Students learning with digital mathematical tools – three levels of instrumental genesis

There is a widespread aphorism that if your only tool is a hammer every problem looks like a nail. The solution to mathematical problems does not always follow the same pattern but may require the use of multiple tools or tool components. It is therefore important as a learner to be aware of the variety of possibilities that are available and to be able to select and use the optimal tool in a problem situation. However, a previously unknown tool is not directly operational for a learner. For the solution of existing problems, only tools whose operation is known can be used. This text examines the ways in which differences in the progress of instrumental genesis are expressed and when digital tools support learners' thinking. This raises the following research question: How far must instrumental genesis be advanced until it can be used with confidence. Three different mathematical problems and a think-aloud-study have been used to identify different steps of the instrumental genesis