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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

UIM: Scenario 2

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

KQ Team September 10, 2012January 26, 2024 Use of instructional materials No Comments Read more

UIM: Scenario 3

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

KQ Team September 10, 2012January 26, 2024 Use of instructional materials 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

Deviation from lesson agenda

Contingency, Deviation from Agenda Descriptors / aspects of DA Good examples: When the teacher displays deeper subject matter knowledge to enhance pupils’ understanding When the teacher displays deeper subject matter knowledge in taking a pupil’s remark as a starting point

KQ Team September 2, 2012January 26, 2024 Deviation from lesson agenda No Comments Read more

CUR: Scenario 1

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

KQ Team August 14, 2012January 26, 2024 Choice of representations No Comments Read more

DS- Scenario 1

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 August 11, 2012January 26, 2024 Decisions about sequencing No Comments Read more

CUR: Scenario 2

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,

KQ Team August 11, 2012January 26, 2024 Choice of representations No Comments Read more

CUR: Scenario 3

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 August 11, 2012January 26, 2024 Choice of representations 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

OSK: Scenario 2

Scenario: Mirella teaching two-digit divisions by invariantive law Country: Italy Grade (student age): Year 3 (age 7-8) Contributed by: Marco Bardelli, University of Padova, Italy Context – public primary school, national curriculum In Italy two-digit divisions is a topic that

KQ Team August 10, 2012January 26, 2024 Overt display of subject knowledge No Comments 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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