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ICMI Study 14: Applications and modelling in mathematics education – Discussion document

This paper is the Discussion Documentfor a forthcoming ICMI Study on Applications and Modelling in MathematicsEducation. As will be well-known, fromtime to time ICMI (the InternationalCommission on Mathematical Instruction)mounts specific studies in order toinvestigate, both in depth and in detail,particular fields of interest inmathematics education. The purpose of thisDiscussion Document is to raise someimportant issues related to the theory andpractice of teaching and learningmathematical modelling and applications,and in particular to stimulate reactionsand contributions to these issues and tothe topic of applications and modelling asa whole (see Section 4). Based onthese reactions and contributions, alimited number (approximately 75) ofparticipants will be invited to aconference (the Study Conference)which is to take place in February 2004 inDortmund (Germany). Finally, using thecontributions to this conference, a bookwill be produced (the Study Volume)whose content will reflect thestate-of-the-art in the topic ofapplications and modelling in mathematicseducation and suggest directions for futuredevelopments in research and practice.The authors of this Discussion Document are themembers of the International ProgrammeCommittee for this ICMI Study. Thecommittee consists of 14 people from 12countries, listed at the end of Section4. The structure of the Document isas follows. In Section 1, we identifysome reasons why it seems appropriate tohold a study on applications and modelling.Section 2 sets a conceptual frameworkfor the theme of this Study, and Section3 contains a selection of importantissues, challenges and questions related tothis theme. In Section 4 we describepossible modes and ways of reacting to theDiscussion Document, and in the finalSection 5 we provide a shortbibliography relevant to the theme of thisStudy. This revised version was published online in July 2006 with corrections to the Cover Date.     

The (Social) Construction of Information Security

While the philosophical foundations of information security have been unexamined, there is an implicit philosophy of what protection of information is. This philosophy is based on the notion of containment, taken from analogies with things that offer physical security (e.g., buildings, safes, fences). I argue that this implicit philosophy is unsatisfactory in the current age of increased connectivity, and provide an alternative foundation. I do so from a constructionist point of view, where the coevolution of social and technical mechanisms is seen as the source of the security of an information system, rather than rational design choices only. I employ the concept of causal insulation from system theory in order to give an account of the fundamental characteristics of information security research. This generates definitions that can be used for philosophically informed discussions on the protection of information in new systems.     

Relationships among field-test measures and physical match performance in elite-standard soccer referees

Abstract

The aim of this study was to assess the extent to which measures derived from the new FIFA referees’ fitness tests can be used to monitor a referee's match-related physical capacity. Match-analysis data were collected (Prozone®, Leeds, UK) from 17 soccer referees for 5.0 (s = 1.7) FA Premier League matches per referee during the first 4 months of the 2007–08 season. Physical match performance categories included total distance covered, high-intensity running distance (speed >5.5 m · s^?1), and sprinting distance (>7.0 m · s^?1). The two tests were a 6 × 40-m sprint test and a 150-m interval test. Heart rate demand was correlated with total match distance covered (r = ?0.70, P = 0.002) and high-intensity running (r = ?0.57, P = 0.018) in the interval test. The fastest 40-m sprint was related to total distance covered (r = ?0.69, P = 0.002), high-intensity running (r = ?0.76, P < 0.001), and sprinting distance (r = ?0.75, P = 0.001), while mean time for the 40-m sprints was related to total distance covered (r = ?0.70, P = 0.002), high-intensity running (r = ?0.77, P < 0.001), and sprinting distance (r = ?0.77, P < 0.001). The referees who recorded the best interval-test heart rate demand and fastest 40-m time produced the best physical match performances. However, only the sprint test and in particular the fastest 40-m time had appropriate construct validity for the physical assessment of soccer referees.     

Teaching methods for modelling problems and students’ task-specific enjoyment, value, interest and self-efficacy expectations

In this study which was part of the DISUM-project, 224 ninth graders from 14 German classes from middle track schools (Realschule) were asked about their enjoyment, interest, value and self-efficacy expectations concerning three types of mathematical problems: intra-mathematical problems, word problems and modelling problems. Enjoyment, interest, value and self-efficacy were assessed before and after a ten-lesson teaching unit promoting modelling competency related to the topics “Pythagoras’ theorem” and “linear functions”. The study aimed to answer the following research questions: (1) Do students’ enjoyment, value, interest and self-efficacy expectations differ depending on the type of task? (2) Does the treatment of modelling problems in classroom instruction influence these variables? (3) Are there any differential effects for different ways of teaching modelling problems, including a “directive”, teacher-centred instruction and an “operative-strategic”, more student-centred instruction emphasising group work and strategic scaffolding by the teacher? The findings show that there were no differences in students’ enjoyment, interest, value and self-efficacy between the three types of tasks. However, teaching oriented towards modelling problems had positive effects on some of the student variables, with the student-centred teaching method producing the most beneficial effects.     

Student teachers’ pedagogical content knowledge for teaching systems thinking: effects of different interventions

ABSTRACT

Systems’ thinking has become increasingly relevant not only in education for sustainable development but also in everyday life. Even if teachers know the dynamics and complexity of living systems in biology and geography, they might not be able to effectively explain it to students. Teachers need an understanding of systems and their behaviour (content knowledge), and they also need to know how systems thinking can be fostered in students (pedagogical content knowledge (PCK)). But the effective development of teachers’ professional knowledge in teaching systems thinking is empirically uncertain. From a larger study (SysThema) that investigated teaching systems thinking, this article reports the effects of the three different interventions (technical course, didactic course and mixed course) in student teachers’ PCK for teaching systems thinking. The results show that student teachers’ PCK for teaching systems thinking can be promoted in teacher education. The conclusion to be drawn from our findings is that a technically orientated course without didactical aspects seems to be less effective in fostering student teachers’ PCK for teaching systems thinking. The results inform educators in enhancing curricula of future academic track and non-academic track teacher education.     

The Use of Bibliometrics to Measure Research Performance in Education Sciences

This paper investigates the fitness-for-purpose and soundness of bibliometric parameters for measuring and elucidating the research performance of individual researchers in the field of education sciences in Switzerland. In order to take into account the specificities of publication practices of researchers in education sciences, the analyses are based on two separate databases: Web of Science and Google Scholar. Both databases show a very unequal distribution of the individual research output, and the indicators used to measure research performance (quantity of publications and citation impact) from the two data sources are highly positively correlated. However, individual characteristics of the researchers, such as age, gender and academic position, that serve to explain the great variance in research performance, can only be identified if the Web of Science is used as a benchmark of research performance. The results indicate that Google Scholar is so inclusive that it impedes a meaningful interpretation of the data. However, the Web of Science inclusion policy for journals is also associated with certain shortcomings that put some researchers at an unjustified disadvantage. Therefore, problems currently exist in regard to both citation databases when used to benchmark individual research performance.     

Knowledge management supporting education and research at a university cleanroom

At the university, each institute or chair can be seen as a small independent enterprise in respect of education and research. For this reason, the efficiency of management as well as the improvement of education and research within this unit is more and more at a premium. The students need a good working environment and the opportunity to gain and share information in order to carry out successful research and course work. This paper shows how education at a university semiconductor laboratory can be improved by using a content management system to build a knowledge management system. The structuring and implementation will be shown as well as students’ rating of it. The results support the conclusion that the knowledge base is a great step forward for improving education and research in a complex environment.     

Muskuläre Regulation bei ermüdungsinduzierter Vorbelastung im Krafttraining

International sport strives for increasing the level of performance in sports. Risks of manipulating the performance are not unusual. At the same time, improvements in science, engineering and data processing offer further opportunities for planning effective, low-risk and year-round training programmes for specific sports. This paper presents new approaches based on the example of techniques for strength training. Selected experimental results highlight the limitations and provide conclusions for the scientific foundation and individualization of high performance training. The approach of “muscle pre-fatigue” is verified in a training study with high jumpers. The statements show how important scientifically controlled analysis is for individual training programmes and what high significance they have for optimizing the training process. These will be essential requirements for a legal improvement of high performance in international sport.