Exponential Function in Physics Education from the view of Knowledge in Pieces Theory

Learning is deeply rooted in the social environment of pupils and can flourish in a well-designed optimal learning environment in schools. Participative teaching-learning requires activities set in many different contexts, developing the grain-size pieces of knowledge and chaining of the fragments by causal chaining, time sequences and mathematical similarities. Based on the Knowledge-in-Pieces theory by diSessa, we focus on the development of the ability to think in terms of the exponential function, in Physics education from the age of 12. Main ideas are supported by experience with one activity with a bouncing ball designed for pupils at the age of 12. The activity is focused on topics such as measuring quantity, unit, method of measurement. Pupils propose which features of the ball can be investigated and measured. After this introduction, a quantity related to the bouncing is put forward in the activity. It is a dimensionless quantity, which pupils can express as a percentage. Pupils empirically investigate the bouncing of a ball. In the extension, at a higher age, the graph of maximal height vs the number of bounces, pupils discover the same shape they have seen in a water-cooling experiment. The activity was tested on a small sample of pupils, and some interesting results have been noticed. At the end of this contribution, we offer a list of other contexts naturally involving the exponential shape graph applicable in science education.