1.  Accessible Mathematics

“Without question, one of the most common responses I have when sitting in the back of a mathematics class is screaming under my breath, “Draw a picture!” or “Use a number line!” or “Ask them what it looks like!”.  The failure to capture the mathematics being taught with a picture that helps students visualize what is going on is one of the most serious missed opportunities I observe.”

P 19 Accessible Mathematics 10 Instructional Shifts that Raise

Student Achievement by Steven Leinwand, former president

 of the National Council of Supervisors of Mathematics


2.  Learning and Teaching Early Math - The Learning Trajectories Approach

“There are different types of images, and they range from helpful to harmful, depending on their nature and the way children use them.  High-achieving children build images with a conceptual and relational core….low achieving children’s images tend to be dominated by surface features.

(p. 128) by Douglas Clements

3.  Paying Attention to Spatial Reasoning

“By making students aware of visualization and providing opportunities to practise and develop this skill, we give students yet another strategy to rely on when problem solving.” p. 21


4.  Link to Visualization Game


5.  Representations Ministry Webcast


6.  YouCubed

“Researchers even found that after four 15-minute sessions of playing a game with a number line, differences in knowledge between students from low-income backgrounds and those from middle-income backgrounds were eliminated”.


7.  Mathies


8.  Number Sense Routines

Sample chapter


Number Sense Routines


9. Cathy Fosnot - Landscape of Representations

From: Learning to Support Young

Mathematicians at Work by Fosnot et al.


10.  Principals to Action Ensuring Mathematical Success for All

NCTM principle:

Establish mathematics goals to focus learning  Effective teaching of mathematics establishes clear goals for the mathematics that students are learning, situates goals within learning progressions, and uses goals to guide instruction.  p. 10.


11.  Solve Me Mobiles -Game


12.  Alex Lawson Monograph