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
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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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No
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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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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.
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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
Explore
meaning
of problem
Look
for entry(MP1)
points to a solution
solving
them
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
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-classdiscussion-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
Setting up
the
Classroom
Work in
Progress
Working
Great
To do list
Tools from Whole Class Discussion
book
(Chapter 2)
*P.36 Checklist
Setting up
Physical
Space
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Cultivating
Not
Classroom
Met
Environment/Routi
nes
Routines for
Preparing for
Discussion
Routines for
Communicating
Routines for
Listening/Reflecting
Work in
Progress
Working Note: Routines for
Great (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
Standards of
Mathematical
Practice
1,4,5,7,8
Standards of
Mathematical
Practice 2,3
Standards of
Mathematical
Practice 1
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Lesson Planning
First level Planning
(Long term & Short
Term Goals)
Concepts (big ideas)
Unit Plan
(Sequencing/learning
trajectory)
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)
*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
Not
Planning
met
(Adapting
discussion to
support
student
understanding/
needs)
Making
decisions on
what to talk
about based on
student
reasoning
during lessons
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
Phase 3: Developing New
Mathematical Insights
(Abstract Mathematical Concepts)
Phase 2: Analyzing Each Other's
Solution
(Analyzing Low Level to More
Sophisticated Reasoning)
Phase 1: Making Thinking Explicit
(Explaining Reasoning)
Mathematical
Connections
Continuum: Levels of Understanding and Student Strategies
Inefficient strategies
.
11111 11111 11111 11111
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Efficient Strategies
5+5+5+5
5x4=20 20 ÷5=4
Simpler Representations (Concrete)
Abstract
Representations
** + **
2 apples and 2 apples
2 +2
two groups of two apples
two plus two
Teacher Questioning/
Supporting Mathematical
Connections
Not Met
Still Working
Workin Note: These levels of Sense
g Great 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
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Improving Teaching
Through Reflection
Reflecting on Your
Teaching
(Making Teaching
Visible)
(Chapter 6)
Making teaching Visible
What are you currently
focusing on?
What
What is
are you working/wh
currentl at is not?
y
doing?
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@unr.edu
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