Towards Personalized Mathematics Learning: Developing an Instrument to Map Students' Mathematical Content Knowledge (MCK) about Function as a Foundation for Permutation Group Concepts

Abstract

Mathematics learning at the college level requires an in-depth knowledge of the prerequisite concepts that have been previously studied. Function is a fundamental concept that serves as an introduction to understanding the permutation group. This study describes the development of an instrument that measures the students’ mathematical content knowledge (MCK) level about function. The processes of development consist of four steps that include: identifying aspects of knowledge about function, developing the questions, checking the content validity, and improving the quality of questions. Four aspects were synthesized that include: basic function knowledge, operation in function, composite function, and properties of function. Ten questions were arranged as the initial product then were validated by two experts in terms of the content. Based on their suggestions, spelling errors were corrected, question sentences were simplified, the number of questions was decreased, the information about the curve was added, and to guarantee that the developed instrument measured what it should be measuring. The final instrument consisted of six questions. The readability test was conducted by the students to see the practicality of the instrument. The result of this study shows that the developed instrument can be used to measure the level of students’ MCK about function.