DT Scenario 1

Teacher demonstration
Scenario: Laura teaching column multiplication Country: UK Grade (student age): Year 5 (age 9-10) Contributed by: Tim Rowland, University of Cambridge, UK Context: national, curricular, professional, other At the time when this lesson was recorded, mathematics in primary schools was prescribed by a National Numeracy Strategy (DfEE, 1999) and a related curriculum framework. The framework suggests progression from mental methods to informal and "expanded" written methods, thence to standard, contracted algorithms. The key focus of this lesson was on teaching column multiplication of whole numbers, specifically multiplying a two-digit number by a single digit number. The intended method is a kind of staging-post between a transparent 'grid' method (see below) and the fully-contracted algorithm. Laura was a graduate pre-service teacher, and the lesson took place in a school-based placement towards…
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MCP: Scenario 2

Making connections between procedures
Scenario: Jess teaching about the relationship between multiplication and division within the context of a lesson about solving word problems Country: UK Grade (student age): Year 5 (age 9-10) Contributed by: Fay Turner, University of Cambridge, UK Context – national, curricular, professional, other Jess had completed a one year graduate teacher programme the previous year.  The lesson took place in the second term of her first year of teaching.  The curriculum guidance for England at this time (2006) gave an objective that stated pupils in year 5 should ‘understand the effect of and relationship between the four operations, and the principles (not the names) of the arithmetic laws as they apply to multiplication’.  The main objective for this lesson was ‘Choose and use appropriate number operations and appropriate ways of…
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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…
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TUP: Scenario 1

Theoretical underpinning of pedagogy
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 properties of 3D shapes in Key Stage 3 (years 7-9, pupil age 11-14) including surface area and volume of 3D shapes based on prisms. John had introduced the idea of surface area and volume of 3D shapes in a previous lesson and was moving on to consider the properties of a cylinder in this lesson. 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 age 11-18) in…
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TUP: Scenario 2

Theoretical underpinning of pedagogy
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. Having completed a mathematics degree, which included an optional mathematics education element, Heidi was a graduate on a pre-service training course. 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 secondary school (pupil age 11-18) in a village in the UK. The school…
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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…
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MCC: Scenario 1

Making connections between concepts
Scenario: Bella discussing connections Country: UK Grade (student age): Trainee teacher Contributed by: Gwen Ineson, Brunel University, UK Context –professional Bella is at the end of her one year post-graduate teacher training course.  She has completed nineteen weeks of sustained school experience and her most recent experience was in a year 1 class of five and six year olds.  She was engaging in a discussion about her mathematical subject knowledge for teaching and how she would respond to pupils encountering difficulty with various numerical problems.  Questions included subtraction of a two digit number from a three digit number (234 – 48), multiplication of two digit numbers (52 x 34), multiplication of decimals (3.4 x 4.9) and division of fractions (1 ¾ ÷ ½) . The transcript included below is an…
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AP: Scenario 3

Awareness of purpose
Scenario: Jim teaching construction of bar charts from tally charts Country: UK Grade (student age): Year 6 (age 9-11) Contributed by: Fay Turner, University of Cambridge, UK Context – national, curricular, professional, other Jim was a student teacher in the final term of a postgraduate teacher education course. During his final school placement, he was teaching a unit about data handling to a Year 6 class.  In a previous lesson he had shown them how to make tally charts to record the frequency of different phenomena. One of the displays in the classroom consisted of a number of different bar charts that the pupils had made previously.  At this time, curriculum guidance for mathematics in England suggested that pupils should be able to use tally charts by Year 4 and…
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AC: Scenario 2

Anticipation of complexity
Scenario: Chloe teaching strategies for subtracting 9, 11, 19 and 21 Country: UK Grade (student age): Year 1/2 (age 5-7) Contributed by: Fay Turner, University of Cambridge, UK Context – national, curricular, professional, other Chloe was a student teacher in the final term of a one year postgraduate teacher education programme.  The lesson took place during her final school placement.  In planning this lesson Chloe referred to curriculum guidance in the National Numeracy Strategy framework (DfEE, 1999) in place at that time.  A mental calculation strategy suggested for Year 2 in this guidance was ‘add/subtract 9 or 11: add subtract 10 and adjust by 1.  Begin to add/subtract 19 or 21: add/subtract 20 and adjust by 1’.  Chloe was following up a lesson in which her class had used these…
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TUP: Scenario 3

Theoretical underpinning of pedagogy
Scenario: Amy teaching a lesson about counting Country: UK Grade (student age): Reception/Kindergarten (age 4-5) Contributed by: Fay Turner, University of Cambridge, UK Context – national, curricular, professional, other This lesson took place during the second half of Amy’s first term teaching in a large city primary school.  It was a lesson with Amy’s Reception class about counting.  The national curriculum for England at this time (2006) put great emphasis in the early years on counting.  Two key objectives for pupils in their first formal year of school were that they should be able to: Say and use the number names in order in familiar contexts Count reliably up to ten everyday objects By the end of Year 1, pupils were expected to count up to 20 objects and to…
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