Mathematical thinking of undergraduate students when using three types of software

Abstract

The research investigates how conceptual understanding of mathematics is promoted when using three types of software: black-box (no mathematical intermediate steps shown), glass-box (intermediate steps shown) and open-box (interaction at each intermediate step). Thirty-eight students were asked to think-aloud and give detailed explanations whilst answering three types of tasks: mechanical (mostly procedural), interpretive (mostly conceptual) and constructive (mixture of conceptual and procedural). The software types had no impact on how students answered the mechanical tasks; however students using the black-box did better on the constructive tasks because of their increased explorations. Students with low maths confidence resorted to using real-life explanations when answering tasks that were application related