“The essence of metaphor is understanding and experiencing one kind of thing in terms of another.”
-George Lakoff and Mark Johnson, Metaphors We Live By
The classroom is an artist's studio.
The class is a group critique in an artists’ studio.
As I explained on the Home page, I constructed metaphors to help me implement authentic mathematical practices. I wanted to see students engaging in genuine mathematical inquiry, I wanted them to see the activity of problem solving as a creative process, and most importantly, I wanted them to see themselves as mathematical thinkers. How could students see mathematics as a creative process when they rarely get to discuss their own unique ways of solving problems? In order to create an environment where their varying ways of problem solving was valued, they had to be the writers/discoverers of the content. They had to present their work--even incorrect work--to help bring the class closer to solving the problems.
I spent some time unpacking the language of the statement analytically, to see the types of activities that would be implied. I began by taking the two key words "art" and "critique", and wrote out all of the thoughts that come to mind when I think of them. Then, I wrote out their dictionary definitions and saw how they matched up with my thoughts. Lastly, I applied the words to more closely define the kind of environment and the types of activities that students would be engaging in through the viewpoint that this metaphor provides.
Unpack: Group Critique
Judging an artwork’s success
Expounding on other’s judgments
Agreeing and disagreeing
Making comparisons between pieces
Is more or less elegant
Has it’s own internal logic
Apply: Implied Meanings/Activities
Doing mathematics is a Creative Activity. Different solutions to problems have differing Aesthetic Value, where some are More or Less Elegant. As paintings have an internal logic that conforms to harmony, rhythm, and composition, so too do our solutions to mathematics problems.
Students Analyze their work and make Judgments on the Success of the different solutions on the board. Criteria for judgments are based on explicitness of argument, exactness of language, and efficiency of argument. They Listen to each other’s remarks, Agree or Disagree with each other, and come to consensus about the strength of their arguments and precision through which their ideas are conveyed. They Make Comparisons Between solutions, and assess their Value as not only valid, but Elegant.