PEDAGOGY OF CALCULUS IN INDIA: AN EMPIRICAL INVESTIGATION

Abstract

When students learn a calculus construct, both a concept image as well as a concept definition is imprinted in their mind, and because of it, concrete and real-life examples become a prerequisite for a contextually rich learning environment for the abstractions inherently present in calculus. In the light of aforementioned propositions, the current study focusses on delving into several issues, few of the prominent ones include the epistemological nature of calculus curriculum in India’s senior-secondary schools, role of Indian calculus teachers in students’ cognition, possibility of enumeration of characteristics of a successful calculus teacher with regards to India’s socio-cultural milieu, challenges regarding complete immersion of calculus in manipulation of symbols that eventually give rise to cognitive obstacles, interrelationship between teachers’ calculus content knowledge and their pedagogical practices, effect of secondary school calculus on performance of Indian students’ college calculus, and the nature of effect on Indian learners having calculus in school on their procedural and conceptual performance. For this extensive study, data were collected from PGTs and Assistant/Associate Professors having more than 8 years of calculus teaching experience drawn from 76 different schools, colleges and universities belonging to 23 different states and union territories of India. A total of 323 teachers took part in this study. Multiple methods of data collection were used including naturalistic observation, structured interviews, classroom observations, focussed group interviews, and informal discussions, and these were done both before and after the classroom teaching. The researcher transcribed the interviews, identified emerging and repeated themes, and used NVivo and Concordance software to conduct content and classroom discourse analysis, with simple counting methods and applied grounded theory approach using which empirical data were thematically categorized and in the process of it, employed the induction approach. The researcher analyzed the transcripts using N5 (NUD*IST 5.0; QSR International, Melbourne) with the grounded theory approach. This research study is purely qualitative in nature and its framework lies within the interpretative paradigm. The current study was carried out between June 2016 and March 2019. Findings indicate that there are lots of cognitive obstacles in understanding the concepts inbuilt in calculus: two of the prominent ones that came out from the study include the one related to intuitions and the other related to linguistic/representational aspects.