Tuesday, November 25, 2014

How did those third-graders determine the turkey's cost?

All images are from New Perspectives on Learning
used with the permission of the authors
Having anticipated third-graders' thinking for the scenario provided above (the first of the Five Practices which was attended to in the first post in this series), my preservice elementary teachers are ready to engage in the next Practice - Monitoring students' thinking. Unfortunately, the university has yet to meet my request for a lab school which means that elementary-aged children are in short supply in my classroom. Given my desire to create as authentic experience as possible for my teachers, this creates a problem.

Luckily, Dr. Catherine Fosnot and her colleagues have gathered classroom videos and student-work from elementary kids working on problems from their Context for Learning Mathematics (Fosnot et. al.) series (including from the turkey cost lesson). While it's not the same as monitoring actual students, it does represent the same experiences inservice teachers might have in Professional Development (PD) sessions using Dr. Fosnot's materials.

This PD involves helping teachers to develop phronesis. "Phronesis is situation-specific knowledge related to the context in which it is used—in this case, the process of teaching and learning." (from p. 147 of Young Mathematicians at Work: Constructing Multiplication and Division) By watching the video and examining the students' work, teachers are able to observe an authentic lesson and reflect on the teaching moves that support students who are immersed in doing mathematics.

The preservice teachers in my class watch the video and observe the students finding the turkey cost. Just as many of them predicted, the third-graders are splitting the $1.25 per pound into a dollar and a quarter. Students' papers (like the one on the right) show that they understand the 24-pound turkey will cost $24 plus 24 quarters. Pairs of students use a variety of approaches to determine the total cost of the turkey. As my teachers review the third-graders' efforts, the teachers move toward the next phase of the Five Practices - Selecting students to share their work based on the Standards for Mathematical Practice (SMP) selected at the beginning of this process. 

We will continue this work in the next post. But first, which SMPs would you say the work of Emma and Emma highlights?

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