Misconceptions in Mathematics Multiplication and Division Essay Example
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
Multiplication always makes a number larger or it stays the same stays the samesolution larger than original number. 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. olution smaller than original number 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 numb
...er 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 with fractions they should be happy with the following statement when you multiply 2 fractions together you multiply the numerators and the denominators to produce the resultant solution to the problem. i. e. or with numbers One can then approach the multiplication of a positive integer by a fraction less then one as follows; a numbered example;
When c<d and the square root of c x d is non complex then the solution to the problem will always be smaller than a This can be done for division as well, there is an associated point of misunderstanding relating to division of fractions, for a discussion of this see appendix A. An individual that is familiar with division of fractions should be familiar with the result; with a numbered example; One can then approach the division of a positive integer by a positive fraction less than 1 as follows; with a numbered example.
