Equity through Group Work:Complex Instruction Benefiting Diverse Learners

Kathleen Ross, Belin Tsinnajinnie, Marta CivilNCTM Annual Meeting

TODOS: Mathematics for AllStrand

April 24, 2010

Session OverviewIntroduction

Goal: Explore features of Complex Instruction from theperspective of the teacher as “educational engineer”(Cohen, 1994, p. 3) in a heterogeneous classroom withdiverse mathematical and English languageproficiencies.

Collective inquiry of norms, roles, and sample tasks

Cohen, E. (1994). Designing groupwork: Strategies for the heterogeneousclassroom. New York: Teachers College Press.

Why groupwork?

What are the benefits of groupwork?

When and why is groupwork ineffective?

What are the challenges of groupwork (bothas a participant and as a teacher)?

Complex Instruction PrinciplesCohen, E. G., & Lotan, R. A. (Eds.). (1997). Working for equity in

heterogeneous classrooms: Sociological theory in practice. New York:Teachers College Press.

• Groupworthy Tasks: Providetasks that are open-ended,rich in multiple abilities, andsupport learning importantmathematical concepts andskills central to a big idea.

• Instructional Strategies:Develop autonomy of andinterdependence within eachgroup through the use ofnorms, roles, and teacherinterventions.

• Status and Accountability:Raise intellectual expectationsfor all students, holdindividuals and small groupsaccountable for learning, andintervene in status issues.

Collective Inquiry 1:Is the task groupworthy?

What mathematical concepts and skillsare targeted in the sample task?

Are they important?

Are they central to a big idea?

Is it open-ended and rich in multiple abilities?

Find the number that each shape represents.

from Get it Together, (1989). EQUALS, Lawrence Hall of Science

OBJECTIVE OFOBJECTIVE OF TASKTASK

• Students will be able to:

• solve one-step first degree equation by adding orsubtracting

• work in groups to solve one-step equations

• describe the procedure they used for solving one-stepequations

• use the appropriate mathematical language whenreading and solving one-step equations.

Multiple AMultiple AbilitiesbilitiesCommunicate and explain mathematical ideas in Englishand/or native language with use of gestures, written and oralpresentations.

Conceptual understanding of unknowns and solving a systemof equations

Solving the equations algebraically/numerically

Different mathematical proficiencies (conceptualunderstanding, strategic competence, procedural fluency,adaptive reasoning, productive disposition)

National Research Council (2001). Adding it up: Helping children learnmathematics. Washington, D.C.: National Academy Press.

Collective Inquiry 2:Do task roles support group

autonomy and interdependence?In an elementary or middle school math classthat is diverse in mathematical and Englishlanguage proficiencies:

What factors would you consider in placing studentsinto groups?

How could you assign roles to support groupautonomy, interdependence, learning?

How would you hold individuals and small groupsaccountable for learning?

Find the number that each shape represents.

from Get it Together, (1989). EQUALS, Lawrence Hall of Science

Reflections on Ta Reflections on TaskskImplementationImplementation

Issues of status, gender, and competitiveness stillexist.

Roles and norms have not been internalized.

Still evidence of students trying to dominatediscourse.

Task not based on context familiar to students.

The expectations for group work and mathematicaldiscussions have not yet been established.

Collective Inquiry 3:What expectations and rules need

to be developed first?

What individual, social, and cooperative learning rules areneeded so that:

all students participate,

the responsibility for learning rests with the group, and

the responsibility for learning rests with each individual?

What mathematical processes need to be developed forautonomous cooperative learning to be successful?

Expectations

• Productive Disposition—Habitual inclination to seemathematics as useful, worthwhile, sensible; PLUS belief indiligence and own efficacy.

• NCTM Process Standards (2000)- Problem Solving, reasoningand proof, communication, connections, and representation

• Expectation to use mathematical processes (conjecturing,justifying, generalizing, communicating, etc.)

• Expectation for students to act as resources for each other, tobe accountable as individuals and as a group.

Complex Instruction PrinciplesCohen, E. G., & Lotan, R. A. (Eds.). (1997). Working for equity in

heterogeneous classrooms: Sociological theory in practice. New York:Teachers College Press.

• Groupworthy Tasks: Provide tasksthat are open-ended, rich in multipleabilities, and support learningimportant mathematical conceptsand skills central to a big idea.

• Instructional Strategies: Developautonomy of and interdependencewithin each group through the use ofnorms, roles, and teacherinterventions.

• Status and Accountability: Raiseintellectual expectations for allstudents, hold individuals and smallgroups accountable for learning, andintervene in status issues.