This is the third year I have been here to teach the summer institute. This year I am teaching the middle school program where the teachers are teaching Grades 4 to 7. We began after a brief opening ceremony.
In the opening session, I tried to discuss Bruner's enactive, iconic and symbolic representations using division of whole numbers by fractions and long division algorithms. The teachers asked questions related to teaching of division of fractions by fractions, multiplication of decimals and operations involving negative integers. We ended the day with a game of 'either one or three'- in a game where two players take turn to remove exactly one or three paper clips from apile of clips and the winner is the person who remove the last clip(s) - what is the winning strategy?
What if the rule is changes to wither 'one or two'?
We begin Day Two with Dienes' Theory of Variation ... but not before I pose the class the Fido Problem. Tell you more later.