Detecting Unsolvable Algebra Word Problems

When do students detect algebra word problems with missing information, and how do they do it? To determine whether such detection operates automatically or requires conscious effort and attention, this study manipulated whether a hint was provided that problems might be unsolvable. A signal detection analysis revealed that the hint resulted in a large improvement in the detection of unsolvable problems, implying that many individuals possess the means to detect missing information but that conscious effort is required for those means to be deployed. Participants with moderate mathematical ability had good success at detecting missing information when given the hint, but only when the problems had familiar cover stories. High math ability individuals were successful regardless of the cover story's familiarity. In addition, participants were more likely to conclude that a solvable problem was unsolvable when the hint was provided, when the problems' cover story was unfamiliar, and with the passage of time. As a result, problem solving of solvable problems was sometimes abandoned prematurely.