A good math lesson is like a good story or movie: it comes in three parts.
ACT ONE: Introduce the central conflict of your story/task clearly and visually with as few words as possible. (I can see how the focus on the math problem, rather than a "word problem" makes it more interesting and accessible to all learners (eg. ELL students). What do students wonder about?)
ACT TWO: The protagonist overcomes obstacles, looks for resources, and develops new tools. (Students try to figure out if they understand the problem and whether or not they have the necessary information and tools to solve the problem.)
ACT THREE: Resolve the conflict and set up a sequel/extension. (Solve the problem and add more challenging levels.)
This workshop was led by Chris Hunter and Marc Garneau, and is based on the Estimation 180 website and Graham Fletcher's website. We started with a problem of solving the height of a lamppost using a man as a reference point. Quite interesting. Then we worked on estimating how many Whoppers fit in a jar. The last problem was the tiles covering a shape on the floor. Probably the most interesting part is the group work, and how sharing of ideas within and outside a group is so critical for success.
They talked about Ten Design Principles for Engaging Math Tasks:
1) Perplexity: make students confused and curious, wondering what's going on
2) Concise questions: Keep it simple
3) Pure math can be engaging while applied boring. (Or vice-versa).
4) Photos and video.
5) Use original images.
6) Low floor for entry; high ceiling for exit. Anyone can join in, but at the challenging levels--watch out!
7) Progressive disclosure: reveal when asked or needed.
8) Ask for guesses.
9) Math is social.
10) Show that students need to learn new skills and knowledge.
Finally the Student Inquiry Process is what the Three Acts is about: Focus; Explore; Analyze and Share Learning. During this time, there is constant reflection and feedback.
Daniel H. Lee
This blog will be dedicated to sharing in three areas: happenings in my classroom and school; analysis and distillation of other educators' wealth of knowledge in various texts; insights from other disciplines and areas of expertise that relate and connect with educational practices.