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Problem Fractions = 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 Fractions It is important that learners think about relationships between fractions, rather than just trying to memorize methods for processing them. FACTUAL CONCECPTUAL FACTUAL We should move towards a more holistic approach when teaching fractions.
Teachers’ Mistakes Syntactic 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 Representations Students 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) Provide exposure to other types of interpretations Ignoring other ideas leaves incomplete understanding
Multiple Representations Learners need to be familiar with multiple representations of fractions, and should always be given more than one representation. 1/3 of the class are boys.
Multiple Representations Use a variety of mediums to illustrate the same fraction Sharing Cakes Clock Manipulatives
Multiple Representations What fraction of the hats are red?
Multiple Representations What fraction of the circles are blue?
Multiple Representations Pictorial 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 Use manipulatives when introducing fractions. Practice cutting different shapes into fractions.
How to teach Fractions Students 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 connections Integrate into other math topics solving money problems sharing a bill comparing prices calculating journey times
Making Conncetions Cooking checking the weight of ingredients
Making Connections Interpreting data in pictograms and bar charts Using a metre rule Measuring a room Comparing each other’s heights
Making Connections Ask learners to think of some fractions they encounter in an everyday context
Classifying Fraction Classifying 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 fractions Learners 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 classroom Many 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 classroom The 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
Games Fraction War Game Show (Jeopardy) Fairytales Fraction Blackjack