I want my students to learn how to write about their thinking. Therefore, my assignments have to be written in full sentences, explain everything in detail and convey the mathematical concepts. They can also contain the story of how the student discovered the solution, including all struggles and mistakes.
This semester we are video taping our IBL classes and as I am watching the videos I am reflecting (again) on all the pieces necessary for a productive whole class discussion. My goal for a discussion is to make the “Big Mathematical Ideas” visible by having students construct connections between different solution strategies or attempts.
We found all positions for two dancers that exhibit both reflectional and 180 degree rotational symmetry. After the students discovered their conjectures, I asked them to prove that their conjectures were correct. This was our first activity of the semester and the students were new to the cycle of exploration - definitions - conjectures - proof.
In 2012 the Discovering the Art of Mathematics team started reaching out to the two-year colleges. At the NEMATYC conference in 2013 we learned that many faculty are interested in support around algebra related courses.