Ideas foundational to calculus learning and their links to students’ difficulties

‘Scaffolding’ or ‘Filtering’: A Review of Studies on the Diverse Roles of Calculus Courses for Students, Professionals and Teachers

“…The Institutional Role of Calculus Courses in the Transition Across Educational Levels: Scaffolding and Filtering Calculus courses are often institutionally located at critical positions in students' pathways through secondary and post-compulsory education and towards their preparation for STEM studies (Thompson & Harel, 2021;Törner et al, 2014). In the studies we reviewed, we observed two (intended or unintended) roles of calculus courses in post-compulsory and/or early tertiary level: (a) calculus courses support students towards their preparation for STEM studies, and (b) success to those courses is part of the selection process towards STEM studies at tertiary level.…”

“…Calculus is an essential aspect of the preparation and professional development of teachers in many countries around the world (Tatto et al, 2010;Thompson & Harel, 2021). For example, in the US, the Conference Board of the Mathematical Sciences (CBMS, 2012) has recommended that preparation of high school teachers comprises at least a three-course sequence of single-and multi-variable calculus, complemented by a proof-based calculus course.…”

Calculus at the intersection of institutions, disciplines and communities: a special issue Guest Editorial

“…IJRUME co-editor in chief Elena Nardi, also co-chair of the conference with Tommy Dreyfus and John Monaghan, acted as handling editor of the Special Issue. In what follows, Guest Editors Irene Biza, Alejandro S. González-Martín and Alon Pinto introduce the Special Issue.Calculus courses are widely considered an important gateway, or gate keeper, in many academic and professional paths (Bressoud et al, 2016;Thompson & Harel, 2021). Calculus is also widely recognized as a critical stage in various transition processes, such as the transition from secondary mathematics to tertiary mathematics, the transition within and across university courses, or the transition from university to the workplace (Hochmuth et al, 2021).…”

“…Calculus courses are widely considered an important gateway, or gate keeper, in many academic and professional paths (Bressoud et al, 2016;Thompson & Harel, 2021). Calculus is also widely recognized as a critical stage in various transition processes, such as the transition from secondary mathematics to tertiary mathematics, the transition within and across university courses, or the transition from university to the workplace (Hochmuth et al, 2021).…”

“…In this vein, and going further, the ZDM special issue on calculus (2014) states: "research [in calculus education] that takes up the institutional and cultural context and how these aspects constrain and enable sustained uptake of advances in calculus learning and teaching is sorely needed […] this represents a new research theme, one yet to be realized to any large extent" (Rasmussen et al, 2014, p. 513). More recently, a ZDM special issue was dedicated to different approaches in calculus education around the world (Thompson & Harel, 2021) and highlighted the diversity in approaches across educational systems and institutions.…”