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EDSC 1262nd sem, 09-10TRANSCRIPT
How to Teach Fractions
ProblemFractions = one of the most difficult
concepts for children to grasp Notation of fractions Formal vocabulary Learners may be able to draw and
label fractions correctly, but not be able to put them in order of size, or use them to solve problems.
Do not behave like ‘normal’ numbers
How to Teach FractionsIt is important that learners think
about relationships between fractions, rather than just trying to memorize methods for processing them.
FACTUAL
FACTUALCONCECPTUAL
We should move towards a more holistic approach when teaching
fractions.
Teachers’ MistakesSyntactic vs. Semantic emphasis
◦Technical procedures instead of understanding/meaning
Adult- vs. Student- centered approach◦Ignore ‘prefactional’ knowledge◦Adult concepts are very different from
children’s
Confusing representation
Multiple RepresentationsStudents given multiple
explanations can have…◦Greater conceptual understanding◦Transfer knowledge to tasks not
directly taught to them
Different Interpretations for the Fraction ¾ (Lamon, 2001)
Interpretation Example
Part/Whole 3 out of 4 equal parts of a whole or a set of objects
Measure ¾ means a distance of 3 (1/4 units) from 0 on the number line
Operator ¾ of something, stretching or shrinking
Quotient 3 divided by 4, ¾ is the amount each person receives
Ratio 3 parts cement to 4 parts sand
Provide exposure to other types of interpretations Ignoring other ideas leaves incomplete understanding
Multiple RepresentationsLearners need to be familiar with multiple representations of fractions, andshould always be given more than one representation.
1/3 of the class are boys.
Multiple RepresentationsUse a variety of mediums to
illustrate the same fractionSharing CakesClockManipulatives
Multiple RepresentationsWhat fraction of the hats are red?
Multiple RepresentationsWhat fraction of the circles are
blue?
Multiple RepresentationsPictorial representations of a particular
fraction may be of different sizes and different shapes. For example, don’t always use shaded sections of circles.
When you divide things into fractions it doesn't matter how you do this as long as the parts are all equal in size.
Multiple Representations
Multiple RepresentationsUse manipulatives when
introducing fractions. Practice cutting different shapes
into fractions.
How to teach FractionsStudents learn more if they
actually enjoy the activity, have a chance to discuss what they do, explain their work, and reach a shared understanding.
Conceptual Understanding
Making connectionsIntegrate into other math topicssolving money problemssharing a billcomparing pricescalculating journey times
Making ConncetionsCookingchecking the weight of
ingredients
Making ConnectionsInterpreting data in pictograms
and bar chartsUsing a metre ruleMeasuring a roomComparing each other’s heights
Making ConnectionsAsk learners to think of some
fractions they encounter in an everyday context
Classifying FractionClassifying different
representations of fractions, or statements about them, can be a very effective method of encouraging learners to reflect on and discuss their properties
Evaluating statements about fractionsLearners are given some
generalisations about fractions, perhaps printed out on separate cards, and are asked to choose whether they consider these to be ‘always’, ‘sometimes’ or ‘never’ true, and to justify their choices, with examples and convincing explanation.
Links outside the classroomMany learners do not use their
understanding of fractions outside the classroom, and are unwilling or unable to transfer it to ‘real life’ problems.
Encourage children to give names to the fractions they see in everyday life.
Did your family have meatloaf for dinner last night? How many pieces was it cut into? How many pieces did you eat?
Encourage kids to share.
Links outside the classroom
Links outside the classroomThe proportions of the human
body provide links with art, and with dressmaking/tailoring.
Artists assume the eyes are half-way down the face, the nose half-way between the eyes and the chin.
Fraction Quotes A man is like a fraction whose
numerator is what he is and whose denominator is what he thinks of himself. The larger the denominator, the smaller the fraction.
—Leo Tolstoy“We live but a fraction of our
lives”— Henry David Thoreau
GamesFraction War Game Show (Jeopardy)FairytalesFraction Blackjack