The central idea of teaching with variation is to highlight the essential features of a concept or idea through varying the non-essential features

Variation is not the same as variety – careful attention needs to be paid to what aspects are being varied (and what is not being varied) and for what purpose.

NCETM The 5 Big Ideas of Teaching for Mastery

Procedural variation provides the opportunity

  • for practice (intelligent rather than mechanical);

  • to focus on relationships, not just the procedure;

  • to make connections between problems.

Intelligent Practice

When constructing a set of activities or questions it is important to consider what connects the examples; what mathematical structures are being highlighted?

Students are encouraged to avoid mechanical practice and, instead, to practice the thinking process (intelligent practice)

Research suggests that mathematical thinking occurs when students are thinking about mathematical structure.

Conceptual Variation

Multiple Representations

  • Multiple representations allow students to gain a deeper understanding of the mathematical structure.

  • Comparing multiple methods allows students make connections and use the most appropriate method with fluency.

  • Comparing different representations uncovers the structure of the mathematics and allows students to make generalisations.

Carefully planned variation reveals mathematical structure.