Validation of cognitive models for subtraction of time involving years and centuries

Abstract

Years and Centuries are the measurement units used to quantify a longer time duration, while subtraction is the operation required to determine the duration based on two given time points. However, subtraction of time is a difficult skill to be mastered by many elementary students. To identify the root cause of the student's failure in performing subtraction involving the unit of time, we developed and validated the three cognitive models related to this skill by conducting a descriptive study which involved 119 Grade Five students from three Malaysian elementary schools. The cognitive diagnostic assessment developed based on the three cognitive models was used to elicit the participants' responses. Then, Attribute Hierarchy Method and Classical Test Theory were employed to analyse the data. The findings indicated that the hierarchical structures of all cognitive models are supported by the student's responses. The three student-based cognitive models were also highly consistent with the corresponding expert-based cognitive models. The cognitive models developed could guide diagnostic assessment development and diagnostic inference making.