Expert-Based cognitive models vs theory-based cognitive models: Which cognitive models match students’ cognition on ‘Parallel and Perpendicular Lines’ Better?

Abstract

The cognitive model is a prominent element for supporting teachers' instructional needs regarding the confusing geometry topic named ‘Parallel and Perpendicular Lines’. Nonetheless, the mismatch between the derived cognitive models and the students’ cognition would threaten the validity of the diagnostic inferences made. While cognitive models could be developed by using different approaches, this study evaluated the model-data fit of the expert-based cognitive models which were developed by conducting expert task analysis and the theory-based cognitive models which were developed by reviewing the available theory. The study was conducted by adopting a cross-sectional research design. A total of 1 069 Grade Four students were selected by using two-stage cluster sampling. The findings indicated that the average model-data fit increased with the abilities of students for both theory-based and expert-based cognitive models on ‘Parallel and Perpendicular Lines’. Nonetheless, the theory-based cognitive models have a better model-data fit compared to the expert-based cognitive models. The findings imply the significance of the available theory of cognition in guiding the development of cognitive models. With satisfactory model-data fit, the theory-based cognitive models could serve as a guide for making diagnostic inferences on students' skill acquisition in the topic of 'Parallel and Perpendicular Lines'.