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Supporting Rigorous Mathematics Teaching and Learning Making Sense of Numbers and Operations

Supporting Rigorous Mathematics Teaching and Learning Making Sense of Numbers and Operations Fraction Standards via a Set of Tasks. Tennessee Department of Education Elementary School Mathematics Grade 3-5

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Supporting Rigorous Mathematics Teaching and Learning Making Sense of Numbers and Operations

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  1. Supporting Rigorous Mathematics Teaching and Learning Making Sense of Numbers and Operations Fraction Standards via a Set of Tasks Tennessee Department of Education Elementary School Mathematics Grade 3-5 [*Note: Slides for Math CCSS Grades 6-8 are the same except for the tasks and the grade level standards. 6th & 7th grade Focus – Making Sense of the Number System Standard via a Set of Tasks.]

  2. Rationale Tasks form the basis for students’opportunities to learn what mathematics is and how one does it, yet not all tasks afford the same levels and opportunities for student thinking. [They] are central to students’learning, shaping not only their opportunity to learn but also their view of the subject matter. Adding It Up, National Research Council, 2001, p. 335 By analyzing instructional and assessment tasks that are for the same domain of mathematics, teachers will begin to identify the characteristics of high-level tasks, differentiate between those that require problem-solving, and those that assess for specific mathematical reasoning.

  3. Session Goals

  4. Overview of Activities

  5. Analyzing Tasks as a Means of Making Sense of the CCSSNumber and OperationsFractions

  6. Linking to Research/Literature: The QUASAR Project The Mathematical Tasks Framework TASKS as set up by the teachers TASKS as implemented by students TASKS as they appear in curricular/ instructional materials Student Learning Stein, Smith, Henningsen, & Silver, 2000

  7. Linking to Research/Literature: The QUASAR Project The Mathematical Tasks Framework TASKS as set up by the teachers TASKS as implemented by students TASKS as they appear in curricular/ instructional materials Student Learning Stein, Smith, Henningsen, & Silver, 2000 Setting Goals Selecting Tasks Anticipating Student Responses • Orchestrating Productive Discussion • Monitoring students as they work • Asking assessing and advancing questions • Selecting solution paths • Sequencing student responses • Connecting student responses via Accountable Talk® discussions Accountable Talk®is a registered trademark of the University of Pittsburgh

  8. Analyzing Tasks: Aligning with the CCSS(Small Group Discussion) Determine which Content Standards students would have opportunities to make sense of when working on the task. Determine which Mathematical Practice Standards students would need to make use of when solving the task.

  9. Analyzing Tasks: Aligning with the CCSS(Whole Group Discussion) How do the tasks differ from each other with respect to the content that students will have opportunities to learn? Do some tasks require that students use Standards for Mathematical Practice that other tasks don’t require students to use?

  10. The CCSS for Mathematical Content − Grade 3 Common Core State Standards, 2010, p. 54, NGA Center/CCSSO

  11. The CCSS for Mathematical Content − Grade 3 Common Core State Standards, 2010, p. 55, NGA Center/CCSSO

  12. The CCSS for Mathematical Practice Common Core State Standards, 2010, p. 6-8, NGA Center/CCSSO • Make sense of problems and persevere in solving them. • Reason abstractly and quantitatively. • Construct viable arguments and critique the reasoning of others. • Model with mathematics. • Use appropriate tools strategically. • Attend to precision. • Look for and make use of structure. • Look for and express regularity in repeated reasoning.

  13. Reflecting and Making Connections • Are all of the CCSS for Mathematical Content in this cluster addressed by one or more of these tasks? • Are all of the CCSS for Mathematical Practice addressed by one or more of these tasks? • What is the connection between the cognitive demand of the written task and the alignment of the task to the Standards for Mathematical Content and Practice?

  14. Differentiating Between Instructional Tasks and Assessment Tasks Are some tasks more likely to be assessment tasks than instructional tasks? If so, which and why are you calling them assessment tasks?

  15. Instructional Tasks Versus Assessment Tasks

  16. Reflection So, what is the point? What have you learned about assessment tasks and instructional tasks that you will use to select tasks to use in your classroom next school year?

  17. Bridge to Practice Select a high-level task. Analyze the task and determine the alignment to the Mathematical Content Standards and the Standards for Mathematical Practice. Describe if the task is an instructional task or an assessment task and explain why you decided on the label. If necessary, refer back to slide 33 for assistance. Use the set of examples of tasks to differentiate between the two types of tasks .

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