Abstract:

The assessment of student learning has traditionally emphasized objective performance measures, often overlooking the role of metacognition in the learning process. However, students’ ability to reflect on and evaluate their own knowledge is an essential component of self-regulated learning and academic growth. With this in mind, this study proposes a Metacognitive Calibration Assisted Model (MCAM), aimed at exploring the relationship between students’ self-perception and their actual performance in educational contexts.

The model brings together statistical analysis and fuzzy logic to offer an interpretable way of identifying discrepancies between perceived and actual knowledge. Methodologically, it combines quartile analysis, histograms, bar charts, and scatter plots to examine how performance is distributed and how calibration patterns evolve across different stages, such as pre-test, test, and post-test. While quartile analysis helps reveal performance groupings, histograms and bar charts provide complementary views at both group and individual levels.

To better understand the relationship between perceived and actual knowledge, scatter plots are used as a visual aid. In this representation, students positioned below the reference line tend to overestimate their performance, whereas those above it tend to underestimate it. Points located near the line suggest a more balanced calibration. This type of visualization makes it easier to observe learner profiles and identify possible metacognitive biases.

An important element of the model is the fuzzy inference system, which allows discrepancy levels to be classified in a gradual and more flexible way. Instead of relying on rigid categories, numerical differences are translated into linguistic labels such as low, moderate, and high discrepancy. This approach better captures the continuous nature of cognitive miscalibration and makes the results easier to interpret in educational settings.

In addition, a Receiver Operating Characteristic (ROC) curve is used to examine decision thresholds and to better understand the trade-off between true positive and false positive rates when identifying miscalibration patterns. By varying cutoff values, it becomes possible to select decision criteria that are more balanced and context-appropriate.

Results based on simulated data suggest that the model can effectively distinguish between different learner profiles, including tendencies toward overestimation and underestimation. The combination of statistical techniques and fuzzy logic offers a comprehensive yet accessible framework for analyzing student learning.

Overall, the findings reinforce the importance of considering not only students’ performance but also how they perceive their own learning. The proposed model contributes to the development of more diagnostic and adaptive assessment approaches, helping educators identify learning gaps and encourage metacognitive awareness. Future studies could explore its application in real educational settings, as well as the use of normalized data to further improve robustness and generalization.

Keywords:

Metacognition, Learning Assessment, Fuzzy Logic, Technology-Enhanced Learning, Dunning-Kruger Effect.