We discuss the main obstacles in the learning of fractions - the numerator denominator notation, linkage between whole number knowledge and fraction calculation as well as the to distinct use of fractions.
Do students know the numerator is the 'number' and denominator is the name of the parts which are derived from a whole? If they do then they can easily compute 3 fifths - 1 fifth because it is no different from 3 cookies - 1 cookies.
Do students link what they do in whole numbers to what they do in fractions? If they do then they know why they need to have common denominator in 3 fifths - 2 tents. It's the same as in 1 ten - 3 ones, you need to have the same noun before subtraction. 10 ones - 3 ones.
Do students know that factions can be used as a quantity eg 1/2 lb as well as a proportion eg 1/2 of the class? If they do then calculating 1/3 of 6 sevenths is easy. It is no different from calculating 1/3 of 6 apples.
We also discuss how to help students identify correct operations in solving word problems.