Presentation on theme: "Cooperative Learning The students will learn what educational research has shown about cooperative learning. The students will learn effective methods."— Presentation transcript:
1Cooperative LearningThe students will learn what educational research has shown about cooperative learning. The students will learn effective methods to implement cooperative learning into their classrooms.
2Introduction 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.
4Societal FactorsMost 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 math2 years of 19th century algebra1 year of 3rd century BC geometryEven calculus is 300 years old!Fractals, discrete math, knot theory, statistics, probability are not included in the curriculum.
5Societal FactorsIt is a difficult subject mastered by a very few that have an innate ability.Given 100 ninth grade students75 graduate from high school45 go to college18 graduate in four years.1 or 2 major in mathematics or the sciences.
6Curriculum 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” curriculumTextbooks need updating – add probability, statistics, modeling, etc.
7Teacher Preparation Elementary 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.continued
8Teacher Preparation Secondary 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.
9We Learn . . . 10% of what we read 20% of what we hear 30% of what we see50% of what we both see and hear70% of what is discussed with others80% of what we experience95% of what we TEACH to someone elseWilliam Glasser
10Individualistic Model We Are Each In This Alone Work aloneStrive for own successWhat benefits self does not affect othersOwn success is celebratedRewards are limitedEvaluated by comparing performance to preset criteria.
11Competition Model I Swim, You Sink; I Sink, You Swim Work aloneStrive to be better than classmateWhat benefits self deprives othersOwn success and others’ failure is celebratedRewards are limitedGraded on a curve or ranked from best to worst.
12In reality, no one can teach mathematics 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 )
13Cooperation We Sink Or Swim Together Work in small, often heterogeneous groupsStrive for all group members’ successWhat benefits self benefits othersJoint success is celebratedRewards are viewed as unlimitedEvaluated by comparing performance to preset criteria.
14Basic 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.
15Learning Outcomes Promoted 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,continued
16Learning Outcomes Promoted by Cooperative Learning More positive attitude toward mathematics, learning and schoolMore 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.
17When to Incorporate Cooperative Learning Homework reviewTest preview/reviewTask oriented lessonsEnrichment.
18The Teachers’ Role In Cooperative 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
19Cooperative Learning Teacher’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.
20Teacher’s Role Decisions 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.
21Teacher’s Role Setting 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.
22Teacher’s Role Activities during the lesson. Monitor student progress.Monitor student behavior.Provide assistance.Play the devils advocate.Intervene to teach collaborative skills.
23Teacher’s Role Assessment and process at the end. Evaluate group success/failure.Evaluate student learning.Provide for group interaction.Provide closure.
24Structuring Cooperative Learning Group Formation Heterogeneous by ability and personalityTask oriented with non-task orientedHigh ability with low abilitiesMixed by genderetc.
25Structuring Cooperative Learning Task Design Emphasis on working and learning togetherIndividual accountability to the group and the teacherTasks are divided so that each individual has some responsibility for some of the work
26Structuring Cooperative Learning Group Processing All members of the group should feel free to present ideasMembers are allowed to criticize ideas but not peopleStudents must exercise self-controlStudents must show a willingness to compromiseUse conflict management techniques
27Structuring Cooperative Learning Reward Structure Evaluations by both the teacher and the groupRandomly select students to explain group workCan use letter grades, rank, or use a rubricThe quality of verbal interaction is an important factor in the group’s success
28Reward StructureA 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.
29Reward 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.)
30SummaryThe research show many positive rewards associated with cooperative learning. Know what they are.Cooperative learning should be incorporated into most lessonsThe role of the teacher is changing from presenter of knowledge to facilitator of learning.continued
31SummaryStudents make better citizens when they know how to work cooperatively with othersSolutions to problems are more complete when they come from cooperative groups
32Assignment Read: Posamentier Chapter 3, pages 62-71. Johnson Chapter 2.
34- record all the group’s work. RECORDER/SECRETARY- record all the group’s work.CHECKER & PRAISER/CHEERLEADER- check all calculations- provide positive reinforcement.TASKMASTER & PRESENTERKeep members of the group on taskpresent the group’s solution to the class.
35THE 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.
36Individual 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?
37Scoring Ruberic Understanding the problem Planning a solution 0: Complete misunderstanding of the problem1: Part of the problem is misunderstood or misinterpreted2: Complete understanding of the problemPlanning 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