Development and implementation of a web-based mathematical misconception diagnostic tool

The aim of this study is to develop a web-based assessment tool to diagnose middle school students' misconceptions regarding exponentiation. Accordingly, the Web-Based Mathematics Misconception Diagnostic Tool (WEBMKTA) was designed within the framework of design-based research and its development, improvement, and implementation processes were evaluated. In the first phase, a 30-item multiple-choice test was prepared to identify misconceptions about exponentiation, administered to 569 students, and found to have a KR-20 reliability coefficient of 0.73. Content validity was ensured through expert review. The test was then administered online via WEBMKTA; the system analyzed the responses and produced diagnostic results as "no misconception," "learning deficiency," or "misconception," identifying misconceptions categorically. Interviews conducted with 79 students revealed that the diagnoses were accurate in 88.6% of cases. In addition, system adjustments were made regarding user interfaces, the administrator panel, and exam screens. In the second phase, the improved system was re-administered, and students' feedback was used to evaluate accessibility and ease of use. As a result, WEBMKTA was determined to be a functional assessment tool capable of accurately diagnosing misconceptions about exponentiation, with user-friendly features, flexible test assignment, and category-based reporting capabilities. The system's diagnostic findings revealed that students experienced significant difficulties in their conceptual understanding of exponentiation. In particular, misconceptions such as "multiplying the base and the exponent" and "expressing as a positive/negative integer" were found to be prevalent across multiple categories. Moreover, when dealing with more abstract concepts such as zero exponents and negative exponents, students often failed to evaluate rote-learned rules within a conceptual framework, frequently making incorrect generalizations such as "a⁰ = a" or "(-a)ⁿ = -aⁿ." It is considered that web-based diagnostic systems can also be adapted to other mathematics topics.