Making Sense of Mathematics for Teaching to Inform Instructional Quality. Juli K. Dixon
have the opportunity to engage in high-level thinking, teachers must regularly select and implement tasks that promote reasoning and problem solving.
—National Council of Teachers of Mathematics
In this chapter, you will explore how teachers can implement mathematical tasks during mathematics lessons in ways that support or possibly diminish students’ opportunities to engage in thinking and reasoning. By the end of the chapter, you will be able to answer the following questions.
■ What happens when teachers enact high-level tasks in the classroom? How do teachers maintain (or limit) opportunities for thinking and reasoning during the lesson?
■ What teacher actions seem to support (or diminish) students’ opportunities for thinking and reasoning as well as provide (or take away) access for students to engage in the task?
■ What does student work indicate about students’ engagement in thinking and reasoning during the lesson and their level of access to the lesson?
■ What does students’ work indicate about instruction and teaching during the lesson?
Introductory Activities
Let’s get started by analyzing mathematics lessons and observing how the implementation of a task can affect student learning. In activity 2.1, we ask you and your collaborative team to observe two mathematics lessons that use the same task, but in noticeably different ways. You will then consider the thinking and problem-solving strategies that each teacher’s implementation elicited.
Activity 2.1: Comparing Two Mathematics Lessons
Before engaging in this activity, consider what opportunities for mathematical learning the Leftover Pizza task could offer students and how you might implement the task in the classroom.
Engage
In chapter 1, activity 1.1 (page 7), you considered the level of thinking and reasoning that could potentially be provided by the Leftover Pizza task for students in grade 6. In activity 2.1, you will explore how the task plays out in two different lessons.
■ Revisit the Leftover Pizza task (see figure 1.1, page 8).
■ Watch the video of the Leftover Pizza lesson version 1.
■ Read the transcript of the Leftover Pizza lesson version 2 (see figure 2.1).
Discuss your responses with your collaborative team before moving on to the activity 2.1 discussion.
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Leftover Pizza Lesson Version 1: www.SolutionTree.com/Dividing_Fractions_in_Context |
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Figure 2.1: Leftover Pizza lesson version 2.
Discuss
How do your responses compare with those in your collaborative team? What themes emerged during your discussion? In this section, we present ideas for you to consider.
Rate the Leftover Pizza task using the Potential of the Task rubric.
The Leftover Pizza task would rate a level 3 on the Potential of the Task rubric. As discussed in activity 1.1, the task provides a context and encourages a model for students to make sense of dividing fractions. The task does not include an explicit prompt to explain.
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