Numbers and variables often follow the same principles of arithmetic operations, yet numbers can be computed to a value whereas variables cannot. We examined the effect of symbols—numbers versus variables—on middle school students’ problem-solving behaviors in a dynamic algebra notation system by presenting problems in numbers (e.g., 3+5−3) or variables (e.g., x+y−x). We found that compared to problems presented in numbers, students attempted the problems more times and took more total steps when the problems were presented in variables. We did not find differences in pre-solving pause time or strategy efficiency on the two types of problems, indicating that students might notice problem structure in both types of problems. The results have implications for research on cognitive processes of symbols as well as the design of educational technologies.

In the development and analysis of interventions designed to improve student learning, it is important to consider potential influences of student behavior. Unproductive behaviors, such as “gaming the system,” have been studied for their potential impacts on the measurement and assessment of student knowledge within these interventions. Conversely, less attention has been given to factors that may influence gaming behavior. Gaming may be attributed to student-level traits, but could also be a temporary state brought on by systemic causes such as the perceived difficulty or presentation of a problem. We leverage prior research in this area to develop a data-driven measure of gaming and address whether this behavior occurs as a “state” or “trait” within a randomized controlled trial. We find that these factors are differential across the two study conditions, suggesting that context contributes to the underlying causes of gaming behavior.