Unit 3: Reasoning and Explaining (MP2 and MP3)

# 3.4 Making Arguments More Viable

As students become more mathematically proficient and their reasoning skills increase they should be able to identify flaws in their own and others' thinking: thus prompting revision of thinking that leads to better problem solving."

Daro, 2012

During the writing process, an author can expect to make several revisions in order to develop a thoughtful, coherent piece. Often an editor reads the piece and offers suggestions and an outside perspective. The same expectation should be held of young mathematicians as they revise and improve their reasoning while developing a coherent argument.

Opportunities for rehearsal and revisions to improve arguments

Duri, the 5th grade teacher, offered her students multiple opportunities to share their reasoning with teachers, partners, visiting educators, small groups, and the entire class. Over a period of two weeks, students had multiple opportunities to rehearse and refine their arguments with advice from these outside perspectives.

Public definitions of odd and even

Before the revision work began, the class agreed to the following definitions of odd and even:

• An even number ends in 0, 2, 4, 6, or 8
• If you count by twos, you will land on an even number
• An even number can be divided by 2 and has no remainder
• An odd number ends with 1, 3, 5, 7, or 9
• When you put numbers into pairs, and there is a leftover, the number is odd.

Their sequence of work contained the following steps:

Step 1: Complete the assigned MARS task
Step 2: Meet individually with the teacher, then revise work
Step 3: Share solution with a partner and revise
Step 4: Share solution with whole class and revise
Step 5: Work with a small group to combine arguments into a poster
Step 6: Share rough draft of poster with another group and revise
Step 7: Share completed poster at public research lesson