Transfer functions are convenient representations to analyse cause-and-effect relationships of linear time-invariant dynamic systems. Traditionally, transfer functions are introduced using the Laplace transform. In this paper, we argue that the Laplace transform method is not a necessary prerequisite to understanding the topic 'transfer…

In this paper we consider the problem of modelling when students end their session in an online mathematics educational system. Being able to model this accurately will help us optimize the way content is presented and consumed. This is done by modelling the probability of an action being the last in a session, which we denote as the…

This article reports on a combined quantitative and in-depth qualitative study of 315 Danish upper secondary (grades 10-12) mathematics students' answers to six modelling tasks that place emphasis on the early phases of the so-called modelling cycle. In order to focus attention on the extra-mathematical aspects of modelling, the technical…

The analysis of log data generated by online educational systems is an important task for improving the systems, and furthering our knowledge of how students learn. This paper uses previously unseen log data from Edulab, the largest provider of digital learning for mathematics in Denmark, to analyse the sessions of its users, where 1.08 million…

The article addresses the problématique of where mathematization is taught in the educational system, and who teaches it. Mathematization is usually not a part of mathematics programs at the upper secondary level, but we argue that physics teaching has something to offer in this respect, if it focuses on solving so-called unformalized problems,…

This article reproduces correspondence between Georg Rasch of The University of Copenhagen and Benjamin Wright of The University of Chicago in the period from January 1966 to July 1967. This correspondence reveals their struggle to operationalize a unidimensional measurement model with sufficient statistics for responses in a set of ordered…

Mathematics plays a crucial role in physics. This role is brought about predominantly through the building, employment, and assessment of mathematical models, and teachers and educators should capture this relationship in the classroom in an effort to improve students' achievement and attitude in both physics and mathematics. But although there…

Mathematical models and mathematical modeling play different roles in the different areas and problems in which they are used. The function and status of mathematical modeling and models in the different areas depend on the scientific practice as well as the underlying philosophical and theoretical position held by the modeler(s) and the…

Critical to many science, technology, engineering, and mathematics (STEM) career paths is mathematical modeling--specifically, the creation and adaptation of mathematical models to solve problems in complex settings. Conventional standardized measures of mathematics achievement are not structured to directly assess this type of mathematical…

In this paper, a course on applied superconductivity is described. The course structure is outlined and the learning objectives and the learning activities are described. The teaching was multidisciplinary given by four departments each contributing with their expertise. Being applied superconductivity, the focus was on an application, which could…

The negotiation of meaning presupposes a taken-to-be-shared understanding of a situation. Uses an example to illustrate how negotiation of meaning and task may be linked in ways inappropriate to the learning of modeling and critical reflections. Contains 16 references. (Author/ASK)

Under certain conditions it may be possible to determine the difficulty of previously untested test items. Although no recipe can be provided, reflections on this topic are presented, drawing on concepts of item banking. A functional constructive method is suggested as having the most potential. (SLD)

The focus is on the metacognitive awareness of ten high-achieving high school pupils in mathematics in Denmark and England and their understanding of their cognitive learning processes and strategies. Mainly unstructured focus group interviews investigate how they explain that they learn a mathematical concept that is new to them. I develop the…

The tests for zero partial association in a multiple contingency table have gained new importance with the introduction of graphical models. It is shown how these may be performed as exact conditional tests, using as test criteria either the ordinary likelihood ratio, the standard x squared statistic, or any other appropriate statistics. A…

Approximately 1200 Danish school children aged 8, 11, and 14 participated in a questionnaire study under the caption, "Why I like to read." Data from Denmark formed part of an international study, in which 12 other countries used the same questionnaire to explore various functions of reading and to compare them over different countries.…