In this paper we aim to contribute to the process of networking between theoretical frames in mathematics education by means of forging connections between Constructionism and Instrumental Theory to discuss a design for instrumentalisation. We specifically focus on instrumentalisation, i.e. the ways in which students make changes to digital artifacts and generate meanings in reference to these, as something which will not inevitably happen during activity with digital media. We discuss the issue of designing artifacts and corresponding activities in order to facilitate an instrumentalisation process which will be rich in the generation of mathematical meanings. We report findings from research aimed at shedding light on the meanings of angle in 3D space generated by 13 year olds pupils while using a specially designed Turtle Geometry microworld. The analysis indicates that connections between the two theories on the issue of designing for instrumentalisation enhances our efficiency to explore the links between tool design and students' instrumental genesis in technology-rich environments.