Education, politics, and anything else that catches my attention.
Sunday, July 15, 2007
Multiplication Method
I've seen this done before, but it looks more complicated and less elegant than the standard method.
Still, there's no reason not to try it if the standard method doesn't work for some students.
12 comments:
Anonymous
said...
But, Darren ... when should one expect a student to get past the lattice method of multiplication? Unfortunately what I've found is that the ones who are still multiplying with lattice in the 6th grade move only to a calculator and by the eighth grade they are lost to math.
In my class, the lattice multipliers take about 4 times as long to multiply as the "standard" method users.
As I said, it's an alternative *after* the standard method just isn't working for a kid. I'd probably teach such kids both methods in tandem, to see if there's any "crossover" learning that takes place.
My point is that teaching the same method over and over without success calls for a different tactic.
I tried it out and it works just fine. You just put a zero in the hundreds column. (487*029) Understand that I am not advocating this algorithm over any other, but since we all seemed to be sharing alternatives, I thought I'd toss in this one.
You confuse what I recommend with the fuzzies. They throw a bunch of methods out and let kids pick what they like best, or let kids invent their own. I would teach a standard algorithm, and if a student couldn't learn to do it properly, try another method. My way would be drawing on a student's learning in one area (the trellis method) to reinforce learning in the standard, more efficient method.
What's your recommendation for students who haven't learned to multiply? Just keep doing it over and over?
It's sort of hard to answer the question about what to do if a kid couldn't learn multiplication (assuming you are speaking specifically about multi digit multiplication, and assuming the kid had mastered his multiplication facts).
I quite simply find it impossible to believe that any kid couldn't master the standard method. If for some reason they couldn't then I doubt that it would even be possible to learn an alternate method. Any method is made up of specific recurring steps that must be done in order.
I also wonder where we would get the time to effectively teach another method. It's my understanding that instructional time is precious. There is also the slippery slope that goes, if the hypothetical child couldn't learn the first two methods, then should we continue to keep trying methods until one works...
Short answer: If a kid couldn't learn how to use the standard method; more time, more practice, change how you teach, but don't change what you teach.
Side note: I do appreciate these other methods, and I have no problem if they are taught to kids in Algebra class, but only after the kids have mastered the standard method. I am a "math" guy. Hell, I even enjoyed proofs. I think math can be magical, and problems are a puzzle to be solved, but I am a traditionalist.
12 comments:
But, Darren ... when should one expect a student to get past the lattice method of multiplication? Unfortunately what I've found is that the ones who are still multiplying with lattice in the 6th grade move only to a calculator and by the eighth grade they are lost to math.
In my class, the lattice multipliers take about 4 times as long to multiply as the "standard" method users.
Bob
This method works best for me:
http://www.youtube.com/watch?v=owMjAbkU1eE
: )
As I said, it's an alternative *after* the standard method just isn't working for a kid. I'd probably teach such kids both methods in tandem, to see if there's any "crossover" learning that takes place.
My point is that teaching the same method over and over without success calls for a different tactic.
Eric, you smart alec, I knew what he was going to draw before I even started the video!
How about this one.
http://sciencehack.com/videos/category/10
Nifty. Now how about 487*29?
I tried it out and it works just fine. You just put a zero in the hundreds column. (487*029) Understand that I am not advocating this algorithm over any other, but since we all seemed to be sharing alternatives, I thought I'd toss in this one.
"I'd probably teach such kids both methods in tandem, to see if there's any "crossover" learning that takes place."th
Kids struggle to learn even one method... your idea to teach both is exactly the thinking that "new math" advocates have.
This might be a neat trick to show in a High School class, but why confuse 3rd and 4th graders?
You confuse what I recommend with the fuzzies. They throw a bunch of methods out and let kids pick what they like best, or let kids invent their own. I would teach a standard algorithm, and if a student couldn't learn to do it properly, try another method. My way would be drawing on a student's learning in one area (the trellis method) to reinforce learning in the standard, more efficient method.
What's your recommendation for students who haven't learned to multiply? Just keep doing it over and over?
http://www.youtube.com/watch?v=uPgc2umPCyU&NR=1
works best for me
Don't you know Spanish? It's el boxo DEL Diablo. =)
Darren,
It's sort of hard to answer the question about what to do if a kid couldn't learn multiplication (assuming you are speaking specifically about multi digit multiplication, and assuming the kid had mastered his multiplication facts).
I quite simply find it impossible to believe that any kid couldn't master the standard method. If for some reason they couldn't then I doubt that it would even be possible to learn an alternate method. Any method is made up of specific recurring steps that must be done in order.
I also wonder where we would get the time to effectively teach another method. It's my understanding that instructional time is precious. There is also the slippery slope that goes, if the hypothetical child couldn't learn the first two methods, then should we continue to keep trying methods until one works...
Short answer: If a kid couldn't learn how to use the standard method; more time, more practice, change how you teach, but don't change what you teach.
Side note: I do appreciate these other methods, and I have no problem if they are taught to kids in Algebra class, but only after the kids have mastered the standard method. I am a "math" guy. Hell, I even enjoyed proofs. I think math can be magical, and problems are a puzzle to be solved, but I am a traditionalist.
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