Most of the existing student response systems, such as clickers, have limited input capabilities, typically only offering students a multiple-choice selection. In some instances, students can input a numerical or textual response. However, mathematical equations, diagrams, etc. are all beyond the capabilities of such systems. This paper proposes and presents a novel multi-platform smart device-based student response system, called UniDoodle, that allows for a more generic and flexible input. This system consists of a student application that allows for freeform input through sketching capabilities, a lecturer application that allows easy viewing of multiple sketch-based responses and a cloud-based service for co-ordinating between these two applications. In essence, students can now respond to a question posed by the lecturer using sketches and, hence, mathematical equations, circuit diagrams, graphs, etc. are all possible on the UniDoodle system. In addition, the lecturer can now gain a richer and more useful insight to the students' understanding of the relevant material. This paper also evaluates the UniDoodle system in a large class of first year Engineering Mathematics students. Details of the UniDoodle system, the evaluation process and the feedback obtained are all presented within.