Sense Making and the Development of Other Mathematical Practices http://mathforum.org/workshops/cmc-2014/ Steve Weimar [email protected] What are we currently thinking about and trying to figure out with the mathematical practices and the development of these with students? What I am thinking about What do we mean by “learning the mathematical practices”? (and what does this have to do with learning math, more generally?) What might it look like if the students were explicitly working on this and accountable for competence and improvement in the practices? What I am thinking about Focus on two practices: Sense Making, Looking for Structure What do we mean by these practices? What is the interaction between Sense Making and Looking for Structure? What does it mean to get better at them? How is this facilitated? (graphic organizer for recording) Plan Engage a scenario with sense making (Notice and Wonder) Add notes to our graphic organizer about Sense Making Pick a wonder/problem and work on it Compare and contrast, looking for structure Add notes to our graphic organizer about Looking for Structure Reflect on the process and what helps facilitate Revise/tweak the process Do a different type of problem Interaction of Sense Making and Looking for Structure Notice and Wonder: You have 7 cups of dog food. You use two-thirds of a cup of dog food at each meal. Fraction +1 Scenario Start with a fraction: add 1 to the numerator and 1 to the denominator Three Piece Spaghetti Break a piece of spaghetti into three pieces. Try to make a triangle with the ends of the pieces brought together to make vertices. Find a value for x. When I first posted this problem, I neglected to mention that it can be done with introductory geometry concepts (supplements, transversals, similarity, 180 degrees in a triangle, etc.) and no trig.