Development of an Item Bank for Measuring Students’ Conceptual Understanding of Real Functions

Abstract

It is known that students have many misconceptions about concepts related to function. By discovering misconceptions using an appropriate measurement instrument, we can determine what changes we need to make in the real functions curriculum to improve learning outcomes. Therefore, we designed an item bank for measuring conceptual understandings of real functions with items that require ability to move from one representation of the same concept to another. By surveying university professors, we conducted an expert judgment and content validity of the test. Altogether 36 multiple-choice items based on concepts related to real function with a single correct answer and three distractors have been field-tested by means of a paper and pencil survey, which included 80 freshman students from the Faculty of Science at the University of Sarajevo. By surveying students, we checked technical characteristics of items and their cognitive validity. Results from surveying university professors and students show that the test meets the requirements of content and cognitive validity. Results from the item analysis (item difficulty index, item discrimination index, and point-biserial coefficient) and test analysis (test reliability and Ferguson’s delta) show that 32 out of 36 items have good psychometric characteristics, and they are reliable for measuring students’ understanding and skills in introductory mathematics courses at universities. We noticed that students have a poor understanding of certain concepts, regardless of the representation, and that there is no coordination between representations of the same concept.