Making Mathamatical Thinking Visible

Making Mathematical Reasoning Visible

A district-wide numeracy framework designed to help educators understand how
mathematical reasoning develops over time.

Part-Whole Understanding

K-9 Numeracy Learning Continuum and Teacher Guide

Mathematical understanding grows through uncovering relationships among concepts, strategies, representations, and ways of reasoning. To help make those relationships visible, I developed the Part-Whole Understanding teacher guide as part of a larger K-9 Numeracy Learning Continuum. The guide helps educators recognize indicators of conceptual understanding and understand how reasoning develops across grade levels. Practical sample activities and assessment activities were also a key feature of the guide, making an all-in-one go-to guide for elementary teachers.

My Role in the Project: Project Leader • Learning Architect • Continuum Designer

What was hidden

Relationships among concepts were not obvious.
Teachers lacked a shared language for numeracy.
Differences between strategies and algorithms were often unclear.
Student thinking was difficult to interpret.
Development and connections across grades was difficult to see.

What became visible

Shared definitions and terminology were provided.
Reasoning was made visible through visual models, representations and strategies.
Indicators of Learning were made visible though developmental progressions
Connections across grade levels were linked and made more explicit.

What became possible

Richer professional conversations took place within and across grades.
Teacher's gained confidence in their own mathematical understanding.
Greater coherence emerged across the district.
Student thinking became more visible and easier to discuss, interpret, and respond to.
Assessment became more responsive, focusing on understanding rather than simply correctness.