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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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Foundation

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

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

AP: Scenario 1

Scenario: Finding three fractions that adds up to one whole Country: Norway Grade (student age): Grade 7 (age 12-13) Contributed by: Ove Gunnar Drageset, University of Tromsoe, Norway Context The teacher has five years teaching experience. The lesson is halfway

KQ Team October 8, 2012January 26, 2024 Awareness of purpose No Comments Read more

AP: Scenario 2

Scenario: Franca solving a story problem with the students. Country: Italy Grade (student age): Year 4 (age 9-10) Contributed by: Marco Bardelli, University of Padova, Italy Context – public primary school, national curriculum The Italian National Curriculum emphasizes the development

KQ Team October 8, 2012January 26, 2024 Awareness of purpose No Comments Read more

AP: Scenario 3

Scenario: Jim teaching construction of bar charts from tally charts Country: UK Grade (student age): Year 6 (age 9-11) Contributed by: Fay Turner, University of Cambridge, UK Context – national, curricular, professional, other Jim was a student teacher in the

KQ Team October 8, 2012January 26, 2024 Awareness of purpose No Comments Read more

Adherence to textbook

KQ Team October 2, 2012January 26, 2024 Adherence to textbook No Comments Read more

Identifying errors

KQ Team September 20, 2012January 26, 2024 Identifying pupil errors No Comments Read more

TUP: Scenario 3

Scenario: Amy teaching a lesson about counting Country: UK Grade (student age): Reception/Kindergarten (age 4-5) Contributed by: Fay Turner, University of Cambridge, UK Context – national, curricular, professional, other This lesson took place during the second half of Amy’s first

KQ Team September 2, 2012January 26, 2024 Theoretical underpinning of pedagogy No Comments Read more

OSK: Scenario 1

Scenario: Lucy teaching trigonometric ratios Country: UK Grade (student age): Year 10 (age 14-15) Contributed by: Anne Thwaites, University of Cambridge, UK Context – national, curricular, professional, other The National Curriculum for mathematics in England introduces trigonometric relationships in Key

KQ Team August 10, 2012January 26, 2024 Overt display of subject knowledge No Comments Read more
  • « Previous
  • 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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