Computer technology and complex problem solving: Issues in the study of complex cognitive activity

Goals and plans organize much of complex problem solving behavior and are o ften inferable from action sequences. This paper addresses the strengths an d limitations of inferring goals and plans from information that can be der ived from computer traces of software used to solve mathematics problems. W e examined mathematics problem solving activity about distance, rate, time relationships in a computer software environment designed to support unders tanding of functional relationships among these variables (e. g., distance = rate x time; time = distance/ rate) using graphical representations of th e results of simulations. Ten adolescent-aged students used the software to solve two distance, rate, time problems, and provided think-aloud protocol s. To determine the inferability of understanding from the action traces, c oders analyzed students' understanding from the computer traces alone (Trac e-only raters) and compared these to analyses based on the traces plus the verbal protocols (Trace-plus raters). Inferability of understanding from th e action traces was related to level of student understanding how they used the graphing tool. When students had a good understanding of distance, rat e, time relationships, it could be accurately inferred from the computer tr aces if they used the simulation tool in conjunction with the graphing tool . When students had a weak understanding, the verbal protocols were necessa ry to make accurate inferences about what was and was not understood. The c omputer trace also failed to capture dynamic exploration of the visual envi ronment so students who relied on the graphing tool were inaccurately chara cterized by the Trace-only coders. Discussion concerns types of scaffolds t hat would be helpful learning environment for complex problems, the kind of information that is needed to adequately track student understanding in th is content domain, and instructional models for integrating learning enviro nments like these into classrooms.