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Ses Case1 Ron Castleman 062009 Pk Formatted

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Ses Case1 Ron Castleman 062009 Pk Formatted

1. 1. Overview of Session <ul><li>Working on a Mathematical Task </li></ul><ul><li>Analyzing the Ron Castleman Case </li></ul>
2. 2. Goals of the Session <ul><li>To develop an understanding of differences between ratios and fractions </li></ul><ul><li>To identify solution strategies for proportional situations </li></ul><ul><li>To recognize the factors that support and undermine student learning </li></ul>
3. 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)
4. 4. Working on a Mathematical Task <ul><li>Solve the problem in more than one way </li></ul><ul><li>Be sure to label what each quantity represents </li></ul><ul><li>Explain why your strategy works </li></ul>
5. 5. <ul><li>Shade 6 of the small squares shown below. </li></ul><ul><li>Determine the percent of the area that is shaded and use the diagram to explain/justify your solution. </li></ul>Working on a Mathematical Task: Ron Castleman Problem Ron Castleman Problem
6. 6. Strategies for The Task <ul><li>What strategies might be used in solving this task? </li></ul><ul><li>Scaling up/down </li></ul><ul><ul><li>Using ratio tables </li></ul></ul><ul><ul><li>Using equivalent fractions </li></ul></ul><ul><li>Using unit ratio </li></ul>
7. 7. Goals of The Task <ul><li>What might be the mathematical goals of this task? </li></ul><ul><li>To identify differences between concepts, language, notation and operations related to ratios and fractions </li></ul><ul><li>To develop meanings meanings of fractions, decimals, and percents and make connections among them </li></ul>
8. 8. Reading the Case <ul><li>Read the case of Ron Castleman </li></ul><ul><li>Pay special attention to </li></ul><ul><ul><li>students’ understanding of the mathematics </li></ul></ul><ul><ul><li>teacher moves that support or undermine student learning </li></ul></ul>
9. 9. Analyzing the Case: Student Thinking <ul><li>What were the expectations for students in each class? </li></ul><ul><li>What did the students seem to learn in each class? </li></ul>
10. 10. Analyzing the Case: The Instruction <ul><li>What does Ron Castleman do to support student opportunities for learning? </li></ul><ul><li>What does he do to undermine opportunities? </li></ul>
11. 11. Factors that Undermine the Cognitive Demand of a Task <ul><li>Routinizing problematic aspects of the task </li></ul><ul><li>Shifting the emphasis from meaning, concepts, or understanding, to the correctness or the completeness of the answer </li></ul><ul><li>Not providing enough time </li></ul><ul><li>Not holding students accountable for high-level products or processes </li></ul><ul><li>(Stein, Smith, Henningsen, & Silver, 2000) </li></ul>
12. 12. Factors that Support Maintaining High Cognitive Demand <ul><li>Building on students’ prior knowledge of concepts and meanings </li></ul><ul><li>Scaffolding students’ thinking </li></ul><ul><li>Providing appropriate amount of time </li></ul><ul><li>Modeling high-level performance </li></ul><ul><li>Sustaining pressure for justification, explanations and meaning </li></ul><ul><li>Drawing frequent conceptual conceptions </li></ul><ul><li>(Stein, Smith, Henningsen, & Silver, 2000) </li></ul>
13. 13. Reflection <ul><li>What were the important mathematical ideas you encountered today? </li></ul><ul><li>Did this experience generate any insights/connections relate to teaching? (What about the day prompted these?) </li></ul>