2. Good morning… Complete the Teacher Beliefs Survey that can be found on the table. Find a seat and create a name plate with the cardstock. Lisa Joe

3. Principles to Actions: Ensuring Mathematical Success For All NC DPI Mathematics Section Fall 2015 Lisa Ashe lisa.ashe@dpi.nc.govlisa.ashe@dpi.nc.gov Joseph Reaper joseph.reaper@dpi.nc.govjoseph.reaper@dpi.nc.gov

4. Welcome “Who’s in the Room”

5. Session Goals  To explore the effective teaching practices that contribute to higher student achievement using Principles to Actions.  To explore the links between the Mathematics Teaching Practices and the Standards for Mathematical Practice.  To examine the classroom “look-fors” that promote student learning.

6. Norms Assume positive intentions Disagree with ideas, not people Maintain Professionalism Participate Actively

7. A 25-year History of Standards-Based Mathematics Education Reform

8. Standards Have Contributed to Higher Achievement The percent of 4th graders scoring proficient or above on NAEP (National Assessment of Educational Progress) rose from 13% in 1990 to 42% in 2013. The percent of 8th graders scoring proficient or above on NAEP rose from 15% in 1990 to 36% in 2013. Between 1990 and 2012, the mean SAT-Math score increased from 501 to 514 and the mean ACT-Math score increased from 19.9 to 21.0.

9. Trend in fourth-and-eighth grade NAEP Mathematics Average Scores http://nces.ed.gov/nationsreportcard/subject/publications/main2013/pdf/2014451.pdf

10. North Carolina NAEP Trends in Mathematics GradeSource19902013Change 4NC223254Up 31 4US227250Up 23 8NC250286Up 36 8US262284Up 22 NAEP Scale Score 1990 –First year NAEP reported NC Scores 2013 – Latest NC NAEP Test Data http://nces.ed.gov/nationsreportcard/subject/publications/main2013/pdf/2014451.pdf

11. Average NAEP Scores for NC 8 th Graders http://nces.ed.gov/nationsreportcard/subject/publications/stt2013/pdf/2014465NC8.pdf

12. NC EOG/EOC Percent Solid or Superior Command (CCR) Grade2012-20132013-20142014-2015 346.848.248.8 447.647.148.5 547.750.351.3 638.939.641.0 738.539.040.0 834.234.635.8 Math I42.646.948.5 http://www.ncpublicschools.org/accountability/reporting/

13. Although We Have Made Progress, Challenges Remain The average mathematics NAEP score for 17- year-olds has been essentially flat since 1973. Among 34 countries participating in the 2012 Programme for International Student Assessment (PISA) of 15-year-olds, the U.S. ranked 26th in mathematics. While many countries have increased their mean scores on the PISA assessments between 2003 and 2012, the U.S. mean score declined. Significant learning differentials remain.

14. Program for International Student Assessment (PISA)

15. Brainstorm Beliefs about Teaching and Learning Administrators & Leadership StudentsMediaCommunityTeachersFamily

16. “Teachers’ beliefs influence the decisions they make about the manner in which they teach mathematics.” Principles to Actions pg. 10-11 Beliefs About Teaching and Learning Mathematics “Students’ beliefs influence their perception of what it means to learn mathematics and how they feel toward the subject.” Examine the comic strip. What do you see?

17. Our Current Realities Too much focus is on learning procedures without any connection to meaning, understanding, or the applications that require these procedures. Too many students are limited by the lower expectations and narrow curricula of remedial tracks from which few ever emerge. Too many teachers have limited access to the instructional materials, tools, and technology that they need. Too much weight is placed on results from assessments – particularly large-scale, high-stakes assessments – that emphasize skills and fact recall and fail to give sufficient attention to problem solving and reasoning. Too many teachers of mathematics remain professionally isolated, without the benefit of collaborative structures and coaching, and with inadequate opportunities for professional development related to mathematics teaching and learning. Principles to Actions pg. 3

18. Principles to Actions: Ensuring Mathematical Success for All The primary purpose of Principles to Actions is to fill the gap between the adoption of rigorous standards and the enactment of practices, policies, programs, and actions required for successful implementation of those standards. NCTM. (2014). Principles to Actions: Ensuring Mathematical Success for All. Reston, VA: NCTM.

19. Teaching and Learning Access and EquityCurriculumTools and TechnologyAssessmentProfessionalism Guiding Principles for School Mathematics Guiding Principles for School Mathematics

20. “Effective teaching is the non-negotiable core that ensures that all students learn mathematics at high levels.” Overarching Message Principles to Actions (NCTM, 2014, p. 4)

21. Teaching and Learning Principle “An excellent mathematics program requires effective teaching that engages students in meaningful learning through individual and collaborative experiences that promote their ability to make sense of mathematical ideas and reason mathematically.” Principles to Actions (NCTM, 2014, p. 7)

22. Student learning of mathematics “depends fundamentally on what happens inside the classroom as teachers and learners interact over the curriculum.” (Ball & Forzani, 2011, p. 17) Ball, D. L, & Forzani, F. M. (2011). Building a common core for learning to teach, and connecting professional learning to practice. American Educator, 35(2), 17-21. Why Focus on Teaching?

23. Effective Mathematics Teaching Practices

24. Effective Mathematics Teaching Practices 1.Establish mathematics goals to focus learning. 2.Implement tasks that promote reasoning and problem solving. 3.Use and connect mathematical representations. 4.Facilitate meaningful mathematical discourse. 5.Pose purposeful questions. 6.Build procedural fluency from conceptual understanding. 7.Support productive struggle in learning mathematics. 8.Elicit and use evidence of student thinking.

25. Effective Mathematics Teaching Practices 1.Establish mathematics goals to focus learning. 2.Implement tasks that promote reasoning and problem solving. 3.Use and connect mathematical representations. 4.Facilitate meaningful mathematical discourse. 5.Pose purposeful questions. 6.Build procedural fluency from conceptual understanding. 7.Support productive struggle in learning mathematics. 8.Elicit and use evidence of student thinking.

27. Obstacles to Implementing High-Leverage Instructional Practices Many parents and educators believe that students should be taught as they were taught, through memorizing facts, formulas, and procedures and then practicing skills over and over again. Principles to Actions (NCTM, 2014, p. 9)

28. Let’s Do Some Math!

29. The Calling Plans Task Long-distance company A charges a base rate of $5.00 per month plus 4 cents for each minute that you are on the phone. Long-distance company B charges a base rate of only $2.00 per month but charges you 10 cents for every minute used. How much time per month would you have to talk on the phone before subscribing to company A would save you money? Create a phone plan, Company C, that costs the same as Companies A and B at 50 minutes, but has a lower monthly fee than either Company A or B.

30. The Calling Plans Task (MS) The Context of Video Clip 1 Prior to the lesson: Students solved the Calling Plans Task – Part 1. The tables, graphs and equations they produced in response to that task were posted in the classroom. Video Clip 1 begins immediately after Mrs. Brovey explained that students would be working on the Calling Plans Task – Part 2 and read the problem to students. Students first worked individually and subsequently worked in small groups.

31. The Calling Plans Video As you watch the video, make note of what the teacher does to support student learning and engagement as they work on the task. Work with a partner. One of you will focus on the teacher and the other will focus on the students. o What is the teacher doing/saying? o What are the students doing/saying?

32. Math Teaching Practice 1 Establish mathematics goals to focus learning. Formulating clear, explicit learning goals sets the stage for everything else. (Hiebert, Morris, Berk, & Janssen, 2007, p. 57)

33. Establishing mathematics goals to focus learning. As you read pgs. 12-14 and Table on pg. 16, use the following symbols in your reading. SymbolMeaning ✓ Confirms your thinking. ✕ Contradicts your thinking. ?Raises questions you would like to discuss with others. * Important…answers a question. !New, interesting or surprising End Start 20 minute Timer :

34. Table Talk Each person in the group share one interesting thing that you read. No responses at this time. You may want to record or take notes to respond later. After everyone has shared, each person in the group share a response to someone else’s comment. Once everyone has responded, then you may openly discuss.

35. Learning Goals should: Clearly state what it is students are to learn and understand about mathematics as the result of instruction. Be situated within learning progressions. Frame the decisions that teachers make during a lesson. Daro, Mosher, & Corcoran, 2011; Hattie, 2009; Hiebert, Morris, Berk, & Jensen., 2007; Wiliam, 2011 Establish mathematics goals to focus learning Establish mathematics goals to focus learning

36. What learning goals can you create for the task? When complete, share with your table. Each table needs to be prepared to share 1 goal. Reflecting on Calling Plans Task

37. Mrs. Brovey’s Mathematics Learning Goals Students will understand that: 1.the point of intersection is a solution to each equation (Companies A, B, and C); 2.the rate of change (cost per minute) determines the steepness of the line; 3.if the y-intercept (monthly base rate) is lowered then the rate of change (cost per minute) must increase in order for the new equation to intersect the other two at the same point.

38. Connections to the CCSS Content Standards National Governors Association Center for Best Practices & Council of Chief State School Officers (2010). Common core state standards for mathematics. Washington, DC: Authors. Define, Evaluate and Compare Functions 8.F Uses Functions to Model Relationships Between Quantities 4.Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. 5.Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

39. Mr. Torchon’s Mathematics Learning Goals Students will understand that: 1.The point of intersection is a solution to each equation (Plans A and B); 2.A system of equations may be solved with a table or a graph; 3.When the graph of one function is below the graph of another function, the function with the lower graph has y-values that are less than the other function.

40. Connections to the CCSS Content Standards National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common core state standards for mathematics. Washington, DC: Authors. Solve Systems of Equations 6. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Represent and solve equations and inequalities graphically 11.Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately. ★ Reasoning with Equations and Inequalities A-REI

41. Connections to the CCSS Content Standards National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common core state standards for mathematics. Washington, DC: Authors. Interpret functions that arise in applications in terms of the context 4. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. ★ 5. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. ★ Interpreting Functions F-IF

42. Teaching Practices Jigsaw 1.Everyone grab a flip-flop cut out and note-taking handout from your table. 2.Expert Groups: Move to find others in the room with the same cut out. 3.Read your assigned practice. Come to a shared understanding of the teaching practice and be prepared to share back at your table. 10 minutes End Start

43. Teaching Practice Reading 2.Implement Tasks – Page 17 3.Use and Connect Representations – Page 24 4.Facilitate discourse – Page 29 5.Pose questions – Page 35 6.Build procedural fluency – Page 42 7.Support productive struggle – Page 48 8.Elicit and use evidence – Page 53 10 minutes End Start

44. Teaching Practices Share 1.Share Group: Now create a group that has at least one of every flip flop type. 2.Share important points about each teaching practice. 3.Use the graphic organizer to take notes on each practice. 15 minutes End Start

45. Implement tasks that promote reasoning and problem solving. Student learning is greatest in classrooms where the tasks consistently encourage high-level student thinking and reasoning and least in classrooms where the tasks are routinely procedural in nature. (Boaler & Staples, 2008; Stein & Lane, 1996) Math Teaching Practice 2

46. Math Tasks There is no decision that teachers make that has a greater impact on students’ opportunities to learn, and on their perception about what mathematics is, than the selection or creation of the tasks with which the teacher engages students in shaping mathematics.

47. Mathematical tasks should: Allow students to explore mathematical ideas or use procedures in ways that are connected to understanding concepts. Build on students’ current understanding and experiences. Have multiple entry points. Allow for varied solution strategies. Boaler & Staples, 2008; Hiebert et al., 1997; Stein, Smith, Henningsen, & Silver, 2009 Implement tasks that promote reasoning and problem solving

48. High or Low Cognitive Demanding Task? High Low

49. Low Cognitive Demand TasksHigh Cognitive Demand Tasks Memorization Procedures with Connections Procedures without Connections Doing Mathematics Stein, Smith, Henningsen, & Silver (2000)

50. Cognitive Demand Sort 1.Individually study the Cognitive Demand chart at your tables. 2.Grab a “tool” cut out from your table 3.Find your group. 4.Using the chart as a guide, sort the tasks in the envelope labeled Task Sort by cognitive demand. 10 minutes End Start

51. High Low HighLow Moderate TaskImplementation Student Learning

52. Reflecting on Calling Plans Task Reflecting on your experience with the task or the video, in what ways can the implementation of the task allow for multiple entry points and engage students in reasoning and problem solving?

53. Students are working on the Calling Plans Task. Mr. Torchon is initially working with groups of students, asking questions to help them focus on their thinking and to progress toward a solution. The tables, graphs (and, in at least one case an equation) students produce in response to the task are then posted in the classroom and a whole class discuss ensues. The Calling Plans 1 Task The Context of Video Clip

54. Lens for Watching the HS Video First Viewing As you watch the video, make note of what the teacher does to support student learning and engagement as they work on the task. In particular, identify any of the Effective Mathematics Teaching Practices that you notice Mr. Torchon using. Be prepared to give examples and to cite line numbers from the transcript to support your claims.

55. Use and connect mathematical representations. Math Teaching Practice 3 Because of the abstract nature of mathematics, people have access to mathematical ideas only through the representations of those ideas. (National Research Council, 2001, p. 94)

56. Use and connect mathematical representations Different Representations should: Be introduced, discussed, and connected. Be used to focus students’ attention on the structure of mathematical ideas by examining essential features. Support students’ ability to justify and explain their reasoning. Lesh, Post, & Behr, 1987; Marshall, Superfine, & Canty, 2010; Tripathi, 2008; Webb, Boswinkel, & Dekker, 2008

57. Contextual Physical Visual Symbolic Verbal Important Mathematical Connections between and within different types of representations Principles to Actions (NCTM, 2014, p. 25) (Adapted from Lesh, Post, & Behr, 1987)

58. Lens for Watching the Video Second Viewing As you watch the video this time, pay attention to the ways in which representations are used and connected. Specifically: Does the task allow students to use multiple representations? What representations are students using? In what ways are students making connections among the mathematical representations? In what ways are students contextualizing mathematical ideas in real-world situations?

59. What mathematical representations were students working within the lesson? How did Mr. Torchon support students in making connections between and within different types of representations? Contextual Physical Visual Symbolic Verbal

60. Facilitate meaningful mathematical discourse. Math Teaching Practice 4 Discussions that focus on cognitively challenging mathematical tasks, namely those that promote thinking, reasoning, and problem solving, are a primary mechanism for promoting conceptual understanding of mathematics. (Hatano & Inagaki, 1991; Michaels, O’Connor, & Resnick, 2008)

61. Mathematical Discourse should: Build on and honor students’ thinking. Let students share ideas, clarify understandings, and develop convincing arguments. Engage students in analyzing and comparing student approaches. Advance the math learning of the whole class. Carpenter, Franke, & Levi, 2003; Fuson & Sherin, 2014; Smith & Stein, 2011 Facilitate meaningful mathematical discourse

62. 1. Anticipating 2. Monitoring 3. Selecting 4. Sequencing 5. Connecting 5 Practices for Orchestrating Productive Mathematics Discussions (Smith & Stein, 2011)

63. Given the Calling Plans Task, using the MS goal or the HS goal, how would you structure the student presentations to connect mathematical ideas and encourage discourse? Selecting specific student representations and strategies for discussion and analysis. Sequencing the various student approaches for analysis and comparison. Connecting student approaches to key math ideas and relationships. Structuring Mathematical Discourse...

64. Pose purposeful questions. Math Teaching Practice 5 Teachers’ questions are crucial in helping students make connections and learn important mathematics and science concepts. (Weiss & Pasley, 2004)

65. Effective Questions should: Reveal students’ current understandings. Encourage students to explain, elaborate, or clarify their thinking. Make the targeted mathematical ideas more visible and accessible for student examination and discussion. Boaler & Brodie, 2004; Chapin & O’Connor, 2007; Herbel-Eisenmann & Breyfogle, 2005 Pose purposeful questions

66. Following individual and small group work, Mrs. Brovey pulls the class together for a whole group discussion. Several different equations that satisfy the conditions of the problem are offered by students. Jake, a student in the class then proposed a theory that every time the rate increases by 1 cent the base rate decreases by 50 cents. Mrs. Brovey records the four possible phone plans for Company C (shown below) on the board and ask the class what patterns they see. C =.14m C =.13m + $.50 C =.12m + $1.00 C =.11m + $1.50 Video Clip 2 focuses on the discussion between teacher and students regarding the patterns they notice.. The Calling Plans Task – Part 2 The Context of Video Clip 2

67. Lens for Watching the MS Video Clip 2 As you watch the second video of the MS this time, pay attention to the questions the teacher asks. Specifically: What do the questions reveal about students’ current understandings? To what extent do the questions encourage students to explain, elaborate, or clarify their thinking? To what extent to the questions make mathematics more visible and accessible for student examination and discussion? How are the questions in this clip similar to or different from the questions asked in video clip 1?

68. Build procedural fluency from conceptual understanding. Math Teaching Practice 6 A rush to fluency undermines students’ confidence and interest in mathematics and is considered a cause of mathematics anxiety. (Ashcraft 2002; Ramirez Gunderson, Levine, & Beilock, 2013)

69. Procedural Fluency should: Build on a foundation of conceptual understanding. Over time (months, years), result in known facts and generalized methods for solving problems. Enable students to flexibly choose among methods to solve contextual and mathematical problems. Baroody, 2006; Fuson & Beckmann, 2012/2013; Fuson, Kalchman, & Bransford, 2005; Russell, 2006 Build procedural fluency from conceptual understanding

70. “Fluency builds from initial exploration and discussion of number concepts to using informal reasoning strategies based on meanings and properties of the operations to the eventual use of general methods as tools in solving problems.” Principles to Actions (NCTM, 2014, p. 42) Build procedural fluency from conceptual understanding

71. Algebra Tiles activities on GCF and Factoring

72. Math Teaching Practice 7 Support productive struggle in learning mathematics. The struggle we have in mind comes from solving problems that are within reach and grappling with key mathematical ideas that are comprehendible but not yet well formed. (Hiebert, Carpenter, Fennema, Fuson, Human, Murray, Olivier, & Wearne, 1996)

73. Productive Struggle should: Be considered essential to learning mathematics with understanding. Develop students’ capacity to persevere in the face of challenge. Help students realize that they are capable of doing well in mathematics with effort. Black, Trzesniewski, & Dweck, 2007; Dweck, 2008; Hiebert & Grouws, 2007; Kapur, 2010; Warshauer, 2011 Support productive struggle in learning mathematics

74. Where in this task would you predict as areas of productive struggle? How would you prepare for those struggles? Reflecting on Calling Plans Task

76. Elicit and use evidence of student thinking. Math Teaching Practice 8 Teachers using assessment for learning continually looking for ways in which they can generate evidence of student learning, and they use this evidence to adapt their instruction to better meet their students’ learning needs. (Leahy, Lyon, Thompson, & Wiliam, 2005, p. 23)

77. Evidence should: Provide a window into students’ thinking. Help the teacher determine the extent to which students are reaching the math learning goals. Be used to make instructional decisions during the lesson and to prepare for subsequent lessons. Chamberlin, 2005; Jacobs, Lamb, & Philipp, 2010; Sleep & Boerst, 2010; van Es, 2010’ Wiliam, 2007 Elicit and use evidence of student thinking

78. Identify specific places during either video where the teacher elicited evidence of student learning. Discuss how she/he used or might use that evidence to adjust their instruction to support and extend student learning. Elicit and use evidence of student thinking

79. Pair-Share Discuss the strategy used in this video. What did you like about the teachers’ method of assessing student understanding? What formative assessment strategies do you use in your classroom? “My Favorite No: Learning From Mistakes”

80. “Although the important work of teaching is not limited to the eight Mathematics Teaching Practices, this core set of research-informed practices is offered as a framework for strengthening the teaching and learning of mathematics.” Principles to Actions (NCTM, 2014, p. 57) NCTM’s Core Set of Effective Mathematics Teaching Practices

81. What might be the math learning goals? Math Goals What representations might students use in reasoning through and solving the problem? Tasks & Representations How might we question students and structure class discourse to advance student learning? Discourse & Questions How might we develop student understanding to build toward aspects of procedural fluency? Fluency from Understanding How might we check in on student thinking and struggles and use it to inform instruction? Struggle & Evidence

82. Sort the Beliefs Unproductive Beliefs Check your arrangement on Principles to Actions pg. 11

83. Principles to Action – pg. 11 Beliefs About Teaching and Learning Mathematics

84. Reflections and Next Steps

85. Start Small, Build Momentum, and Persevere The process of creating a new cultural norm characterized by professional collaboration, openness of practice, and continual learning and improvement can begin with a single team of grade-level or subject-based mathematics teachers making the commitment to collaborate on a single lesson plan.

86. What action are you taking? Your role: –Leaders and policymakers pgs 110-112 –Principals, coaches, specialists, other school leaders pgs 112-114 –Teachers pgs 114-117 –Group Discussion about next steps Principles to Actions

87. As you reflect on this framework for the teaching and learning of mathematics, identify 1-2 mathematics teaching practices that want to begin strengthening in your own instruction. Working with a partner, develop a list of actions to begin the next steps of your journey toward ensuring mathematical success for all of your students. Principles to Actions

88. Food for thought…. ① We are being asked to teach in distinctly different ways from how we were taught. ② The traditional curriculum was designed to meet societal needs that no longer exist. ③ It is unreasonable to ask a professional to change more than 10 percent a year, but it is unprofessional to change by much less than 10 percent a year. ④ If you don’t feel inadequate, you’re probably not doing the job. http://steveleinwand.com/wp-content/uploads/2014/08/FourPostulatesforChange.pdf

90. NCCTM Fall Leadership Conference November 4th Koury Convention Center Featuring: Daniel Brahier, lead author for NCTM’s Principles to Actions Diane Briars, President of NCTM Jon Wray, Howard County Public Schools

91. 45 th Annual State Math Conference Principles to Actions in Action November 5 th and 6 th Koury Convention Center Greensboro, NC Anyone here being honored as their district’s NCCTM Outstanding Elementary Mathematics Educator?

92. 2013 PAEMST Math State Winner

93. What questions do you have?

94. maccss.ncdpi.wikispaces.net

95. Follow Us! NC Mathematics www.facebook.com/NorthCarolinaMathematics @ncmathematics http://maccss.ncdpi.wikispaces.net

96. DPI Mathematics Section Kitty Rutherford Elementary Mathematics Consultant 919-807-3841 kitty.rutherford@dpi.nc.gov Denise Schulz Elementary Mathematics Consultant 919-807-3842 denise.schulz@dpi.nc.gov Lisa Ashe Secondary Mathematics Consultant 919-807-3909 lisa.ashe@dpi.nc.gov Joseph Reaper Secondary Mathematics Consultant 919-807-3691 joseph.reaper@dpi.nc.gov Dr. Jennifer Curtis K – 12 Mathematics Section Chief 919-807-3838 jennifer.curtis@dpi.nc.gov Susan Hart Mathematics Program Assistant 919-807-3846 susan.hart@dpi.nc.gov

97. For all you do for our students!