Mathematical Development 5-8 Years: Numeracy and Mathematics Study Notes

Introduction

  • Lecturer and tutor: Mistel Ball
  • Focus: Mathematical development for ages five to eight in numeracy and mathematics.
  • Lecture format: May be organized into one long part or two to three smaller parts.
  • Purpose: To break down large ideas so students are not overwhelmed.

Weekly Structure

  • Each lecture concludes with a reflective activity.
  • Students are expected to:
    • Bring a response or answer for the tutorial discussion.
    • Watch the lectures and look for the reflective activity before attending tutorials.
    • Read recommended texts and articles in preparation for discussions.

Expectations for Lectures and Tutorials

  • Visuals highlight the importance of being open-minded and exploratory as educators.
  • Openness is crucial for:
    • Embracing diversity in children’s backgrounds (cultural and linguistic).
    • Adapting to rapidly changing educational practices.
    • Responding flexibly to young learners' unpredictable nature.
    • Fostering inclusive environments where all children feel valued.
    • Encouraging creativity and collaborating with families and colleagues.
  • Key qualities to model for children: empathy, resilience, and lifelong learning.

Explorer Mindset in Education

  • Importance of seeing educators as explorers:
    • Approaching teaching with curiosity and creativity.
    • Supporting children's investigation of the world.
    • Embracing roles as co-explorers of learning journeys.
  • Benefits of this mindset include:
    • Encouraging experimentation with new ideas.
    • Adapting to the evolving needs of learners.
    • Fostering environments where inquiry is celebrated, and mistakes are learning opportunities.
    • Empowering children and educators to model curiosity and a love for learning.

Estimation Task Introduction

  • Introduction of a mathematical estimation task from the Multiplicity Lab.
  • Dismisses formal testing as the only method of understanding students' abilities; advocates for conversation as a means of engagement.
  • Estimation tasks provide insights into:
    • Students' approaches to problem-solving and their number sense.
    • Understanding through conversation and observation rather than tests.

Estimation Task Mechanics

  • Example scenario:
    • Children shown an image of scattered buttons and asked to estimate how many are visible.
  • Challenges children face:
    • Variability in button size and overlap.
    • Uneven distribution and varying density.
  • Estimation Strategies:
    1. Direct counting where visible and guessing the rest.
    2. Instinctual estimation without a clear strategy.
    3. Benchmarking using groups of ten for building estimation (e.g., drawing circles around clusters).
    4. Dividing the image into sections, counting one part, and multiplying to estimate the total.
  • Each strategy reveals different insights into students' mathematical reasoning and comfort levels.

Course Requirements Overview

  • Weekly Layout:
    • Lectures: Fully online (must be watched before tutorials).
    • Tutorials: Face-to-face attendance is mandatory.
    • Rolls will be taken.
    • Email in advance for absence; missing over 15% may lead to a non-completion mark.
  • Assessment Structure:
    • Four main assessments with detailed discussions in tutorials.
    • Weekly readings on Blackboard (1-3 readings weekly based on content).
    • Expectation to have completed readings before attending tutorials to facilitate discussion.

Assessment Details

  1. Competency Test:

    • Timing: Week 3 during tutorial.

  2. Assessment Recording Tool:

    • Due: End of Week 6, March 29.
    • Discussion and samples in tutorials.

  3. In-Class Presentation and Weekly Planning Document:

    • Big assignment due in Week 11.
    • Further discussion in tutorials prior to submission.
    • Presentation scheduled for Week 11.

  4. Mathematical Concepts Test:

    • Timing: Week 13 tutorial.
    • Review key ideas in the previous week’s lecture.

Weekly Breakdown

  • Weekly focus includes:
    • Key concepts and assessment timelines.
    • Information available on Blackboard for further clarity on discussions and assessments.