Habit 3
Construct viable arguments and critique the reasoning of others
The Mathematical Habits of Mind describe ways in which developing students of mathematics increasingly engage with the subject matter as they grow in mathematical maturity and expertise throughout the elementary, middle and high school years.
MHM3. Construct viable arguments and critique the reasoning of others.
Analyze problems and use stated mathematical assumptions, definitions, and established results in constructing arguments.
Justify conclusions with mathematical ideas.
Listen to the arguments of others and ask useful questions to determine if an argument makes sense.
Ask clarifying questions or suggest ideas to improve/revise the argument.
Compare two arguments and determine correct or flawed logic.
Questions to Develop Mathematical Thinking Related to Habit 3
What mathematical evidence would support your solution?
How can we be sure that _____? / How could you prove that _____? Will it still work if _____?
What were you considering when _____?
How did you decide to try that strategy?
How did you test whether your approach worked?
How did you decide what the problem was asking you to find? (What was unknown?)
Did you try a method that did not work? Why didn’t it work?
Would it ever work? Why or why not?
What is the same and what is different about _____?
How could you demonstrate a counter-example?