AP: Scenario 2

Awareness of purpose
Scenario: Franca solving a story problem with the students. Country: Italy Grade (student age): Year 4 (age 9-10) Contributed by: Marco Bardelli, University of Padova, Italy Context – public primary school, national curriculum The Italian National Curriculum emphasizes the development of students’ number sense through realistic mathematical problems where the estimate of numbers can be performed. The mental calculation has taken great importance  and the students should manage the control of their reasoning.  Moreover the National Curriculum underlines that students should be able to solve mathematical problems with different strategies. Franca is teaching volume measures to her pupils. She has already explained the litre and its submultiples as a measure of capacity. In this lesson she wants to show her pupils how to use mental calculation in a story problem…
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OSK: Scenario 2

Overt display of subject knowledge
Scenario: Mirella teaching two-digit divisions by invariantive law Country: Italy Grade (student age): Year 3 (age 7-8) Contributed by: Marco Bardelli, University of Padova, Italy Context – public primary school, national curriculum In Italy two-digit divisions is a topic that is usually taught in year 4. The new national curriculum in Italy  (2007), named “Indicazioni per il Curriculum,“ gives just some directions to the teachers about the competences that must be reached in each subject matter at the end of third, fifth and eighth grade of schooling and about the skills the  students have to manage in order to reach those competences. At the end of the third year of schooling  knowledge of the algorithm of the division with two-digit and remainder is not required. Students have to know how…
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