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Integrating the Standards for Mathematical Practice as a Natural part of Teaching Through Whole Class Mathematics Discussions. Teruni Lamberg, Ph.D. University of Nevada, Reno Terunil@unr.edu 1

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The ultimate goal of teaching is to support student LEARNING! 2

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Three things to keep in mind as you teach: What do I want my students to learn? What are they learning? Am I being effective? 3

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What is learning? How do you know that learning is taking place? 4

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According to National Research Council learning When students learn concepts with UNDERSTANDING, that knowledge becomes a TOOL to solve problems in novel situations. Learning is an ACTIVE process! New knowledge builds on students’ pre existing knowledge- need to pay attention to students' prior conceptions and understandings. Making meaningful connections and seeing patterns is an important part of developing expertise. National Research Council. How People Learn: Brain, Mind, Experience, and School: Expanded Edition. Washington, DC: The National Academies Press, 2000 5

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Improving teaching to support student learning: Involves thinking about the process of planning and teaching including setting up the classroom environment. Effective whole class discussions that support learning involves situating the discussion within the larger mathematical goals. 6

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Students’ Role in Discussion Students must effectively communicate their mathematical thinking using representations. Listen and reflect to ideas presented. Ask questions if unclear about idea presented. Be willing to refine and revise thinking. 8

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Teacher’s Role in Whole Class Discussions The teacher’s role in whole class discussion is to select problems to pose. Use questions to engage students in mathematical reasoning. Carefully sequence discussion and questioning so that students make mathematical connections. 9

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Classroom discussion time must be used effectively and efficiently to Support learning Discussion must build a bridge between student thinking, mathematical concepts and skills. Students must develop new mathematical insights and make deeper mathematical connections as a result of participating in a discussion. 10

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Integrating the Standards of Mathematical Practice through Whole Class discussions as a natural part of teaching. 11

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Make Sense of Problems and Persevere in solving them (MP1) Explore meaning of problem Look for entry points to a solution Analyze givens, constraints, relationships, and goals. Think about possible solution and plan a pathway Consider similar problems or simpler problems Monitor and evaluate their progress and change course if necessary 12

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Reason abstractly and quantitatively (MP2) Mathematically proficient students make sense of quantities and their relationships in problem situations. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. 13

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Construct viable arguments and critique the reasoning of others. (MP3) Mathematically proficient students can justify their conclusions, communicate them to others, and respond to the arguments of others. 14

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Model with mathematics (MP4) They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. 16

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Use appropriate tools strategically (MP 5) Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models …. 17

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Attend to precision. (MP6) Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. 18

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Look for and make use of structure. (MP7) Mathematically proficient students look closely to discern a pattern or structure 19

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Look for and express regularity in repeated reasoning. (MP 8) Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. 20

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Facilitating effective discussions involves thinking about the process of teaching! Setting up the physical space Classroom Routines Lesson Planning Teacher questioning (To start and facilitate discussion) 21

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Lamberg (2012) Framework from Whole Class Mathematics discussion book. Can download copy from my blog: http://mathdiscussions.wordpress.com/whole-class- discussion-framework-checklist/ http://mathdiscussions.wordpress.com/whole-class- discussion-framework-checklist/ Blog contains many resources and links to support your teaching and use the framework This Framework allows you to see the “big picture” of teaching and how the parts such as whole class discussion fits in. Facilitating discussions that support learning involves having all these pieces work together. 22

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23 Not met Work in Progress Working Great To do list Tools from Whole Class Discussion book Setting up the Classroom (Chapter 2) *P.36 Checklist Setting up Physical Space

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Cultivating Classroom Environment/Routi nes Not Met Work in Progress Working Great Note: Routines for (Communicating/Listeni ng Takes place during whole class discussion. These routines take time to develop.) (Chapter 3) *P.60 Strategies for Your Classroom, Ideas for Developing classroom Routines Routines for Preparing for Discussion Standards of Mathematical Practice 1,4,5,7,8 Routines for Communicating Standards of Mathematical Practice 2,3 Routines for Listening/Reflecting Standards of Mathematical Practice 1 24

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Lesson Planning Note: Third level of planning takes place during lesson/discussion. The purpose of the first 2 levels of planning is to situate the discussion in larger goals to support deeper learning. (Chapter 4) *P.91 Strategies for Your Classroom (Three Levels of Planning) First level Planning (Long term & Short Term Goals) Concepts (big ideas) Unit Plan (Sequencing/learning trajectory) *P.92 Concept Map *P.93 Rubric for Unit Planning 25

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Second Level of Planning 5 E-Lesson Plan- (Anticipating Student Reasoning/Misconceptions Errors, Format for using a problem solving approach to teaching and structuring time) *P.94 Rubric for 5E Lesson Plan: Level 2 26

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Takes Place During the Lesson Third Level of Planning (Adapting discussion to support student understanding/ needs) Making decisions on what to talk about based on student reasoning during lessons Not met Still Working Working Great *Rubric for Planning the Discussion: Level 3 27

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The Whole Class Discussion 28

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Three Levels of Analysis and Sense making Phase 1: Making Thinking Explicit (Explaining Reasoning) Phase 2: Analyzing Each Other's Solution (Analyzing Low Level to More Sophisticated Reasoning) Phase 3: Developing New Mathematical Insights (Abstract Mathematical Concepts) 29

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Continuum: Levels of Understanding and Student Strategies Inefficient strategies Efficient Strategies 11111 11111 11111 11111 5+5+5+5 5x4=20 20 ÷5=4 Simpler Representations (Concrete) Abstract Representations ** + ** 2 + 2 2 apples and 2 apples two groups of two apples two plus two 30. Mathematical Connections

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Teacher Questioning/ Supporting Mathematical Connections Not Met Still Working Workin g Great Note: These levels of Sense Making make up the Whole discussion. The teacher poses a problem and issue for class to discuss. The teacher uses questions to help students make mathematical connections. Students communicate their ideas; reflect on their own ideas and others being presented to make connections. (See classroom routines section). (Chapter 5) See p. 69 Figure 4.1 (Identify topic for discussion based on goals) Three Levels of Sense Making *P.116 Strategies for You Classroom: The Three Levels of Sense Making Phase 1: Making Thinking explicit Standards of Mathematical Practice 2, 3, 4 Phase II: Analyzing Each other’s solutions Helping students make connections from low level strategies to sophisticated strategies See p. 102-103 Address Errors/Misconceptions Standards of Mathematical Practice 1,3,4,6,7,8 Phase III: Developing New Mathematical Insights See Case Study p.103-107 Identify “big ideas” in Lesson and create a record Standards of Mathematical Practice 1,2,4,5,6,7,8 31

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Improving Teaching Through Reflection Reflecting on Your Teaching (Making Teaching Visible) (Chapter 6) What are you currentl y doing? What is working/wh at is not? Making teaching Visible What are you currently focusing on? See: Reflecting on Practice Questions throughout chapters & *Reflecting on Your Practice Worksheets in End of Chapter Study Guides 32

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Working Smarter not Harder! Integrate discussion as a natural part of teaching to support mathematical learning. Use time efficiently Remember facilitating effective discussions is a journey and a process. 33

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Whole Class Mathematics Discussions: Improving in-depth Mathematical thinking and Learning Slides, Video Clips and downloadable worksheets are available in PDToolkit http://pdtoolkit.pearsoncmg.com/login Video clip 1.4 Video Clip 1. 2 Blog: www.mathdiscussions.wordpress.comwww.mathdiscussions.wordpress.com Teruni Lamberg, Ph.D. University of Nevada, Reno Terunil@unr.edu 34

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