Bayesian Assessment of Undergraduate Students About the Real Function Mathematical Concept

Abstract

The evaluation of learning in mathematics is a worldwide problem, therefore, new methods are required to assess the understanding of mathematical concepts. In this paper, we propose to use the Item Response Theory to analyze the understanding level of undergraduate students about the real function mathematical concept. The Bayesian approach was used to make inferences about the parameters of interest. We designed a test containing twelve items, to which a reliability analysis and validation test were applied. The experiment consisted in administer our test to 48 undergraduate students (18-20 years old) who are in a math career. We concluded that 25% of the students reached a high level of understanding, 39.6% a medium level of understanding and, 35.4% a low level of understanding. Furthermore, that students obtained low levels of understanding for tasks with high cognitive demand, and they obtained high levels of understanding for tasks with low cognitive demand.