I recently read an article about an English teacher giving her students Shakespeare’s Sonnet 116. They then looked for patterns that they thought would be present in all sonnets. After groups wrote the observations on the board and reviewed all of them, she led a discussion and critique of which ideas seemed the most likely to be useful. Finally, she allowed them to use their BYOT devices to see if they were correct or if they were missing anything. So the natural question is, how does this work in a mathematics classroom?
One of the pushes of Common Core is Multiple Representations (table, graph, equation, description). Could we give these to groups and have them crowd source patterns that they see? All the usual suspects of lines, quadratics, exponentials, jump to mind. What about factoring?could we show them several pairs of factored and unfactored quadratics and see if they come up with their own ideas for what links them together?