Implementing the CCSSM
Planning for Instruction
CCSSM are....
• Student Habits of Mind-Standards for
Mathematics Practice
• Learning Outcomes-Mathematics Content
CCSSM are not......
• A List of Things to "Cover"
• A Pacing Guide
• A Curriculum
• The learning constellations for each
grade/course are determined and organized
based upon the CCSSM and learning
• Formative assessments are used to determine
where students are in the learning trajectory and
determine next instructional moves.
Constellations of Learning
• Term I heard first used by Deborah Schifter.
• New term that does not bring the baggage of prior usage
(not unit, not cluster, not domain but related to these in
some ways).
• Teachers will almost never be attending to a single
standard, but instead working on a constellation of
learning that is focused and coherent.
• Teachers will be working on multiple constellations
Tools for Developing Curriculum
• Standards (Content) Progressions
• Learning Trajectories (Construct Maps)
• Essential Understandings
Standards Progressions are...
• Standards written in narrative form.
Standards Progressions can be used to…
• Develop teacher knowledge about the
standard(s) and/or domain(s).
• See how content knowledge grows over
time - Vertical articulation.
• Take the second step toward curriculum
development for CCSSM.
You may be asking, what was the first step?
• Teachers developing a deep
understanding of the Standards for
Mathematical Practice.
Standards Progressions
• McCallum
• Wu
Learning Trajectories…
•Identify bridging standards.
•Identify underlying cognitive principals.
•Identify student misconceptions, strategies and
•Identify models, related representation and
•Describe students' movement from naive to
sophisticated ideas.
Construct Maps…..
• Do all the things Learning Trajectories do.
• Describe student behaviors at each step in the
Learning Trajectories can be used to...
•Inform the planning of the instructional
•Design formative assessments to locate
students in the trajectory.
•Inform instruction planning to move classes
and individual students along the trajectory.
•Take the third step in curriculum development.
Learning Trajectories are empirically developed.....
•Developers use their content knowledge,
experiences, etc. to propose a learning trajectory.
•Instruction is designed based on the proposed
•Instructional sequence is implemented.
•Trajectory is modified during and following this
•Several rounds of modification and
implementation may be required.
Learning Trajectories
Hess (Progressions)
Confrey (Trajectories)
Lehrer (Construct Maps)
Battista (Building on Student Reasoning)
Essential Understandings are...
•Resources that can help us take the
fourth step in curriculum development.
•A series of books from NCTM that will
help us think deeply about what are the
essential understanding that are
necessary to achieve the learning
outcomes mandated by CCSSM.
Planning for Instruction (Curriculum Development)
•Faculty study the Standards for Mathematical Practice
•Faculty study the Mathematics Content Standards using the
standards progressions
•Faculty identify and sequence constellations of learning
using learning trajectories and essential understandings.
•Faculty work collaboratively to design or identify formative
assessment tasks for each constellations.
•Teachers use formative assessment results to plan next
instructional moves including differentiation.
Show Video
Mrs. White
Purposeful Pedagogy and Discourse Instructional Model:
Student Thinking Matters Most
• Jacobs, Lamb, and Philipp on professional noticing and
professional responding;
• Smith, Stein, Hughes, and Engle on orchestrating
productive mathematical discussions;
• Ball, Hill, and Thames on types of teacher mathematical
• Levi and Behrend (Teacher Development Group) on
Purposeful Pedagogy Model for Cognitively Guided
Some musings....
• Change is a process and not an event.
• Curriculum development is a process and not an
• Sequencing may not be linear.
• Basing instruction on formative assessment
results requires flexibility from day to day.
• Role of interim assessment may change.
Links to Book Resources
• NCTM Essential Understandings
• Heinemann – Battista books Cognition-Based
Assessment and Teaching
Link to Jere Confrey’s work
• Optimized for use with the Safari and Chrome
browsers. Less smooth with Firefox and Internet
Link to Text Analysis Tool
• Item 2b Math Analysis Tool

Implementing the CCSSM Planning for Instruction CCSSM are