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.
Pupils need to be able to identify what is the same and what is different. This may be in terms of how something is represented using different apparatus (an example of conceptual variation) or within questions which are offered to pupils (procedural variation).
Conceptual variation
- provides pupils with different perspectives and experiences of maths concepts.
Procedural variation provides the opportunity
- for practice (intelligent rather than mechanical);
- to focus on relationships, not just the procedure;
- to make connections between problems.
Procedural variation provides a process for formation of concepts stage by stage through varying problems in a rich manner.
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)