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Next Steps in Implementing Mathematics (and Science) Initiatives at the National and State Levels: Focusing on Common Core Standards . Jere Confrey, Joseph D. Moore University Distinguished Professor, Mathematics Education

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Next Steps in Implementing Mathematics (and Science) Initiatives at the National and State Levels: Focusing on Common Core Standards

Jere Confrey, Joseph D. Moore University Distinguished Professor, Mathematics Education

Friday Institute for Educational Innovation, College of Education, North Carolina State University

U.S. Department of Education's Mathematics and Science Partnerships 2011Conference

February 15, 2011

Baltimore, Maryland

The instructional practices and assessments discussed or shown

are not an endorsement by the U.S. Department of Education

Common Core State Standards represent an opportunity – once in a lifetime to form effective coalitions for change

The MSP programs can play a critical role in maximizing this opportunity:

    • To strengthen the movement towards Common Core Standards implementation
    • To get your innovations to move to scale to the degree to which they can tie into a broader policy agenda
features of the common core
Features of the Common Core
  • They focus attention on core concepts in number and numeration and their relationships to operations with a focus on the structure of the number system;
  • Aggressive timelines for teaching particular concepts in elementary and middle grades;
  • They introduce multiple measurement systems (metric, non-standard and English) simultaneously and tie the number line directly to scales to improve students’ visualization of some number relationships;
  • They support the articulation of some key learning trajectories in numeration and geometry; and
  • They remain agnostic about sequencing and organization of high school math.
decisions that should be re examined over time
Decisions that Should Be Re-examined over time:
  • The practices of mathematics are presented independently from the content standards: the practices could be isolated and under-emphasized without careful professional development;
  • There is limited detail to engaging students in mathematics through modeling with robust use of technology, and developing the related skills and concepts of modeling;
  • New standards for Probability and Statistics in early grades should supplant the current weak treatment of the topic in Measurement;
  • The CCSS construe Number narrowly tend to overemphasize additive structures—limiting early and foundational development of multiplicative/divisional structures related to ratio and rate, and many algebraic patterns of growth;

Even with their flaws, the Standards are “good enough” to embrace.

There is a narrow window of opportunity to prepare for and interpret the Next Steps.

window of opportunity
Window of Opportunity
  • Window open from now until 2014- 2015 when assessments are put into place.
  • The current circumstance is unstable and ambiguous at the state level:
    • Example: NC has its third set of standards in three years; with 2001 assessments and 2008 assessment policy and membership in two assessment coalitions and the passage of the CCSS. What should they be telling teachers? What should they be doing on assessment?
goal for stem education
Goal for STEM education

Schooling is about modeling our world (scientifically, technologically, mathematically, and statistically), encouraging active citizenry, building opportunities for expressiveness, fostering collaboration, designing and testing solutions, feeling engaged and empowered, and being well-prepared to earn a satisfying and sufficient living.

six priorities around the instructional core

Priority 1: Phasing

Six Priorities around the Instructional Core

Priority 4: Professional Development Systems

Priority 2: Linking Assessment,

Curriculum and Instruction

Priority 3: 15% and Literacy

Priority 5: Curricular Effectiveness and Change

Priority 6: Care and Feeding of Standards

priority one phasing implementation
Priority One: Phasing Implementation

and -- Include the mathematical practices

in all aspects of implementation.

phasing by learning trajectories
Phasing by Learning Trajectories

Posters of K-5, 6-8 and 9-12 CCSS in learning trajectories format available at

phasing the implementation
Phasing the Implementation


new curricular development,

general support systems,


building technological infrastructure, and

professional development systems.

lack of engagement
Lack of Engagement
  • Lack of engagement in learning is the greatest problem in mathematics classes
  • How do the CCSS help us with this?
    • The Mathematical Practices as a way to leverage discourse
    • Formative Assessment or Assessment for Learning
    • New technologies for networking
assessment for learning
Assessment for Learning

Assessment for Learning Defined: Stiggins et al. (2005)

The UK Assessment Reform Group (1999) identifies


The provision of effective feedback to students.

The active involvement of students in their own learning.

Adjusting teaching to take account of the results of assessment.

Recognition of the profound influence assessment has on the motivation and self esteem of pupils, both of which are critical influences on learning.

The need for students to be able to assess themselves and understand how to improve.


Formative Assessment

…a process used by teachers and students during instruction that provides feedback to adjust ongoing teaching and learning to improve students’ achievement of intended instructional outcomes.

  • rely on learning progressions (Heritage 2008)
  • share explicit learning goals
  • provide students with descriptive feedback
  • promote a collaborative environment
  • include peer and self assessments

(CCSSO, 2008)


Defining Diagnostic Assessment

  • Diagnostic Assessment requires an explicit theory of how a student’s thinking progresses over time.
  • Comes from a combination of dia, to split apart, and gnosi, to learn, or knowledge
  • Efficient, effective use of students’ responses, both to document growth in their learning and understanding (content and process) and to promote that growth, from initial states to more powerful, coherent and aligned conceptions

Issues in Diagnostic Assessment

  • Focus on big ideas in mathematics
  • Focus on how children’s mathematics understanding evolves over time, rather than replicating the ‘structure of mathematics’
  • Rapid feedback to teachers on individual and group status of understanding
  • Provide recommendations and interventions for improving growth, remedying gaps in conceptual understanding
  • Professional Development: continuous instructional improvement
a learning trajectory progression is
A learning trajectory/progression is:

…a researcher-conjectured, empirically-supported description of the ordered network of constructs a student encounters through instruction (i.e. activities, tasks, tools, forms of interaction and methods of evaluation), in order to move from informal ideas, through successive refinements of representation, articulation, and reflection, towards increasingly complex concepts over time

(Confrey et al., 2009)

classroom assessment
Classroom Assessment

Draws on students’ proclivity for interactions and social networking

Supplements teachers’ knowledge of student thinking and content

Reaches students directly to involve them in learning

Supports reasonable levels of customization

Builds on the base of knowledge of empirically supported learning trajectories

Supports rather than supplants curriculum


Applets for Diagnostics

and Activities: Packet 1

Equipartitioning Learning Trajectory

Proficiency levels:

1 (Collections)

3 (Justification)

4 (Naming)


Priority Three: Defining and deploying a broader college-and-career STEM agenda by appropriating the fifteen percent of a state’s standards that does not have to comply with the CCSS;


What adoption means

  • A state adopts 100% of the common core K-12 standards in ELA and mathematics (word for word).
  • With option of adding up to an additional 15% of standards on top of the core.
ela standards reading in science and technical subjects
ELA standards: Reading in Science and Technical Subjects

Key ideas and details

Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks.

Reading Standards for Literacy in Science and Technical Subjects

Craft and Structure:

Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 6–8 texts and topics.

Integration of Knowledge and Ideas:

Compare and contrast the information gained from experiments, simulations, video, or multimedia sources with that gained from reading a text on the same topic (grades 6-8)

Range of Reading and Level of Text Complexity

writing standards for science and technical subjects
Writing Standards for Science and Technical Subjects
  • Text Type and Purposes

-- Write arguments focused on discipline-specific content

  • Production and Distribution of Writing
    • Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on addressing what is most significant for a specific purpose and audience
  • Research to Build and Present Knowledge
    • Conduct short as well as more sustained research projects to answer a question (including a self-generated question) or solve a problem; narrow or broaden the inquiry when appropriate; synthesize multiple sources on the subject, demonstrating understanding of the subject under investigation

The math CCSS are conservative, and delayed on modeling, probability and statistics, and rate of change and early functions as an introduction to algebra.

Further, they only modestly focus on the use of new learning technologies: this could leave our students foundering in exciting arenas incorporating visualization, integration of topics, engineering, and design and the use of simulations. These topics constitute a critical agenda for our field, and we need a strategy to avoid their marginalization.




weighing evidence, and

interpreting representations

Could be achieved by inclusion of simulations, dynamic displays, and extensions of problems from informal and formal contexts

trojan horse approach
Trojan Horse Approach

Build innovative curricula for the 15% and for the Science and Technical Reading and Writing Standards

Ways to implement:

Use school time that is often blank (inter-sessions, post summative assessment time, near holiday time) and

Develop high school courses along the lines of “Theory of Knowledge” in International Baccalaureate Programs

priority 4 developing advanced systems for professional development around points 1 3
Priority 4 : Developing advanced systems for professional development around points 1-3;
  • Professional development needs to be:
    • Content and curricular specific
    • Closely linked to classroom practices
    • Include intensive learning opportunities with year round follow up
    • Obligatory
    • Linked to building professional communities
  • It needs to tie to standards, including their interpretation.
  • States need professional development systems connecting district resources, departments of public instruction and universities, colleges and community colleges.
Priority Five: Using longitudinal data systems to decipher and study curricular effectiveness and provide empirical support for change.
Priority Six: Using longitudinal data systems to decipher and study curricular effectiveness and provide empirical support for change.

On Evaluating



(NRC 2004)

recent advances
Recent Advances

Implementation fidelity(Huntley, 2010)

Opportunity to learn and related constructs (McNaught et al. 2010)

Fair Tests for comparison (Chavez et al. 2010)

Complexity of relationships among teacher and student variables and curricular effects Tarr et al. (

We need to continue to build on these to ensure that we can substantiate future effectiveness

care and feeding of the standards
“Care and Feeding of the Standards”
  • Should be an NRC type process with documented responses to feedback
  • Should include:
    • members of professional organizations
    • teachers
    • researchers,
    • assessment experts
  • Should have a three part timeline: immediate fixes, minor revisions and major reviews

The Common Core State Standards present considerable opportunities for innovative thinking around curriculum

  • Require a plan for phasing in the CCSS by grades and domains
  • Need to elaborate the learning trajectories
  • Need to inter-relate curriculum, instruction, and assessment using new technologies as a priority to improve engagement and fair opportunities
  • Wise to expand our target to 15% and ELA
  • Continue progress on evaluating curricular effectiveness

The success of the standards depends on the ability of teachers to assist students in learning the specified “fewer” standards at grade level.

Therefore, the success of the standards should be measured heavily, though not exclusively, on the narrowing of the performance gaps

“It is time to recognize that Standards are not just promises to our children, but promises we intend to keep.” CCSS 2010, p. 5

Photo: Tyler Confrey Maloney

“It is time to recognize that Standards are not just promises to our children, but promises we intend to keep.” CCSS 2010, p. 5