Clip 20/21: Standard 7: Look for & Make Use of Structure Using Quadrilaterals Part F
Overview
Mathematically proficient students look closely to discern a pattern or structure.
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. Humphreys asks to meet with the students who are playing the role of “facilitators” in their groups to ensure that the Burton and Mason argumentation structure is followed. This clip is also indicative of standard 3 (construct viable arguments & critique the reasoning of others), standard 6 (attend to precision), and standard 8 (look for & express regularity in repeated reasoning).