Observations of Student Learning
My goal for this lesson was for the practice of making numeric combinations to become more meaningful for students by solving these problems within the framework of the lesson design. Students seemed to respond well to 'pizza math' throughout the lesson. They seemed to demonstrate computational fluency with addition and numeric combinations, and seemed to demonstrate an increased comfort with numeric reasoning as the lesson progressed. In reviewing the lesson, I feel that I was successful in beginning to accomplish the pedagogical and mathematical goals that I set for the students. The dimension of discourse was very helpful in enabling me as a teacher. I was able to make students' mathematical thinking visible by asking questions that facilitated students' articulation of their knowledge and thought processes.
During the lesson, I observed students move through the three key ideas of fluency (as used in NCTM's Principles and Standards): efficiency, accuracy, and flexibility. While I acted as facilitator, students worked in pairs to create numeric combinations in ways that made sense to them. I modeled how to use the price sheet by listing prices per topping in the workspace, but I did not model strategies for counting or adding the prices together. Students worked in pairs and engaged in decision making to select the toppings they wanted. The video clip below shows two students working together to fill out the price sheets. Students used their own strategies for addition to keep track of subtotals.
During the lesson, I observed students move through the three key ideas of fluency (as used in NCTM's Principles and Standards): efficiency, accuracy, and flexibility. While I acted as facilitator, students worked in pairs to create numeric combinations in ways that made sense to them. I modeled how to use the price sheet by listing prices per topping in the workspace, but I did not model strategies for counting or adding the prices together. Students worked in pairs and engaged in decision making to select the toppings they wanted. The video clip below shows two students working together to fill out the price sheets. Students used their own strategies for addition to keep track of subtotals.
As shown in the assessment checklist, students displayed different strategies for creating numeric combinations, which highlight the different stages they are currently in regarding their development of computational fluency. They seemed to be at different stages of development of perceptual and conceptual knowledge as well. I observed many students using numeric reasoning to answer addition questions. Many students demonstrated knowledge of skip counting, while others counted by one's out loud, often using fingers as tools to guide them. Additionally, every student used the price sheet appropriately, and demonstrated an ability to keep track of one's work and to make sense of numbers as symbols.
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