Tina Cardone, Geometry Lead & Gabriel Rosenberg, Curriculum Writer
There is no doubt that proof plays a central role in the human endeavor of mathematics, but there remains much debate on what role it should play in high school mathematics. At least two standards for mathematical practice in the common core focus on this concept. Certainly MP3, “Construct viable arguments and critique the reasoning of others”, is about the need for students to be able to write their own proofs and to analyze the proofs of others. MP6, “attend to precision” goes deeper, though, by noting the need for precision, including the use of clear definitions, when communicating their reasoning. This is what we mean by rigor in mathematical proof.
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People use routines for all kinds of things. Routines give structure to time and interactions. People like structure. When a child comes home from school, there might be a routine. She expects a snack, homework time, play time, dinner, some television, a bath, pajamas, a book, and to get tucked into bed. She might have responsibilities, like setting the table for dinner, and engage in predictable dialog along the way, like sharing something that happened at school. She might expect her father to sing her a song. (Over and over and over again, in the case of my daughters—Bill.) The routine makes her comfortable and makes necessary chores go smoothly.
