Investigating the Frameworks of Students' Understanding of the relationship between the Derivative and Antiderivative Function graphs: A Qualitative Meta-analysis

AbstractThe derivative is one of the most important topics in calculus that is used in various sciences.  One of the topics in this field is the interpretation of the derivative function graph with the help of its antiderivative function and vice versa. Research shows that because students understanding of derivative graphs requires high-level thinking skills, students have difficulty in understanding the relationship. The present study investigates the methodology and content of these studies to determine their underlying theory. This study is a descriptive study and qualitative meta-analysis method to show an insight into the coherence of these studies. The research field included all related research that were done by regularly searching for keywords and also by searching among citations of articles in national and international databases based on PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses). Based on the inclusion criteria, 182 studies were identified between 1992 and 2022 and finally, based on the exclusion criteria, 26 studies were selected for final review and analysis. The qualitative meta-analytic findings identified 13 main frameworks among the research that focuses on the three Krutetskii thinkers (analytical, visual, and harmonic), Dubinsky APOS (action-process-object-schema) theory and the three layers of graph disclosure (objects-relationships- functional relationships) is Swidan. The new method used in the qualitative meta-analysis of the present study can be used by researchers in different fields of education. Also, the findings of this meta-analysis for teaching and learning the relationship between the graph of the derivative function and its antiderivative function for teachers, and professors; will be useful for authors of textbooks and researchers.