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Do you need to understand that addition is commutative, or even what commutative means, to use the schoolboy multiplication algorithm? How is that anything oth
by bradleyjg 3y ago
Do you need to understand that addition is commutative, or even what commutative means, to use the schoolboy multiplication algorithm?
How is that anything other than a “step by step methods that allow[s] you to arrive at a solution without needing to understand what you are doing?”
- dotnet00 3y agoThe point is that math is not typically taught as just memorizing the schoolboy multiplication algorithm without being given an understanding that addition is commutative and what commutative means.
- bradleyjg 3y agoI challenge you to select a random high schooler and report back on his or her knowledge of commutativity.
- peteradio 3y agoIf you ask them if A+B=B+A I'm sure they'd tell you yes for the most part. Quizzing on vocabulary is hardly the point.
- bradleyjg 3y agoAnd be able to explain why that must be true for schoolboy multiplication to work. Come on, this argument is ridiculous. There was no golden age of mass mathematics education.
- jjk166 3y agoThat is moving the goal posts to a different stadium. I don't think I could explain that now, there's no reason for a child to be required to do so.
- bradleyjg 3y agoReal understanding of concepts has been replaced with step by step methods that allow you to arrive at a solution without needing to understand what you are doing. This is exactly what happens with multiplication (and simplify fractions and taking derivatives). That’s been exactly my claim all along. Virtually no 16 year olds know why the procedure they were taught to multiply 123 x 456 produces the correct answer. Not today, not 20 years ago, not 50 years ago. They know how to execute the algorithm. That’s it.
- dotnet00 3y ago"This argument is ridiculous" only because you keep shifting goalposts and refusing to actually back up anything you're saying while just repeating your personal belief that mathematics has always been rote memorization of algorithms. If it was that way, there would not be so much variation between performance in math around the world, as they'd all just be having kids memorize the same stuff.