Construction of Three-Tier Diagnostic Test for Identifying Student Misconceptions in Exponential Properties

Abstract

Misconceptions are considered the most detrimental errors. A mathematics topic that students commonly experience misconceptions is in understanding exponential properties. This study aims to develop a three-tier diagnostic test. The development methodology follows a 3D model, Define, Design, and Develop. The resulting test comprises both essay and multiple-choice questions. Expert validation indicates that the essay questions are deemed suitable for use, with an 84.24% validation rate and a total of 20 questions. For the multiple-choice format, 9 questions meet moderate validity criteria, while 11 questions achieve high validity. Subsequent limited trial analysis, considering validity, reliability, difficulty, and discriminant power, identifies 8 questions as suitable for identifying student misconceptions in exponential properties. The construction of these questions consist of four types of misconceptions, generalisation, notation, spesialisation, and language. Reffering to exponential properties, the test item was developed asking students to apply the properties on real numbers.