Framework for Examining the Transformation of Mathematics and Mathematics Learning in the Transition from School to University

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

“…It is also reported that participation in the various teaching formats (such as lectures, study groups, tutorials, mathematics skills help centres) offered at some universities has decreased in recent years (local information). Comparatively low pass rates for first year undergraduate mathematics courses have also been observed in other countries (Dieter and Törner 2010;Engineering Council 2000;De Guzman et al 1998;Vollstedt et al 2014). The issue has gained more importance with policies that aim at widening participation in higher education for under-represented groups, mostly framed in terms of gender, ethnicity and social class (Pampaka et al 2012).…”

“…Hoyles et al 2001;Robert 1998, cited in Gueudet 2008Vollstedt et al 2014). For instance, according to Jooganah and Williams (2010), mathematics in school is mainly procedural requiring from the students only little conceptual depth, while university mathematics places Bemphasis on proof and rigour requiring them to engage with and critically think about concept definitions^(p. 116).…”

The Transition from School to University in Mathematics: Which Influence Do School-Related Variables Have?

“…This means, for example, that a person who wants to apply a mathematical rule in a specific context must be sure that this rule provides a result which can be considered as acceptably accurate for this specific context. So, for many mathematical statements in school mathematics, in principle empirical evidence is sufficient to take validity for granted-that may be one reason why there are only rare opportunities to prove a statement in German school textbooks (Vollstedt et al, 2014). In contrast, at university, the scientific mathematical community has developed strict standards whose kind of argument is accepted as evidence for mathematics as a scientific discipline.…”

“…Although this general observation seems to be true for many countries, the specific differences of mathematics at school and at university might vary between countries due to traditions concerning curricula or learning goals. The subsequent presentation refers to the situation in Germany which was analyzed in empirical studies (Vollstedt, Heinze, Gojdka, & Rach, 2014;Witzke, 2015) and which is relevant for the empirical study we present below. Nevertheless, several of the described features might be true for other countries as well.…”

“…the concept definition plays the essential role, Engelbrecht, 2010). In particular, concept images in the sense of specific mental representations are rarely induced by university teachers or academic textbooks (Vollstedt et al, 2014) so that students must apply specific elaboration strategies for an individual construction of the meaning of formally defined concepts. A second consequence of the different characters of school and university mathematics is the different role of proofs.…”