Bridging a cultural gap

Abstract

There has been a broad wave of change in tertiary calculus courses in the past decade. However, the much-needed change in tertiary pre-calculus programmesaimed at bridging the gap between high-school mathematics and tertiary mathematics-is happening at a far slower pace. Following a discussion on the nature of the gap and the objectives of a potential bridging programme, this paper aims at demonstrating that the gap can be bridged, by presenting an ongoing modular bridging programme especially designed for the diverse types of student populations in teachers training colleges. We also present here some innovative teaching and assessment methods that were judged essential for the success of these programmes-focusing mainly on the "Questionnaire Based Instruction Method". Finally we suggest directions of follow up and research.

Mathematical Prerequisites for STEM Programs: What do University Instructors Expect from New STEM Undergraduates?

“…However, the activities have different foci. In school, typically, the solving of real-life problems is emphasized (see the PISA studies, e.g., OECD 2016), whereas in university mathematics the focus is on inner-mathematical problems (e.g., Engelbrecht 2010;Leviatan 2008;De Guzmán et al 1998). Similarly, the focus shifts from describing concepts to precisely defining concepts or from convincing via argumentation to mathematical proving (Tall 1991;Thomas et al 2015).…”

“Much Palaver About Greater Than Zero and Such Stuff” – First Year Engineering Students’ Recognition of University Mathematics

“…Also, the notion of Ba fundamental conceptual divide between school and university mathematics^ (Hoyles et al 2001, p. 832) has been used in this context. Leviatan (2008) goes as far as to describe the shift in criteria as a Bcultural gap^:…”

Key Mathematical Concepts in the Transition from Secondary School to University

“…There is some evidence that bridging courses can assist in transition (Varsavsky 2010), by addressing skill deficiencies in basic mathematical topics (Tempelaar et al 2012) and building student confidence (Carmichael and Taylor 2005). Other successful transition courses (e.g., Leviatan 2008) introduce students to the mathematical "culture" and its typical activities (generalizations, deductions, definitions, proofs, etc. ), as well as central concepts and tools.…”

“…This requires logical deductive reasoning (Engelbrecht 2010) and rigour (Leviatan 2008). Research highlighting examples of this includes conceptualisation related to the use of quantifiers (Chellougui 2004), the relationship between syntax and semantics in the proving process (Barrier 2009;Blossier et al 2009) and logical competencies (Durand-Guerrier and Njomgang Ngansop 2010).…”