Exploring unitizing strategies in middle school students: Insights from number line, fraction circle, and word problem tasks

The concept of a unit is fundamental to mathematics, deeply intertwined with the notion of "one" and other key mathematical constructs. This study investigates middle school students' strategies for "unitizing" — defining and using units — across three different tasks: number lines, fractional circles, and word problems. The research employs an explanatory mixed-methods approach, combining quantitative and qualitative data. First, a total of ninety-one students in grades 5, 6, and 7 completed a Fraction Test to evaluate their achievement and a Unitizing Test to assess their strategies. Tasks include identifying fractions on number lines, using fractional circles, and solving word problems. Selected students then participated in interviews to explore their reasoning processes in greater depth. Nine students across grade levels and performance levels attended the interviews. The findings revealed that students struggled with the Unitizing Test, as their solutions reflected a notably higher proportion of none or unknown strategies. For others, two main strategies had emerged, namely Effective Unitizing and Procedural Unitizing. Students' use of either strategy varied for different grade levels and task types. Finally, the study highlighted the relationship between students' fraction performance and their unitizing strategies, suggesting that students with higher fraction achievement levels were able to use more sophisticated and successful unitizing strategies, and students with lower fraction achievement levels were more likely to show none or unknown strategies. These findings altogether can provide valuable insights into improving mathematical curricula by highlighting the diverse ways students conceptualize and use units.