# Variation

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

**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**

**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)**

**Re****search suggests that mathematical thinking occurs when students are thinking about mathematical structure.**

**Conceptual Variation**

**Conceptual Variation**

**Multiple Representations**

**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.