An innovative diagnostic instrument for assessing students’ reasoning in quadratic functions

Reasoning refers to the capacity for critical thinking, problem-solving, and adapting to new ideas independently of prior knowledge, and it is fundamental to the learning process. However, existing assessments in quadratic functions tend to emphasise procedural accuracy rather than reasoning processes, limiting teachers’ ability to evaluate students’ conceptual understanding. This study aimed to develop and validate a reasoning-based assessment instrument grounded in the Structure of the Observed Learning Outcome (SOLO) taxonomy to evaluate the reasoning levels of Form Four students. The instrument utilizes a superitem test format, focusing on four reasoning processes, recognizing patterns, manipulating symbols, drawing logical inferences, and making generalizations across the content domains of quadratic expressions, equations, and graphs. A pilot study was conducted with 100 Form Four students from four secondary schools in Penang. Data were analyzed using the Rasch Partial Credit Model through WINSTEPS software to examine the instrument's psychometric properties. Findings from the pilot study confirmed the instrument's high degree of measurement consistency, yielding a personal reliability of 0.90 and an item reliability of 0.95. The separation indices further indicated that the instrument could effectively distinguish between different levels of student ability and stable item difficulty. While the results demonstrated that students could successfully navigate unistructural and multistructural tasks, they revealed significant challenges at relational and extended abstract levels. This study provides a validated diagnostic tool for educators to identify specific reasoning gaps and informs the development of differentiated instructional strategies to foster higher-order thinking in the secondary mathematics curriculum.