MCP: Scenario 3

Making connections between procedures
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 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 school (pupil age 11-18) in a small town in the UK. The school divides each year into…
Read More

RSI: Scenario 5

Responding to students' ideas
Scenario: Heidi revising percentages Country: UK Grade (student age): Year 8 (age 12-13) Contributed by: Anne Thwaites, University of Cambridge, UK Context – national, curricular, professional, other The National Curriculum for mathematics in England includes work on fractions, decimals and percentages in Key Stage 3 (years 7-9, pupil age 11-14). Heidi was revising the four operations with fractions, before moving on to discuss some word problems related to percentages. Heidi 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 Heidi, a graduate student-teacher, was teaching in an open entry school (pupil age 11-18) in a village in the UK. The school divides the year group into maths sets (by ability) and Heidi was teaching one of…
Read More

CUR: Scenario 2

Choice of representations
Scenario: Umay teaches the limit concept Country: Turkey Grade (student age): K 12 (age 17-18) Contributed by: Semiha KULA, Esra BUKOVA GÜZEL, University of Dokuz Eylül, Turkey Context – national, curricular, professional, other Secondary school lasts four years in Turkey, between the ages 15 and 18. According to the national secondary school mathematics curriculum, the limit concept is thought during the last year of secondary school. Teacher education program for secondary mathematics education is a five year program; the first three-and-half years are undergraduate studies and remaining year and half is a non-thesis masters’ program. In these programs, subject matter knowledge, general pedagogical knowledge, and pedagogical content knowledge oriented lessons are taught. There are also lessons related to school-based placement in the last three semesters. Umay is a pre-service teacher…
Read More

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.…
Read More

RAT: Scenario 2

Responding to the (un)availability of tools and resources
Scenario: John teaching properties of 3-D shapes Country: UK Grade (student age): Year 9 (age 13-14) Contributed by: Anne Thwaites, University of Cambridge, UK Context – national, curricular, professional, other The National Curriculum for mathematics in England includes solutions of quadratic equations in Key Stage 4 (years 10-11, pupil age 14-16). These pupils were near the end of year 9 and John had been working on graphical representation of quadratic expressions in a previous lesson and then on ‘completing the square’ [i.e. expressing in an equivalent form ], as specified in the 16-18 pupil age curriculum. John was a graduate pre-service teacher, and the lesson took place in a school-based placement towards the end of his one-year teacher preparation. Scenario John was teaching in an open entry secondary school (pupil…
Read More