Influence of Proportional Number Relationships on Item Accessibility and Students’ Strategies

Proportional reasoning is important to students’ future success in mathematics and science endeavors. More specifically, students’ fluent and flexible use of scalar and functional relationships to solve problems is critical to their ability to reason proportionally. The purpose of this study is to investigate the influence of systematically manipulating the location of an integer multiplier—to press the scalar or functional relationship—on item difficulty and student solution strategies. We administered short-answer assessment forms to 473 students in grades 6–8 (approximate ages 11–14) and analyzed the data quantitatively with the Rasch model to examine item accessibility and qualitatively to examine student solution strategies. We found that manipulating the location of the integer multiplier encouraged students to make use of different aspects of proportional relationships without decreasing item accessibility. Implications for proportional reasoning curricular materials, instruction, and assessment are addressed.