```Date: May 7, 2013 11:21 PM
Author: Jonathan J. Crabtree
Subject: Dear professor, please stop telling teachers multiplication is<br> scaling.

Multiplication as taught in schools to children is not (only) repeated addition, yet that does not make it scaling.Multiplication makes one thing multiple things or one thing multiple parts of a thing. Quantity spans both the discrete and the continuous.Quantity is the interplay of multitude and magnitude.Questions of math involve, 'How many?' and 'What size?'Multiplication is to discrete multitudes as scaling is to continuous magnitude.Multiplication is not scaling. Scaling is scaling.One small pie multiplied by two equals two small pies.One small pie scaled by two equals one bigger pie.The quantity of two small pies may equal the quantity of one bigger pie, yet the processes (operations) are not the same.Multiplication and scaling can result in the same quantity, yet that does not mean they are the same thing.Multiplication affects the number associated with a quantity leaving the magnitude unchanged.Scaling affects the magnitude associated with a quantity leaving the number unchanged.So dear professor, please stop telling teachers, parents and children that multiplication is scaling.It isn't.Thank you.Jonathan CrabtreeMelbourne Australia
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