jere confrey, joseph d. moore university distinguished professor, mathematics education friday...

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 2011ConferenceFebruary 15, 2011

Baltimore, Maryland

Next Steps in Implementing Mathematics (and Science)

Initiatives at the National and State Levels: Focusing on Common Core Standards

The instructional practices and assessments discussed or shown are not an endorsement by the U.S. Department of Education

Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606

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• 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:• 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;


Nonetheless…

• 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 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

• 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

Priority 5: Curricular

Effectiveness and Change

Priority 2: Linking

Assessment,Curriculum

and Instruction

Priority 4: Professional

Development Systems

Priority 6: Care and

Feeding of Standards

Priority 3: 15% and Literacy


Priority One: Phasing the Implementation


Priority One: Phasing Implementation

Year Grade Level2010-11 K-12011-12 2-32012-13 4-52013-14 6-72014-15 8

and -- Include the mathematical practices in all aspects of implementation.


Phasing by Learning Trajectories

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

mailto:[email protected]


Phasing the Implementation

Simultaneously, • new curricular development, • general support systems, • assessments, • building technological infrastructure, and

professional development systems.


Priority Two: Smartly coupling curriculum and classroom assessment

via the CCSS


Priority Two: Smartly coupling curriculum and classroom assessment via the CCSS


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 LearningThe UK Assessment Reform Group (1999) identifies

FIVE PRINCIPLES OF ASSESSMENT FOR LEARNING

1. The provision of effective feedback to students. 2. The active involvement of students in their own learning.3. Adjusting teaching to take account of the results of assessment. 4. Recognition of the profound influence assessment has on the

motivation and self esteem of pupils, both of which are critical influences on learning.

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

Assessment for Learning Defined: Stiggins et al. (2005) http://www.assessmentinst.com/wp-content/uploads/2009/05/afldefined.pdf

http://www.assessmentinst.com/wp-content/uploads/2009/05/afldefined.pdf


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.

1. rely on learning progressions (Heritage 2008)

2. share explicit learning goals

3. provide students with descriptive feedback

4. promote a collaborative environment

5. 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 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

• 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


Prototyping a Diagnostic Assessment System: LPPSync


Applets for Diagnosticsand Activities: Packet 1Equipartitioning 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

Key ideas and detailsFollow precisely a multistep procedure when carrying out experiments, taking

measurements, or performing technical tasks. Reading Standards for Literacy in Science and Technical SubjectsCraft 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

• 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.


Solution

• argumentation, • reasoning, • 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

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

Ways to implement: a) Use school time that is often blank (inter-sessions, post

summative assessment time, near holiday time) and b) 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;

• 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 Curricular

Effectiveness (NRC 2004)


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. (http://cosmic.missouri.edu/aera10/)

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

http://cosmic.missouri.edu/aera10/


Priority Six: The 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


ConclusionsThe 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

jere confrey, joseph d. moore university distinguished professor, mathematics education friday...

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