## Responding to students' ideas

Responding to Students’ Ideas (RSI)   This code includes the ability to make cogent, reasoned and well-informed responses to unanticipated ideas or suggestions from students These teachers’ responses are to students’ contributions to the (mathematical) development of the lesson. These contributions are typically oral, but could be written. Our analysis of the data available to us identifies three sub-types of triggers in this category: student’s response to a question from the teacher; student’s spontaneous response to an activity or discussion; student’s  incorrect answer - to a question, or as a contribution to a discussion. Furthermore, our data show that the teacher’s response is one of three kinds: to ignore; to acknowledge but put aside; to acknowledge and incorporate.

## RSI: Scenario 1

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 The scenario described below comes from a lesson taught by Elsa. Elsa, a final year university student in a teacher preparation programme, was teching problem solving using Schema-Based Instruction with a…

## RSI: Scenario 2

Scenario: Róisín teaching equivalence of fractions Country: Ireland Grade (student age): 3rd class (age 8-9) Contributed by: Dolores Corcoran, St Patrick’s College, Drumcondra, Ireland Context – national, curricular, professional, other The Irish primary curriculum proposes that “the child should be enabled to identify fractions and equivalent forms of fractions with denominators 2, 4, 8 and 10” first among a list of six objectives for children in third class. Róisín, who was a second year Bachelor of Education student, with a relatively strong background in mathematics devised an ambitious lesson to develop an understanding of equivalent fractions with this class of 21 girls in the third week of her spring teaching placement. The lesson lasted 40 minutes. Scenario Róisín set the lesson in a pizzeria, with five friends sharing a “ten…

## RSI: Scenario 3

Scenario: Christiana teaching average Country: Cyprus Grade (student age): Year 6 (age 11-12) Contributed by: Marilena Petrou Context – national, curricular, professional, other Christiana was a final year university student in a teacher praparation programme , Teacher training in Cyprus involves taking part in a 4 year university degree in elementary education. Teachers are trained to teach all subjects of the school curriculum and during their last year the take part in a school based placement where they teach a series of lessons in all subjects throughout the year. With the completion of the programme the teachers are qualified to teach. The lesson took place in a school-based placement towards the end of her four-year teacher preparation. Scenario Christiana, was teaching mean with a Year 6 (pupils age 11-12) class.…

## RSI: Scenario 4

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…

## RSI: Scenario 5

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. Heidi 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 Heidi, a graduate student-teacher, was teaching in an open entry school (pupil age 11-18) in a village in the UK. The school divides the year group into maths sets (by ability) and Heidi was teaching one of…