Dad didn't make it any easier on me because,eventho I was right,he was pissed for the F and I was stamped as a "rebellious" kid by the school because I refused to acknoledge wrong when I was RIGHT.
Failed math class therefore,year after year.
If you watch the Day After Tomorrow... the kid has the same problem at the beginning of the film...
I was the same way - I hit algebra in the fourth grade, and could compute things way faster than anyone else in the class, but when my teacher asked me to help mentor some of the other kids, show them my work, I didn't have work to show. I had little tricks that helped me remember things, special digit flips and such, but no one understood them like I did.
Chances are, Anita's kid is one of those special kids (and when I say special, I mean special) that should be given more challenging things to chomp on, instead of being held back by the rest of the class.
I'll join this chorus.
I started long division in 3rd grade and quickly learned how to do it -- not in my head -- but the class dwelled on the topic for MONTHS. After only a few weeks, I began just making up numbers because I lacked the patience to continually divide numbers out to 43 places. It was, in my young mind, a waste of time, energy, and paper when the concept was established and calculators readily available.
After years of that sort of math instruction, I got to 9th grade and still had not mastered the concept behind fractions. (Ironic, I know.)
Fortunately, one teacher took the time to explain math to me and was able to set me on the path to righteousness. Sadly, the damage was done and to this day I'm not very good at math even though I'm good at logic.
I would definitely urge Anita not give in to this misguided educator. There is simply no possible way her son could ever get the right answer if he had not already mastered this all-powerful process. To suggest that someone doing math in their head is not doing math is beyond idiotic.
Wow. This is good to know about, Jim. I don't think I've known anyone who could do long division in his/her head. Certainly not worth battling about if it has the potential to squelch someone's interest in math.
Trey hinted at the true nature of the problem: the teachers. If you are lucky enough to have a teacher who loves their subject and understands it, as I did in maths, they can show not just the how, but the why as well. Even more important is to recognise that not everybody has the same ability; some kids will be like Jim and work out different ways of doing things. That's to be encouraged, but it takes a huge amount of effort for a teacher of a class of 25 kids to recognise 25 sets of abilities.
The biggest problem is the teachers themselves. I fear many of them only know the process they've been taught and don't have the understanding or tools to cope with lateral solutions. In maths teaching it forces many kids to be put off the subject because they are squeezed into a rote learning of method model. Teach the teachers better and the consequences take care of themselves.