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  1. 1. Mathematics on the campus: the “degree-tree” in Tanzania
  2. 2. Mathematics in the daily news: elections in South Africa (April 1994)
  3. 3. How many elephants?
  4. 4. Example from ‘Comparing Quantities’
  5. 5. T-shirts and cola: solutions 1
  6. 6. T-shirts and cola: solutions 2
  7. 7. T-shirts and cola: solutions 3
  8. 8. <ul><li>teaching- techniques.doc </li></ul>
  9. 9. Example from Ghana SSS Mathematics 3, page 124 On pairs of similar figures. The area of ∆ ACD = 64 cm2. Find the area of ∆ ABE. 4 cm 6 cm 5 cm 12 cm A B E D C
  10. 10. The Legend of the Tower of Hanoi (or Brahma) <ul><li>Legend says that at the beginning of time the priests in the temple were given a stack of 64 gold disks, each one a little smaller than the one beneath it. Their assignment was to transfer the 64 disks from one of the three poles to another, with one important restriction: a large disk could never be placed on top of a smaller one. The priests worked very efficiently, day and night. When they finished their work, the myth said, the temple would crumble into dust and the world would vanish. </li></ul><ul><li>How long would this take, assuming that one move would take an average of 1 second? </li></ul>
  11. 11. <ul><li>The rules: </li></ul><ul><li>In every move, you can only move one disc to another peg </li></ul><ul><li>You may never place a bigger disc on a smaller one </li></ul><ul><li>All pegs may be used </li></ul>Tower of Hanoi
  12. 12. Summary <ul><li>Use real world problems as a starting point. </li></ul><ul><li>Connect to pupils’ current knowledge. </li></ul><ul><li>From informal through preformal to formal. </li></ul><ul><li>Take enough time for each step. </li></ul><ul><li>Use own productions. </li></ul><ul><li>The formal level of one stage can be used as an informal introduction to the next stage. </li></ul>