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Cooperative Learning. The students will learn what educational research has shown about cooperative learning. The students will learn effective methods to implement cooperative learning into their classrooms. Introduction Something to Think About.

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Cooperative learning
Cooperative Learning

The students will learn what educational research has shown about cooperative learning. The students will learn effective methods to implement cooperative learning into their classrooms.

Introduction something to think about
Introduction Something to Think About.

There are 125 sheep and 5 dogs in a flock. How old is the shepherd?

3 of 4 students in late elementary and middle school produce an answer.

Clearly, there are some problems with the current way in which we do things.

Three factors
Three Factors










Societal factors
Societal Factors

Most students believe that mathematics is a rule-oriented body of knowledge acquired through memorization.

Mathematics is a static body of knowledge!

  • 8 years of 18th century shopkeeper math

  • 2 years of 19th century algebra

  • 1 year of 3rd century BC geometry

  • Even calculus is 300 years old!

  • Fractals, discrete math, knot theory, statistics, probability are not included in the curriculum.

Societal factors1
Societal Factors

It is a difficult subject mastered by a very few that have an innate ability.

Given 100 ninth grade students

  • 75 graduate from high school

  • 45 go to college

  • 18 graduate in four years.

  • 1 or 2 major in mathematics or the sciences.

Curriculum factors
Curriculum Factors

Textbooks determine what is taught in schools.

  • 95% of students relate it as the only source of information.

  • Texas/California drive the textbook market.

  • Textbooks stress computation, algorithmic procedures and artificial story problems.

There is an over reliance on “Spiral” curriculum

Textbooks need updating – add probability, statistics, modeling, etc.

Teacher preparation
Teacher Preparation


  • One in eight teachers has had three or fewer credits of college level mathematics.

  • Few take algebra or higher level courses at the college level.

  • Mathematics coordinators are rare.


Teacher preparation1
Teacher Preparation


  • One in eight teachers are assigned duties outside their competency and certification.

  • Few courses relate to what you will be teaching in 2016.

  • Most of you will teach the way you have been taught - lecture.

We learn
We Learn . . .

  • 10% of what we read

  • 20% of what we hear

  • 30% of what we see

  • 50% of what we both see and hear

  • 70% of what is discussed with others

  • 80% of what we experience

  • 95% of what we TEACH to someone else

William Glasser

Individualistic model we are each in this alone
Individualistic ModelWe Are Each In This Alone

  • Work alone

  • Strive for own success

  • What benefits self does not affect others

  • Own success is celebrated

  • Rewards are limited

  • Evaluated by comparing performance to preset criteria.

Competition model i swim you sink i sink you swim
Competition ModelI Swim, You Sink; I Sink, You Swim

  • Work alone

  • Strive to be better than classmate

  • What benefits self deprives others

  • Own success and others’ failure is celebrated

  • Rewards are limited

  • Graded on a curve or ranked from best to worst.

Cooperative learning

In reality, no one can teach mathematics. Effective teachers are those who can stimulate students to learn mathematics. Education research offers compelling evidence that students learn mathematics well only when they construct their own mathematical understanding. To understand what they learn, they must enact for themselves verbs that permeate the mathematics curriculum: “examine,” “represent,” “transform,” “solve,” “apply,” “prove,” “communicate.” This happens most readily when students work in groups, engage in discussion, make presentations, and in other ways take charge of their own learning.

Everybody Counts (National Research Council 1989, pp. 58-59)

Cooperation we sink or swim together
CooperationWe Sink Or Swim Together

  • Work in small, often heterogeneous groups

  • Strive for all group members’ success

  • What benefits self benefits others

  • Joint success is celebrated

  • Rewards are viewed as unlimited

  • Evaluated by comparing performance to preset criteria.

Basic elements of cooperative learning
Basic Elements of Cooperative Learning

  • Positive Interdependence – mutual goals, joint rewards, shared resources, assigned roles.

  • Face-to-Face Interactions – students explain, discuss and teach.

  • Interpersonal and Small Group Skills – socialization skills.

  • Group Processing – group discuss goals and achievements. Teacher monitors group and gives feedback.

Learning outcomes promoted by cooperative learning
Learning OutcomesPromoted by Cooperative Learning

  • Higher achievement,

  • Increased retention,

  • Greater use of higher level reasoning strategies,

  • Increased critical reasoning competencies,

  • View situations from other’s perspective,

  • Greater intrinsic motivation,

  • More positive, accepting, and supportive relationships with all peers,


Learning outcomes promoted by cooperative learning1
Learning OutcomesPromoted by Cooperative Learning

  • More positive attitude toward mathematics, learning and school

  • More positive attitude toward teachers, principals and school personnel,

  • Higher self-esteem based on self acceptance,

  • Greater social support,

  • More positive psychological adjustment and health,

  • Less disruption and more on-task behavior,

  • Greater collaborative skills and attitudes necessary for working with others.

When to incorporate cooperative learning
When to IncorporateCooperative Learning

  • Homework review

  • Test preview/review

  • Task oriented lessons

  • Enrichment.

The teachers role in cooperative learning
The Teachers’ Role InCooperative Learning

“The teachers’ role should include those of consultant, moderator, and interlocutor, not just presenter and authority. Classroom activities must encourage students to express their approaches, both orally and in writing. Students must engage mathematics as a human activity; they must learn to work cooperatively in small teams to solve problems as well as argue convincingly for their approach amid conflicting ideas and strategies.”

Everybody Counts: A Report to the Nation On The Future of Mathematics Education, National Research Council, 1989

Cooperative learning teacher s role
Cooperative LearningTeacher’s Role

What follows will constitute four of the ways a teacher is involved in a cooperative problem-solving lesson.

  • Decisions prior to the activity.

  • Setting up the lesson for the students.

  • Teacher activities during the lesson.

  • Assessment and process at the end.

Teacher s role decisions prior to the activity
Teacher’s RoleDecisions prior to the activity.

  • Define the academic objectives.

  • Define the collaborative objectives.

  • Assign students to groups.

  • Arrange the classroom appropriately.

  • Plan for any needed materials.

  • Decide on the roles for students.

Teacher s role setting up the lesson for the students
Teacher’s RoleSetting up the lesson for the students.

  • Explain the problem.

  • Explain the academic tasks.

  • Structure the individual accountability.

  • Structure the positive interdependence. The inter-group cooperation.

  • Explain the criteria for success.

  • Specify the expected behavior.

Teacher s role activities during the lesson
Teacher’s RoleActivities during the lesson.

  • Monitor student progress.

  • Monitor student behavior.

  • Provide assistance.

  • Play the devils advocate.

  • Intervene to teach collaborative skills.

Teacher s role assessment and process at the end
Teacher’s RoleAssessment and process at the end.

  • Evaluate group success/failure.

  • Evaluate student learning.

  • Provide for group interaction.

  • Provide closure.

Structuring cooperative learning group formation
Structuring Cooperative LearningGroup Formation

  • Heterogeneous by ability and personality

  • Task oriented with non-task oriented

  • High ability with low abilities

  • Mixed by gender

  • etc.

Structuring cooperative learning task design
Structuring Cooperative LearningTask Design

  • Emphasis on working and learning together

  • Individual accountability to the group and the teacher

  • Tasks are divided so that each individual has some responsibility for some of the work

Structuring cooperative learning group processing
Structuring Cooperative LearningGroup Processing

  • All members of the group should feel free to present ideas

  • Members are allowed to criticize ideas but not people

  • Students must exercise self-control

  • Students must show a willingness to compromise

  • Use conflict management techniques

Structuring cooperative learning reward structure
Structuring Cooperative LearningReward Structure

  • Evaluations by both the teacher and the group

  • Randomly select students to explain group work

  • Can use letter grades, rank, or use a rubric

  • The quality of verbal interaction is an important factor in the group’s success

Reward structure
Reward Structure

A duel assessment scheme can be used to include both group and individual accountability.

1. Students work in their assigned groups to solve a problem and write a single group solution.

2. Students work individually to answer questions about their group’s solution and to solve similar problems.

Reward structure continued
Reward Structure (continued)

A similar duel scheme is used for grading.

1. The teacher grades each group’s solution and all students in the group receive the same score for that solution.

2. The teacher grades individual student work consisting of three types of problems. A. A question for understanding. B. A parallel problem. C. An extension problem. (May be a home assignment.)


  • The research show many positive rewards associated with cooperative learning. Know what they are.

  • Cooperative learning should be incorporated into most lessons

  • The role of the teacher is changing from presenter of knowledge to facilitator of learning.



  • Students make better citizens when they know how to work cooperatively with others

  • Solutions to problems are more complete when they come from cooperative groups



  • Posamentier Chapter 3, pages 62-71.

  • Johnson Chapter 2.

Cooperative learning


- record all the group’s work.


- check all calculations

- provide positive reinforcement.


  • Keep members of the group on task

  • present the group’s solution to the class.

The triangle arrangement problem

The three sides of a triangle have lengths a, b, and c. All three lengths are whole numbers and a ≤ b ≤ c.

  • Suppose that c = 9. Find the number of different triangles that are possible.

  • For any given value of c, find a general law that expresses the number of possible triangles.

Individual follow up questions for the triangle arrangement problem
Individual follow-up questions for the triangle arrangement problem:

  • (2 points) In the problem your group just solved, would c = 9, b = 5, and a = 4 be possible values fro c, b, and a? Justify your answer.

  • (4 points) If c = 4, how many triangles would be possible?

  • (4 points) If the number of possible triangles is 36, what is the value of c?

Scoring ruberic
Scoring Ruberic problem:

  • Understanding the problem

    0: Complete misunderstanding of the problem

    1: Part of the problem is misunderstood or misinterpreted

    2: Complete understanding of the problem

  • Planning a solution

    0: No attempt or inappropriate plan

    1: Partially correct plan based on a correct interpretation.

    2: Plan could have or did lead to a correct solution.

  • Getting an Answer

    0: No answer or wrong due to a poor plan

    1: Copying error; computational error; partial correct answer

    2: Correct answer with correct label