Ses Case1 Ron Castleman 062009 Pk Formatted
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Ses Case1 Ron Castleman 062009 Pk Formatted
- 3. The Mathematical Tasks Framework TASKS as presented in curriculum/ materials TASKS as set up by the teachers TASKS as enacted by students and teacher in the classroom Student Learning (Adapted from Stein, Smith, Henningsen, & Silver, 2000)
Notes de l'éditeur
- Slides 1-4 (10 min) Our work today will involve working on a mathematical task and analyzing a case around that task. It will be important to listen to and make sense of others’ ideas and to challenge others to provide explanations.
- Slides 1-4 (10 min) We have chosen to focus on these goals because understanding rational numbers, including fractions, percents, decimals, and ratios is requisite for students’ success in middle school and beyond. We also believe it is important to think about the kinds of tasks and the instruction around these tasks that helps students develop this understanding.
- Slides 1-4 (10 min) This framework “specifies several points at which a teacher mediates students’ engagement with the tasks found in curriculum materials and highlights the ways that task demands may change as a teacher uses them with students. A teacher decides which tasks to assign and which to omit, and he or she may transform tasks substantially when reading and interpreting the curriculum materials, when setting up the tasks during instruction, and while interacting with students during enactment of these tasks.” (Silver, Ghousseini, Charalambous, & Mills, 2005, p. 248)
- Slides 1-4 (10 min) Explain the expectations for working on a mathematical task.
- Independent work (10 min) & Small Group (10 min ) Handout: Ron Castleman Task O Take time to work on the task individually and then share your solutions with others in your group. O How does the grid help you think about this problem? O Can you come up with a different way to solve this problem? Stress the expectation that they must use the diagram in solving the problem and/or in providing an explanation for their strategy. As they are working on the task, circulate and select the strategies to be shared during whole group discussion.
- Whole Group (45 min) [This slide comes in two phases] Phase 1--Question only We would suggest that you have participants share two or three strategies that you’ve selected. O How did you approach this task? O How did the grid help you think about this problem? After discussing each strategy, have the whole group step back and make connections among different strategies and representations. O How are the solutions alike? Different? Following the discussion on commonalities and differences, ask about the kind of thinking involved in their strategies. Record their responses on a poster. (See next slide) Phase 2--List of strategies Compare their ideas with those on the slide.
- Whole Group (5 min) [This slide comes in two phases] Phase 1--Question only Before showing the bullets with the goals of the task, have the participants generate their own goals for the task. Now, let us consider the mathematical goals of the task. O What do you see as the mathematical goals of this task? Phase 2--List of strategies Compare their ideas with those on the slide.
- Individual Work (30 min) Handout: Linking Fractions, Decimals, and Percents Using an Area Model (The Case of Ron Castleman) Now that we have worked on the problem and made sense of our own strategies, we are ready to think about how using this task might look in a classroom. We will have you read the case of Ron Castleman, a teacher who is committed to use cognitively demanding tasks in his classroom but he is finding it highly challenging.
- Small group (30 min) Handout: Ron Castleman Case Analysis Protocol Have participants complete the protocol working in small groups.
- Whole Group (15 min) Use a graphic organizer to record their ideas in a way that highlights the contrasts between the teacher moves from one class to the next (e.g., providing sufficient time vs. letting his concern about time affect his decisions).
- (1-2 min) These last two slides help review the teacher moves or decisions that affect students’ opportunities for learning. Use as needed. Ask participants to compare this list with the one generated by the participants. What is the same, or different?
- (1-2 min) This slides help summarizes teacher moves or decisions that affect students’ opportunities for learning. Use as needed. Again, ask participants to compare this list with the one generated by the participants. What is the same, or different?
- (5 min.) Use 5 minutes to summarize the key ideas from the session or allow time for individual refection.