Classroom Sneak Peek #3 - Construct viable arguments and critique the reasoning of others

The past couple of weeks I began blogging about the 8 Mathematical Practices from the Common core.  I finished Mathematical Practice # 1 and Mathematical Practice # 2.  This week the focus is on CCSS Mathematical Practice #3 - Construct viable arguments and critique the reasoning of others.  I'll address what this looks like in the classroom, what students will be doing, what teachers will be doing, and the most important, the type of questions teachers will be asking.. 

3. Construct viable arguments and critique the reasoning of others.

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.

What does this really look like?  The chart below is a work in progress.  I've designed this with the expertise of many classroom teachers.  If you have other ideas, please don't hesitate to email me and share your expertise as well.  If you are interested in using this process with your staff, read What Do The Common Core Standards Look Like in the Math Classroom.

Mathematical Practice: Construct viable arguments and critique the reasoning of others.

Student Actions:	Teacher Actions:	Open-Ended Questions:
Use correct math vocabulary when discussing ideas. Write their understanding of math terms in journals using their words. Make conjectures and explore if their conjectures are true or false. Communicate and justify their solutions. Listen to reasoning of others and ask clarifying questions. Compare two arguments or solutions. Question where data comes from. Question how solutions came about. Question the reasoning of other students. Look for and can identify faulty arguments. Explain flaws in arguments. Use pictures and tools to prove or disprove an idea. Listen and read arguments of others.	Use appropriate strategies for working with vocabulary (McRel Instructional Strategies) Create a word wall that is developed using student language. Use anchor charts to focus on conjectures around operations and patterns in our number system. (a + 0 = a) Focus on non-examples as well as examples with math vocabulary. (Frayer Model) Provide time to look at solutions that are incorrect. Facilitate discussions on why incorrect solutions have faulty logic. Provide time for communication and discussion.	How can you draw a picture of the math term and describe the math term? What might be a non-example? How is your strategy the same or different than ____________? Why do you believe that is always true? How could you prove that this is true for all cases? What might be a possible problem with the strategy or solution? How might their thinking be clarified? What parts of _______ explanation might need clarifying? What parts of ____________ strategy or solution confuses you? How might a picture or math tool help you prove your conjecture?