The students were asked to think-aloud whilst they solved three task types. Thirty-eight students were randomly assigned to one of the software boxes in an experimental design where all audio and video data were collected via a web-conference remote observation method. The effect of mathematics confidence on students' approaches and performance was also considered. Three approaches that students may undertake when solving the tasks were investigated: students' processing levels, their software exploration and their self-explanations. This research investigated students' performance and their approaches to solving three mathematical task types when assigned to the software boxes. The glass-box and open-box software modes are often recommended over the black-box software to help understanding but there is limited research comparing all three. Three mathematical software modes are investigated in this thesis: black-box software showing no mathematical steps glass-box software showing the intermediate mathematical steps and open-box software showing and allowing interaction at the intermediate mathematical steps.
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