3. Construct viable arguments and critique the reasoning of others.
How are middle school teachers helping their students construct viable arguments and critique the reasoning of others?
How can students be helped to:
- understand and use stated assumptions, definitions, and previously established results in constructing arguments
- make conjectures and build a logical progression of statements to explore the truth of their conjectures
- analyze situations by breaking them into cases
- recognize and use counterexamples
- justify their conclusions, communicate them to others, and respond to the arguments of others
- reason inductively about data
- make plausible arguments that take into account the context from which the data arose
- 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
The CCSS states:
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.
What are you doing to help students develop this practice? What makes it hard? What challenges are you encountering?
This mathematical standard is one of the most exciting for me as a teacher. I love to build a case, argue about it, and then refine reasoning. As a teacher of alternative education, with a variety of oppositional students, I love teaching students to argue with thought and intelligence versus emotion. I often equate mathematical arguments and reasoning to their science classes. I restate their statements adding in missed or misused vocabulary. I help them to effectively state their position on a problem and then convince others.