From Stated Knowledge to Certainty of Thought: A Study on Four-Level Tests in Mathematics Teaching
DOI:
https://doi.org/10.70232/jesds.v2i2.53Keywords:
Four-Level Diagnostic Test, Mathematics, Conceptual Misunderstandings, Confidence in Thought, Sustainability, Student AssessmentAbstract
Traditional approaches to assessment in mathematics are often limited to measuring final results, without providing sufficient insight into students’ cognitive processes and confidence in their answers. The Four-Tier Diagnostic Test (FTDT) represents an innovative assessment instrument designed to evaluate not only the correctness of knowledge but also students’ confidence levels, reasoning accuracy, and ability to distinguish between accurate understanding and misconceptions. This study aims to analyze the application of FTDT in mathematics teaching, focusing on identifying conceptual difficulties and the structure of students’ beliefs regarding their knowledge. The research was conducted with 70 lower secondary school students from “Heronjtë e Lumës” in Vërmica, Prizren, Kosovo, through a specially designed diagnostic instrument covering topics such as algebra, geometry, probability, and statistics. Data were analyzed using descriptive and inferential statistics, including Chi-square, Pearson correlation, and t-tests, supported by qualitative analysis of reasoning patterns. The results revealed that the FTDT enables a precise distinction between errors caused by lack of knowledge, uncertainty of thought, and persistent misconceptions. Students were classified into three cognitive profiles: those with stable knowledge, those with unstable knowledge, and those with strong misconceptions. A significant positive correlation (r = .66, p < .001) was found between confidence in answers and reasoning, confirming that confidence is a reliable indicator of conceptual stability. The findings demonstrate that FTDT serves as a valuable diagnostic and pedagogical tool for mathematics teachers, supporting the design of personalized teaching strategies and targeted interventions. This study contributes to the growing body of research emphasizing diagnostic assessment as a cornerstone for improving the quality and sustainability of mathematics education. Ultimately, the ability to gauge one’s certainty accurately is essential for making informed, sustainable decisions in complex, real-world problem-solving scenarios.
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