## OSK: Scenario 1

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.…

## OSK: Scenario 2

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…

## Use of terminology

‘Good’ examples Demonstrate knowledge of the correct mathematical terms & their precise meanings Correct use of mathematical terms and evidence of efforts to teach these terms Use alternative ways & more precise words to describe shapes for example, if child says ‘round’ then suggest ‘curved’ while linking new word to child’s word or words Link use of alternative ways of saying things, e.g.,1/4  can be called  ‘one quarter’ and ‘one fourth’ Add the correct term to help children express what they mean, e.g. Child says threes when describing thirds; child says10 teacher adds ‘centimetres’ Clarity around use of correct terminology when discussing different forms of all four operations on number Precise use of mathematical symbols ‘Bad’ examples Calling a parallelogram a ‘rectangle pulled out of shape’ Calling a sphere a…

## UT: Scenario 1

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…

## ATB: Scenario 1

Scenario: Holly teaching probability Country: USA Grade (student age): Grade 4 (age 9-10) Contributed by: Tracy Weston, The University of Alabama, USA Context –curricular, professional, other As is the case in the United States, North Carolina has state mandated goals and objectives for mathematics instruction at each grade level.  The North Carolina Standard Course of Study (NCSCOS) indicates that in grade 4 students are to “maintain” skills in permutation and combinations from Grade 3, which state “the learner will understand and use simple probability concepts,” which are further explained as determining the number of permutations and combinations of up to three items and solving probability problems using permutations and combinations. (NCSOS). This school used the EnVisions curriculum, as mandated by the district (local authority).  Students in this school were not…

## ATB: Scenario 2

Scenario: Eoin revising perimeter and area concepts Country: Ireland Grade (student age): 6th class (age 11-12 years) Contributed by: Dolores Corcoran, St Patrick’s College, Drumcondra, Ireland Context – national, curricular, professional, other While espousing a reform approach with the mandated development of mathematics process skills, the Irish primary mathematics curriculum is relatively specific in that content to be taught is divided into five mathematical strands (number, algebra, measures, shape and space and data and chance). These are further divided into strand units with lists of content objectives (followed by very brief exemplars) specified for each strand for each class level over the eight years of Irish primary schooling. Mathematics textbook series from one of three different publishing companies are currently available in Irish schools and these are ubiquitous in Irish…

## COP: Scenario 1

Scenario: Maeve discussing the use of formal standard algorithms Country: UK Grade (student age): Pre-service teacher Contributed by: Gwen Ineson, Brunel University, UK Context – professional The session described below took place in week five of a one year postgraduate teacher training programme.  Trainees had not completed either of their sustained school experiences but they had undertaken an observation period of two weeks in primary classrooms as preparation for the course.  They had received 14 hours of mathematics input, which included an overview of the national curriculum, planning and assessment as well as subject knowledge relating to calculation, measures and shape. A feature of the course is the strong emphasis on a range of calculation approaches for the number operations. It would be useful to explain what is in the…

## COP: Scenario 2

Scenario: Eleanor discussing approaches to helping pupils solve a multiplication problem Country: UK Grade (student age): Primary Contributed by: Gwen Ineson, Brunel University, UK Context – professional Eleanor was at the end of her one year graduate pre-service teacher training course and had completed all of her sustained school experience.  She was interviewed at the end of her programme about her approaches to calculation and about her approaches to teaching calculation.  The scenario below involves the multiplication of 2-digit numbers. Scenario Eleanor was asked what her approach would be to help pupils working on multiplication of 2-digit numbers.  The specific examples are 52 x 34 and 3.4 x 4.9. Interviewer:     What strategies would you use to teach your pupils to solve the following problem: 52 multiplied by 34?   Eleanor:…