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Learning in Co-operative Groups in mathematics

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OECD / France Workshop Jan Terwel VU University Amsterdam Faculty of Psychology and Education Paper 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?

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Learning in Co-operative Groups

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Co-operation in Vocational Education

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Computer Supported Collaborative Learning (CSCL)

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Becoming an Authentic Learner New Learning Situated cognition Community of practice Socially shared cognition Cognitive apprenticeship

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Providing versus generating? searching for a third way instructional model for cooperative learning and adaptive instruction for students between the ages of 12-16 (AGO-model) instructional approach for primary mathematics called ‘guided co- construction’.

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Co-operative Learning and Adaptive Instruction The AGO-model is a whole-class model that allows for student diversity through remediation and enrichment within small groups. 1.Whole ‑ class introduction of a mathematics topic 2.Small ‑ group cooperation in groups of four students 3.Teacher assessments and diagnostic test 4.Alternative learning paths 5.Individual work at own level in groups 6.Whole-class reflection and evaluation of the topic 7.Final test.

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Guided co-construction of mathematics The instructional approach Guided co-construction of mathematics entails the following three core elements ‘Guided’ refers to the explicit role of the teacher for whole-class instruction and the scaffolding of students either in groups or individually. ‘Co-’ refers to cooperative learning as an essential component of mathematics as a social, human activity and a cultural tool. In contrast to mathematics as a closed system to be transmitted to students. ‘Construction’ refers to the recognition and construction of concepts, principles, models, symbols by students related to their prior knowledge and experiences.

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The dynamics of group work: five explaining factors Socio-cognitive conflicts Resource sharing Cognitive reorganization Motivation theory/peer group interaction. Hans Freudenthal's theory of levels in the learning process in mathematics Elizabeth Cohen’s Status Theory

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Distance-Time Graphs as Representations in Mathematics

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

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Socio-cognitive conflict Rick says: "Lucy goes on and on without rest and Evelyn runs irregular, she starts fast, then she slows down, and so on. ”0, yes?" said José, “why does she bend over that, stupid?” Rick says: "You don’t understand, dummy", and José slaps back: "That makes no sense, fatty." José sees Evelyn’s graph as a road with curves. He functions on another level than Rick.

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Designing models

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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.

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Student’s productions: The global water cycle Nienke’s Model of the global water cycle

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Student’s productions: The global water cycle Daniel’s model of the global water cycle

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Conclusions We conclude that cooperative learning and guided co-construction are feasible and effective instructional approaches in mathematics education. There are reasons to believe in a happy marriage between cooperative learning and mathematics education. However these approaches are no cure for all. And cooperative learning should always be accompanied by other instructional strategies like whole class introductions and reflections which should be led by the teacher. Without special attention to low-achieving students, they may profit less from cooperative learning than their more able counterparts. The curriculum materials should be special designed for guided co- construction.

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