Standards of Mathematical Practices - One Standard at a Time

  

"I used the array model to figure out the problem.  First, I broke apart 32 x 45..."

Mathematical Practices are embedded in every math lesson we teach.  The Standards for Mathematical Practice describe varieties of expertise that math educators at all levels (K-12) should seek to develop in their students.  These practices rest on important "processes and proficiencies" with longstanding importance in mathematics education. 

Mathematical Practice #3

Construct viable arguments and critique the 

reasoning of others.

What should students be able to do?

• 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 the Teacher Can Ask to Develop Mathematical Thinking:

• 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? (Was it 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?