Assessing Difficulty Levels of Mathematical Tasks through Subjective and Behavioral Criteria

Abstract

This paper aims to assess the difficulty levels of mathematical tasks in relation to the appearance of unconscious patterns of thinking in students’ cognitive processes that play a role in learning. The data analyzed using a mixed-methods approach was collected from a population of undergraduate engineering and science students enrolled in Calculus courses at the university while answering three questionnaires as part of their online class activities. Two criteria were used to find categories of difficulty levels: one subjective, given by an evaluation carried out by the subjects, and another behavioral, related to obtaining the correct answers. The relationships of these criteria with the appearance of these unconscious patterns of thinking were identified: a significant and strong correlation was noticed between the number of erroneous unconscious patterns detected and task difficulty levels determined by the percentage of correct answers, as well as a significant and strong correlation between task difficulty levels determined by the subjective evaluation and the number of these patterns recognized. Based on the results obtained, it can be stated that these unconscious erroneous patterns in students’ reasoning about a mathematical concept are related to the index of the difficulty of a task and could be considered indicators of mental effort according to the cognitive load theory. The analysis showed the recognition of these unconscious patterns in students’ cognitive mechanisms is relevant when solving mathematical tasks that require information processing at a higher level and could play a role in assessing the difficulty levels of a task related to the study of mathematical concepts in Calculus courses, which constitutes the main novelty of this study.