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The Knowledge Quartet

The Knowledge Quartet

a theoretical framework for the analysis and development of mathematics teaching

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Author: KQ Team

Theoretical underpinning of pedagogy

One aspect of Mathematical Knowledge for Teaching is a teacher’s use of a theoretical foundation to guide instructional decisions, rather than relying on imitation of another teacher or trial and error. Therefore, it is important for teachers to know factors

KQ Team November 2, 2012January 26, 2024 Theoretical underpinning of pedagogy Read more

TUP: Scenario 1

Scenario: John teaching properties of 3-D shapes Country: UK Grade (student age): Year 9 (age 13-14) Contributed by: Anne Thwaites, University of Cambridge, UK Context – national, curricular, professional, other The National Curriculum for mathematics in England includes properties of

KQ Team October 22, 2012January 26, 2024 Theoretical underpinning of pedagogy Read more

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

KQ Team October 13, 2012January 26, 2024 Responding to students' ideas Read more

TUP: Scenario 2

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

KQ Team October 12, 2012January 26, 2024 Theoretical underpinning of pedagogy Read more

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

KQ Team October 11, 2012January 26, 2024 Responding to students' ideas Read more

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

KQ Team October 11, 2012January 26, 2024 Responding to students' ideas Read more

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

KQ Team October 11, 2012January 26, 2024 Responding to students' ideas Read more

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,

KQ Team October 11, 2012January 26, 2024 Responding to students' ideas Read more

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

KQ Team October 11, 2012January 26, 2024 Responding to students' ideas Read more

MCC: Scenario 1

Scenario: Bella discussing connections Country: UK Grade (student age): Trainee teacher Contributed by: Gwen Ineson, Brunel University, UK Context –professional Bella is at the end of her one year post-graduate teacher training course.  She has completed nineteen weeks of sustained

KQ Team October 11, 2012January 26, 2024 Making connections between concepts Read more
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  • Foundation (17)
    • Theoretical underpinning of pedagogy (4)
    • Awareness of purpose (3)
    • Identifying pupil errors (1)
    • Overt display of subject knowledge (2)
    • Use of mathematical terminology (2)
    • Adherence to textbook (3)
    • Concentration on procedures (2)
  • Transformation (15)
    • Teacher demonstration (2)
    • Use of instructional materials (4)
    • Choice of representations (3)
    • Choice of examples (6)
  • Connection (9)
    • Making connections between procedures (3)
    • Making connections between concepts (1)
    • Anticipation of complexity (3)
    • Decisions about sequencing (1)
    • Recognition of conceptual appropriateness (1)
  • Contingency (12)
    • Responding to students' ideas (6)
    • Deviation from lesson agenda (1)
    • Teacher insight (1)
    • Responding to the (un)availability of tools and resources (4)
  • Uncategorized (5)

Tags

Counting (1) Cyprus (5) Data (1) Fractions (8) Geometry (1) Ireland (2) Italy (2) Norway (6) Operations (6) Percentages (2) Problem Solving (2) Reception/Kindergarten (1) Secondary (5) Turkey (1) UK (14) USA (3)
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