Moving to Action: Effective
Mathematics Teaching
Practices in the Middle
Grades
Michael D. Steele
University of Wisconsin-Milwaukee
Elizabeth Cutter
Whitnall (WI) School District
Session Overview
•  NCTM’s Principles to Actions:
Background, Rationale and Development
•  Supporting the Development of Effective
Mathematics Teaching Practices
•  Engaging in Sample Activities:
The Hexagon Task
•  Using the Materials with Teachers and
Districts
•  Questions and Discussion
A 25-year History of Standards-Based
Mathematics Education Reform
1989 Curriculum and
Evaluation Standards for
School Mathematics
2000 Principles and
Standards for School
Mathematics
2006 Curriculum Focal
Points
2009 Focus in High School
Mathematics
2010 Common
Core State
Standards for
Mathematics
Standards have led to higher
achievement…
4th grade NAEP 8th grade NAEP Mean SAT-‐Math Mean ACT-‐Math 1990 13% proﬁcient 15% proﬁcient 501 19.9 2012-‐2013 42% proﬁcient 36% proﬁcient 514 21.0 …but challenges remain.
•  The average mathematics NAEP score for 17year-olds has been essentially flat since 1973.
•  Among 34 countries participating in the 2012
Programme for International Student
Assessment (PISA) of 15-year-olds, the U.S.
ranked 26th in mathematics.
•  While many countries have increased their
mean scores on the PISA assessments between
2003 and 2012, the U.S. mean score declined.
•  Significant learning differentials remain.
From Standards to Pedagogy
High-quality standards are
necessary for effective teaching and
learning, but not sufficient.
The Common Core does not describe
or prescribe the essential conditions
required to make sure mathematics
works for all students.
Principles to Actions:
Ensuring Mathematical Success for All
The primary purpose of
Principles to Actions is to fill
the gap between the
adoption of rigorous
standards and the
enactment of practices,
policies, programs, and
actions required for
successful implementation of
those standards.
NCTM. (2014). Principles to Actions: Ensuring
Mathematical Success for All. Reston, VA: NCTM.
Organization of P2A
Guiding Principles for
School Mathematics
1. 
2. 
3. 
4. 
5. 
6. 
Teaching and Learning
Access and Equity
Curriculum
Tools and Technology
Assessment
Professionalism
For each principle…
•  Productive and
Unproductive Beliefs are
Listed
•  Obstacles to
Implementing the
Principle are Outlined
•  Overcoming the Obstacles
•  Taking Action
o  Leaders and Policymakers
o  Principles, Coaches,
Specialists, Other School
Leaders
o  Teachers
Teaching and Learning
Principle
Eight High-Leverage Mathematics Teaching Practices
1.  Establish mathematics goals to focus learning
2.  Implement tasks that promote reasoning and problem
solving
3.  Use and connect mathematical representations
4.  Facilitate meaningful mathematical discourse
5.  Pose purposeful questions
6.  Build procedural fluency from conceptual understanding
7.  Support productive struggle in learning mathematics
8.  Elicit and use evidence of student thinking
The challenge: How to support meaningful
change in classrooms around these eight practices?
A set of professional development resources
SUPPORTING DEVELOPMENT OF
THE MATHEMATICS TEACHING
PRACTICES
The case for content-focused
professional development
•  Teachers must see aspects of their own
teaching in new practices
•  Case-based professional development
allows teachers to generalize about
teaching from the particulars of practice
•  Seeing the mathematics teaching
practices in action is a critical component
to foster meaningful change
The case for content-focused
professional development
The typical US teacher receives less than 2
days per school year of content-specific
professional development.
Steele et al. (2015). Learning about new demands in schools: considering algebra policy environments Principles to Actions Professional
Development Modules
•  High-quality classroom video from the
University of Pittsburgh Institute for
Learning
•  Focus on one or more of the P2A
Mathematics Teaching Practices
•  High cognitive demand mathematical
task
•  Designed to be used by departments,
districts, and cross-district teacher
professional learning communities
Sixth Grade
Exploring the Hexagon Pattern Task
THE CASE OF PATRICIA
ROSSMAN
Developed by Michael D. Steele at the University of Wisconsin-‐Milwaukee. Video courtesy of PiPsburgh Public Schools and the InsRtute for Learning. The Hexagon Task
Trains 1, 2, 3, and 4 are the first 4 trains in the hexagon
pattern. The first train in this pattern consists of one
regular hexagon. For each subsequent train, one additional
hexagon is added. For the hexagon pattern:
1.  Compute the perimeter for the first 4 trains.
2.  Determine the perimeter for the tenth train without
constructing it.
3.  Write a description that could be used to compute the
perimeter of any train in the pattern.
(Use the edge length of any pattern block or the length
of a side of a hexagon as your unit of measure.)
Hexagon Task:
Some Possible Solutions
1  2 1  2 1  2 1  2 1  2 1  2 3 4 3 4 3 4 3 4 3 4 3 4 A Tops & BoPoms, plus 2 ends y = 4x + 2 B Insides and Outsides y = 4(x – 2) + 10 C Shared sides subtracted y = 6x – 2(x – 1) The two outside hexagons each contribute 5 sides The inside hexagons each contribute 4 Number of inside hexagons is train number minus 2 Each hexagon contributes 6 sides For each new hexagon past train 1, there is a pair of inside sides that have to be subtracted The number of shared pairs is the train number minus 1 The Hexagon Task Video
School: Austin Independent School District
Teacher: Ms. Patricia Rossman
Class:
6th grade
Many of the students in the classroom have
recently arrived to the United States. The
students are in a dual language program.
This task is an introduction to a unit titled
Number Sense, Patterns, and Algebraic
Thinking. It is the first time students have been
asked to engage in a task that requires them
analyze and look for patterns in a visual
diagram.
Ms. Rossman’s
Mathematics Learning Goals
Students will:
1.  Create a generalization that describes the
relationship between the train number and the
perimeter of the train and explain how the
different components of their generalization can
be seen in the visual pattern
2.  Identify a constant rate of change between the
quantities in the relationship -- as the train
number increases by one, the train's perimeter
increases by four
3.  Understand that the rate of change between the
quantities can be seen in a table as the first
difference, in a graph as the slope of the line, and
in an equation as a the coefficient of the input
quantity
Connections to the CCSS
Content Standards
Expressions and EquaRons★ 6.EE.6 Represent and analyze quantitative relationships
between dependent and independent variables.
9. Use variables to represent two quantities in a real-world
problem that change in the relationship to one another;
write an equation to express one quantity, thought of as
the dependent variable, in terms of the other quantity,
thought of as the independent variable. Analyze the
relationship between the dependent and independent
variables using graphs and tables, and relate these to
the equation.
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 Hexagon Task: Video Context
Prior to this clip:
•  Ms. Rossman launched the task, ensuring that
students understood the words in the task
•  Ms. Rossman communicated that all students in a
group should understand the methods they discuss
In this clip, we see a small group working on their
explanation and interacting with Ms. Rossman,
followed by an excerpt of the whole-class discussion in
which the same group shares their method.
Lens for Watching the Video:
Time 1
As you watch the video, make note of what
the teacher does to support student learning
and engagement as they work on the task.
In particular, identify any of the Effective
Mathematics Teaching Practices that you
notice Mrs. Rossman using.
Be prepared to give examples and to cite
line numbers from the transcript to support
your claims.
Effective Mathematics
Teaching Practices
1. 
Establish mathematics goals to focus learning.
2. 
Implement tasks that promote reasoning and problem
solving.
3. 
Use and connect mathematical representations.
4. 
Facilitate meaningful mathematical discourse.
5. 
Pose purposeful questions.
6. 
Build procedural fluency from conceptual
understanding.
7. 
Support productive struggle in learning
mathematics.
8. 
Elicit and use evidence of student thinking.
Effective Mathematics
Teaching Practices
1. 
Establish mathematics goals to focus learning.
2. 
Implement tasks that promote reasoning and problem
solving.
3. 
Use and connect mathematical representations.
4. 
Facilitate meaningful mathematical discourse.
5. 
Pose purposeful questions.
6. 
Build procedural fluency from conceptual
understanding.
7. 
Support productive struggle in learning
mathematics.
8. 
Elicit and use evidence of student thinking.
Facilitate Meaningful
Mathematics Discourse
Discourse in math classrooms should:
•  Analyze and compare student approaches and
arguments;
•  Make use of student thinking in ways that keep
key mathematical ideas prominent;
•  Build students’ responsibility and agency as
knowers and doers of mathematics
Students who learn to articulate and justify their own
mathematical ideas, reason through their own and others’
mathematical explanations, and provide a rationale for their
answers develop a deep understanding that is critical to
their future success in mathematics and related fields.
(Carpenter, Franke, & Levi, 2003, p. 6)
Lens for Watching the Video:
Time 2
As you watch the video this time, pay
attention to discourse moves the teacher
makes.
As you do, consider:
•  In what ways did the teacher’s discourse
move support moving her mathematical
goals forward?
•  In what ways did the teacher’s discourse
move support students’ developing
mathematical identities as learners?
What have you learned
and how do these ideas
apply to your classroom
work?
REFLECTING ON THE
EXPERIENCE
Principles to Actions Professional
Development Modules
•  High-quality classroom video from the
University of Pittsburgh Institute for
Learning
•  Focus on one or more of the P2A
Mathematics Teaching Practices
•  High cognitive demand mathematical
task
•  Designed to be used by departments,
districts, and cross-district teacher
professional learning communities
Reflections and Questions…
…on the Effective Teaching Practices?
…on the Principles to Action document?
…on Principles to Action Professional
Development modules?
Principles to Action webpage:
http://www.nctm.org/
PrinciplestoActions/
Getting Started
with P2A
•  Learn more about the effective teaching practices
from reading the book, exploring other resources,
and talking with your colleagues and administrators.
•  Engage in observations and analysis of teaching (live
or in narrative or video form) and discuss the extent
to which the eight practices appear to have been
utilized by the teacher and what impact they had on
teaching and learning.
•  Co-plan lessons with colleagues using the eight
effective teaching practices as a framework. Invite
the math coach (if you have one) to participate.
•  Observe and debrief lessons with particular attention
to what practices were used in the lesson and how
the practices did or did not support students’
learning.
Getting Started
with P2A PD modules
•  Learn more about the effective teaching practices
from reading the book, exploring other resources,
and talking with your colleagues and administrators.
•  Engage in observations and analysis of teaching (live
or in narrative or video form) and discuss the extent
to which the eight practices appear to have been
utilized by the teacher and what impact they had on
teaching and learning.
•  Co-plan lessons with colleagues using the eight
effective teaching practices as a framework. Invite
the math coach (if you have one) to participate.
•  Observe and debrief lessons with particular attention
to what practices were used in the lesson and how
the practices did or did not support students’
learning.
Using the Principles to Actions
Professional Development Modules
•  Book Clubs around P2A:
–  Teachers can read about an effective teaching
practice, then meet to engage in a PD module
highlighting that practice.
•  On-line access to videos and PD materials:
–  Enable collaboration between teachers in different
districts and geographic locations.
–  Optimize use of limited face-to-face meeting time
(though we recommend face-to-face interaction for
solving the task, when possible).
Using the Principles to Actions
Professional Development Modules
•  Provide PD materials for teacher-based
groups within or across schools and
districts:
–  For school-based teams during common meeting time.
–  To support a District-wide focus on a specific effective
teaching practice.
–  For vertical groups: Teachers across different gradelevels could read and discuss an effective teaching
practice, then engage with the PD materials for their
specific grade-band.
–  For horizontal groups: Teachers in common gradebands or subjects (across schools or districts) could
collaborate in face-to-face or on-line groups.
Start Small, Build Momentum,
and Persevere
The process of creating a new cultural
norm characterized by professional
collaboration, openness of practice, and
continual learning and improvement can
begin with a single team of grade-level or
subject-based mathematics teachers
making the commitment to collaborate on
a single lesson plan.
The Title Is Principles to Actions