In time I hope to add specific pedagogical notes to each activity explaining the thought process behinds each sequence of questions and what you, the teacher, may choose to draw students’ attention to. Likewise, on the Practice, Rule, Pattern and Demonstration pages you will find pedagogical notes about delivering the various activity types.

However, I just wanted to make one general – and hopefully obvious – point here.

It is important to note that an intelligently varied sequence of examples or practice questions will not magically make students understand something better. Whilst the structure and sequencing of the questions, together with the explicit processes of reflect, expect, check certainly makes it far more likely that students’ attention will be focused upon the thing you want them to focus on, there is certainly no guarantee of this. These examples and questions need to be accompanied by a pedagogy that supports them.  Anne Watson describes this point beautifully:

This is important for the way that variation theory is seen within the mathematics education field, because a superficial look at it might suggest that the theory as applied to design is purely cognitive and concerned only with what is presented to learners in order for them to construct meaning individually through inductive reasoning. The addition of teachers’ gestures and speech to the mix indicates a need to think also about attention and the disposition of learners to  discern what is intended.

For me it is the teacher pausing when answering a question, and the way they explicitly indicate which feature of the previous example they are focusing on when considering the new answer. It is the carefully planned discussion that follows the completion of an exercise, avoiding unnecessarily vague questions such as “what did you notice?” in favour of more pertinent ones like “how did the answer to the previous question help you answer this one?”, or “which answer surprised you the most?”. It is these teacher actions that give intelligently varied sequences of examples and questions their power.

And in terms of creating and presenting the activities, this image by Ben Gordon sums it up better than I ever could: