## Theoretical underpinning of pedagogy

One aspect of Mathematical Knowledge for Teaching is a teacher’s use of a theoretical foundation to guide instructional decisions, rather than relying on imitation of another teacher or trial and error. Therefore, it is important for teachers to know factors that are significant in the teaching and learning of mathematics (Rowland et al., 2009; Ball, Lubienski & Mewborn, 2001). Descriptors/Aspects of TUP (Theoretical Underpinning of Pedagogy) "Strong" examples: Draws on knowledge of well-established results in mathematics education research regarding the way pupils learn the topic in hand to underpin the planning and/or delivery of the lesson (whether this is implicit through lesson observation or revealed explicitly later through post-observation interview). Draws on knowledge of well-established results in mathematics education research regarding pupils’ misconceptions to underpin the planning and/or delivery of…

## TUP: Scenario 1

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…

## TUP: Scenario 2

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…

## TUP: Scenario 3

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…