Operations – Knowledge Quartet

11Nov 2012 by Tracy Weston No Comments

MCP: Scenario 2

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…

11Sep 2012 by Tracy Weston No Comments

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…

10Sep 2012 by Tracy Weston No Comments

UIM: Scenario 3

Use of instructional materials

Scenario: Christiana’s teaching multiplication by powers of ten Country: Cyprus Grade (student age): Year 4 (age 9-10) Contributed by: Marilena Petrou Context – national, curricular, professional, other In Cyprus textbooks are used on a daily basis in the classroom, and are produced by policy makers. The mathematics textbooks in Cyprus are year-based, and all students at a particular grade are taught the same mathematics for the same length of time from the same textbook. These textbooks are consistent with fundamental principles of constructivist views of learning and teaching mathematics. Activities are designed with the purpose of helping students to construct their own understanding of different topics, while teachers are seen as facilitators in the process of learning, whose aim is to create a teaching environment that supports exploration of different…

10Aug 2012 by Tracy Weston No Comments

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…

14Jun 2012 by Tracy Weston No Comments

CUE: Scenario 5

Choice of examples

Scenario: Suzy teaching multiplication methods Country: UK Grade (student age): Year 5 (age 9-10) Contributed by: Ray Huntley, Brunel University, UK Context – national, curricular, professional, other Suzy was reviewing ideas about multiplication of tens and hundreds with her class, before moving on to discuss other examples which extended the method into thousands. Suzy was a final year undergraduate pre-service teacher, and the lesson took place in a school-based placement towards the end of her three-year teacher preparation. Scenario Suzy, an undergraduate student-teacher, was reviewing multiplication methods with a Year 5 (pupil age 9-10) class. She was teaching the children to multiply using the ‘grid method’, and it is the third lesson of a sequence of lessons on multiplication that is described here. It opens with a worked example, 34 x…

10Jun 2012 by Tracy Weston No Comments

RAT: Scenario 3

Responding to the (un)availability of tools and resources

Scenario: Chloe teaching a mental arithmetic strategy Country: UK Grade (student age): Year 1/2 (age 5-7) 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 and a related curriculum framework. In the early years, in keeping with Dutch RME principles, arithmetic emphasises children’s mental methods, and introduces a number of related strategies. The focus for this lesson is subtracting near-multiples of 10 (specifically, 9, 11, 19, 21) by subtracting 10 (or 20) and then adjusting by 1. Chloë 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 The objectives of the lesson…