Construction and Validation of a Test for Measuring Students’ Proportional Reasoning on Rates, Ratios, & Proportions

Abstract

This study aimed to develop and validate a proportional reasoning test (PRT) to measure students’ proportional reasoning skills on rates, ratios, and proportions in mathematics. The test items were carefully designed to reflect the aspects of proportional reasoning identified in the existing literature and aligned them to the instructional objectives as stated in the Kenya secondary mathematics curriculum. The test underwent different developmental processes to establish content-related validity before it was piloted. The pilot was conducted on a sample of 45 form three students from one school in Kenya. The results showed an acceptable internal consistency level (Cronbach’s α= .83). The item analysis revealed that all the items had a moderate difficulty level ranging from .39 to .50. The discrimination index for most items ranged from .22 to .44. The findings suggest that the PRT is a valid and reliable instrument that can be used to measure the domain-specific skills on proportional reasoning. More specifically, the instrument can be used to measure the impact of a formative assessment intervention on students’ achievement on proportional reasoning skills.