Assessing first-year engineering students' pre-university mathematics knowledge: Preliminary validity results based on an item response theory model

Abstract

The importance of students’ prior knowledge to their current learning outcomes cannot be overemphasised. Students with adequate prior knowledge are better prepared for the current learning materials than those without the knowledge. However, assessment of engineering students' prior mathematics knowledge has been beset with a lack of uniformity in measuring instruments and inadequate validity studies. This study attempts to provide evidence of validity and reliability of a Norwegian national test of prior mathematics knowledge using an explanatory sequential mixed-methods approach. This approach involves use of an item response theory model followed by cognitive interviews of some students among 201 first-year engineering students that constitute the sample of the study. The findings confirm an acceptable construct validity for the test with reliable items and a high-reliability coefficient of .92 on the whole test. Mixed results are found on discrimination and difficulty indices of questions on the test with some questions having unacceptable discriminations and require improvement, some are easy, and some appear too tricky questions for students. Results from the cognitive interviews reveal the likely reasons for students' difficulty on some questions to be lack of proper understanding of the questions, text misreading, improper grasping of word-problem tasks, and unavailability of calculators. The findings underscore the significance of validity and reliability checks of test instruments and their effect on scoring and computing aggregate scores. The methodological approaches to validity and reliability checks in the present study can be applied to other national contexts.