Search results for "university mathematics"
showing 10 items of 21 documents
Learning complex analysis in different branches – Project Spotlight-Y for future teachers
2018
International audience; At the University of Bremen in teaching complex analysis, we split the last part of the lecture into two branches according to profession: While future mathematicians deepen their understanding in a branch for them, future teachers take a branch of the lecture where they prepare a task with dynamical geometry software for pupils which is based on phenomena of complex analysis. Here, we describe the design of the course, some general aims and first results obtained from the branch for future teachers.
Didactical resource purposes as an aspect of students’ decision making regarding resources used to learn mathematics
2019
International audience
Cross-linking maths: Using keynotes to structure a curriculum for future teachers
2018
International audience; The paper gives an outline of a concept for university maths teacher education, that is based on three keynotes, which are central scientific notions, history and language. Amongst other benefits, the keynotes serve as cross-links between the different courses the students go through in their studies.
Adapting Formal Logic for Everyday Mathematics
2022
Although logic is considered central to mathematics and computer science, there is evidence that teaching logic has not been a great success. We identify three issues where what is typically taught conflicts with what is needed by those who are supposed to apply logic. First, what is taught about the notion of implication often disagrees with human intuition. We argue that in some cases human intuition is wrong, and in some others teaching is to blame. Second, the formal concepts of logical consequence, logical equivalence and tautology are not the similar concepts that everyday mathematicians and computer scientists need. The difference is small enough to go unnoticed but big enough to cau…
Automated Checking of Flexible Mathematical Reasoning in the Case of Systems of (In)Equations and the Absolute Value Operator
2021
We present an approach and a tool for automatically providing feedback on solutions that involve complicated reasoning patterns. Currently the tool supports linear systems of equations and inequations that may also contain the absolute value operator and a restricted form of rational functions. This suffices for designing problems that are laborious to solve with standard mechanical procedures, but much easier using short-cuts that students may find by creative thinking. Earlier research has found that struggling with important mathematics promotes conceptual development. Our goal is to encourage students to such struggling. A crucial feature is to give them great freedom to choose the path…
Engaging with feedback: How do students remediate errors on their weekly quiz
2018
International audience; Maths for Business is a first-year mathematics module for approximately 500 non-mathematics specialists. It has continuous assessment consisting of ten weekly quizzes, worth 40% of the final mark. In 2016/17, students who did not receive the maximum five marks on their weekly quiz were offered the opportunity to resubmit their quiz, with correction(s) and an explanation of their error(s), for one additional mark. We refer to this process as ‘remediation'. In this paper, we examine how students remediate their errors in order to identify features of a ‘good' remediation. These features are identification, description, and correction of errors. By analysing a subset of…
Students' usage patterns of video recorded lectures in an undergraduate mathematics course
2018
International audience; It is customary for some universities to offer recordings of live lectures to students. Whether this improves learning and academic performance is debated in the literature. As with most technology, correct usage can lead to increased academic performance, but there are also usage patterns that can be considered counter productive, especially for learning mathematics. In order to investigate patterns in students' usage of such online recorded live lectures, we analyze log files from a server holding the recordings of an undergraduate mathematics course. This poster presents results from the statistical analysis and discusses some of the usage patterns found in light …
Predictors of performance in engineering mathematics
2018
International audience; Mathematics in university courses was identified as a main obstacle for engineering students in the beginning of their study. Since difficulties with mathematics could lead to a dropout, our research aims to analyse students' profiles referring to individual characteristics that allow identifying possible risks for students' achievement or success in the first year of study. As a first step to identify possibly risky profiles, we started to find possible predictors of students' performance. For this, we give a short overview of the research state and our derived research interest. We discuss theoretical constructs that are possibly crucial characteristics of students…
Discussing Mathematical Learning and Mathematical Praxeologies from a Subject Scientific Perspective
2018
International audience; This programmatic contribution discusses the link between concepts from Anthropological Theory of Didactics (ATD) and the “subject-scientific point of view” according to Holzkamp (1985, 1993). The main common concern of ATD and the subject-scientific approach is to conceptualize and analyse “objects” like “institutionalized mathematical knowledge” and “university” not as conditions that cause reactions but essentially as meanings in the sense of generalized societal reified action possibilities. The link of both approaches is illustrated by the issue of “real numbers” in the transition from school to university: Hypotheses are derived for further actual-empirical res…
From single to multi-variable Calculus: a transition?
2018
International audience; We recently used the notion of praxeology from the Anthropological Theory of the Didactic to model the knowledge that is necessary for students to learn in order to succeed in an undergraduate multivariable Calculus course. We considered the presence and absence of elements of the knowledge to be taught, as proposed by curricular documents, in the knowledge to be learned, as indicated by final exams. Our results indicate that the mathematical activities expected of students at this level align with the activities observed in differential and integral Calculus, where exercise-driven assessments set students' work mainly in the recognition of types of tasks and recolle…