It is important for students to be explicitly taught how to use reasoning and logical justification to communicate their ideas effectively.

Developmental Stages of Mathematical Proficiency

Numeracy is more than number sense and procedural fluency. It is the foundation upon which we see and represent the world. Numeracy opens doors to creativity, connection, critical thinking, and lifelong learning. Viewing the stages of development as nested and inclusive of each other helps reinforce the idea that working on productive challenges at any stage of the continuum supports further growth and understanding in other areas. Learners typically approach new ideas by recognizing that they are grappling with something new and then making comparisons to the knowledge they already have about a topic. This act of grounding oneself is integral to the process of acquiring new skills and knowledge. Scaffolding instruction to effectively build from one stage to the next is a key part of developing a structured, cohesive, and robust numeracy program.

Numerate citizens have opportunities/solve problems/ find solutions using logic and reasoning. One way to visualize the development of numeracy is as a multi-step process with spatial reasoning and modelling as a central hub. Anchoring students’ learning to hands-on, real-world, and observable phenomena helps students to develop increasingly complex ways of thinking about mathematical ideas.

Concreteness Fading

Concreteness fading is an instructional method where learners are introduced to a concept through increasingly abstract representations, moving from concrete, tangible examples to more symbolic or generalized forms. This approach aims to enhance understanding and promote transfer of knowledge by first grounding the concept in familiar, concrete experiences and then gradually shifting to more abstract, symbolic representations. 

Key Vocabulary and Notation for Math K-9

Reinforcement of key vocabulary can support student success in mathematics. In addition to traditional print glossaries (English and French), teachers have access to interactive, illustrated glossaries as well as locally developed logic games and puzzles.

Authentic Tasks and Contextualized Learning Experiences

All activities that expand world knowledge (e.g. reading informational texts, learning new vocabulary, exploring new environments and places) are likely to be beneficial to the development of children's reasoning skills.

SD72 Teachers use a variety of critical thinking resources to teach reasoning and logical justification. Examples include Peter Liljedahl's Thinking Classroom approach, Carole Fullerton's "Good Questions", Number Talks, Esti-Mysteries, Open-Middle problems, University of Waterloo Problems of the Week, and Contextual Investigations (Math Labs).

All four key curricular competencies can be assessed when students are engaged in rich thinking tasks.

Many “Three-Act Tasks” combine both spatial and statistical reasoning

 Understanding & Solving: Understand contextualized problems

 Reasoning & Analyzing: Model mathematics in contextualized experiences

 Communicating & Representing: Use mathematical vocabulary; explain and justify mathematical ideas and decisions

 Connecting & Reflecting: Use mathematical arguments to support personal choices

Resources for Unpacking BCs Math Curricular Competencies: