1. Task Analysis Guide (TAG)

2. Framework for Viewing  What does the teacher do to foster learning?  What is the impact on student learning?

3. What Are Mathematical Tasks? Mathematical tasks are a set of problems or a single complex problem the purpose of which is to focus students’ attention on a particular mathematical idea.

4. Why Focus on Mathematical Tasks?  Tasks form the basis for students’ opportunities to learn what mathematics is and how one does it.  Tasks influence learners by directing their attention to particular aspects of content and by specifying ways to process information.

5. Why Focus on Mathematical Tasks?  The level and kind of thinking required by mathematical instructional tasks influences what students learn.  Differences in the level and kind of thinking of tasks used by different teachers, schools, and districts, is a major source of inequity in students’ opportunities to learn mathematics.

6. “Not all tasks are created equal, and different tasks will provoke different levels and kinds of student thinking.” Stein, Smith, Henningsen, & Silver, 2000 “The level and kind of thinking in which students engage determines what they will learn.” Hiebert et al., 1997

7. Page 54

8. The Cognitive Level of Tasks Lower-Level Tasks  Memorization  Procedures without connections Higher-Level Tasks  Procedures with connections  Doing mathematics

9. Task Analysis Guide Read over the Task Analysis Guide and highlight important words, phrases or ideas for each level. Discuss at your table. Page 54

10. Memorization Tasks  Involves either producing previously learned facts, rules, formulae, or definitions OR committing facts, rules, formulae, or definitions to memory.  Cannot be solved using procedures because a procedure does not exist or because the time frame in which the task is being completed is too short to use a procedure.  Are not ambiguous – such tasks involve exact reproduction of previously seen material and what is to be reproduced is clearly and directly stated.  Have no connection to the concepts or meaning that underlie the facts, rules, formulae, or definitions being learned or reproduced.

11. Procedures Without Connections Tasks  Are algorithmic. Use of the procedure is either specifically called for or its use is evident based on prior instruction, experience, or placement of the task.  Require limited cognitive demand for successful completion. There is little ambiguity about what needs to be done and how to do it.  Have no connection to the concepts or meaning that underlie the procedure being used.  Are focused on producing correct answers rather than developing mathematical understanding.  Require no explanations, or explanations that focus solely on describing the procedure that was used.

12. Procedures With Connections Tasks  Focus students’ attention on the use of procedures for the purpose of developing deeper levels of understanding of mathematical concepts and ideas.  Suggest pathways to follow (explicitly or implicitly) that are broad general procedures that have close connections to underlying conceptual ideas as opposed to narrow algorithms that are opaque with respect to underlying concepts.  Usually are represented in multiple ways (e.g., visual diagrams, manipulatives, symbols, problem situations). Making connections among multiple representations helps to develop meaning.  Require some degree of cognitive effort. Although general procedures may be followed, they cannot be followed mindlessly. Students need to engage with the conceptual ideas that underlie the procedures in order to successfully complete the task and develop understanding.

13. Doing Mathematics Tasks  Requires complex and non-algorithmic thinking (i.e., there is not a predictable, well-rehearsed approach or pathway explicitly suggested by the task, task instructions, or a worked-out example).  Requires students to explore and to understand the nature of mathematical concepts, processes, or relationships.  Demands self-monitoring or self-regulation of one’s own cognitive processes.  Requires students to access relevant knowledge and experiences and make appropriate use of them in working through the task.  Requires students to analyze the task and actively examine task constraints that may limit possible solution strategies and solutions.  Requires considerable cognitive effort and may involve some level of anxiety for the student due to the unpredictable nature of the solution process required.

14. Task Analysis Guide What type of task was the “Percentage Task and the “Sweater Task?” Why? Take 3 minutes to discuss this at your table. Page 55

15. You Decide…  Use your TAG on page 54.  As a group, categorize each task by the cognitive levels Lower-Level Tasks  Memorization  Procedures without connections Higher-Level Tasks  Procedures with connections  Doing mathematics

16. There is no decision that teachers make that has a greater impact on students’ opportunities to learn and on their perceptions about what mathematics is than the selection or creation of the tasks with which the teacher engages students in studying mathematics. Lappan & Briars, 1995

17. Structure and Practicality

18. Page 56

19. The importance of the start Low High Low High Moderate High Task Set – UP Task Implementation Student Learning

20. The Explore Phase: Private Work (Think) Time  Generate Solutions  Teacher monitors:  Variety of representations  Errors  Misconceptions

21. The Explore Phase: Small Group – Problem Solving  Generate and Compare Solutions  Small groups work to find best solution  Assess and Advance Student Learning

22. Share Discuss and Analyze the Lesson  Share and Model  Compare Solutions  Focus the Discussion on Key Mathematical Ideas  Engage in a Quick Write

25. 25 We will narrow the focus of the TCAP and expand use of Constructed Response Assessments NAEP PARCC NAEP 2011-20122012-2013 2013-2014 2014-2015 TCAP We will remove 15-25% of SPIs that are not reflected in Common Core State Standards from the TCAP NEXT year. The specific list of SPI’s will be shared on May 1. Constructed Response We will expand the constructed response assessment for allgrades 3-8, focused on the TNCore focus standards for math.

26. 26 2012-2013 assessment plan, math 3-8 Official Constructed Response Assessment (paper-based only, scored by state, results reported in July) May CRA 2 (paper and online option, scored by teachers in Field Service Center region, reported by school team) February CRA 1 (paper and online option, scored by teachers in Field Service Center region, reported by school team) October Small Field Test, May 2012 Student performance on the Constructed Response Assessments will not affect teacher, school, or district accountability for the next two years.

27. Where will your students be in 2014-2015?

28. Moral Obligation  The time is always right to do what is right. Martin Luther King Jr.  Be sure you put your feet in the right place, then stand firm. Abraham Lincoln

29. Questioning

30. Questioning Resources  DOK Question Stems  Page 58  Pearson Ring (Assessing & Advancing)  Page 50-60  Pearson Effective Question Stem Cards  Page 61-65

35. Assessing Questions  Based closely on the work the student has produced.  Clarify what the student has done and what the student understands about what s/he has done.  Provide information to the teacher about what the student understands.

36. Advancing Questions  Use what students have produced as a basis for making progress toward the target goal.  Move students beyond their current thinking by pressing students to extend what they know to a new situation.  Press students to think about something they are not currently thinking about.

37. Marking Function  Direct attention to the value and importance of a student’s contribution. Example  “That’s an important point.”

38. Challenging students Function  Redirect a question back to the students or use student’s contributions as a source for a further challenge or inquiry. Example  “What do YOU think?”

39. Modeling Function  Make one’s thinking public and demonstrate expert forms or reasoning through talk. Example  “Here’s what good readers do...”

40. Recapping Function  Make public in a concise, coherent form, the group’s achievement at creating a shared understanding of the phenomenon under discussion. Example  “What have we discovered?”

41. Keeping the channels open Function  Ensure that students can hear each other, and remind them that they must hear what others have said. Example  “Did everyone hear that?”

42. Keeping everyone together Function  Ensure that everyone not only heard, but also understood what a speaker said. Example  “Who can repeat...?

43. Linking contributions Function  Make explicit the relationship between a new contribution and what has gone before. Example  “Who wants to add on...?

44. Verifying and clarifying Function  Revoice a student’s contribution, thereby helping both speakers and listeners to engage more profitably in the conversation. Example  “So, are you saying...?

45. Pressing for accuracy Function  Hold students accountable for the accuracy, credibility, and clarity of their contributions. Example  “Where can we find that...?

46. Building on prior knowledge Function  Tie a current contribution back to knowledge accumulated by the class at a previous time. Example  “How does this connect...?

47. Pressing for reasoning Function  Elicit evidence and establish what contribution a student’s utterance is intended to make within the group’s larger enterprise. Example  “Why do you think that...?

48. Expanding reasoning Function  Open up extra time and space in the conversation for student reasoning. Example  “Take your time... say more.”

49. 49 Reflection What have you learned about assessing and advancing questions that you can use in your classroom? Turn and Talk

50. Common Core and TEAM Model

52. 1. Make sense of problems and persevere in solving them. Questioning

53. 1. Make sense of problems and persevere in solving them. Questioning plan a solution pathway rather than simply jumping into a solution attempt

54. 1. Make sense of problems and persevere in solving them. Questioning plan a solution pathway rather than simply jumping into a solution attempt check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?

55. 1. Make sense of problems and persevere in solving them. Academic Feedback

56. 1. Make sense of problems and persevere in solving them. Academic Feedback explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends

57. 1. Make sense of problems and persevere in solving them. Thinking

58. 1. Make sense of problems and persevere in solving them. Thinking analyze givens, constraints, relationships, and goals

59. 1. Make sense of problems and persevere in solving them. Problem Solving

60. 1. Make sense of problems and persevere in solving them. Problem Solving make conjectures about the form and meaning of the solution

61. 1. Make sense of problems and persevere in solving them. Problem Solving make conjectures about the form and meaning of the solution try special cases and simpler forms of the original problem

62. 1. Make sense of problems and persevere in solving them. Problem Solving make conjectures about the form and meaning of the solution try special cases and simpler forms of the original problem understand the approaches of others to solving complex problems

63. 2. Reason abstractly and quantitatively. Thinking

64. 2. Reason abstractly and quantitatively. Thinking make sense of quantities and their relationships in problem situations

65. 2. Reason abstractly and quantitatively. Thinking make sense of quantities and their relationships in problem situations creating a coherent representation of the problem at hand

66. 2. Reason abstractly and quantitatively. Problem Solving

67. 2. Reason abstractly and quantitatively. Problem Solving abstract a given situation and represent it symbolically

68. 2. Reason abstractly and quantitatively. Problem Solving abstract a given situation and represent it symbolically considering the units involved; attending to the meaning of quantities

69. 2. Reason abstractly and quantitatively. Problem Solving abstract a given situation and represent it symbolically considering the units involved; attending to the meaning of quantities knowing and flexibly using different properties of operations and objects

70. 3. Construct viable arguments and critique the reasoning of others. Questioning

71. 3. Construct viable arguments and critique the reasoning of others. Questioning Making plausible arguments

72. 3. Construct viable arguments and critique the reasoning of others. Questioning Making plausible arguments listen or read the arguments of others

73. 3. Construct viable arguments and critique the reasoning of others. Questioning Making plausible arguments listen or read the arguments of others ask useful questions to clarify or improve the arguments

74. 3. Construct viable arguments and critique the reasoning of others. Academic Feedback

75. 3. Construct viable arguments and critique the reasoning of others. Academic Feedback communicate them to others, and respond to the arguments of others

76. 3. Construct viable arguments and critique the reasoning of others. Academic Feedback communicate them to others, and respond to the arguments of others if there is a flaw in an argument— explain what it is

77. 3. Construct viable arguments and critique the reasoning of others. Thinking

78. 3. Construct viable arguments and critique the reasoning of others. Thinking analyze situations by breaking them into cases

79. 3. Construct viable arguments and critique the reasoning of others. Thinking analyze situations by breaking them into cases compare the effectiveness of two plausible arguments

80. 3. Construct viable arguments and critique the reasoning of others. Problem Solving

81. 3. Construct viable arguments and critique the reasoning of others. Problem Solving can recognize and use counter examples

82. 3. Construct viable arguments and critique the reasoning of others. Problem Solving can recognize and use counter examples justify their conclusions

83. 3. Construct viable arguments and critique the reasoning of others. Problem Solving can recognize and use counter examples justify their conclusions distinguish correct logic or reasoning from that which is flawed

84. 4. Model with mathematics. Questioning

85. 4. Model with mathematics. Questioning reflect on whether the results make sense

86. 4. Model with mathematics. Thinking

87. 4. Model with mathematics. Thinking making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later

88. 4. Model with mathematics. Thinking making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later interpret their mathematical results in the context of the situation

89. 4. Model with mathematics. Problem Solving

90. 4. Model with mathematics. Problem Solving identify important quantities in a practical situation

91. 4. Model with mathematics. Problem Solving identify important quantities in a practical situation draw conclusions

92. 4. Model with mathematics. Problem Solving identify important quantities in a practical situation draw conclusions possibly improving the model if it has not served its purpose

93. 6. Attend to precision. Academic Feedback

94. 6. Attend to precision. Academic Feedback communicate precisely to others

95. 6. Attend to precision. Academic Feedback communicate precisely to others use clear definitions in discussion with others and in their own reasoning

96. 8. Look for and express regularity in repeated reasoning. Thinking

97. 8. Look for and express regularity in repeated reasoning. Thinking notice if calculations are repeated

98. 8. Look for and express regularity in repeated reasoning. Thinking notice if calculations are repeated look both for general methods and for shortcuts

99. Resources Beth Gilbert