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### Students Critiquing and Revising Arguments

This clip shows 2 student critiques of the proportional reasoning argument, pointing out that the method counts sides that are not part of the perimeter of the larger chain of hexagons. The teacher strives to make sure that the different groups make their reasoning and critiques as clear and explicit as possible.

### Ms. Hauser's Reflection on the Students' Critiques and Revisions

Ms. Hauser discusses challenges of helping a student critique and revise her own argument. During this lesson Ms. Hauser says that she learned about getting students to revise arguments. As you listen to this interview consider the following--
• What did Ms. Hauser learn?
• What are the implications for this when facilitating tasks designed to elicit CCRA?

### Commentary from Mathematics Educators on Establishing Classroom Environment Conducive to CCRA

Listen to mathematics educators Megan Staples and Mark Ellis as they discuss the teacher's role in creating an environment in which students are focused on critiquing and revising arguments that originated from their peers.

Student Work Samples: A Focus on Revising Arguments
The video clip above, which is near the end of Day 1 of the task, shows students in the midst of critiquing and revising arguments. An important question is how these critiques and arguments were then developed and solidified over time. Two sets of student work samples are shared here. Each set comprises student work for the original task (their initial thinking), a warm-up on day 2 (their thinking after the discussion shown in these video clips) and their final write up (done for HW after day 2). Set 1 has work from two students who initially used a proportional argument to justify their claims about the perimeter of the 25th figure. Set 2 has work form three students who had a correct answer initially, but whose arguments may have developed or changed over time.

Set 1: Amanda, Abby

Set 2: Bernardo, Brit, Bill

QUESTIONS:

For Set 1: Students who initially had used a proportional argument...

Q: What evidence do you see, if any, that these students have revised their thinking about their initial method?

For Set 2: Students who had the correct answer for their initial write up...

Q: What evidence do you see, if any, that these students revised their thinking about the task and/or revised the way they constructed their arguments?

Q: A main purpose of this 7th-grade course is to help students transition from arithmetic to algebra. Based on the student work samples, what evidence do you see, if any, that these students’ arguments are moving from arithmetic to algebraic arguments?

Q: As you consider each “final” student work sample, with the revised argument, what do you see as strengths and weaknesses (areas for improvement) for each student’s argument?

FINAL QUESTION: What are qualities of a “good” argument, particularly for a 7th-grade student on this task?