Numbers vs. Variables: The Effect of Symbols on Students’ Math Problem-Solving

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