2/17/15 Teaching Ma+ers! NCTM Tools to Support Implementa9on of Effec9ve Mathema9cs Teaching Prac9ces Diane J. Briars Cathy Mar9n Jeff Ziegler Urban Mathema9cs Leadership Network February 10, 2015 FYI
Electronic copies of slides are available by request dbriars@nctm.org 1 2/17/15 National Council of Teachers of Mathematics
www.nctm.org
Na9onal ouncil o
Teachers of
of Mathematics
Mathema9cs National CCouncil
off Teachers
www.nctm.org
www.nctm.org For $144 per year, your school will get a FREE print-­‐only subscrip9on to one of the following award-­‐winning journals: Five FREE E-­‐Memberships for teachers in your school All the benefits of an e-­‐membership including full access to the digital ediBon of Teaching Children Mathema1cs or Mathema1cs Teaching in the Middle School (a $72 value!) FREE! To involve more teachers, addiBonal e-­‐memberships can be added for just $10 each. 2 2/17/15 Na9onal ouncil o
Teachers of
of Mathematics
Mathema9cs National CCouncil
off Teachers
www.nctm.org
www.nctm.org New Member Discount $20 off for full membership $10 off e-­‐membership $5 off student membership Use Code: BDB2015 NCTM Conferences
www.nctm.org
2015 Annual Meeting and Exposition
April 15–18, 2015
Boston
2016 Annual Meeting and Exposition
April 13–16, 2016
San Francisco
3 2/17/15 NCTM Interactive Institutes
www.nctm.org
•  Algebra Readiness for Every Student
July 20-22, 2015, Chicago, IL
•  Connecting Number and Operations
in Classrooms
July 23-25, 2015, Chicago, IL
•  Engaging Students in Learning:
Mathematical Practices, July 27-July
29, 2015, Anaheim, CA
•  Engaging Students in Learning:
Mathematical Practices and Process
Standards
July 30-August 1, 2015, Anaheim,
CA
NCTM Regional Conferences
www.nctm.org
•  Atlantic City, ,NJ
October 21-23, 2015
•  Minneapolis, MN
November 11-13, 2015
•  Nashville, TN
November 18-20, 2015
4 2/17/15 Agenda
•  Introduce NCTM’s Principles to Ac1ons: Ensuring Mathema1cal Success for All and related forthcoming professional learning materials. •  Share ways in which you have used, or might use, Principles to AcBons to support improved mathemaBcs educaBon in your district. •  Analyze a video case of a teacher (Mr. Ziegler) implemenBng the S-­‐Pa]ern Task in terms of the effecBve teaching pracBces as described in Principles to Ac1ons. •  Discuss access and equity issues as described in Principles to Ac1ons •  Discuss your acBon steps related to Principles to Ac1ons. •  Provide an update on the naBonal mathemaBcs educaBon landscape •  Discuss ways in which NCTM can support you in your work. 5 2/17/15 Principles to Actions:
Ensuring Mathematical Success for All
•  Describes the supportive conditions,
structures, and policies required to give all
students the power of mathematics
•  Focuses on teaching and learning
•  Emphasizes engaging students in
mathematical thinking
•  Describes how to ensure that mathematics
achievement is maximized for every student
•  Is not specific to any standards; it’s universal
We Must Focus on Instruction
•  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)
•  “Teaching has 6 to 10 times as much
impact on achievement as all other factors
combined ... Just three years of effective
teaching accounts on average for an
improvement of 35 to 50 percentile points.”
Schmoker (2006, p.9)
6 2/17/15 Guiding Principles
for School Mathematics
1.  Teaching and Learning
Effective teaching is the non-negotiable
core that ensures that all students learn
mathematics at high levels.
Guiding Principles
for School Mathematics
1.  Teaching and
Learning
2.  Access and Equity
3.  Curriculum
4.  Tools and Technology
Essential
Elements
of Effective
Math
Programs
5.  Assessment
6.  Professionalism
7 2/17/15 For Each Principle
•  Productive and Unproductive Beliefs are
Listed
•  Obstacles to Implementing the Principle
are Outlined
•  Overcoming the Obstacles
•  Taking Action
─  Leaders and Policymakers
─  Principles, Coaches, Specialists, Other
School Leaders
─  Teachers
Guiding Principles
for School Mathematics
1.  Teaching and Learning
2.  Access and Equity
3.  Curriculum
4.  Tools and Technology
5.  Assessment
6.  Professionalism
8 2/17/15 Effective
Mathematics Teaching Practices
1.
2.
3.
4.
5.
6.
7.
Establish mathematics goals to focus learning.
Implement tasks that promote reasoning and
problem solving.
Use and connect mathematical representations.
Facilitate meaningful mathematical discourse.
Pose purposeful questions.
Build procedural fluency from conceptual
understanding.
Support productive struggle in learning
mathematics.
8.  Elicit and use evidence of student thinking.
How Have You Used P2A in
Your District?
•  Make a poster showing
–  What have you used from P2A?
–  How have you used it?
–  What issue/challenge were you
addressing?
•  Museum Walk
–  Designate a docent
–  Divide and conquer
•  Reconvene to discuss what you
learned with your team
9 2/17/15 http://www.nctm.org/PrinciplestoActions/
Reflection Guide
10 2/17/15 Principles to Actions
Professional Learning Toolkit
•  Principles to Actions overview presentation
•  Mathematics Teaching Practices
presentations
–  Middle school case, proportional reasoning (Mr.
Donnelly)
–  High school case, exponential functions (Ms. Culver)
–  Elementary case, multiplication (Mr. Harris)*
•  Teaching Practices modules by grade band*:
–  PowerPoint slides, illustrative cases/video clips, tasks,
activities
•  Guiding Principles modules*
•  Principles to Actions Spanish translation*
http://education.ti.com/en/us/
activities/nctm-activities
11 2/17/15 http://education.ti.com/en/us/
activities/nctm-activities
Effective Mathematics
Teaching Practices
THE CASE OF JEFF ZIEGLER
HIGH SCHOOL
Developed by Margaret Smith and Victoria Bill at the University of Pi]sburgh. Video courtesy of Pi]sburgh Public Schools and the InsBtute for Learning. 12 2/17/15 The S Pattern Task
1
1 2 4 3 5 1. What patterns do you notice in the set of figures?
2. How many square tiles are in figure 7? Write a description that could be used to determine
the shape of and total number of square tiles in figure 7. Your description should be clear
enough so that another person could read it and use it to think about another figure.
3. Determine an equation for the total number of squares in any figure. Explain your rule and
show how it relates to the visual diagram of the figures.
4. Find a second way to describe the pattern and write the equation that matches the
description. Compare the two equations and show in the visual representation how one
equation is equivalent to the other.
5. If you knew that a figure had 9802 squares tiles in it, how could you determine the figure
number? Explain.
6.  Does the pattern describe a linear relationship between the figure number and the total
number of squares? Why or why not?
1
This task was adapted from Visual Mathema1cs Course II, Lessons 1-­‐10 published by The Math Learning Center, Salem, OR. Connections to the CCSS Standards for
Mathematical Practice
1.  Make sense of problems and persevere in
solving them.
2.  Reason abstractly and quantitatively.
3.  Construct viable arguments and critique the
reasoning of others.
4.  Model with mathematics.
5.  Use appropriate tools strategically.
6.  Attend to precision.
7.  Look for and make use of structure.
8.  Look for and express regularity in repeated
reasoning. 13 2/17/15 Connections to the CCSS Standards for
Mathematical Practice
1.  Make sense of problems and persevere in
solving them.
2.  Reason abstractly and quantitatively.
3.  Construct viable arguments and critique the
reasoning of others.
4.  Model with mathematics.
5.  Use appropriate tools strategically.
6.  Attend to precision.
7.  Look for and make use of structure.
8.  Look for and express regularity in
repeated reasoning. The S-Pattern Task
Video Context
School:
Teacher:
Principal:
Class:
Langley High School, Pittsburgh Public Schools
Mr. Jeffrey Ziegler
Linda Baehr
11th-12th Grade Students
At the time the video was filmed, Jeffery Ziegler was a
coach at Langley High School in the Pittsburgh Public
School District. The students are 11th and 12th grade and
struggle with mathematics.
(Jeffrey Ziegler is currently a curriculum supervisor for
grades 6-12 mathematics in the Pittsburgh Public School
district.)
14 2/17/15 Mr. Ziegler’s
Mathematics Learning Goals
Students will understand that:
1.  An equation can be written that describes
the relationship between 2 quantities;
2.  Different but equivalent equations can be
written that represent the same situation;
and
3.  The symbolic and pictorial representations
can be connected.
Connections to the CCSS Content
Standards
Creating Equations★
A-CED
Create equations that describe numbers
or relationships.
2. Create equations in two or more variables
to represent relationships between
quantities; graph equations on coordinate
axes with labels and scales.
NaBonal Governors AssociaBon Center for Best PracBces & Council of Chief State School Officers. (2010). Common core state standards for mathema1cs. Washington, DC: Authors. 15 2/17/15 The S-Pattern Task
The Context of Video Clips
The lesson begins with Mr. Ziegler engaging
students in a brief discussion of the task. They
establish the fact that this was a growth pattern
that is growing in two dimensions, getting both
“taller” and “bigger”. Before they begin their work,
Mr. Ziegler tells students:
“Now there are 6 prompts... Kind of the first one, the second one, third one is to kind of get you started but it is on you guys to work with your groups to come up with a way to find the pa]erns. You don’t necessarily have to word-­‐for-­‐word answer these quesBons, but they’re there to help you maybe get started.
The clip begins as small groups begin to work on
the task and Mr. Ziegler visits Groups 1 and 2.
Lens for Watching the Video Clip 1
As you watch the video, make note of what the
teacher does as he interacts with groups 1 and 2.
In particular, identify any of the Effective
Mathematics Teaching Practices that you notice Mr.
Ziegler using.
Be prepared to give examples and to cite line
numbers from the transcript to support your claims.
Also, record any questions that you have
(wonderings)
16 2/17/15 Effective
Mathematics Teaching Practices
1.
2.
3.
4.
5.
6.
7.
Establish mathematics goals to focus learning.
Implement tasks that promote reasoning and
problem solving.
Use and connect mathematical representations.
Facilitate meaningful mathematical discourse.
Pose purposeful questions.
Build procedural fluency from conceptual
understanding.
Support productive struggle in learning
mathematics.
8.  Elicit and use evidence of student thinking.
Video Clip 1
..\..\Diane NCTM\PtA\PtA resources\PtA Toolkit\Ziegler case\4. ZieglerClip1.mp4 17 2/17/15 Lens for Watching the Video Clip 1
As you watch the video, make note of what the
teacher does as he interacts with groups 1 and 2.
In particular, identify any of the Effective
Mathematics Teaching Practices that you notice Mr.
Ziegler using.
Be prepared to give examples and to cite line
numbers from the transcript to support your claims.
Also, record any questions that you have on note
cards (“I wonder . . . ).
Effective
Mathematics Teaching Practices
1.
2.
3.
4.
5.
6.
7.
Establish mathematics goals to focus learning.
Implement tasks that promote reasoning and
problem solving.
Use and connect mathematical representations.
Facilitate meaningful mathematical discourse.
Pose purposeful questions.
Build procedural fluency from conceptual
understanding.
Support productive struggle in learning
mathematics.
8.  Elicit and use evidence of student thinking.
18 2/17/15 Support Productive Struggle
in Learning Mathematics
Productive Struggle should:
•  Be considered essential to learning
mathematics with understanding;
•  Develop students’ capacity to persevere in the
face of challenge; and
•  Help students realize that they are capable of
doing well in mathematics with effort.
By struggling with important mathematics we
mean the opposite of simply being presented
information to be memorized or being asked only
to practice what has been demonstrated.
Hiebert & Grouws, 2007, pp. 387-388
Lens for Watching the Video
Clip 2
In the second video clip Mr. Ziegler visits Groups 1
and 1 for a second time.
Considering the teacher’s actions and interactions
with Groups 1 and 2 in both clips, identify what the
teacher does to support his student’s productive
struggle.
Be prepared to give examples and to cite line
numbers from the transcript to support your claims.
Also, record any questions that you have on note
cards (“I wonder . . . ).
19 2/17/15 Video Clip 2
..\..\Diane NCTM\PtA\PtA resources\PtA Toolkit\Ziegler case\6. ZieglerClip2.mp4 Lens for Watching the Video
Clip 2
In the second video clip Mr. Ziegler visits
Groups 1 and 2 for a second time.
Considering the teacher’s actions and
interactions with Groups 1 and 2 in both clips,
identify what the teacher does to support his
student’s productive struggle.
Also, record any questions that you have
(wonderings)
20 2/17/15 What Did You Wonder
About This Lesson?
Effective
Mathematics Teaching Practices
1.
2.
3.
4.
5.
6.
7.
8.
Establish mathematics goals to focus learning.
Implement tasks that promote reasoning and
problem solving.
Use and connect mathematical representations.
Facilitate meaningful mathematical discourse.
Pose purposeful questions.
Build procedural fluency from conceptual
understanding.
Support productive struggle in learning
mathematics.
Elicit and use evidence of student thinking.
21 2/17/15 What have you learned and how
do these ideas apply to teachers
classroom work?
Guiding Principles
ACCESS AND EQUITY
Developed by Robert Q. Berry III, University of Virginia, and Marilyn Strutchens, Auburn University. 22 2/17/15 Guiding Principles for School
Mathematics: Access and Equity
Access and Equity
An excellent mathematics program
requires that all students have access to
high-quality mathematics curriculum,
effective teaching and learning, high
expectations, and the support and
resources needed to maximize their
learning potential.
Beliefs about
Access and Equity?
Complete the survey (p. 10):
•  Rate the extent to which you
agree with each statement.
•  Compare with others at your
table.
•  How might these beliefs affect
your work?
•  Who else’s beliefs about access
and equity affects your work?
23 2/17/15 Unproductive vs Productive
Beliefs about Access and Equity
•  Beliefs should not be viewed as
good or bad.
•  Beliefs are unproductive when
they hinder implementation of
effective instructional practice or
limit student access to important
mathematics content and
practices.
pp 63-­‐64 24 2/17/15 pp 63-­‐64 Brief Discussion
What does it mean for students if
teachers and/or administrators
ascribe to any of the
aforementioned beliefs?
Pick one to discuss with your
elbow partners.
25 2/17/15 Focus on Students’
Mathematics Identities
•  Please write down at least three
adjectives which describe you as
a mathematics learner.
–  Also think about the factors which
helped to shape these beliefs about
yourself as a learner.
Read the Overview of Factors
Impacting Mathematics
Identities
•  What are the major points?
•  What are strategies that support
positive mathematics identities?
26 2/17/15 Mathematics Identity
•  Mathematics identity includes:
–  beliefs about one’s self as a mathematics
learner;
–  one’s perceptions of how others perceive
them as a mathematics learner,
–  beliefs about the nature of mathematics,
–  engagement in mathematics, and
–  perception of self as a potential
participant in mathematics.
(Solomon, 2009)
Vignette: Caroline and Craig
•  Read the Caroline’s and Craig’s
Vignettes.
•  Talker-Listener Exchange:
How Caroline’s and Craig’s
mathematics identities were being
formed.
Adapted from Chval & Davis, 2008 27 2/17/15 Overcoming Obstacles
•  Access to rigorous, high-quality
mathematics, taught by teachers who
not only understand mathematics but
also understand and appreciate
learners’ social and cultural contexts in
meaningful ways.
•  Classroom environments that foster a
sense of community that allows
students to express their mathematical
ideas.
55 Interwoven
MathemaBcs IdenBty Agency IdenBty Affirming 56 28 2/17/15 The Title is Principles to Actions
Actions for:
•  Leaders and policymakers
•  Principals, Coaches, Specialists, and
Other School Leaders
•  Teachers
The Title Is Principles to Actions
Your
Actions?
29 2/17/15 NATIONAL UPDATE
CCSSM Advocacy
•  Mathematics Common Core
Coalition Advocacy materials
•  NCTM-Hunt Institute parent
(teacher) videos
•  CCSS Advocacy speaker support
30 2/17/15 From the NRC Board on Mathema9cal Science and Their Applica9ons •  Examines the mathematical
science now and how it
needs to evolve to produce
the best value for the
country by 2025.
•  Describes the remarkable
success of the
mathematical sciences in
the opening years of the
21st century.
•  Highlights the increasing
importance of statistics,
modeling and discrete
mathematics.
Our high schools focus
on getting people
prepared for calculus . . .
But we do little to teach
statistics, probability,
and uncertainty . . .
This is one of the biggest
issues facing U.S.
mathematical sciences; it
is also a big problem in
terms of national
competitiveness.
h]p://www.nap.edu/catalog.php?record_id=15269 31 2/17/15 Companion Book for Teachers and Students Describes ongoing
advances in the
mathematical science
and how these
advances are
changing our
understanding of the
world, creating new
technologies and
transforming
industries.
Purpose:
•  Communicate
the possibilities
of applied
mathematics.
•  Interest K-12
students in
STEM careers.
32 2/17/15 Inside the “Vignettes”
Eigenvectors Compressed Sensing National Academy
Press
•  25% Discount
Use Code MATH14
Sale price: $14.96
•  Free download:
http://
www.nap.edu/
catalog.php?
record_id=13373
33 2/17/15 New National Developments:
Collegiate Mathematics
•  Transforming Post-Secondary Education in
Mathematics (TPSE)
•  Common Vision for Undergraduate
Mathematics in 2025
–
–
–
–
–
Mathematical Association of America
American Mathematical Society
American Statistical Association
Society of Applied and Industrial Mathematics
American Mathematical Association of Two-Year
Colleges
New National
Developments: Modeling
•  Guidelines on Assessment and Instruction in
Mathematical Modeling Education (GAIMME)
–  SIAM lead organization; COMAP is playing a lead role
–  Consistent with CCSSM
–  NCTM representation: Rose Zbiek, Board Liaison
•  The International Mathematical Modeling Challenge
(IMMC), another COMAP initiative
–  Goal: Promote the teaching of mathematical modeling and
applications at all educational levels for all students.
–  One problem that all selected teams (2 teams, up to 4
students each); will work on in their home countries
–  Summer, all teams come to host country to present and
defend their solutions before the judging panel.
34 2/17/15 New National
Developments
•  Statistics Education of Teachers (SET)
report
–  Modeled after MET reports
–  Standards for Mathematical Practice though a
statistical lens
•  IES What Works Clearing House
Practice Guide: Teaching High School
Algebra (April 7, 2015)
How Can NCTM Support
Your Work?
•  Think
•  Talk
•  Post:
https://todaysmeet.com/NCTMsupport
Please use your district name as your
nickname
35 2/17/15 https://todaysmeet.com/NCTMsupport
How Can NCTM Support
Your Work?
•  Think
•  Talk
•  Post:
https://todaysmeet.com/NCTMsupport
Please use your district name as your
nickname
36 2/17/15 Thank You!
37