Lecture Notes Flashcards

Page 1: Five Principles of Counting

• Key Ideas

  • Counting is more than learning ABCs; it involves understanding five principles or rules.

  • Understanding can be implicit (doing without realizing) or explicit (articulating the process).

• Five Principles of Counting

  • Stable Word Order

  • One-to-One

  • Cardinal Principle

  • Order Irrelevance

  • Abstract Principle

  • Stable word order and one-to-one are often explicitly taught to children.

Early Arithmetical Strategies

• Overview

  • Children develop strategies for counting collections to perform addition and subtraction.

  • Progression from counting one by one to more sophisticated group counting strategies.

• Stages of Development

  • Count by Ones

  • Count by Groups (Facile)

Page 2: Strategies for Counting

• Key Ideas

  • Initial addition/subtraction involves counting each item (counting by ones).

  • Strategies progress from naive to sophisticated:

    • Emergent - cannot count a collection.

    • Perceptual - count using concrete materials or fingers.

    • Figurative - count without concrete materials.

    • Counting-On - start counting from an existing number.

  • Teaching goal: transition from counting by ones to counting in groups.

• Facile Counting Strategies

  • Focus on using properties of numbers for efficient arithmetic tasks using groups/chunks.

  • These strategies are flexible and enhance ease of solving arithmetic problems.

Page 3: Learning Progressions

• Introduction

  • Focus on three sub-elements in Number Sense and Algebra:

    • Counting Processes (CPr)

    • Number Place Value (NPV)

    • Additive Strategies (AdS)

    • Multiplicative Strategies (MuS)

  • Teaching numeracy builds a strong mathematical foundation.

  • NSW Government support for teaching numeracy effectively includes:

    • Continuum for student strategies.

    • Syllabus linked to continuum.

    • Assessments: SENA1 and SENA2.

  • Familiarize with Learning Progressions; complete knowledge isn’t required now.

  • Explore Early Years Learning Framework for preschool mathematics.

Page 4: CPA Framework

• Key Ideas

  • CPA: Concrete-Pictorial-Abstract; a teaching framework applicable in all study areas.

  • Developed by Jerome Bruner (Enactive-Iconic-Symbolic framework).

• Representation Types

  • Concrete: Hands-on tasks using manipulatives with no abstraction.

  • Pictorial: Uses images to represent concrete items, slightly abstracted.

    • Example: Drawing a triangle without specifying color/size.

  • Abstract: Involves symbols for general concepts; can be challenging if introduced too early.

    • Important to understand the meaning behind symbols (e.g., '4' for four-ness).