OSK: Scenario 1

Overt display of subject knowledge
Scenario: Lucy teaching trigonometric ratios Country: UK Grade (student age): Year 10 (age 14-15) Contributed by: Anne Thwaites, University of Cambridge, UK Context – national, curricular, professional, other The National Curriculum for mathematics in England introduces trigonometric relationships in Key Stage 4 (years 10 and 11, pupil age 14-16). Lucy was reviewing the idea of a trigonometric ratio with her class, before moving on to discuss how to calculate the size of an angle in a right-angled triangle, given the lengths of two sides. Lucy was a graduate pre-service teacher, and the lesson took place in a school-based placement towards the end of her one-year teacher preparation. Scenario Lucy, a graduate student-teacher, was teaching in an open entry secondary school (pupil age 11-18) in a small town in the UK.…
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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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