Identifying Competency Demands in Calculus Textbook Examples: the Case of Integrals

This study investigates how three widely used calculus textbooks realise integrals as a potential to prompt mathematical competencies, adapting the rating scheme used in Boesen et al. (The Journal of Mathematical Behavior, 33:72–87, 2014), Pettersen and Braeken (International Journal of Science and Mathematics Education, 17(2):405–425, 2019) and Turner, Blum and Niss (2015). For this purpose, the study analysed examples ( n = 444) about integrals—specifically, to assess the extent to which solving those examples calls for the activation of a particular set of mathematical competencies: Communication ; Devising Strategies ; Mathematising ; Representation ; Using Symbols , Operations and Formal Language [ Symbols and Formalism ]; Reasoning and Argument . The competency demand of the examples was also identified on a scale from 0 (lowest demand) to 3 (highest demand) for each of six mathematical competencies. The findings revealed substantial similarities among the three calculus textbooks with regard to the level of competency demands: high level of Communication and Symbols and Formalism and low level of Devising Strategies , Representation , Reasoning and Argument and Mathematising . Relationships between these findings, implementations and future research directions are also discussed.