To gain a better understanding of the process through which technology users become technology creators, we designed a paper-based, tangible Turing Machine and introduced it to 54 teenage students. The information collected through tinkering tasks and a questionnaire is discussed both via statistics and qualitative analysis. This initial study suggests that simple paper tangibles and tinkering have a place in future, technology-enhanced learning, and that central technological concepts can be discussed on the basis of low-cost tabletop-like games. We also notice a general interest in the historical development of technologies, that seems to enhance motivation and participation.