At our last webinar, I had asked people to choose one of the practices we have discussed, (1-6) and spend one planning session for math thinking about how to concentrate on that one specific practice. What insights did you have from this experience? If you feel comfortable, please share your thoughts in the chat box while we wait to get started! Implementation of the Practices
Today’s Targets Continue to discuss the larger picture- today’s side topic…Questioning Dig deeper into practices seven and eight: 1.Look for and make use of structure. 2.Look for and express regularity in repeated reasoning. Identify key implications for classroom instruction..
Thoughts? What is the first word that comes to mind when you read this paragraph taken from a NCTM (National Council of Teachers of Mathematics) publication?
Practice Number Seven Teachers who are developing students’ capacity to "look for and make use of structure" help learners identify and evaluate efficient strategies for solution. An early childhood teacher might help students identify why using "counting on" is preferable to counting each addend by one, or why multiplication or division can be preferable to repeated addition or subtraction. An elementary teacher might help his students discern patterns in a function table to "guess my rule." A teacher of middle school students might focus on the application of rules and reasoning behind why rules work.
Thoughts about Implementation In the chat box, list anything from your current curriculum that requires students to “generalize” a pattern, structure or strategy that will work for them in many situations. For example- “Multiplication is repeated addition.” “Fractions with the same numerator and denominator are equal to one whole.” (Of course, we also want them to know WHY this is true!!!!)
Chat box discussion! (This was actually a recent discussion I listened to at a staff meeting where the teachers were talking about why everyone had to help with the new ELA standards- no matter what they taught.) How Much Writing Should Students do in Math Class? (Julia won’t be weighing in!)
Practice Eight Integrating Standard Eight into classroom practice is not only a matter of planning for lessons that require students to look for general methods and shortcuts. It also requires teachers to attend to and listen closely to their students’ noticings and “a-ha moments,” and to follow those a-ha moments so that they generalize to the classroom as a whole. Teachers can create the conditions for students to look for and express regularity in repeated reasoning, and follow and elaborate students’ thinking when they begin to make these connections.
The Eight Mathematical Practices 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning.