A successful method of teaching fractions to primary children is vividly captured in Just a Fraction. This programme (click on link to watch the programme) follows a group of seven-year-old pupils at Janvrin School in Jersey, UK.
The technique used is visualisation. For this only the simplest resources are needed: paper cups carefully cut into halves and quarters, cards representing different fractions - and two tables!
The children are invited to write down a maths "story" on a white board. Demonstrators drawn from the class then play out the maths story with paper cups.
The sum set is 1¼ + 3 - 2¼. So one whole cup, then one quarter-cup, are moved from the resources table to the maths table. As the story involves an addition, three more cups are taken to the maths table, then for a subtraction two and a quarter cups are taken from the maths table to the resources table. Next, the children add up the cups on the maths table to complete the story. They move on to see how cards containing the usual notation for a half and a quarter can be transported in the same way.
By the end of the lesson, some children understand the concept and can go from the concrete to the abstract, but still visualise the concrete when they are unsure of a calculation. The change of emphasis away from calculation is easy for any child to understand.
This programme demonstrates:
How to introduce children to fractions using concrete representation (cups)
How to move from the concrete to the symbolic (number cards)
How to translate symoblic ability to abstract thought