MrDingMaths

Research Map

8 min read

Research map of educational practice and cognitive science

Overview

This collection contains interconnected research notes on educational practice, cognitive science, and teaching methodology. The research is grounded in cognitive load theory and memory science, focusing on evidence-based instructional methods and their practical classroom application.

Core thesis: Learning occurs through changes in long-term memory. Working memory has a limited capacity of approximately four elements, so instruction must be designed to accommodate this constraint through explicit teaching, worked examples, and systematic practice.

Research orientation: This collection defends knowledge-based, explicitly taught curricula against progressive or discovery-based approaches, drawing on cognitive science research and classroom implementation studies.

Foundation concepts

These core concepts provide the basis for the research:

  • Cognitive Load Theory - The central theoretical framework explaining how working memory limitations constrain learning
  • Memory - The two-component architecture (working and long-term memory) that underlies all learning
  • Learning - Defined as change in long-term memory, distinct from performance
  • Schema - How knowledge organises into interconnected networks in long-term memory
  • Prior Knowledge - The foundation upon which new learning builds

Thematic categories

1. Cognitive science foundations

Theoretical basis for instructional design:

2. Core instructional methods

Evidence-based approaches to teaching:

3. Cognitive effects and phenomena

Specific research findings that inform instruction:

Memory and practice effects:

Instructional design effects:

Presentation effects:

4. Assessment and feedback

Monitoring and responding to student understanding:

5. Classroom management and behaviour

Creating conditions that enable learning:

6. Classroom techniques and micro-practices

Specific tactical implementations:

Questioning and participation:

Listening and communication:

Problem design:

7. Pedagogical philosophies and curriculum approaches

Competing educational philosophies and their critiques:

8. Subject-specific applications

Domain-specific pedagogies and debates:

Mathematics:

Literacy:

General:

9. Student development and individual differences

How students develop and what affects their learning:

Psychological foundations:

Cognitive development:

Individual needs:

Common errors:

10. Historical figures and theoretical traditions

Key thinkers and their contributions:

11. Research literacy and critical thinking

Understanding research quality and common errors:

12. Specialised topics

Additional areas of focus:

Conceptual hierarchy

The research contains dependencies between concepts that affect the order in which they are best understood:

Foundational theory (level 1)

These concepts explain the cognitive architecture that constrains all learning:

  1. Memory - Two-component memory system
  2. Cognitive Load Theory - Working memory limitations
  3. Learning - Change in long-term memory
  4. Schema - Knowledge organisation

Core principles (level 2)

These principles show how teaching responds to cognitive constraints:

  1. Prior Knowledge - Learning builds on existing schemas
  2. Experts and Novices Think Differently - Experience changes cognition
  3. Element Interactivity - Task difficulty and cognitive load

Instructional methods (level 3)

Evidence-based teaching approaches that apply these principles:

  1. Explicit Teaching - Systematic direct instruction
  2. Worked Examples - Demonstrating solution processes
  3. Practice - Consolidating knowledge
  4. Scaffolding - Supporting complex learning

Implementation techniques (level 4)

Specific classroom techniques that deploy these methods:

  1. Check for Understanding - Monitoring learning
  2. Cold-Call, Mini-Whiteboards - Assessment tools
  3. Retrieval Practice - Strengthening memory
  4. Classroom Management - Creating learning conditions

Refinement and context (level 5)

Deeper understanding that refines practice:

  1. Expertise Reversal Effect - Adapting to learner expertise
  2. Responsive Teaching - Adjusting to student needs
  3. Culture of Error - Creating safe learning environments

Key learning pathways

Different entry points depending on focus:

For understanding instructional design:

  1. Cognitive Load Theory
  2. Worked Examples
  3. Expertise Reversal Effect
  4. Element Interactivity
  5. Split-Attention Effect, Redundancy Effect, Modality Effect

For implementing explicit teaching:

  1. Explicit Teaching
  2. I Do, We Do
  3. Check for Understanding
  4. Worked Examples
  5. Scaffolding

For improving assessment:

  1. Retrieval Practice
  2. Spacing Effect
  3. Diagnostic Questions
  4. Mini-Whiteboards
  5. Formative Assessment

For building classroom management:

  1. Classroom Management
  2. Routines, Rules, Norms
  3. Script Language of Behaviour
  4. Relationships and Regulation
  5. Culture of Error

For understanding mathematics teaching:

  1. Maths Wars
  2. Procedural Alongside Conceptual
  3. Concrete Pictorial Abstract
  4. Fluency
  5. Problem-Solving