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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.

Cooperative Learning

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

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.

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Three Factors

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

Mathematics is a static body of knowledge!

Societal Factors

• 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.

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

Given 100 ninth grade students

Societal Factors

• 75 graduate from high school• 45 go to college• 18 graduate in four years.

• 1 or 2 major in mathematics or the sciences.

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Textbooks determine what is taught in schools.• 95% of students relate it as the only source of information.

Curriculum Factors

• 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.

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

Teacher Preparation

• Few take algebra or higher level courses at the college level.• Mathematics coordinators are rare.

continued

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Teacher Preparation

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

Secondary

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

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

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• 10% of what we read

We Learn . . .

William Glasser

• 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

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• 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.

Individualistic ModelWe Are Each In This Alone

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• 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.

Competition ModelI Swim, You Sink; I Sink, You Swim

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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)

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• 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.

CooperationWe Sink Or Swim Together

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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.

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• Higher achievement,

Learning OutcomesPromoted by Cooperative Learning

• 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,

continued

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• More positive attitude toward mathematics, learning and school

Learning OutcomesPromoted by Cooperative Learning

• 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.

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When to IncorporateCooperative Learning

• Homework review

• Test preview/review

• Task oriented lessons

• Enrichment.

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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

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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.

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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.

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Teacher’s RoleSetting up the lesson for the students.

• Explain the problem.

• Explain the academic tasks.

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

• Structure the individual accountability.

• Explain the criteria for success.

• Specify the expected behavior.

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Teacher’s Role Activities during the lesson.

• Monitor student progress.

• Monitor student behavior.

• Provide assistance.

• Play the devils advocate.

• Intervene to teach collaborative skills.

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Teacher’s Role Assessment and process at the end.

• Evaluate group success/failure.

• Evaluate student learning.

• Provide for group interaction.

• Provide closure.

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• Mixed by gender

Structuring Cooperative LearningGroup Formation

• Heterogeneous by ability and personality

• Task oriented with non-task oriented

• High ability with low abilities

• etc.

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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

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• Members are allowed to criticize ideas but not people

Structuring Cooperative LearningGroup Processing

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

• Students must exercise self-control

• Students must show a willingness to compromise• Use conflict management techniques

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

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

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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.

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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.)

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Summary

• 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.

continued

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Summary

• 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

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Assignment Read:

• Posamentier Chapter 3, pages 62-71.

• Johnson Chapter 2.

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INCLASS COOPERATIVE LEARNING ASSIGNMENT

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RECORDER/SECRETARY

- record all the group’s work.

CHECKER & PRAISER/CHEERLEADER

- check all calculations

- provide positive reinforcement.

TASKMASTER & PRESENTER

-Keep members of the group on task

- present the group’s solution to the class.

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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.

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

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

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Individual follow-up questions for the triangle arrangement problem:

1. (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.

2. (4 points) If c = 4, how many triangles would be possible?

3. (4 points) If the number of possible triangles is 36, what is the value of c?

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Scoring Ruberic• Understanding the problem

0: Complete misunderstanding of the problem1: Part of the problem is misunderstood or misinterpreted2: Complete understanding of the problem

• Planning a solution0: No attempt or inappropriate plan1: Partially correct plan based on a correct interpretation.2: Plan could have or did lead to a correct solution.

• Getting an Answer0: No answer or wrong due to a poor plan1: Copying error; computational error; partial correct answer2: Correct answer with correct label