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Supporting Rigorous Mathematics Teaching and Learning

Supporting Rigorous Mathematics Teaching and Learning Engaging In and Analyzing Teaching and Learning. Tennessee Department of Education Elementary School Mathematics Grade 2. Rationale. Common Core State Standards for Mathematics , 2010.

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Supporting Rigorous Mathematics Teaching and Learning

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  1. Supporting Rigorous Mathematics Teaching and Learning Engaging In and Analyzing Teaching and Learning Tennessee Department of Education Elementary School Mathematics Grade 2

  2. Rationale Common Core State Standards for Mathematics, 2010 Asking a student to understand something means asking a teacher to assess whether the student has understood it. But what does mathematical understanding look like? One hallmark of mathematical understanding is the ability to justify, in a way appropriate to the student’s mathematical maturity, why a particular mathematical statement is true - Mathematical understanding and procedural skill are equally important, and both are assessable using mathematical tasks of sufficient richness. By engaging in a task, teachers will have the opportunity to consider the potential of the task and engagement in the task for helping learners develop the facility for expressing a relationship between quantities in different representational forms, and for making connections between those forms.

  3. Session Goals Participants will: • develop a shared understanding of teaching and learning; and • deepen content and pedagogical knowledge of mathematics as it relates to the Common Core State Standards (CCSS) for Mathematics.

  4. Overview of Activities Participants will: • engage in a lesson; and • reflect on learning in relationship to the CCSS.

  5. Looking Over the Standards • Read the task. Before you solve the task, look over the second grade standards for Operations and Algebraic Thinking and Number Operations in Base Ten. • We will return to the standards at the end of the lesson and consider what it means to say: • In what ways did we have opportunities to learn about the concepts underlying the standards? • What gets “counted” as learning?

  6. Eduardo’s and Katrina’s Strategies Eduardo solves the story problem below by using subtraction. Show Eduardo’s equation. You have 100 stickers. You put 48 of the stickers into your sticker album. How many stickers do you still need to put in an album? When Eduardo compares his work to Katrina’s, he sees that she used addition to solve the problem. Explain to Eduardo why Katrina can use addition to solve this problem.

  7. The CCSS for Mathematics: Grade 2 Common Core State Standards, 2010, p. 19, NGA Center/CCSSO

  8. The CCSS for Mathematics: Grade 2 Common Core State Standards, 2010, p. 19, NGA Center/CCSSO

  9. The CCSS for Mathematics: Grade 2 Common Core State Standards, 2010, p. 19, NGA Center/CCSSO

  10. The CCSS for Mathematics: Grade 2 Common Core State Standards, 2010, p. 19, NGA Center/CCSSO

  11. The CCSS for Mathematics: Grade 2 Common Core State Standards, 2010, p. 19, NGA Center/CCSSO

  12. Table 1: Common Addition and Subtraction Situations Common Core State Standards, 2010

  13. Engage In and Reflect on a Lesson

  14. The Structures and Routines of a Lesson Set Up the Task Set Up of the Task MONITOR: Teacher selects examples for the Share, Discuss, and Analyze Phase based on: • Different solution paths to the • same task • Different representations • Errors • Misconceptions The Explore Phase/Private Work Time Generate Solutions The Explore Phase/Small Group Problem Solving Generate and Compare Solutions Assess and Advance Student Learning SHARE: Students explain their methods, repeat others’ ideas, put ideas into their own words, add on to ideas and ask for clarification. REPEAT THE CYCLE FOR EACH SOLUTION PATH COMPARE: Students discuss similarities and difference between solution paths. FOCUS: Discuss the meaning of mathematical ideas in each representation. REFLECT by engaging students in a quick write or a discussion of the process. Share, Discuss, and Analyze Phase of the Lesson 1. Share and Model 2. Compare Solutions 3. Focus the Discussion on Key Mathematical Ideas 4. Engage in a Quick Write

  15. Solve the Task(Private Think Time) • Work privately on the Eduardo’s and Katrina’s Strategies Task. • Work with others at your table. Compare your solution paths. • Make observations about relationships that you notice.

  16. Eduardo’s and Katrina’s Strategies Eduardo solves the story problem below by using subtraction. Show Eduardo’s equation. You have 100 stickers. You put 48 of the stickers into your sticker album. How many stickers do you still need to put in an album? When Eduardo compares his work to Katrina’s, he sees that she used addition to solve the problem. Explain to Eduardo why Katrina can use addition to solve this problem. 16

  17. Expectations for Group Discussion • Solution paths will be shared. • Listen with the goals of: • putting the ideas into your own words; • adding on to the ideas of others; • making connections between solution paths; and • asking questions about the ideas shared. • The goal is to understand the mathematical relationships and to make connections among the various strategies used when solving the problems in the task.

  18. Reflecting on Our Learning What supported your learning? Which of the supports listed will EL students benefit from during instruction? Which CCSS for Mathematical Content did we discuss? Which CCSS for Mathematical Practice did you use when solving the task?

  19. Pictures Manipulative Models Written Symbols Real-world Situations Oral Language Linking to Research/LiteratureConnections Between Representations Adapted from Lesh, Post, & Behr, 1987

  20. Reflecting on Our Learning What supported your learning? Which of the supports listed will EL students benefit from during instruction? Which CCSS for Mathematical Content did we discuss? Which CCSS for Mathematical Practice did you use when solving the task?

  21. Reflecting on Our Learning What supported your learning? Which of the supports listed will EL students benefit from during instruction? Which CCSS for Mathematical Content did we discuss? Which CCSS for Mathematical Practice did you use when solving the task?

  22. The CCSS for Mathematical Practice • Common Core State Standards, 2010 • 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.

  23. Research Connection: Findings from Tharp and Gallimore Tharp & Gallimore, 1991 For teaching to have occurred - Teachers must “be aware of the students’ ever-changing relationships to the subject matter.” They [teachers] can assist because, while the learning process is alive and unfolding, they see and feel the students’ progression through the zone, as well as the stumbles and errors that call for support. For the development of thinking skills—the [students’] ability to form, express, and exchange ideas in speech and writing—the critical form of assisting learners is dialogue—thequestioning and sharing of ideas and knowledge that happen in conversation.

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