Student problem solving in the context of a dynamic mathematics environment (DME) has previously been investigated primarily through the lens of whether or not the student could complete a problem-solving task. Herein, we investigate what trajectories students employ in the realms of mathematics, technology, and problem solving as they attempt to complete tasks and which of these trajectories are more helpful than others. Notably, it was determined that these trajectories are idiosyncratic, nonlinear, and iterative and that, while some trajectories help problem solving, others harm the problem solving process. Among other findings, it was determined that student access to technology may not assist their mathematical problem solving and may at times hinder it even further.