It worries me greatly when Mathematics teaching is de-humanised. Sure learning can take place by listening to a lecture, either in person or via technology. But by the interaction of human beings, much more powerful learning can take place. Here is a simple example from one of my classes:
During a Year 9 probability unit the students were set the task of designing a game involving chance. Student X showed me his progress in class. His game was well presented with step by step instructions including diagrams. Part of his game involved a player getting 3 cards from a standard 52 card deck. Student X wondered how many different “hands” were possible. Being of GEN Y of course he “googled” it. Without knowing it he had begun learning about permutations and combinations!
In class I drew this topic out. Soon factorials were easy. Problems like choosing 2 objects from a group of 5 were no longer mysterious. The two way dialogue we had left me with a much better understanding of student X.
One of my treasured possessions is: Mathematics – A Human Endeavour, by Harold R. Jacobs. I have a first edition copy (1970). Jacobs goal in writing the book was “to introduce you to what mathematics is really like, to reveal its extent and power, and to give you some insight into its historical development.
I think he succeeds very well. The simple text, diagrams and cartoons, leave the reader wanting to discover whats on the next page. Jacobs’ method of guided discovery allows students to experience the “aha” feeling.
I think I will ‘show’ student X, chapter 7 “Some Methods of Counting”.