Research on Undergraduate Mathematics Education in Afghanistan: How Students Understand and Learn the Concept of “Function”

The purpose of this study was to explore undergraduate students’ conception of the concept of function in the education faculty of Balkh University, Afghanistan. In particular, the focus was to see what difficulties they had in learning the concept and to determine those factors that impeded/facilitated the learning of the concept in the curriculum. The research methodology was an exploratory approach where both qualitative and quantitative methods were used to analyze the data. The theoretical basis for the study was David Tall’s theory which focuses on understanding one’s knowledge and learning. David Tall’s theory was used to analyze qualitative data and descriptive statistics, t – test for two independent samples, and ANOVA were used to present the results of the qualitative data and to test the hypothesis developed after analyzing the qualitative data. Twenty fourth year undergraduate students worked on a questionnaire which was developed based on different aspects of the concept of function and were interviewed to elaborate their written work on the questionnaire. The participants completed the questionnaire and participated in in-depth interviews to reveal their understanding of the concept of function. The major finding was that those who had a good conceptual understanding of the concept could do better in various representations of the concept than those who did not. Also, the set – theoretic definition of the concept helped some of the students to be successful in dealing with various representations of the concept, but it challenged the majority of the students to comprehend this definition and apply it in certain situations. In addition, the concept was not taught with its theoretical aspects and through applied examples in Algebra and Calculus courses where the concept was introduced using two different approaches