It has been recognised that the general lack of enjoyment of institutional mathematics learning at the secondary level is one of the basic reasons behind the bad reputation of mathematics in society. Increasing students' motivation to learn mathematics through enjoyment and playing, especially in their free time, might therefore be a relevant research focus. This paper considers robot-based investigation spaces for students at the secondary level and the transition from secondary to tertiary level education (or from compulsory to non-compulsory mathematics education) which allow them to explore the facility of real and virtual environments to create behaviours which are both meaningful to them and which naturally motivate a greater use of mathematical language to describe and predict these behaviours more precisely. The value of these environments is assessed from the perspective of the challenges of instrumental orchestration. (Contains 1 table and 4 figures.)