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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Transformation

Dimensions, Transformation
This category concerns knowledge-in-action as demonstrated both in planning to teach and in the act of teaching itself. At the heart of this category, is Shulman’s observation that the knowledge base for teaching is distinguished by “ … the capacity of a teacher to transform the content knowledge he or she possesses into forms that are pedagogically powerful” (1987, p. 15). As Shulman indicates, the presentation of ideas to learners entails their re-presentation (our hyphen) in the form of analogies, illustrations, examples, explanations and demonstrations (Shulman, 1986, p. 9). This second category picks out behaviour that is directed towards a pupil (or a group of pupils) which follows from deliberation and judgement. Of particular importance is the trainees’ choice and use of examples presented to pupils to assist their concept…
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UIM: Scenario 1

Use of instructional materials
Scenario: Teaching of fractions Country: Norway Grade (student age): Year 5 (age 10-11) Contributed by: Ove Gunnar Drageset, University of Tromsoe, Norway Context The teacher has 35 years of experience as a teacher. The lesson is taught mid-way through the school year. The competence goals in the Norwegian curriculum are not formulated for each year, but are given after the completion of grade 4, 7 and 10. The competence goals regarding fractions after grade seven focus on calculations using positive and negative fractions, and placing fractions on a number line.   The teacher writes 1/10 on the blackboard and asks if someone knows another fraction of equal size. A student answers 10/100, and the teacher writes ‘=10/100’ to the right of 1/10. Then the teacher chooses to illustrate this by…
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UIM: Scenario 2

Use of instructional materials
Scenario: Teaching of fractions Country: Norway Grade (student age): Example 1 - year 7 (age 12-13) Contributed by: Ove Gunnar Drageset, University of Tromsoe, Norway Context The teacher in example one has 25 years of experience as a teacher. The lesson is taught mid-way through the school year. The competence goals in the Norwegian curriculum are not formulated for each year, but are given after the completion of grade 4, 7 and 10. The students have only met fractions like ½ and ¼ used in everyday situations prior to fifth grade.   The teacher helps one student with the task of comparing and finding the smallest fraction of ¼ and 5/8. She sits down and tells him to find the fraction bars.                …
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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…
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CUR: Scenario 1

Choice of representations
Scenario: Sharon teaching subtraction Country: UK Grade (student age): Year 4 (age 8-9) Contributed by: Ray Huntley, Brunel University, UK Context – national, curricular, professional, other Subtraction is taught to primary children as being either ‘take-away’ or ‘difference’, with various models and images used to help children understand the processes involved. In terms of finding a difference, the notions of ‘counting back’ or ‘counting on’ are often introduced, and the hundred square can be a useful image to assist with this process. Sharon, a final year undergraduate trainee was reviewing these ideas with her class, starting with subtracting single digits from 10, before going on to discuss other examples which extended the method into subtracting single-digit and  two-digit numbers from multiples of 10. Scenario Sharon was teaching a Year 4…
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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…
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CUR: Scenario 3

Choice of representations
Scenario: Hans teaching fractions greater than one Country: Norway Grade (student age): Year 5 (age 11-12) Contributed by: Bodil Kleve, Oslo and Akershus University College of Applied Sciences Context – national, curricular, professional, other In our present curriculum LK 06, competence aims for the subject are presented after year 2, year 4, year 7 and year 10. This lesson is from year five. With regard to fractions, competence aims after year 4 do not include any. After year 7 fractions are included in Competence aims for numbers and algebra: “The aim for the education is that the pupil shall be able to describe the place value system for decimal numbers, calculate with positive and negative whole numbers, decimal numbers, fractions and percentages, and place them on the real number line…
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