+ Coherence

Connecting new ideas to concepts that have already been understood, and ensuring that, once understood and mastered, new ideas are used again in next steps of learning- all steps being small steps.

+ Representation and Structure

Representations used in lessons expose the mathematical structure being taught. These representations are practical and pictorial models. The aim being that students can do the maths without recourse to the representation.

+ Mathematical Thinking

If maths concepts are to be understood deeply, they must not merely be passively received but must be worked on by the student: thought about, reasoned with and discussed with others.

+ Fluency

Quick and efficient recall of facts and procedures and the flexibility to move between different contexts and representations of mathematics. Procedural fluency is the ability to apply procedures accurately, efficiently, and flexibly; to transfer procedures to different problems and contexts; to build or modify procedures from other procedures; and to recognize when one strategy or procedure is more appropriate to apply than another.

+ Variation

Varying the way a concept is initially presented to students, by giving examples that display a concept as well as those that don’t display it. Also, carefully varying practice questions so that mechanical repetition is avoided, and thinking is encouraged.