Skip to content
The Knowledge Quartet

The Knowledge Quartet

a theoretical framework for the analysis and development of mathematics teaching

Menu

  • Home
  • Introduction
  • Dimensions
  • Scenarios
  • References
  • Contact

Author: KQ Team

DT Scenario 1

Scenario: Laura teaching column multiplication Country: UK Grade (student age): Year 5 (age 9-10) Contributed by: Tim Rowland, University of Cambridge, UK Context: national, curricular, professional, other At the time when this lesson was recorded, mathematics in primary schools was

KQ Team August 3, 2017January 26, 2024 Teacher demonstration Read more

Knowledge Quartet Framework

This is an image that we use to indicate our conceptualization of and the connections between the four dimensions in the Knowledge Quartet.

KQ Team November 16, 2012January 26, 2024 Uncategorized Read more

Foundation

This category consists of knowledge, beliefs and understanding acquired in the academy, in preparation (intentionally or otherwise) for their role in the classroom. Such knowledge and beliefs inform pedagogical choices and strategies in a fundamental way. The key components of

KQ Team November 16, 2012January 26, 2024 Uncategorized Read more

Transformation

This category concerns knowledge-in-action as demonstrated both in planning to teach and in the act of teaching itself. At the heart of this category, is Shulman’s observation that the knowledge base for teaching is distinguished by “ … the capacity

KQ Team November 15, 2012January 26, 2024 Uncategorized Read more

Teacher Demonstration

KQ Team November 14, 2012January 26, 2024 Teacher demonstration Read more

Connection

This category binds together certain choices and decisions that are made for the more or less discrete parts of mathematical content. It concerns the coherence of the planning or teaching displayed across an episode, lesson or series of lessons. Our

KQ Team November 13, 2012January 26, 2024 Uncategorized Read more

Contingency

This category concerns classroom events that are almost impossible to plan for. In commonplace language it is the ability to ‘think on one’s feet’. In particular, the readiness to respond to children’s ideas and a consequent preparedness, when appropriate, to

KQ Team November 12, 2012January 26, 2024 Uncategorized Read more

MCP: Scenario 1

Scenario: Christiana teaching division by multiples of ten Country: Cyprus Grade (student age): Year 5 (age 10-11) Contributed by: Marilena Petrou Context – national, curricular, professional, other Christiana was a final year university student in a 4 year teacher prapeartion

KQ Team November 11, 2012January 26, 2024 Making connections between procedures Read more

MCP: Scenario 2

Scenario: Jess teaching about the relationship between multiplication and division within the context of a lesson about solving word problems Country: UK Grade (student age): Year 5 (age 9-10) Contributed by: Fay Turner, University of Cambridge, UK Context – national,

KQ Team November 11, 2012January 26, 2024 Making connections between procedures Read more

MCP: Scenario 3

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 November 11, 2012January 26, 2024 Making connections between procedures 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)
Copyright © 2025 The Knowledge Quartet. All rights reserved. Theme Spacious by ThemeGrill. Powered by: WordPress.