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Contribution: This study explores the elements engineering students perceive as important for developing their learner agency in the context of intercultural project-based learning (PBL) teams. Background: The concept of learner agency has recently gained prominence due to its relevance for student-centeredness, autonomy, self-regulation, and collaboration. Certain pedagogical approaches are known to specifically support the development of learner agency, including PBL, in which learners are provided with active, self-directed, and collaborative learning tasks. PBL practice is also increasingly diverse, emphasizing intercultural collaboration in teams. However, learner agency has received little research attention in PBL settings, and even less in intercultural PBL. This study contributes to the existing literature on the development of learner agency in intercultural PBL teams. Research Question: What elements do engineering students consider important for supporting their learner agency development in an intercultural PBL team context? Methodology: Theoretically, learner agency is framed within three interrelated dimensions, namely, intrapersonal, behavioral, and environmental. Based on this framework, a survey instrument with 31 items was constructed and responses were obtained from 310 engineering students. The survey used expert review, student piloting, exploratory factor analysis (EFA), and Cronbach's alpha to test content validity, construct validity, and reliability. The descriptive and demographic statistics were examined through t-test and the analysis of variance test. Findings: Five factors emerged from EFA: 1) interest and motivation; 2) self-efficacy; 3) self-regulated behaviors in teams; 4) team dynamics; and 5) external support. The statistical analysis shows that the interest and motivation factor was perceived by the engineering students as the most important. Furthermore, several demographic variables, including gender, nationality, year of study, and type of PBL learner based on their level of experience with PBL, were found to impact engineering students' agency development.

This paper analyses how lower secondary pupils experience their participation in the Danish science and green entrepreneurship competition, called Edison. The study uses a qualitative research method to investigate pupils' descriptions, in retrospect, on the process of their entrepreneurial work. We completed semi-structured interviews with two teachers and six groups of pupils from two schools. Independence and being able to determine their own product were motivating factors. Often the pupils included other actors, particularly family members, on their own initiative as part of their work. The pupils' interest in STEM education did not appear to have been affected except for two pupils who broadened their educational perspective. However, the awareness of sustainability issues has for some of them been supported, one of them with a change of lifestyle. By including engineering design process models in the analyses, the concept of entrepreneurship in science and technology became more process oriented and operational, which may also help both the teachers' facilitation and the pupils' inventing process.

This study explores how engineering students develop learner agency in an intercultural PBL (problem- and project-based learning) environment, along with the factors that affect their development. Theoretically, learner agency is framed within three interrelated dimensions: intrapersonal, behavioural, and environmental. A narrative inquiry approach is adopted to investigate 11 engineering master's students' perceptions of their agency development. The findings reveal 10 elements perceived as ways to develop learner agency of engineering students, namely belief in their own self-efficacy, motivation, global engineering identity, goal-setting, planning, monitoring, reflecting, trust building, team atmosphere, and support from supervisors and institutions. These results also show that different factors affect the building of learner agency for engineering students, such as students' experiences before undertaking a master's degree, their level of advancement in the program, the culture of each study program, communication styles, and the composition of the project group.

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 functions'. We offer an inquiry-based learning method to represent transfer functions without formally using the full machinery of Laplace transforms. The method is used in an introductory engineering course on system modelling and simulation at Aalborg University, Denmark. The paper also presents an initial assessment of the students' understanding of transfer functions without knowledge of Laplace transforms and the experiences gained from implementing inquiry-based learning in the course. Finally, we conclude with a discussion of the impact of CAS tools on mathematics and engineering science teaching and learning.

At Aalborg University, engineering students spend half the time each semester in groups working on projects in a problem-based learning (PBL) curriculum. The projects are assessed through group exams, except for between 2007 and 2013 when the law forbade group-based project exams. Prior to 2007, a survey showed that students preferred the group-based project exams and a new study was consequently conducted after the 2013 reintroduction of group exams. Again, the results demonstrated that students prefer the group exam, but that there are significant differences between students from various engineering programmes. We compare the two programmes "Architecture and Design" and "Software Engineering", and find that students in the latter programme feel more positively towards the group exam. A further result is that one-third of the students testified that facing a new type of exam did not affect their behaviour at all. This might suggest that the "backwash" effect of an exam on student behaviour is not as present in these students as is often expected and argued in education research. We also argue that what the students' base their views upon forms part of the informal or experienced curriculum, which is not necessarily equal to the formal curriculum.

Problem and Project-Based Learning (PBL) emphasise collaborate work on problems relevant to society and emphases the relation between theory and practice. PBL fits engineering students as preparation for their future professions but what about mathematics? Mathematics is not just applied mathematics, but it is also a body of abstract knowledge where the application in society is not always obvious. Does mathematics, including pure mathematics, fit into a PBL curriculum? This paper argues that it does for two reasons: (1) PBL resembles the working methods of research mathematicians. (2) The concept of society includes the society of researchers to whom theoretical mathematics is relevant. The paper describes two cases of university PBL projects in mathematics; one in pure mathematics and the other in applied mathematics. The paper also discusses that future engineers need to understand the world of mathematics as well as how engineers fit into a process of fundamental-research-turned-into-applied-science.

Six US first-year university students in humanities or social science degree programmes were interviewed while solving 4 tasks on continuity and asymptotes in a required mathematics course. The focus was on how the students referred to the definitions or to the concept images when solving the tasks and if partial understandings appeared. Partial understanding denotes when the definition or the concept image has correct parts but essential parts are missing or incoherencies occur. Some students confused continuity with differentiability or perceived it as a graph not having holes, which is also reported by other studies. Another misconception that emerged is to perceive points on the x-axis as non-continuous. The partial understandings of asymptotes were related to the vertical asymptote as it was confused with a function property. Some students referred to the definitions when correctly solving some of the tasks and some students with coherent concept images were successful solving some of the tasks even when they did not refer to the definitions.

This paper reports a study on retention of differential and integral calculus concepts of a second-year student of physical chemistry at a Danish university. The focus was on what knowledge the student retained 14 months after the course and on what effect beliefs about mathematics had on the retention. We argue that if a student can quickly reconstruct the knowledge, given a few hints, this is just as good as retention. The study was conducted using a mixed method approach investigating students' knowledge in three worlds of mathematics. The results showed that the student had a very low retention of concepts, even after hints. However, after completing the calculus course, the student had successfully used calculus in a physical chemistry study programme. Hence, using calculus in new contexts does not in itself strengthen the original calculus learnt; they appeared as disjoint bodies of knowledge.

This article reports the concluding part of a larger study on retention of key procedural and conceptual concepts in differential and integral calculus among Croatian and Danish university students in non-mathematics study programmes. The first parts of the study examined the retention of the students' knowledge through a questionnaire testing core calculus concepts in derivative and integration given two and six months after the students had passed an exam testing those concepts. In the present article we continue to explore the retention of core concepts in derivative through a mixed method approach examining the knowledge of 10 second-year non-mathematics students 14 months after they took the course. The result showed that there were several negative met-befores and met-afters affecting the students' retention. (Contains 1 table and 4 figures.)

During 2007 all Danish university curricula were reformulated to explicitly state course objectives due to the adoption of a new Danish national grading scale which stipulated that grades were to be given based on how well students meet explicit course objectives. The Faculties of Science at University of Aarhus and University of Southern Denmark interpreted "course objectives" as "intended learning outcomes" (ILO) and systematically formulated all such as competencies using the SOLO taxonomy that operates with five numbered progressive levels of competencies. We investigate how the formulation of ILOs using the SOLO taxonomy gives information about competence progression, educational traditions, and the nature of various science subjects. We use all the course curricula (in total 632) from the two faculties to analyze and compare undergraduate and graduate courses within each department, and different departments with each other.

The aim of the Bologna Process is to make higher education systems across Europe more transparent. It is crucial for this purpose that confusion concerning the characteristics of the systems should be replaced by conformity. But, as we will show, conformity brought about at one level may create confusion at another. The curricular aspect of the Bologna Process focuses on a shift to outcome-based and student-centred programmes. Syllabi should now be based on intended learning outcomes (ILOs) and should be adjusted to general level descriptors for qualifications. However, the Bologna documents give no explicit recommendations about the use of grading scales. In Denmark, Norway and Sweden, the reforms of higher education induced by the Bologna process included a change of grading scales and referred to the European Credit Transfer and Accumulation System (ECTS). Through these three case studies, we describe and analyse the political process and argumentation underpinning the decisions to change the grading scales in each country. This includes the problems, both experienced and perceived, with the old grading scales, the various national assessment traditions and the new grading scales. The purpose of the change was not the same in each country, but the ongoing adaptation to a seven-step grading scale was thought to ease the international recognition of the national grades, making mobility easier. Though a seven-step grading scale was implemented in both Danish and Norwegian higher education and also by an increasing number of Swedish higher education institutions, the translation of grades only works on a superficial level. The grading scales designed are fundamentally different as classification systems; they attach different numerical values to grades with identical labels and they relate differently to norm- and standards-referenced judgements of learning outcomes. The information condensed in similar grades from the three countries cannot be equated. The vision of simple transparency turns out to be an illusion. (Contains 1 figure, 8 tables and 2 notes.)

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 "CULTIS model for analysis" (Consciousness, Unconsciousness, Language, Tacit, Individual, Social), which consists of six themes in which various psychological theories of learning are expressed. The model uses the theories of Ernest, von Glasersfeld, Hadamard, Krutetskii, Mason, Piaget, Polya, Sfard, Skemp, and Vygotsky. The model is used to sort the pupils' explanations and it also functions as a tool with which to compare the pupils' explanations with the various theories. I conclude that the pupils can talk about their learning in their own words and each pupil refers to elements that the researcher associates with different theories. Half the pupils furthermore explain that how they are used to learning, or being taught, influences how they later on are able to learn. I also discuss metacognition and whether this can be an aid to enhance learning.

Aalborg University (AAU) in Denmark is one of the universities in the world that practises problem-based learning (PBL) in all study programmes at all faculties. The PBL principles are broadly defined. and each study programme practices PBL in its own way within these frames. In this paper, we study how differently PBL is practiced within the science, engineering and mathematics areas at AAU. In particular, we analyse 21 AAU Bachelor theses in a selection of different engineering, science, and mathematics study programmes. to explore which types of problems from the discipline the students are addressing in their projects. We exemplify this through an analysis of recent Bachelor theses from Chemical Engineering and Biotechnology, Building and Construction Engineering, Mechanical Engineering, Mathematics, and Biologh respectively. The focus is on which types of problem from the discipline the students work with. The research methodology is documentary analysis of curricula and the theses. We first, through a deductive analysis, apply the four shadows of problems' theoretical framework to categorize the problems. This showed that 18 of the 21 theses can be categorized as concerning a contrast problem. This is the case for all five fields of study. Secondly, a more detailed inductive content analysis of these 18 theses' problems showed that these 18 problems had a great variation, and we were able to identify five specific types of contrast problems among these 18 theses. [ABSTRACT FROM AUTHOR]