| 1. |
- Gerlee, Philip, 1980, et al.
(author)
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Scientific Models : Red Atoms, White Lies and Black Boxes in a Yellow Book
- 2016
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Book (other academic/artistic)abstract
- A zebrafish, the hull of a miniature ship, a mathematical equation and a food chain - what do these things have in common? They are examples of models used by scientists to isolate and study particular aspects of the world around us. This book begins by introducing the concept of a scientific model from an intuitive perspective, drawing parallels to mental models and artistic representations. It then recounts the history of modelling from the 16th century up until the present day. The iterative process of model building is described and discussed in the context of complex models with high predictive accuracy versus simpler models that provide more of a conceptual understanding. To illustrate the diversity of opinions within the scientific community, we also present the results of an interview study, in which ten scientists from different disciplines describe their views on modelling and how models feature in their work. Lastly, it includes a number of worked examples that span different modelling approaches and techniques. It provides a comprehensive introduction to scientific models and shows how models are constructed and used in modern science. It also addresses the approach to, and the culture surrounding modelling in different scientific disciplines. It serves as an inspiration for model building and also facilitates interdisciplinary collaborations by showing how models are used in different scientific fields. The book is aimed primarily at students in the sciences and engineering, as well as students at teacher training colleges but will also appeal to interested readers wanting to get an overview of scientific modelling in general and different modelling approaches in particular.
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| 2. |
- Gerlee, Philip, 1980, et al.
(author)
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Scientific Models
- 2016
-
Book (other academic/artistic)abstract
- A zebrafish, the hull of a miniature ship, a mathematical equation and a food chain - what do these things have in common? They are examples of models used by scientists to isolate and study particular aspects of the world around us. This book begins by introducing the concept of a scientific model from an intuitive perspective, drawing parallels to mental models and artistic representations. It then recounts the history of modelling from the 16th century up until the present day. The iterative process of model building is described and discussed in the context of complex models with high predictive accuracy versus simpler models that provide more of a conceptual understanding. To illustrate the diversity of opinions within the scientific community, we also present the results of an interview study, in which ten scientists from different disciplines describe their views on modelling and how models feature in their work. Lastly, it includes a number of worked examples that span different modelling approaches and techniques. It provides a comprehensive introduction to scientific models and shows how models are constructed and used in modern science. It also addresses the approach to, and the culture surrounding modelling in different scientific disciplines. It serves as an inspiration for model building and also facilitates interdisciplinary collaborations by showing how models are used in different scientific fields. The book is aimed primarily at students in the sciences and engineering, as well as students at teacher training colleges but will also appeal to interested readers wanting to get an overview of scientific modelling in general and different modelling approaches in particular.
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| 3. |
- Thunberg, Hans, 1956-, et al.
(author)
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The Widening Gap — A Swedish Perspective
- 2008
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In: Mathematics Education Research Journal. - 1033-2170 .- 2211-050X. ; 20:2, s. 38-56
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Journal article (peer-reviewed)abstract
- Transition problems from secondary to tertiary level in mathematics have been arecurrent issue in Sweden. This paper summarises the development during the lastdecades. Results from two recent research studies that illuminate the transitionproblem are presented. The first one, based on empirical data from a major Swedishtechnical university, characterises the widening gap, in content and in approach,between secondary school and first year university courses. The second study dealswith students’ encounters with mathematical proof and is based on a largeinvestigation at another main Swedish university. We discuss the influence on thecurrent transition problems of school reforms and of the great expansion of highereducation in Sweden during the last 10 – 15 years in view of the results from theresearch studies.
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| 4. |
- Bergqvist, Tomas, 1962-, et al.
(author)
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Upper secondary students’ task reasoning
- 2008
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In: International Journal of Mathematical Education in Science and Technology. - : Informa UK Limited. - 0020-739X .- 1464-5211. ; 39:1
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Journal article (peer-reviewed)abstract
- Upper secondary students’ task solving reasoning was analysed, with a focus on grounds for different strategy choices and implementations. The results indicate that mathematically well-founded considerations were rare. The dominating reasoning types were algorithmic reasoning, where students tried to remember a suitable algorithm, sometimes in a random way, and guided reasoning, where progress was possible only when essentially all important strategy choices were made by the interviewer.
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| 5. |
- Pejlare, Johanna, 1976
(author)
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On Axioms and Images in the History of Mathematics
- 2007
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Doctoral thesis (other academic/artistic)abstract
- This dissertation deals with aspects of axiomatization, intuition and visualization in the history of mathematics. Particular focus is put on the end of the 19th century, before David Hilbert's (1862–1943) work on the axiomatization of Euclidean geometry. The thesis consists of three papers. In the first paper the Swedish mathematician Torsten Brodén (1857–1931) and his work on the foundations of Euclidean geometry from 1890 and 1912, is studied. A thorough analysis of his foundational work is made as well as an investigation into his general view on science and mathematics. Furthermore, his thoughts on geometry and its nature and what consequences his view has for how he proceeds in developing the axiomatic system, is studied. In the second paper different aspects of visualizations in mathematics are investigated. In particular, it is argued that the meaning of a visualization is not revealed by the visualization and that a visualization can be problematic to a person if this person, due to a limited knowledge or limited experience, has a simplified view of what the picture represents. A historical study considers the discussion on the role of intuition in mathematics which followed in the wake of Karl Weierstrass' (1815–1897) construction of a nowhere differentiable function in 1872. In the third paper certain aspects of the thinking of the two scientists Felix Klein (1849–1925) and Heinrich Hertz (1857–1894) are studied. It is investigated how Klein and Hertz related to the idea of naïve images and visual thinking shortly before the development of modern axiomatics. Klein in several of his writings emphasized his belief that intuition plays an important part in mathematics. Hertz argued that we form images in our mind when we experience the world, but these images may contain elements that do not exist in nature.
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| 6. |
- Bergwall, Andreas, 1972-
(author)
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On a generality framework for proving tasks
- 2015
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In: Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education. - Prague : Charles University in Prague, Faculty of Education and ERME. - 9788072908448 ; , s. 86-92
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Conference paper (peer-reviewed)abstract
- In this paper I present an analytic framework for generality in textbook proving tasks that involve functions. The framework is discussed in relation to results obtained when analysing tasks in integral calculus. The results show that the frameworks’ categories are easily distinguishable if the functions are explicitly described. The results are also promising regarding the possibility to clarify differences between textbooks. The analysed sections exemplify that there is not necessarily a correlation between the number of general proving tasks and the opportunities for students to engage in reasoning about arbitrary functions. Limitations and possible refinements of the framework are also discussed.
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| 7. |
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| 8. |
- Höök, Mikael, 1982-, et al.
(author)
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Descriptive and predictive growth curves in energy system analysis
- 2011
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In: Natural Resources Research. - : Springer Science and Business Media LLC. - 1520-7439 .- 1573-8981. ; 20:2, s. 103-116
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Journal article (peer-reviewed)abstract
- This study reviews a variety of growth curve models and the theoretical frameworks that lay behind them. In many systems, growth patterns are, or must, ultimately be subjected to some form of limitation. A number of curve models have been developed to describe and predict such behaviours. Symmetric growth curves have frequently been used for forecasting fossil fuel production, but others have expressed a need for more flexible and asymmetric models. A number of examples show differences and applications of various growth curve models. It is concluded that these growth curve models can be utilised as forecasting tools, but are do not necessarily provide better predictions than any other method. Consequently, growth curve models and other forecasting methods should be used together to provide a triangulated forecast. Furthermore, the growth curve methodology offers a simple tool for resource management to determine what might happen to future production if resource availability poses a problem. In the light of peak oil and the awareness of natural resources as a basis for the continued well-being of society and mankind, resource management should be an important factor in future social planning.
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| 9. |
- Jansson, Fredrik
(author)
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What games support the evolution of an ingroup bias?
- 2015
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In: Journal of Theoretical Biology. - : Elsevier BV. - 0022-5193 .- 1095-8541. ; 373, s. 100-110
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Journal article (peer-reviewed)abstract
- There is an increasing wealth of models trying to explain the evolution of group discrimination and an ingroup bias. This paper sets out to systematically investigate the most fundamental assumption in these models: in what kind of situations do the interactions take place? What strategic structures - games - support the evolution of an ingroup bias? More specifically, the aim here is to find the prerequisites for when a bias also with respect to minimal groups - arbitrarily defined groups void of group-specific qualities - is selected for, and which cannot be ascribed to kin selection.Through analyses and simulations of minimal models of two-person games, this paper indicates that only some games are conducive to the evolution of ingroup favouritism. In particular, this class does not contain the prisoners׳ dilemma, but it does contain anti-co-ordination and co-ordination games. Contrasting to the prisoners׳ dilemma, these are games where it is not a matter of whether to behave altruistically, but rather one of predicting what the other person will be doing, and where I would benefit from you knowing my intentions.In anti-co-ordination games, on average, not only will agents discriminate between groups, but also in such a way that their choices maximise the sum of the available payoffs towards the ingroup more often than towards the outgroup. And in co-ordination games, even if agents do manage to co-ordinate with the whole population, they are more likely to co-ordinate on the socially optimal equilibrium within their group. Simulations show that this occurs most often in games where there is a component of risk-taking, and thus trust, involved. A typical such game is the stag hunt or assurance game.
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| 10. |
- Smolla, Marco, et al.
(author)
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Underappreciated features of cultural evolution
- 2021
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In: Proceedings of the Royal Society of London. Biological Sciences. - : The Royal Society. - 0962-8452 .- 1471-2954 .- 0962-8436 .- 1471-2970. ; 376:1828
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Journal article (peer-reviewed)abstract
- Cultural evolution theory has long been inspired by evolutionary biology. Conceptual analogies between biological and cultural evolution have led to the adoption of a range of formal theoretical approaches from population dynamics and genetics. However, this has resulted in a research programme with a strong focus on cultural transmission. Here, we contrast biological with cultural evolution, and highlight aspects of cultural evolution that have not received sufficient attention previously. We outline possible implications for evolutionary dynamics and argue that not taking them into account will limit our understanding of cultural systems. We propose twelve key questions for future research, among which are calls to improve our understanding of the combinatorial properties of cultural innovation, and the role of development and life history in cultural dynamics. Finally, we discuss how this vibrant research field can make progress by embracing its multidisciplinary nature.
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