EFFICIENT TEACHING OF
A good understanding of common fractions forms the basis for an understanding of decimal
fractions, percentages and the decimal measurement system. It is also necessary for algebra,
algebraic manipulations, probability and statistics.
A good understanding of common fractions forms the basis for an understanding of decimal fractions,
percentages and the decimal measurement system. It is also necessary for algebra, algebraic manipulations,
probability and statistics.
Logico-mathematical knowledge is constructed inside the brain. It refers to the knowledge of relationships,
and relationships don’t exist until we make them. In other words, it refers to internal knowledge constructed
by learners for themselves. Teachers must therefore refrain from direct instruction and design situations from
which learners can construct and develop their own logico-mathematical knowledge.
If the experiences only provide them with limited views of a concept, their minds may be closed to other
aspects of the specific concept. This will result in limiting constructions.
Research strongly indicates that teaching that gives a limited vision on fractions could cause some limiting
constructions in learners.
Here are a few examples of limited visions:
1. During the first few grades learners multiply with only whole numbers (integers). When you multiply two
whole numbers (not 0 or 1), the answer is always greater than either of the numbers. This develops the
limiting construction that ‘multiplication makes bigger’, which severely hampers children’s understanding of
how fractions behave.
Example: ½×½=¼ (the answer is smaller)
2. Some learners perceive the fraction notation as made up of only two whole numbers and, therefore, apply
whole number strategies which are not correct. This can be prevented by suspending the initial exposure to
the fraction notion as soon as possible. Teachers could rather use ‘two thirds’ instead of its fraction form (2/3)
as this will highlight the fact that the nominator is a quantity and the denominator is a unit.
Example: 3 / 5 × 2 / 5 = 5 / 10 (the numerators and denominators are added)
3. When children had a limited exposure to part-whole concepts, they believe that a fraction is only part of a
single circle or square. They cannot solve a complex problem like sharing three pizzas among four friends or
determining one third of a class of 27 learners.
4. The strategy of repeated halving – half, quarter, eights, etc. – to obtain smaller fractions is so dominant in
some learners that they find it difficult to imagine how something can be divided into thirds, fifths, sixths and
other fractions. This misconception is enhanced by repeatedly folding a piece of paper, as they can then only
imagine fractions in parts of a half.
5. When pictures and manipulatives such as apples or pizzas are used to teach equivalent fractions, the concepts
formed in the learner’s mind stay tactile and literal. Learners should develop the ability to reason about
fractions. Therefore, teaching should present realistic problems that encourage children to invent their own
solutions. That way, the understanding of fractions can develop from the learner’s own thinking.
6. When rules and techniques are given as social knowledge and children are required to memorise it, they
may never have a sound understanding of what the fraction concept entails.
16
Example: ‘Invert the last one and multiply’ when doing division with fractions.
CURRO IN THE CLASSROOM | FROM THE CLASSROOM TO THE WORLD | WWW.CURRO.CO.ZA