Misconceptions in Mathematics Multiplication and Division

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The Family of misconceptions that I will examine is the following; multiplication and division always produces larger and smaller values respectively. This is related to the order in which children are taught the concepts of multiplication, Division and extending the set of numbers from integers to non integers and fractions. Misconception| Demonstration of why this is incorrect|

Multiplication always makes a number larger or it stays the same stays the samesolution larger than original number (5)| Multiplication can make numbers smaller multiplication by a decimal less than 1 multiplication by a fraction less then 1multiplication by a negative| Division always makes numbers smaller or they stay the same.solution smaller than original number (12)stays the same| Division can make a number larger division by a decimal less than 1 division by a fraction less than 1division of a negative number by another negative number| The primary reason that children have this misconception is when they first encounter the functions multiplication and division, they are only being exposed to positive integers, thus the examples that they will have been given and the examples they practiced will all have followed the pattern that multiplication makes numbers larger and division makes numbers smaller. The misconception persists when they individual does not draw a connection to the extension to the numbers space and the implications on the functions. Extension of the number space to decimals and fractions should dispel this misconception, as they should then be exposed to counterexamples to their misconception. In some cases the individual will see the examples they are asked to do as exceptions to their rule rather than a change in the way they perceive multiplication and division. If the individual is familiar with fractions then multiplication by positive numbers less than 1 can be couched in terms of fractions, When an individual is familiar...
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