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How to Teach Fractions<br />
Problem<br />Fractions = one of the most difficult concepts for children to grasp<br />   Notation of fractions<br />   Fo...
How to Teach Fractions<br />It is important that learners think about relationships between fractions, rather than just tr...
Teachers’ Mistakes<br />Syntactic vs. Semantic emphasis<br />Technical procedures instead of understanding/meaning<br />Ad...
Multiple Representations<br />Students given multiple explanations can have…<br />Greater conceptual understanding<br />Tr...
Different Interpretations for the Fraction ¾ (Lamon, 2001)<br />   Provide exposure to other types of interpretations <br ...
Multiple Representations<br />Learners need to be familiar with multiple representations of fractions, and<br />should alw...
Multiple Representations<br />Use a variety of mediums to illustrate the same fraction<br />Sharing Cakes<br />Clock<br />...
Multiple Representations<br />What fraction of the hats are red?<br />
Multiple Representations<br />What fraction of the circles are blue?<br />
Multiple Representations<br />Pictorial representations of a particular fraction may be of different sizes and different s...
Multiple Representations<br />
Multiple Representations<br />Use manipulatives when introducing fractions. <br />Practice cutting different shapes into f...
How to teach Fractions<br />Students learn more if they actually enjoy the activity, have a chance to discuss what they do...
Making connections<br />Integrate into other math topics<br />solving money problems<br />sharing a bill<br />comparing pr...
Making Conncetions<br />Cooking<br />checking the weight of ingredients<br />
Making Connections<br />Interpreting data in pictograms and bar charts<br />Using a metre rule<br />Measuring a room<br />...
Making Connections<br />Ask learners to think of some fractions they encounter in an everyday context<br />
Classifying Fraction<br />Classifying different representations of fractions, or statements about them, can be a very effe...
Evaluating statements about fractions<br />Learners are given some generalisations about fractions, perhaps printed out on...
Links outside the classroom<br />Many learners do not use their understanding of fractions outside the classroom, and are ...
Links outside the classroom<br />
Links outside the classroom<br />The proportions of the human body provide links with art, and with dressmaking/tailoring....
Fraction Quotes<br /> A man is like a fraction whose numerator is what he is and whose denominator is what he thinks of hi...
Games<br />Fraction War <br />Game Show (Jeopardy)<br />Fairytales<br />Fraction Blackjack<br />
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Edsc 126

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EDSC 126
2nd sem, 09-10

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Edsc 126

  1. 1. How to Teach Fractions<br />
  2. 2. Problem<br />Fractions = one of the most difficult concepts for children to grasp<br /> Notation of fractions<br /> Formal vocabulary<br /> 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.<br />Do not behave like ‘normal’ numbers<br />
  3. 3. How to Teach Fractions<br />It is important that learners think about relationships between fractions, rather than just trying to memorize methods for processing them.<br />FACTUAL<br />CONCECPTUAL<br />FACTUAL<br />We should move towards a more holistic approach when teaching fractions.<br />
  4. 4. Teachers’ Mistakes<br />Syntactic vs. Semantic emphasis<br />Technical procedures instead of understanding/meaning<br />Adult- vs. Student- centered approach<br />Ignore ‘prefactional’ knowledge<br />Adult concepts are very different from children’s<br />Confusing representation<br />
  5. 5. Multiple Representations<br />Students given multiple explanations can have…<br />Greater conceptual understanding<br />Transfer knowledge to tasks not directly taught to them<br />
  6. 6. Different Interpretations for the Fraction ¾ (Lamon, 2001)<br /> Provide exposure to other types of interpretations <br />Ignoring other ideas leaves incomplete understanding<br />
  7. 7. Multiple Representations<br />Learners need to be familiar with multiple representations of fractions, and<br />should always be given more than one representation. <br />1/3 of the class are boys.<br />
  8. 8. Multiple Representations<br />Use a variety of mediums to illustrate the same fraction<br />Sharing Cakes<br />Clock<br />Manipulatives<br />
  9. 9. Multiple Representations<br />What fraction of the hats are red?<br />
  10. 10. Multiple Representations<br />What fraction of the circles are blue?<br />
  11. 11. Multiple Representations<br />Pictorial representations of a particular fraction may be of different sizes and different shapes. For example, don’t always use shaded sections of circles.<br />When you divide things into fractions it doesn't matter how you do this as long as the parts are all equal in size.<br />
  12. 12. Multiple Representations<br />
  13. 13. Multiple Representations<br />Use manipulatives when introducing fractions. <br />Practice cutting different shapes into fractions.<br />
  14. 14. How to teach Fractions<br />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.<br />Conceptual Understanding<br />
  15. 15. Making connections<br />Integrate into other math topics<br />solving money problems<br />sharing a bill<br />comparing prices<br />calculating journey times<br />
  16. 16. Making Conncetions<br />Cooking<br />checking the weight of ingredients<br />
  17. 17. Making Connections<br />Interpreting data in pictograms and bar charts<br />Using a metre rule<br />Measuring a room<br />Comparing each other’s heights<br />
  18. 18. Making Connections<br />Ask learners to think of some fractions they encounter in an everyday context<br />
  19. 19. Classifying Fraction<br />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<br />
  20. 20.
  21. 21. Evaluating statements about fractions<br />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.<br />
  22. 22. Links outside the classroom<br />Many learners do not use their understanding of fractions outside the classroom, and are unwilling or unable to transfer it to ‘real life’ problems.<br />Encourage children to give names to the fractions they see in everyday life. <br />Did your family have meatloaf for dinner last night? How many pieces was it cut into? How many pieces did you eat? <br />Encourage kids to share.<br />
  23. 23. Links outside the classroom<br />
  24. 24. Links outside the classroom<br />The proportions of the human body provide links with art, and with dressmaking/tailoring. <br />Artists assume the eyes are half-way down the face, the nose half-way between the eyes and the chin.<br />
  25. 25. Fraction Quotes<br /> 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.<br />—Leo Tolstoy<br />“We live but a fraction of our lives”<br />— Henry David Thoreau<br />
  26. 26. Games<br />Fraction War <br />Game Show (Jeopardy)<br />Fairytales<br />Fraction Blackjack<br />

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