Learning in Co-operative Groups in mathematics. OECD / France Workshop Jan Terwel VU University Amsterdam Faculty of Psychology and Education Paper presented.

Learning in Co-operative Groups Learning in Co-operative Groups in mathematics in mathematics

OECD / France WorkshopOECD / France Workshop

Jan TerwelVU University Amsterdam

Faculty of Psychology and EducationPaper presented at the OECD / France workshop, Paris 23-24 May 2011

‘Education for Innovation: The role of Arts and STEM Education’

Cooperative learning and Mathematics Education: A happy marriage?

Learning in Co-operative GroupsLearning in Co-operative Groups

Co-operation in Vocational Co-operation in Vocational EducationEducation

Computer Supported Collaborative Computer Supported Collaborative Learning (CSCL) Learning (CSCL)

Becoming an Authentic LearnerBecoming an Authentic Learner

New Learning

Situated cognition Community of practice

Socially shared cognitionCognitive apprenticeship

Providing versus generating?Providing versus generating?

searching for a third waysearching for a third way

instructional model for cooperative instructional model for cooperative learning and adaptive instruction for learning and adaptive instruction for students between the ages of 12-16 students between the ages of 12-16 (AGO-model) (AGO-model) instructional approach for primary instructional approach for primary mathematics called ‘guided co-mathematics called ‘guided co-construction’.construction’.

Co-operative Learning and Co-operative Learning and Adaptive InstructionAdaptive Instruction

The AGO-model is a whole-class model that allows for The AGO-model is a whole-class model that allows for student diversity through remediation and enrichment student diversity through remediation and enrichment within small groups. within small groups.

1.1. Whole‑class introduction of a mathematics topic Whole‑class introduction of a mathematics topic 2.2. Small‑group cooperation in groups of four studentsSmall‑group cooperation in groups of four students3.3. Teacher assessments and diagnostic test Teacher assessments and diagnostic test 4.4. Alternative learning pathsAlternative learning paths5.5. Individual work at own level in groups Individual work at own level in groups 6.6. Whole-class reflection and evaluation of the topicWhole-class reflection and evaluation of the topic7.7. Final test.Final test.

Guided co-construction of Guided co-construction of mathematicsmathematics

The instructional approach The instructional approach Guided co-construction of mathematicsGuided co-construction of mathematics entails the following three core elementsentails the following three core elements

‘‘Guided’ refers to the explicit role of the teacher for whole-class Guided’ refers to the explicit role of the teacher for whole-class instruction and the scaffolding of students either in groups or instruction and the scaffolding of students either in groups or individually.individually.

‘‘Co-’ refers to cooperative learning as an essential component of Co-’ refers to cooperative learning as an essential component of mathematics as a social, human activity and a cultural tool. In mathematics as a social, human activity and a cultural tool. In contrast to mathematics as a closed system to be transmitted to contrast to mathematics as a closed system to be transmitted to students.students.

‘‘Construction’ refers to the recognition and construction of concepts, Construction’ refers to the recognition and construction of concepts, principles, models, symbols by students related to their prior principles, models, symbols by students related to their prior knowledge and experiences.knowledge and experiences.

The dynamics of group work: The dynamics of group work: five explaining factorsfive explaining factors

Socio-cognitive conflicts Socio-cognitive conflicts

Resource sharingResource sharing

Cognitive reorganization Cognitive reorganization

Motivation theory/peer group interaction.Motivation theory/peer group interaction.

Hans Freudenthal's theory of levels in Hans Freudenthal's theory of levels in the learning process in mathematicsthe learning process in mathematics

Elizabeth Cohen’s Status TheoryElizabeth Cohen’s Status Theory

Distance-Time Graphs as Representations in Mathematics

Lucie and Evelyn Running

Lucie

Evelyn

Could you tell something about the difference in walking style between Lucy and Evelyn?

Socio-cognitive conflictSocio-cognitive conflict

Rick says: "Lucy goes on and on without rest Rick says: "Lucy goes on and on without rest and Evelyn runs irregular, she starts fast, then and Evelyn runs irregular, she starts fast, then she slows down, and so on.she slows down, and so on.

””0, yes?" said José, “why does she bend over 0, yes?" said José, “why does she bend over that, stupid?”that, stupid?”

Rick says: "You don’t understand, dummy", and Rick says: "You don’t understand, dummy", and José slaps back: "That makes no sense, fatty."José slaps back: "That makes no sense, fatty."

José sees Evelyn’s graph as a road with curves. José sees Evelyn’s graph as a road with curves. He functions on another level than Rick.He functions on another level than Rick.

Designing modelsDesigning models

Assignment: The global water cycle

After a short verbal description of the global water cycle, including elements such as the oceans, the sun, evaporation, condensation, clouds, rain, mountains, rivers, sea, et cetera, students were asked:

‘‘Your friend in Groningen has never heard of this cycle in nature. Could you write a letter and make a model (drawing) to explain to your friend how it works?’’ Below we present two alternative solutions to this problem, produced by respectively Nienke and Daniel.

Student’s productions: The global water cycle

Nienke’s Model of the global water cycle

Student’s productions: The global water cycle

Daniel’s model of the global water cycle

ConclusionsConclusionsWe conclude that cooperative learning and guided co-construction are We conclude that cooperative learning and guided co-construction are feasible and effective instructional approaches in mathematics education. feasible and effective instructional approaches in mathematics education.

There are reasons to believe in a happy marriage between cooperative There are reasons to believe in a happy marriage between cooperative learning and mathematics education. learning and mathematics education.

However these approaches are no cure for all. And cooperative learning However these approaches are no cure for all. And cooperative learning should always be accompanied by other instructional strategies like whole should always be accompanied by other instructional strategies like whole class introductions and reflections which should be led by the teacher. class introductions and reflections which should be led by the teacher.

Without special attention to low-achieving students, they may profit less Without special attention to low-achieving students, they may profit less from cooperative learning than their more able counterparts. from cooperative learning than their more able counterparts.

The curriculum materials should be special designed for guided co-The curriculum materials should be special designed for guided co-construction. construction.