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  1. 1. MISCONCEPTION: Which is bigger 1/3 or 1/6 ?
  2. 2. <ul><li>Misconceptions are problems for two reasons. </li></ul><ul><li>a) First, they interfere with learning when students use them to interpret new experiences. </li></ul><ul><li>b) Second, students are emotionally and intellectually attached to their misconceptions, because they have actively constructed them. </li></ul>What are misconceptions… (Mestre, J. ,2000)
  3. 3. Talking about the problem <ul><li>Pupils could not see the real difference between the fraction 1/3 and 1/6. </li></ul><ul><li>They assume that the largest denominator is the largest fraction. </li></ul><ul><li>and 1 </li></ul><ul><li>3 6 </li></ul>denominators
  4. 4. <ul><li>This reveals a gap in their knowledge about what is the bottom number-the denominator of a fraction does. </li></ul><ul><li>such errors and misconceptions are seen as the natural result of children's efforts to construct their own knowledge </li></ul><ul><li>They are intelligent constructions based on correct or incomplete (but not wrong) previous knowledge </li></ul>
  5. 5. Reasons why such misconception occurs…… <ul><li>prototype and the mathematical concepts </li></ul><ul><li>confusion between examples/ experiences and the real mathematical concept </li></ul><ul><li>Pupils think that numbers get bigger when they increase. So, they apply the same understanding into fraction saying that larger number has larger value rather than understanding the concept of fraction. </li></ul>
  6. 6. <ul><li>Primary pupils often involve in such misconceptions because they are still young and easily get influence by their experiences and surroundings. </li></ul><ul><li>When children are young, they tend to act different than when they are older. They are not mature yet and are still easily influenced. </li></ul>
  7. 7. <ul><li>For instance, </li></ul><ul><li>Question: Which one is larger in value? </li></ul><ul><li>A. 1/3 </li></ul><ul><li>B 1/4 </li></ul><ul><li>C. 1/5 </li></ul><ul><li>D. 1/6 </li></ul>Pupils would immediately choose D because it has the biggest value which is 6.
  9. 9. <ul><li>see for themselves that the portion of 1/3 is bigger than 1/6 </li></ul><ul><li>understand what the numerators and denominators stand for </li></ul><ul><li>The idea of denominator as the number of parts that make up the whole shape can be difficult to grab without proper teaching aids </li></ul>
  10. 11. <ul><li>leave a longer lasting memory </li></ul><ul><li>tend to remember what they from experience much better </li></ul><ul><li>bring real things to the class to show them the clear difference between the various fractions </li></ul>Hands-on Activities
  11. 13. <ul><li>Activity </li></ul><ul><li>Divide the class into groups, each group with a different number of students.  Then, explain that each group will share a pie (or cake). Talk about being fair and giving each member of the group the same size piece. No one is permitted to eat anything until everyone in the class has a piece. </li></ul><ul><li>After the pies (or cakes)are divided, talk about the size of each groups’ pieces (halves are going to be much larger than the fourths, etc.).  After all the discussion and observations, eat the lesson. </li></ul>
  12. 14. <ul><li>using these realias has a drawback </li></ul><ul><li>can be used only once </li></ul><ul><li>Plasticine, clay or play-dough </li></ul><ul><ul><ul><ul><ul><li>– repeated use </li></ul></ul></ul></ul></ul><ul><li>Co-operation with arts teacher </li></ul>Play-dough pizza Clay cake Clay Sandwiches
  13. 15. Blocks of shapes <ul><li>easier to handle </li></ul><ul><li>allow pupils to use them and form fractions with them </li></ul><ul><li>understand the differences between the seemingly similar shapes </li></ul>
  14. 16. Technology <ul><li>use LCD Projector/ SMART board to show 3D shapes that can be divided into various portions </li></ul><ul><li>various online games , songs, etc. </li></ul><ul><li>suitable to introduce the concept of fractions </li></ul>
  15. 17. <ul><li>Using SMART board </li></ul><ul><li>Fractions video song </li></ul><ul><li>Online game </li></ul><ul><ul><li>http://www.arcytech.org/java/patterns/patterns_j.shtml </li></ul></ul>
  16. 18. C. Proposing method for evaluating effectiveness of the intervention
  17. 19. Name: Jamal Year: 3 The test subject
  18. 20. 1/6 No, this is one is bigger because… Now, which is bigger among these? 1/5 1/2 Which is bigger?
  19. 21. Pictures <ul><li>Easy, fun and interesting and also practical and suitable to be used in the Malaysian primary classrooms. </li></ul><ul><li>According to Gardner’s theory , pupils have different learning styles like visual ability </li></ul><ul><li>Therefore, by looking at the pictures (visual) their understanding on the concept will be taken to a higher pace </li></ul>
  20. 22. <ul><li>They would be able to grasp the concept better </li></ul><ul><li>Therefore, using pictures can be implemented </li></ul><ul><li>Pictures are attention grabbing, interesting, unique way to learn, suitable, practical and are able to deter the misconceptions in the pupils </li></ul>
  21. 23. Relia <ul><li>Realia like cakes, pizza, pie, and sandwich and so on can be used to help pupils to deal with the misconceptions </li></ul><ul><li>All these can be implemented but they cannot be used all the time, throughout the year. </li></ul><ul><li>Not applicable as it consumes a lot of money </li></ul><ul><li>Pupils might be distracted looking at the food rather than concentrating at the lesson. </li></ul>
  22. 24. <ul><li>It can also turn out to be messy if after the lesson the teacher gives away the food to pupils, the classroom would turn into a temporary market. </li></ul><ul><li>The real problem is bringing it too often as it is not that practical and is costly </li></ul><ul><li>Pupils might get bored looking at the realia throughout the year. </li></ul><ul><li>In short, realia can be used but there are limits on how often teachers can bring the realia to the classrooms. </li></ul>
  23. 25. Plasticine <ul><li>Practical and useful to be used in the classrooms </li></ul><ul><li>Not that costly and can be used often or recycled in the classroom. </li></ul><ul><li>They are constructing the knowledge by themselves that is making the pie and separating the pieces. </li></ul><ul><li>Reliable tool to be used in order to help pupils with the misconceptions </li></ul>
  24. 26. Technology <ul><li>Useful and practical to be used in Malaysian classroom. </li></ul><ul><li>However, it is not practical to be used all around Malaysia as not schools are equipped with facilities like computer lab, LCD projector, wireless connection and many more. </li></ul><ul><li>This method is practical and beneficial to be used but its use is limited to some places in Malaysia and not everywhere. </li></ul>
  25. 27. Blocks of shapes <ul><li>Practical and suitable </li></ul><ul><li>They are not costly </li></ul><ul><li>Schools do provide them and it is easy to be used </li></ul><ul><li>Pupils will be able to understand the concept better as the teacher will take out blocks one by one to show them about fractions </li></ul>
  26. 28. THE END