# Animated questions

Sunday 8 May 2011

Dynamic geometry and similar dynamic software have been a major influence on my own understanding of mathematics and consequently my own teaching. Start with the notion that all squares actually meet the minimum requirements to qualify as all other quadrilaterals^{[1]}. How often does this notion upset students who somehow want rectangles and squares to be discretely different from each other? I suggest that a mathematical object or phenomenon is best described by its properties and that these properties can best be explored in a dynamic environment. The ability to bend, stretch, and explore a dynamic situation demands that we consider generalities and their limits where static representations provide us only a particular case. Why then, are so many questions in mathematics classrooms asked through a static, fixed and often printed medium? Developments in technology have prompted me to explore the setting of ‘Animated questions’ where students are shown short animations of particular mathematical phenomena and asked to explore and define them by attempting to recreate them. In this workshop I propose to engage the audience with a number of examples of these ‘animated questions’ exploring geometry, functions, sequences and more. In exploring the problems I hope the group is prompted to recognise the benefits of asking questions in this way in terms of exploring generality, engagement and problem solving.

I work in a school where students carry their own laptops with them at all times, which aids such experimentation, but this is not a prerequisite for being able to ask these questions. What it does do is make me increasingly curious about how long it will be before external assessment tools for mathematics will be set using technology as a medium and thus allowing a broader, more versatile style of questioning of which these ‘animated questions’ are just an example.

The above is the abstract for a session I am planning to run at the ICTMT 10 conference in Portsmouth in July.

#### Examples

The following are a few examples of such animations as described above. In each case, the question is essentially quite simple. Can you recreate the animation?

#### Activities

Please follow the links below to see some examples of how this can be done in the classroom.

Quadratic Movers - Learning about quadratics in a dynamic environment

Kaleidoscope - Investigating rotation in a dynamic environment

#### Footnotes

- 1. National variations in the definition of a trapezium or trapezoid do provide an interesting challenge to this notion

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