Clip 37/43: Standard 6: Attend to Precision Using Quadrilaterals Part F
Overview
Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning... By the time they reach high school they ... make explicit use of definitions.
In the closing of the group work on the first day, Humphreys refers her students to the idea of “mathematical friends.” This notion came from Thinking Mathematically by Burton and Mason, a book about mathematical problem solving in which the authors talk about a hierarchy of certainty when trying to write a convincing argument. Convince yourself (the easiest), convince a [mathematical] friend, and finally, convince a skeptic. Developing a skeptical mindset and not jumping to conclusions too quickly is another hallmark of good mathematical thinking. This clip is also indicative of standard 3 (construct viable arguments & critique the reasoning of others), standard 7 (look for & make use of structure), and standard 8 (look for & express regularity in repeated reasoning).