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Teruni Lamberg, Ph.D. University of Nevada, Reno Terunil@unr

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

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Teruni Lamberg, Ph.D. University of Nevada, Reno Terunil@unr

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  1. 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

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

  3. 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?

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

  5. 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

  6. 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.

  7. No

  8. 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.

  9. 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.

  10. 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.

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

  12. 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

  13. 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.

  14. 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.

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

  19. 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. 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. Lamberg (2012) Framework from Whole Class Mathematics discussion book. • Can download copy from my blog: • 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. Takes Place During the Lesson

  23. The Whole Class Discussion

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

  25. Mathematical Connections Continuum: Levels of Understanding and Student Strategies .

  26. 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.

  27. 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@unr.edu

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