Teaching Students to “Construct Viable Arguments and Critique the Reasoning of Others” and fostering “Rough Draft” Thinking.
The Common Core says this about math practice #3:
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 are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.
The ability to “construct viable arguments and critique the reasoning of others” is often weak or entirely lacking in many students. Some overconfident students may just blurt out answers within their teams and expect others to trust that they are correct, without question. Other students may have a fear of being wrong, so they shy away from sharing their thinking or reasoning. Even for your most self-aware students, articulating how they arrived at a solution or the process they used to make sense of a concept can be difficult. Students need to know that their study team is a place for “rough draft” thinking. Help them understand that this means they should be sharing thoughts without worry of right or wrong and that they should be questioning each others thinking in order to make sense and persevere.
A few study team strategies that can help create time for these practices include Swapmeet, Traveling Salesman, and Tuning Protocol. It is interesting to note that often when you ask a team “Would your team be willing to share that thinking with the whole class?” (part of selecting and sequencing) many teams will then begin to rehearse and revise their argument before the time comes to share with the whole class. Be sure to provide such time as it allows them the opportunity to work on constructing viable arguments and the skill of critiquing the reasoning of others.