Laten doen: How many elephants do you see? How did you find this out? Antwoord volgens Arthur: 336 Aanleiding tot concept van gemiddelde
18,446,744,073,709,551,615 moves! If the priests worked day and night, making one move every second it would take slightly more than 580 billion years to accomplish the job! The generally accepted age for the Earth and the rest of the solar system is about 4.55 billion years (plus or minus about 1%).
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Mathematics on the campus: the “degree-tree” in Tanzania
Mathematics in the daily news: elections in South Africa (April 1994)
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
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>
<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
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>
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