Modeling university students’ derivative conceptions in calculus

Kula, Fulya
The aim of this study is to understand how prerequisite knowledge of derivative considered with the cognitive levels is related to the attainment of derivative concepts among the Turkish university students with the consideration of student related characteristics. The cognitive levels addressed in the study are retrieval, comprehension, analysis, and knowledge utilization cognitive processes. Moreover student related characteristics are socioeconomic status, mathematics motivation, mathematics anxiety, derivative self-efficacy, and the demographic profiles. Structural equation modeling was used to test the hypothesized relationships of student related characteristics, the four cognitive levels in the prerequisite concepts of derivative, and in the concept of derivative. Exploratory and confirmatory factor analysis were carried out to determine the observed variables representing the latent variables. According to the present study, for higher achivement in derivative, different groups of skills should be considered. Almost all of the cognitive levels are important to achieve learning in derivative, including the retrieval outcomes. All the groups have different relations with the achievement in derivative with different magnitudes. In terms of prerequisite skills, the most important variable is the knowledge utilization. In general, both analysis and knowledge utilization are the two domains which are definitely required for the learning achievement of derivative concepts. For a successful teaching of derivative, the prerequisite knowledge and skills, and four groups of cognitive tasks should be considered in the course plannings. Students’ affective variables and their socio economic status did not give strong relations with the cognitive variables. With the help of the findings, it can be concluded that different groups of cognitive skills should be considered in calculus teaching settings. Teachers should consider the cognitive skills of the students into account during their teaching. Teachers should be avare of the fact that students need to achieve knowledge utilization in prerequisite skills for being successful in the derivative concept. In general, both analysis and knowledge utilization are the two domains which are definitely required for the learning achievement of derivative concepts. The teaching should go beyond stressing the retrieval cognitive level in the settings in which derivative is teached.


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Citation Formats
F. Kula, “Modeling university students’ derivative conceptions in calculus,” Ph.D. - Doctoral Program, Middle East Technical University, 2013.