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Research based Teaching The relationship between theory and practice Lisser Rye Ejersbo Lisser Rye Ejersbo, Learning Lab Denmark, DPU

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The Guiding Principles On the in-service course, each teaching session is based on a particular theoretical concept from the research literature. The theoretical concept is transformed into practical activities so that –the theoretical concept is made into a tool; –the teachers can use the method in their own classes; –the teachers’ tacit knowledge becomes apparent; –room for reflection is shaped along with the activities. In the preparation phase, theory precedes activities; in the practical phase, activities precede theory. Lisser Rye Ejersbo, Learning Lab Denmark, DPU

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Three Theoretical Concepts Radford and Puig (2007): Syntax and Meaning as Sensuous, Visual, Historical forms of Algebraic Thinking. Educational Studies in Mathematics 66: 145-164. Voigt J. (1996): Negotiation of Mathematical Meaning in Classroom Processes: Social Interaction and Learning Mathematics. In L.P. Steffe et al (eds): Theories of Mathematical Learning (21-50). Mahwah, New Jersey: Lawrence Erlbaum Associates, Publisher. Yackel E., Cobb P. (1996): Sociomathematical norms, argumentation, and authonomy in mathematics. Journal for Research in Mathematics Education 27, No.4, 458- 477. Lisser Rye Ejersbo, Learning Lab Denmark, DPU

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A Task Golden Apples A prince picked a basketful of golden apples in the enchanted orchard. On his way home, he was stopped by a troll who guarded the orchard. The troll demanded payment of one-half of the apples plus two more. The prince gave him the apples and set off again. A little further on, he was stopped by the second troll guard. This troll demanded payment of one-half of the apples the prince now had plus two more. The prince paid him and set of again. Just before leaving the enchanted orchard, a third troll stopped him and demanded one-half of his remaining apples plus two more. The prince paid him and sadly went home. He had only two golden apples left. How many apples had he picked? (Driscoll, 1999, p. 7) Lisser Rye Ejersbo, Learning Lab Denmark, DPU

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Solutions on the blackboard Lisser Rye Ejersbo, Learning Lab Denmark, DPU

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Different Solutions S-I rest 2 + 2 = 4 4 x 2 = 8 8 +2 = 10 10 x 2 = 20 20 + 2 = 22 22 x 2 = 44 Start S-II ½ + 2 = 24 ½ + 2 = 12 ½ + 2 = 6 = 2 44 208 S-III 2 + 2 + 4 + 2 + 10 + 2 + 22 44 S-IV ((((2 + 2) 2) + 2) 2) + 2) 2 = 44 Lisser Rye Ejersbo, Learning Lab Denmark, DPU

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Results and Discussion What happened for whom: The students The teacher educator The researcher Lisser Rye Ejersbo, Learning Lab Denmark, DPU

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Questions for further discussions Does anyone benefit from the GP? If so, who? Reflection on ‘Reflection in action’: How to prepare the unpredictable? Lisser Rye Ejersbo, Learning Lab Denmark, DPU

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Algebra I Unit 1: Solving Equations in One Variable

Algebra I Unit 1: Solving Equations in One Variable

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