Unit 3: Reasoning and Explaining (MP2 and MP3)

# 3.0.1 Introduction to a 5th-grade classroom: The case for these practices

Throughout Unit 3 you will follow the same 5th-grade students as they learn to engage in viable arguments. Below is a summary of the 2011 classroom project.

The classroom teacher, Lynn Duri, is a participant in professional learning with the California Mathematics Project, the North Bay Math Project, and the California Math Science Partnership Grant, Project LEAD. The professional learning includes: Lesson study, Mathematics Assessment Resource Services (MARS) Tasks (also in Unit 5), and re-engagement lessons.

During the professional learning, teachers read and discussed an odd and even numbers case study titled, Discovering Rules for Odds and Evens (Shifter, et al., 2008). Duri and her students received additional support from the leaders of the project as the group studied how to infuse viable arguments into a classroom culture.

The 5th-grade students featured in this unit focus on the reasoning and explaining practices. The students received coaching from Harold Asturias, Director of the Center for Mathematics Excellence and Equity (Lawrence Hall of Sciences at the University of California, Berkeley), and Patrick Callahan, co-director of the California Mathematics Project. Student representation in the selected school included:

- 44% English learners (40% Spanish speakers and 4% Cambodian or Vietnamese speakers)
- 67% receive free and reduced lunch
- 8% identified as having special needs

Throughout unit 3 you will be asked to engage in “professional noticing of children’s mathematical thinking” (Jacobs, et al., 2010) around the reasoning and explaining practices. You will reflect upon and record the practices you observe illuminated in classroom videos and student work.

If discussions about what constitutes a valid justification do not occur, students often rely on the superficial aspects of an argument, such as the use of formal mathematical symbols, over the mathematical reasoning that underlies the argument ."

Healy & Hoyles, 2000

The video below was filmed on the last full day of instruction and demonstrates how students communicated their thinking and investment in continuing their learning. As you watch, consider how Jeanette, Haley, and Leslie define and value viable arguments.

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In your Metacognitive Journal, list the descriptors of viable arguments that Jeanette, Haley, and Leslie speak about.

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