Integrating the Standards for Mathematical Practice as a Natural part of Teaching Through Whole Class Mathematics Discussions.

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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_at_unr.edu

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

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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?

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What is learning?

• How do you know that learning is taking place?

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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

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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.

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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.

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Teachers Role in Whole Class Discussions

• The teachers 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.

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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.

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

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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.

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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.

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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.

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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 .

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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.

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Look for and make use of structure. (MP7)

• Mathematically proficient students look closely
  to discern a pattern or structure

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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.

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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)

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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-d
  iscussion-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.

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  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/Routines   Not Met   Work in Progress Working Great  Note Routines for (Communicating/Listening 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
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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
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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
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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
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• The Whole Class Discussion

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Three Levels of Analysis and Sense making
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Continuum Levels of Understanding and Student
Strategies
Mathematical Connections

Inefficient strategies Efficient Strategies 11111 11111 11111 11111 5555 5x420 20 54  
Simpler Representations (Concrete) Abstract Representations 2 2
2 apples and 2 apples two groups of two apples two plus two
.
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Teacher Questioning/ Supporting Mathematical Connections   Not Met   Still Working  Working 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 others 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
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        Improving Teaching Through Reflection  
Reflecting on Your Teaching (Making Teaching Visible) (Chapter 6) What are you currently doing? What is working/what 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  
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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.

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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.com
• Teruni Lamberg, Ph.D.
• University of Nevada, Reno
• Terunil_at_unr.edu