ABSTRACT
The mathematical themes of course make use of actions which draw upon natural human powers, and so there are multiple overlaps and interconnections. There are also mathematical actions in problem-solving which draw upon human powers but which are not exclusive to mathematics. The tasks themselves do not suggest how a particular action can support mathematical activity. A really good way to augment the doing of mathematical actions is to try to express the relationships to themselves and, if possible, to someone else. Thus it is useful to bring to articulation for oneself what mathematical themes are likely to emerge from work on a task, what mathematical actions are likely to be fruitful and what mathematical concepts or procedures are intended to be encountered. The teacher can be prepared to draw attention to the possibility of factoring and be in the midst of some form of scaffolding and fading with respect to some mathematical activity.
