SCALE Middle School Math ForumDecember 11-12, 2005

Madison, Wisconsin

Denver Public Schools

Los Angeles Unified School District

Madison Metropolitan School District

Providence (RI) Public Schools

California State University, Dominguez Hills

California State University, Northridge

University of Pittsburgh

University of Wisconsin-Madison

Charge for today

Drawing on the expertise from across the SCALE

partnership,

• generate possible useful solutions to the pressing

issues of middle school mathematics faced by

our K-12 districts

• by considering both technical problems and

adaptive challenges, and their corresponding

exploitation and exploration strategies.

From testimony before Subcommittee on 21st Century Competitiveness

Committee on Education and the Workforce, House Of Representatives

Washington, DC, October 9, 2002

For a partnership to be successful, partners must complement each

other. Universities are great places to dream about the possible; large,

urban school districts are places where practical solutions are needed for

almost impossible problems.

Professors are encouraged to strive for the ideal; teachers and school

administrators must deal with reality.

If we do not consider the ideal, we will be forever stuck with mediocrity;

if we do not consider the reality, we will never move forward.”

Steve Brandick, LAUSD

Complex adaptive systems seek a favorable

balance of exploitation & exploration

R. Axelrod & M.D. Cohen,

Harnessing Complexity (2000)

Exploitation – Exploration Continuum

Exploitation - copying of strategies so far proven “best”

Exploration - creation of new, possibly “better” strategies

Competition for system resources

Exploitation - copying of strategies so far proven “best”

Exploration – creation of new, possibly “better” strategies

A thriving system seeks to establish a favorable balance between exploitation and exploration.

Use “exploitation” for “technical problems,” i.e., when:

The problem faced is one that experts know how to

identify, define, and solve.

The knowledge necessary has been transformed

into operating principles, and legitimized

organizational procedures (templates) guide

what to do. There are role authorizations

guiding who should do what. (Heifetz, 1997)

Likely outcomes are known, based on prior

implementation.

Use “exploration” for “adaptive challenges,” i.e., when:

Even experts cannot clearly define, let alone solve the

challenges

Operating principles are vaguely understood

Problems are long-term, widespread, or involve a

looming disaster

Fast, reliable feedback can be used as a tool

Low risk of catastrophe from the exploration

Charge for today

Drawing on the expertise from across the SCALE

partnership,

• generate possible useful solutions to the pressing

issues of middle school mathematics faced by

our K-12 districts

• by considering both technical problems and

adaptive challenges, and their corresponding

exploitation and exploration strategies.

I. What problems must be solved to improve student learning in 8th grade math/algebra?

- Which problems are well-understood and have solutions we can exploit?

- Which of these are adaptive challenges that need new solutions, developed through collaborative exploration?

II. How will we assess the effectiveness of existing and new solutions?

Listen: Define the ProblemArea What are we

doing, or plan to do?

What would we like to do better?

What problems do we see?

Enacted Curriculum

Professional Learning

Monitoring, Accountability and Assessment