 representing operations performed on numbers in different ways – for example, in concrete, pictorial, and symbolic ways.
– Focusing on the Fundamentals of Math – A Teacher’s Guide, p.4
Video Selections
These curated videos have been selected to help you gain a deeper understanding of the above selection from “Focusing on the Fundamentals of Math – A Teachers Guide”.
Mathematical Representations: Rethinking Representations (2:56)
From "Beyond Pictures Numbers and Words"
Spatializing Instruction and Learning  Overall Description (3:36)
From "Spatial Reasoning in Number Sense and Numeration"
Primary: Linking Language to NonVerbal Reasoning (4:35)
From "Spatial Reasoning in Number Sense and Numeration"
Scaling Up or Down  Key to Proportional Reasoning (5:27)
From "Spatial Reasoning in Number Sense and Numeration"
Fosnot: All Models are Not Created Equal (4:33)
From "Leaders in Educational Thought: Mathematics 2013"
Modelling Fractions (1:55)
From "Leaders in Mathematical Thinking 2016"
Tools Reveal Understanding of Operations (3:37)
From "Spatial Reasoning in NSN, NonVerbal Reasoning"
Text Resources
This curated list of documents have been selected to help you gain a deeper understanding of the above selection from “Focusing on the Fundamentals of Math – A Teachers Guide”. Each link will take you directly to the relevant section within the document.
Fractions Across the Curriculum – Capacity Building Series 

A Guide to Effective Instruction in Mathematics Gr 13 Number Sense and Numeration 

A Guide to Effective Instruction in Mathematics Gr K3, Patterning and Algebra 

A Guide to Effective Instruction in Mathematics, Gr K6, Number Sense and Numeration Vol 1, The Big Ideas 

Paying Attention to Algebraic Reasoning 

Paying Attention to Fractions 

Paying Attention to Spatial Reasoning 

A Guide to Effective Instruction in Mathematics Gr 46, Number Sense and Numeration, Vol 3, Multiplication 

A Guide to Effective Instruction in Mathematics Gr 46, Number Sense and Numeration, Vol 4, Division 