## Choice of Examples

Based on reviewing the original data that gave rise to the codes as well as the new scenarios contributed by our research group, we have generated the following descriptors or aspects of CUE: “Strong” examples of CUE: High cognitive demand Mathematically correct Realistic context and/or numbers Address (or at least don’t add to) misconceptions Numbers are selected intentionally Match the purpose of the lesson “Weak” examples of CUE: Low cognitive demand Wrong mathematically Not realistic context and/or number Encourage misconceptions Selected randomly (number selection) Don’t serve purpose of the lesson

## CUE: Scenario 1

Scenario: Alice teaching nth term of linear sequences Country: UK Grade (student age): Year 10 (age 14-15) Contributed by: Nicola Bretscher, King’s College London, UK Context –curricular, professional, other Alice was an experienced mathematics teacher, working at a private girls’ school. The year 10 group she was teaching had just sat their end of school-year exams. Alice noticed that the majority of the group had incorrectly answered a standard question on the nth term of linear sequences. This lesson was intended as a revision lesson of the topic to correct their mistake in preparation for the terminal GCSE[1] exam in year 11. Scenario Alice, an experienced mathematics teacher, was reviewing how to determine the nth term of a linear sequence with a Year 10 (pupil age 14-15) class. In their…

## CUE: Scenario 2

KNOWLEDGE QUARTET CODING MANUAL Scenario: McKenzie teaching problem solving 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 grades 4, “Students will solve relevant and authentic problems.” This school used the enVisions curriculum, as mandated by the district (local authority).  Students in this school were grouped by ability level for math instruction, and McKenzie’s class was the AG (academically gifted)/most advanced students of the five, fourth grade classes.  An objective present at both fourth and fifth grade that applied to this portion of…

## CUE: Scenario 3

Scenario: Solving problems using Schema-Based Instruction Country: Cyprus Grade (student age): Year 5 (age 10-11) Contributed by: Marilena Petrou Context – national, curricular, professional, other Schema-Based Instruction aims to develop students’ understanding of the basic relations found in arithmetic word problems (Marshall, 1995). Students are taught to map features of word problems onto problem schemata. Figure 1 illustrates the four schemas that are included in mathematics textbooks in Cyprus used to describe the semantic relations found in story problems, namely, ‘change’, ‘group’, ‘compare’, and ‘vary’ Figure 1: Schema- problems   Scenario Elsa, a final year university student in a teacher preparation programme, was teching problem solving using Schema-Based Instruction with a Year 5 (pupils age 10-11) class. The lesson took place in a school-based placement towards the end of her…

## CUE: Scenario 4

Scenario: Naomi teaching multiplication Country: UK Grade (student age): Year 4 (age 8-9) Contributed by: Ray Huntley, Brunel University, UK Context – national, curricular, professional, other Naomi was an undergraduate pre-service teacher, and the lesson took place in a school-based placement towards the end of her three-year teacher preparation. She was working from lesson plans from the Hamilton Trust, a UK based group which provides training and curriculum materials in English, mathematics and science, including detailed unit plans for mathematics with objectives, teaching ideas, resources and so on. Scenario In her lesson, Naomi sets out a number of examples so that children can use a grid method to multiply a 2-digit number by a single digit. The starter example is 34 x 2 which is presented in grid form so…

## CUE: Scenario 5

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…