Clip 38/41: Standard 3: Construct Arguments & Critiques Using Quadrilaterals Part F
Overview
Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures.... They justify their conclusions, communicate them to others, and respond to the arguments of others.... Students at all grades can listen or read the arguments of others, decide whether they make sense...
In the closing of the group work, 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 6 (attend to precision), standard 7 (look for & make use of structure), and standard 8 (look for & express regularity in repeated reasoning).