Which Prior Mathematical Knowledge Is Necessary for Study Success in the University Study Entrance Phase? Results on a N
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Which Prior Mathematical Knowledge Is Necessary for Study Success in the University Study Entrance Phase? Results on a New Model of Knowledge Levels Based on a Reanalysis of Data from Existing Studies Stefanie Rach 1 & Stefan Ufer 2 # The Author(s) 2020
Abstract The transition from school to tertiary mathematics courses, which involve advanced mathematics, is a challenge for many students. Prior research has established the central role of prior mathematical knowledge for successfully dealing with challenges in learning processes during the study entrance phase. However, beyond knowing that more prior knowledge is beneficial for study success, especially passing courses, it is not yet known how a level of prior knowledge can be characterized that is sufficient for a successful start into a mathematics program. The aim of this contribution is to specify the appropriate level of mathematical knowledge that predicts study success in the first semester. Based on theoretical analysis of the demands in tertiary mathematics courses, we develop a mathematical test with 17 items in the domain of Analysis. Thereby, we focus on different levels of conceptual understanding by linking between different (in)formal representation formats and different levels of mathematical argumentations. The empirical results are based on a re-analysis of five studies in which in sum 1553 students of bachelor mathematics and mathematics teacher education programs deal with some of these items in each case. By identifying four levels of knowledge, we indicate that linking multiple representations is an important skill at the study entrance phase. With these levels of knowledge, it might be possible to identify students at risk of failing. So, the findings could contribute to more precise study advice and support before and while studying advanced mathematics at university. Keywords Mathematical knowledge . Study entrance phase . Study success . Level model .
Qualities of knowledge
* Stefanie Rach [email protected] Stefan Ufer [email protected] Extended author information available on the last page of the article
International Journal of Research in Undergraduate Mathematics Education
Introduction The transition from mathematics as a school subject to mathematics as a scientific discipline in academic mathematics programs and mathematics teacher education programs is challenging for most students. In Germany, Dieter (2012) reports a dropout rate of over 30% among first-year students with a major in mathematics (see OECD 2010). In general, high dropout rates are considered as serious problems for the individual student and for society (Rasmussen and Ellis 2013). Empirical studies have shown that students’ cognitive prerequisites, such as prior knowledge, are the most important determinants of study success (e.g. Hailikari et al. 2008; Kosiol et al. 2019). Whereas successful students differ from failing students in mathematical knowledge at the beginning of study, motivational variables seem to play a comparably minor role (Kosiol et al. 2019).
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