| 1. |
- Gerlee, Philip, 1980, et al.
(author)
-
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)
-
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. |
- Bengmark, Samuel, 1965, et al.
(author)
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Success-factors in transition to university mathematics
- 2017
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In: International Journal of Mathematical Education in Science and Technology. - : Taylor & Francis Group. - 0020-739X .- 1464-5211. ; 48:7, s. 988-1001
-
Journal article (peer-reviewed)abstract
- This study examines different factors' relative importance for students' performance in the transition to university mathematics. Students' characteristics (motivation, actions and beliefs) were measured when entering the university and at the end of the first year. Principal component analysis revealed four important constructs: Self-efficacy, Motivation type, Study habits and Views of mathematics. Subsequently, orthogonal partial least squares (OPLS) analysis was used for measuring the constructs' ability to predict students' university mathematics grades. No individual constructs measured at the time of entrance predicted more than 5% of the variation. On the other hand, jointly they predicted 14%, which is almost in pair with upper secondary grades predicting 17%. Constructs measured at the end of the first year were stronger predictors, jointly predicting 37% of the variation in university grades, with Self-efficacy (21%) and Motivation (12%) being the two strongest individual predictors. In general, Study habits were not important for predicting university achievement. However, for students with low upper secondary grades, the textbook and interaction with peers, rather than internet-based resources, contributed positively to achievement. The association between Views of mathematics and performance was weak for all groups and non-existing for students with low grades.
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| 5. |
- Pejlare, Johanna, 1976
(author)
-
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. |
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| 7. |
- Kullberg, Angelika, 1969, et al.
(author)
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Improvements in learning addition and subtraction when using a structural approach in first grade
- 2024
-
In: Educational Studies in Mathematics. - : Springer. - 0013-1954 .- 1573-0816.
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Journal article (peer-reviewed)abstract
- Learning to calculate with natural numbers by structuring seems promising but how this can be taught in a sustainable manner remains an open question. An eight-month-long intervention based on the idea of using a structural approach to addition and subtraction, and particularly bridging through ten, was implemented in four Swedish first-grade classes. One goal was that by the end of first grade, students would be able to solve tasks such as subtracting 8 from 15 by using part-whole number relations. In this paper, we report on learning outcomes from task-based interviews with intervention and control groups before, immediately after, and one year after the intervention, in order to investigate long-term effects and whether students used a structural approach when solving tasks in a higher number range in the second grade. In comparison to controls, students in the intervention group showed higher increases in their learning outcomes. Moreover, the intervention group used a structural approach to a larger extent when solving tasks in higher number ranges, whereas students in the control group more commonly used single-unit counting to solve such tasks. These findings have implications both for teaching and for research on students' development of arithmetic skills.
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| 8. |
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| 9. |
- 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
-
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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| 10. |
- 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
-
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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| 11. |
- Olteanu, Constanta, 1960-
(author)
-
"Vad skulle x kunna vara?" : andragradsekvation och andragradsfunktion som objekt för lärande
- 2007
-
Doctoral thesis (other academic/artistic)abstract
- Algebraic equations and functions play an important role in various mathematical topics, including algebra, trigonometry, linear programming and calculus. Accordingly, various documents, such as the most recent Swedish curriculum (Lpf 94) for upper secondary school and the course syllabi in mathematics, specify what the students should learn in Mathematics Course B. They should be able to solve quadratic equations and apply this knowledge in solving problems, explain the properties of a function, as well as be able to set up, interpret and use some nonlinear functions as models for real processes. To implement these recommendations, it is crucial to understand the students’ way of experiencing quadratic equations and functions, and describe the meaning these have for the students in relation to the possibility they have to their experience of them. The aim of this thesis is to analyse, understand and explain the relation between the handled and learned content, which consists of second-degree equations and quadratic functions, in classroom practice. This means that content is the research object and not the teacher’s conceptions or knowledge of, or about this content. This restriction implies that the handled and learned contents are central in this study and will be analysed from different perspectives. The study includes two teachers and 45 students in two different classes. The data consist of video-recordings of lessons, individual sessions, interviews and the teachers’/researcher’s review of the individual sessions. The students’ tests also constituted an important part of the data collection. When analysing the data, concepts relating to variation theory have been used as analytical tools. Data have been analysed in respect of the teachers’ focus on the lesson content, which aspects are ignored and which patterns of dimensions of variations are constituted when the contents are handled by the teachers in the classroom. Also, data have been analysed in respect of the students’ focus when they solve different exercises in a test situation. It can be shown that the meaning of parameters, the unknown quantity in an equation and the function’s argument change several times when the teacher presents the content in the classroom and when the students solve different exercises. It can also be shown that the teachers and the students develop complicated patterns of variation during the lessons and that the ways in which the teachers open up dimensions of variation play an important role in the learning process. The results indicate that there is a convergent variation leading the students to improve their learning. By focusing on some aspects of the objects of learning and create convergent variations, it is possible for the students to understand the difference between various interpretations of these aspects and thereafter focus on the interpretation that fits in a certain context. Furthermore, this variation leads the students to make generalisations in each object of learning (equations and functions) and between these objects of learning. These generalisations remain over time, despite working with new objects of learning. An important result in this study is that the implicit or explicit arguments of a function can make it possible to discern an equation from a function despite the fact that they are constituted by the same algebraic expression.
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| 12. |
- Eriksson, Urban, Lektor i fysik med inriktning mot fysikdidaktik, 1968-
(author)
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Disciplinary discernment : reading the sky in astronomy education
- 2019
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In: Physical review physics education research. - : American Physical Society. - 2469-9896. ; 15:1
-
Journal article (peer-reviewed)abstract
- This theoretical paper introduces a new way to view and characterize learning astronomy. It describes a framework, based on results from empirical data, analyzed through standard qualitative research method- ology, in which a theoretical model for a vital competency of learning astronomy is proposed: reading the sky, a broad description under with various skills and competencies are included. This model takes into account not only disciplinary knowledge but also disciplinary discernment and extrapolating three dimensionality. Together, these constitute the foundation for the competency referred to as reading the sky. In this paper, these competencies are described and discussed and merged to form a new framework vital for learning astronomy to better match the challenges students face when entering the discipline of astronomy.
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| 13. |
- Lundberg, Anna L.V. 1967
(author)
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Encountering Proportional Reasoning During a Single Algebra Lesson: A Microgenetic Analysis
- 2022
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In: International Electronic Journal of Mathematics Education. - Eastbourne, United Kingdom : Modestum Publishing Ltd. - 1306-3030. ; 17:1
-
Journal article (peer-reviewed)abstract
- This case study explores how 12-13-year-old students encounter proportional reasoning while working with geometric patterning tasks using concrete materials. The focus is on the students’ use of spontaneous concepts when first dealing with such patterns in the context of collaborative work. Based on video recordings of a single lesson, a microgenetic analysis was performed to identify students’ learning trajectories, starting with students familiarizing themselves with pattern structure, followed by engagement in proportional reasoning, and ending with students perceiving a new technique to handle a situation where proportional reasoning did not suffice. While some student groups were able to move along the whole trajectory, most groups, when facing challenges, regressed to simpler techniques. The results provide new insights into students’ learning trajectories, which can be used to support students’ progress in the context of student-teacher interaction.
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| 14. |
- Asratian, Armen, et al.
(author)
-
Proper path-factors and interval edge-coloring of (3,4)-biregular bigraphs
- 2009
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In: Journal of Graph Theory. - : Wiley Periodicals Inc.. - 0364-9024 .- 1097-0118. ; 61:2, s. 88-97
-
Journal article (peer-reviewed)abstract
- An interval coloring of a graph G is a proper coloring of E(G) by positive integers such that the colors on the edges incident to any vertex are consecutive. A (3,4)-biregular bigraph is a bipartite graph in which each vertex of one part has degree 3 and each vertex of the other has degree 4; it is unknown whether these all have interval colorings. We prove that G has an interval coloring using 6 colors when G is a (3,4)-biregular bigraph having a spanning subgraph whose components are paths with endpoints at 3-valent vertices and lengths in {2, 4, 6, 8}. We provide several sufficient conditions for the existence of such a subgraph.
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| 15. |
- Lindahl, Karl-Olof, 1975-
(author)
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Applied Algebraic Dynamics
- 2010
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In: P-Adic Numbers, Ultrametric Analysis, and Applications. - : Pleiades Publishing, Ltd.. - 2070-0466 .- 2070-0474. ; 2:4, s. 360-362
-
Journal article (peer-reviewed)
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| 16. |
- Sorooshian, Shahryar, 1980, et al.
(author)
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Performance of the decision-making trial and evaluation laboratory
- 2023
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In: AIMS Mathematics. - : American Institute of Mathematical Sciences (AIMS). - 2473-6988. ; 8:3, s. 7490-7514
-
Journal article (peer-reviewed)abstract
- Multiple attribute decision-making (MADM) techniques constitute a practical approach for solving complex problems involving multiple and often conflicting criteria. Decision-making trial and evaluation laboratory (DEMATEL) is a popular MADM technique with both admirers and critics. This study presents a comprehensive review of DEMATEL through bibliometric analysis using the Scopus database. This article examined 3,521 papers published in journals, conferences or books between 1981 and 2023. We examined a few parameters for commenting on the performance of the technique. Among them are research outputs, the network of DEMATEL users, implementation subject areas, research zones, financing opportunities and publication hosts and their impact trends. We conclude from the findings of this study that the DEMATEL is capable of dealing with modern problem-solving in future environments. Although the growth of new MADMs is obvious, based on the gathered data, we forecast that more than 776 documents will be published in 2025 using DEMATEL for problem-solving. This expanding tendency will continue in the future. As distinct MADMs have diverse constraints, foundations, computing complexity and standpoints, which result in different performances, outmoded low-performance MADM techniques must be reported by researchers to continue this paper’s objective to minimize ambiguity among decision-makers and practitioners. To facilitate such a comparison in the future, a quantitative performance coefficient was also developed here.
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| 17. |
- Pejlare, Johanna, 1976, et al.
(author)
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Programming to learn mathematics - exploring student teachers' instrumental genesis
- 2022
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In: The relation between mathematics education research and teachers' professional development. - Göteborg : Swedish Society for Research in Mathematics Education. - 1651-3274. - 9789198402452 ; 16, s. 69-79
-
Conference paper (peer-reviewed)abstract
- Programming is now a prescribed part of the curriculum in mathematics in both primary and secondary school in Sweden, as in many other countries. Teacher training must thus prepare students for the challenges of teaching mathematics with programming. We explore how student teachers see their own training in programming in relation to mathematics and what opportunities to learn mathematics they believe that programming can offer pupils in school. An instrumental approach is used to analyse observations and a questionnaire on secondary school student teacher’ experience of a programming lab, where they investigate Riemann sums with programming. We find that students feel challenged by both the programming and the mathematical content, and that they see the challenges as useful, both for themselves and for their future pupils.
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| 18. |
- Borg, Andreas, et al.
(author)
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Analysing mathematical programming schemes using different lenses
- 2023
-
In: Nordisk matematikkdidaktikk, NOMAD. - : University of Gothenburg, Sweden. - 1104-2176. ; 28:3–4, s. 199-219
-
Journal article (peer-reviewed)abstract
- The use of programming in mathematics education is undergoing a renaissanceand, in this paper, we analyse students’ handling of programming in mathematicsusing the Instrumental approach as a theoretical lens. We are especially interestedin analysing the development of mental schemes using two analytical frameworkswhich are compared and contrasted according the idea of networking theories. Thestudy illustrates that the frameworks’ detail of richness can have both advantagesand disadvantages and that one of the frameworks are more customed to be appliedwhen analysing students’ instrumental genesis concerning the use of a programmingenvironment as a mathematical artefact.
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| 19. |
- Dyrvold, Anneli, 1970-
(author)
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Difficult to read or difficult to solve? : The role of natural language and other semiotic resources in mathematics tasks
- 2016
-
Doctoral thesis (other academic/artistic)abstract
- When students solve mathematics tasks, the tasks are commonly given as written text, usually consisting of natural language, mathematical notation and different types of images. This is one reason why reading and interpreting such texts are important parts of being mathematically proficient, at least within the school context. The ability utilized when dealing with aspects of mathematical text is denoted in this thesis as a mathematical reading ability; this ability is useful when reading mathematical language, for example, in task text. There is, however, a lack of knowledge of what characterizes this mathematical language, what students need to learn regarding the mathematical language, and exactly which mathematical language that tests should preferably assess. Therefore, the purpose of this thesis is to contribute to the knowledge of aspects of difficulty related to textual features in mathematics tasks. In particular, one aim is to distinguish between a difficulty that has to do with a mathematical ability and another that has not. Different types of text analyses are utilized to capture textural features that might be demanding for the students when reading and solving mathematics tasks. Aspects regarding vocabulary are investigated both in a literature review and in a study where corpora are used to analyse word commonness. Other textual analyses focus on textual features that concern mathematical notation and images, besides natural language. Statistical methods are used to analyse potential relations between the textual features of interest and both task difficulty and task demand on reading ability. The results from the research review are sparse regarding difficult vocabulary, since few of the reviewed studies analyses word aspects separately. Several of the analysed textual features are related to aspects of difficulty. The results show that tasks with more words that are uncommon both in a mathematical context and in an everyday context, may favour students with good reading ability rather than students with good mathematical ability. Another textual feature that is likely to be demanding for students, is if the task texts contains many meaning relations, for example, when several words refer to the same or similar object. These results have implications for the school practice both regarding textual features that are important from an educational perspective and regarding the construction of tests. The research does also contribute to an understanding of what characterizes a mathematical language.
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| 20. |
- Viirman, Olov, et al.
(author)
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Different views – some Swedish mathematics students’ concept images of the function concept
- 2010
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In: Nordisk matematikkdidaktikk. - Göteborg : NCM. - 1104-2176. ; 15:4, s. 5-24
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Journal article (other academic/artistic)abstract
- This study analyses what kind of concept images a group of engineering and teacher students have of the function concept, and how these concept images are related to the historical development of this concept. The study was conducted using questionnaires, and 34 students at a Swedish university participated. It is found that the students primarily rely on operational conceptions of the function concept, with only a minority of students possessing structural conceptions. The definitions given by the students mostly resemble an 18th or 19th century view of functions. The study also indicates that the character of the definitions given in the textbooks used by the students affect their concept images.
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| 21. |
- Viirman, Olov
(author)
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The functions of function discourse : University mathematics teaching from a commognitive standpoint
- 2014
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In: International journal of mathematical education in science and technology. - : Taylor & Francis Group. - 0020-739X .- 1464-5211. ; 45:4, s. 512-527
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Journal article (peer-reviewed)abstract
- This paper addresses a topic within university mathematics education which has been somewhat underexplored: the teaching practices actually used by university mathematics teachers when giving lectures. The study investigates the teaching practices of seven Swedish university teachers on the topic of functions using a discursive approach, the commognitive framework of Sfard. In the paper a categorization of the construction and substantiation routines used by the teachers is presented, for instance various routines for constructing definitions and examples, and for verifying whether an example satisfies a given definition. The findings show that although the overall form of the lectures is similar, with teachers using ‘chalk talk’, and overt student participation limited to asking and answering questions, there are in fact significant differences in the way the teachers present and do mathematics in their lectures. These differences present themselves both on the level of discursive routines and on a more general level in how the process of doing mathematics is made visible in the teachers’ teaching practices. Moreover, I believe that many of the results of the study could be relevant for investigating the teaching of other mathematical topics.
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| 22. |
- Helenius, Ola, 1970, et al.
(author)
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Measuring temperature within the didactic space of preschool
- 2016
-
In: Nordisk matematikkdidaktikk, NOMAD. - : Nationellt centrum för matematikutbildning (NCM). - 1104-2176. ; 21:4, s. 155-176
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Journal article (peer-reviewed)abstract
- The informal character of preschool mathematics, engaged in during children’s play, places complex requirements on preschool teachers. It also leads to challenges in developing appropriate analytical tools for researching teacher work. In this paper a framework, the ”didaktic space”, is described and used to analyse interactions between preschool teachers and children in relationship to mathematical learning situations. An interaction between a preschool teacher and a group of children about how to compare their temperatures is analysed, using this framework. The analysis focuses on how the teacher’s contributions as well as those of the children changed as the role of the mathematics changed. The paper discusses how the didaktic space offers a nuanced understanding of preschool mathematical situations, both to researchers and to teachers.
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| 23. |
- Muhrman, Karolina
(author)
-
Inget klöver utan matematik : En studie av matematik i yrkesutbildning och yrkesliv
- 2016
-
Doctoral thesis (other academic/artistic)abstract
- Syftet med avhandlingen är att öka förståelsen för aspekter som inverkar på relationen mellan yrkeselevers kunskaper och de kunskaper som behövs i yrkeslivet. Detta görs genom att undersöka olika aktörers perspektiv på yrkeslivets behov av matematikkunskaper, matematikundervisning på yrkesprogram och utformningen av läroplanen Gy11. Studien görs inom gymnasiets naturbruksprogram med inriktning mot lantbruksutbildning och inom lantbruksyrket. Det empiriska materialet består av kvalitativa intervjuer med yrkesverksamma lantbrukare, yrkeslärare och matematiklärare samt intervjuer och enkäter med elever. Resultaten från den empiriska studien har analyserats i relation till läroplanen Gy11. För analysen används framförallt Bernsteins läroplansteoretiska perspektiv med begreppen pedagogiska koder och diskurser, i vissa delar tillsammans med D’Ambrosios etnomatematiska perspektiv. Resultaten visar att lantbruksyrket kräver goda matematikkunskaper, men att det i vissa fall finns ett diskursivt gap mellan skolans matematikundervisning och behovet av matematikkunskaper i yrkeslivet. Trots ämnesplanens inriktning mot en matematik som är relaterad till elevernas yrkesinriktning, är matematikundervisningen ofta starkt knuten till en matematikbok utan relation till det yrke eleverna utbildas för. Undervisningens organisering styrs av en mängd ramfaktorer som både kan handla om tid, gruppsammansättningar och schema, men också om lärarnas syn på kunskap. De nationella proven utgör en betydande ramfaktor som i många fall styr undervisningen i högre grad än vad innehållet i ämnesplanen gör. Undervisningens svaga koppling till elevernas yrkesinriktning gör dem omotiverade att lära sig matematik eftersom de har svårt att se hur de ska kunna använda sina kunskaper i sitt kommande yrke. En del elever har också svårigheter med att rekontextualisera sina matematikkunskaper från skolkontexten till yrkeslivets kontext vilket bland annat kan försämra deras anställningsmöjligheter.
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| 24. |
- Jansson, Fredrik
(author)
-
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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| 25. |
- Smolla, Marco, et al.
(author)
-
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
-
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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| 26. |
- Sorooshian, Shahryar, 1980, et al.
(author)
-
Expedited analytical hierarchical process for multicriteria decision making
- 2022
-
In: ICIC Express Letters. - 1881-803X. ; 16:2, s. 145-151
-
Journal article (peer-reviewed)abstract
- In this study, a procedure to overcome analytical hierarchical process (AHP) limitations was developed and tested, and a tool created via pairwise comparison chart and weighted sum method hybridization was introduced. In addition, a multicriteria decision-making software was selected to validate the constructed hybrid decision-making tool. The software was formulated based on an established decision-making technique. Data for the comparison analysis were obtained from an ongoing research, and output from the comparison analysis provided evidence for the accuracy of the constructed tool. The proposed hybridized method aligned with AHP reasoning but demonstrated a faster process; hence, it was called ‘expedited AHP’.
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| 27. |
- Westin, Jonas, et al.
(author)
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Rollspelsövningar för undervisning av matematiska modeller på universitetsnivå
- 2022
-
In: Högre Utbildning. - : Cappelen Damm Akademisk. - 2000-7558. ; 12:1, s. 38-46
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Journal article (other academic/artistic)abstract
- Matematiska modeller används i många sammanhang för att beskriva system, undersöka frågeställningar och skapa beslutsunderlag. Samtidigt ställer denna typ av matematiskt tänkande och problemformulering ofta höga krav på användarens matematiska förmågor. På kurser med inslag av matematisk modellering kan därför en del studenter ha svårt att tillgodogöra sig och förstå abstrakta matematiska modeller och deras kopplingar till den omvärld som modellerna avser att beskriva. I denna artikel beskrivs och diskuteras resultatet av ett pedagogiskt utvecklingsprojekt med syfte att utveckla och utvärdera rollspel som metod för undervisning i matematik och statistik på universitetsnivå. En slutsats från projektet är att det framförallt är studenternas reflektioner och analyser efter själva övningen som skapar en djupare förståelse för de bakomliggande koncepten och idéerna rollspelet avser att spegla genom att länka samman matematiska modeller och teorier med studenternas upplevelser från rollspelsövningen. Användning av rollspelsövningar vid undervisning i högre matematik kan både vara ett verktyg för att repetera kursinnehåll och för att sänka abstraktionsnivån. En tidig version av artikeln har presenterats vid den universitetspedagogiska konferensen vid Umeå universitet 2017.
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| 28. |
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| 29. |
- Pejlare, Johanna, 1976
(author)
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Infinite sums and the calculation of ?, as presented by the Swedish mathematician Anders Gabriel Duhre in the early 18th century
- 2019
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In: Proceedings of the Eighth European Summer University on History and Epistemology in Mathematics Education ESU 8. - Oslo : Oslo Metropolitan University Storbyuniversitetet. - 2535-6984 .- 2535-6992. - 9788283642117
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Conference paper (peer-reviewed)abstract
- Anders Gabriel Duhre, an important mathematician and mathematics educator in Sweden during the 18th century, contributed with two textbooks in mathematics, one in algebra and one in geometry. Among others, he treats infinitesimals based on Nieuwentijts’ theories from Analysis infinitorum and infinite sums based on Wallis’ method of induction from Arithmetica infinitorum. Based on these results, Duhre develops an ingenious method to determine the area enclosed by curves by constructing a corresponding curve. He applies his method to the circle in order to find an expression of ? as an infinite series. The series he finds is a modified version of the Gregory-Leibniz’ series. In the present paper we consider in detail Duhre’s presentation in order to further investigate the influence upon him as well as his influence on the Swedish mathematical society of his time.
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| 30. |
- Sjögren, Jörgen, et al.
(author)
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Concept Formation and Concept Grounding
- 2014
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In: Philosophia. - : Springer Science+Business Media B.V.. - 0048-3893 .- 1574-9274. ; 42:3, s. 827-839
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Journal article (peer-reviewed)abstract
- Recently Carrie S. Jenkins formulated an epistemology of mathematics, or rather arithmetic, respecting apriorism, empiricism, and realism. Central is an idea of concept grounding. The adequacy of this idea has been questioned e.g. concerning the grounding of the mathematically central concept of set (or class), and of composite concepts. In this paper we present a view of concept formation in mathematics, based on ideas from Carnap, leading to modifications of Jenkins’s epistemology that may solve some problematic issues with her ideas. But we also present some further problems with her view, concerning the role of proof for mathematical knowledge.
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| 31. |
- Mamontov, Eugen, 1955
(author)
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Ordinary differential equation system for population of individuals and the corresponding probabilistic model
- 2008
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In: Mathl. Computer Modelling. - : Elsevier BV. - 0895-7177.
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Journal article (peer-reviewed)abstract
- The key model for particle populations in statistical mechanics is the Bogolyubov–Born– Green–Kirkwood–Yvon (BBGKY) equation chain. It is derived mainly from the Hamilton ordinary differential equation (ODE) system for the vectors of the particle states in the particle position-momentum phase space. Many problems beyond physics or chemistry, for instance, in the living-matter sciences (biology, medicine, ecology, and scoiology) make it necessary to extend the notion of a particle to an individual, or active particle. This challenge is met by the generalized kinetic theory. It implements the extension by extending the phase space from the space of the position-momentum vectors to more rich spaces formed by the state vectors with the entries which need not be limited to the entries of the position and momentum: they include other scalar variables (e.g., those associated with modelling homeorhesis or other features inherent to the individuals). One can assume that the dynamics of the state vector in the extended space, i.e. the states of the individuals (rather than common particles) is also described by an ODE system. The latter, however, need not be the Hamilton one. The question is how one can derive the analogue of the BBGKY paradigm for the new settings. The present work proposes an answer to this question. It applies a very limited number of carefully selected tools of probability theory and common statistical mechanics. It in particular uses the well-known feature that the maximum number of the individuals which can mutually interact simultaneously is bounded by a fixed value of a few units. The present approach results in the finite system of equations for the reduced many-individual distribution functions thereby eliminating the so-called closure problem inevitable in the BBGKY theory. The thermodynamic-limit assumption is not needed either. The system includes consistently derived terms of all of the basic types known in kinetic theory, in particular, both the “mean-field” and scattering-integral terms, and admits the kinetic equation of the form allowing a direct chemical-reaction reading. The present approach can deal with Hamilton’s equation systems which are nonmonogenic and not treated in statistical mechanics. The proposed modelling suggests the basis of the generalized kinetic theory and may serve as the stochastic mechanics of population of individuals.
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| 32. |
- Kullberg, Angelika, 1969, et al.
(author)
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Mechanisms enabling knowledge production in learning study
- 2020
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In: International Journal for Lesson and Learning Studies. - : Emerald Group Publishing Limited. - 2046-8253 .- 2046-8261. ; 9:1, s. 78-91
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Journal article (peer-reviewed)abstract
- PurposeThe purpose of this paper is to add to the discussion about practitioner research in schools – by addressing mechanisms and systematic strategies based on theory in a research model, which enables the creation of knowledge products that enhance student learning and are sharable between teachers.Design/methodology/approachThe research question is the following: Can a specific form of teachers’ research produce practice-based knowledge relevant beyond the borders of the local school context? This question is addressed through empirical examples from previously published papers on learning studies in natural sciences, mathematics and language.FindingsThis paper promotes the view that teachers in learning studies can create practical public knowledge relevant beyond their local context. The authors suggest that learning studies and variation theory can offer teachers mechanisms to create such public knowledge.Originality/valueThe paper proposes that teachers’ collaboration in professional learning communities, as in a learning study, not only has the capacity to increase students’ and teachers’ learning, but it can also be used to create practical public knowledge.
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| 33. |
- Pejlare, Johanna, 1976, et al.
(author)
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On the relations between geometry and algebra in Gestrinius' edition of Euclid's Elements
- 2016
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In: Radford, L., Furinghetti, F., & Hausberger, T. (Eds.) (2016). Proceedings of the 2016 ICME Satellite Meeting of the International Study Group on the Relations Between the History and Pedagogy of Mathematics. Montpellier, France: IREM de Montpellier.. - 2909916510 ; , s. 513-523
-
Conference paper (peer-reviewed)abstract
- In 1637 the Swedish mathematician Martinus Erici Gestrinius contributed with a commented edition of Euclid’s Elements. In this article we analyse the relationship between geometry and algebra in Gestrinius’ Elements, as presented in Book II. Of particular interest are Propositions 4, 5, and 6, dealing with straight lines cut into equal and unequal parts, and the three kinds of quadratic equations Gestrinius associates with them. We argue that Gestrinius followed Clavius translation of the Elements, but was influenced by Ramus to include algebra.
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| 34. |
- Ögren, Magnus, 1977-, et al.
(author)
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There’s more to the multimedia effect than meets the eye : is seeing pictures believing?
- 2017
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In: Instructional science. - : Springer Netherlands. - 0020-4277 .- 1573-1952. ; 45:2, s. 263-287
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Journal article (peer-reviewed)abstract
- Textbooks in applied mathematics often use graphs to explain the meaning of formulae, even though their benefit is still not fully explored. To test processes underlying this assumed multimedia effect we collected performance scores, eye movements, and think-aloud protocols from students solving problems in vector calculus with and without graphs. Results showed no overall multimedia effect, but instead an effect to confirm statements that were accompanied by graphs, irrespective of whether these statements were true or false. Eye movement and verbal data shed light on this surprising finding. Students looked proportionally less at the text and the problem statement when a graph was present. Moreover, they experienced more mental effort with the graph, as indicated by more silent pauses in thinking aloud. Hence, students actively processed the graphs. This, however, was not sufficient. Further analysis revealed that the more students looked at the statement, the better they performed. Thus, in the multimedia condition the graph drew students’ attention and cognitive capacities away from focusing on the statement. A good alternative strategy in the multimedia condition was to frequently look between graph and problem statement, and thus to integrate their information. In conclusion, graphs influence where students look and what they process, and may even mislead them into believing accompanying information. Thus, teachers and textbook designers should be very critical on when to use graphs and carefully consider how the graphs are integrated with other parts of the problem.
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| 35. |
- Hamon, Thierry, et al.
(author)
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Combining Compositionality and Pagerank for the Identification of Semantic Relations between Biomedical Words
- 2012
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In: BioNLP. - 9781937284206 - 1937284204 ; , s. 109-117
-
Conference paper (peer-reviewed)abstract
- The acquisition of semantic resources and relations is an important task for several applications, such as query expansion, information retrieval and extraction, machine translation. However, their validity should also be computed and indicated, especially for automatic systems and applications. We exploit the compositionality based methods for the acquisition of synonymy relations and of indicators of these synonyms. We then apply pagerank-derived algorithm to the obtained semantic graph in order to filter out the acquired synonyms. Evaluation performed with two independent experts indicates that the quality of synonyms is systematically improved by 10 to 15% after their filtering.
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| 36. |
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| 37. |
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| 38. |
- Brandes, Julia, et al.
(author)
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On generating functions in additive number theory, II: lower-order terms and applications to PDEs
- 2021
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In: Mathematische Annalen. - : Springer Science and Business Media LLC. - 0025-5831 .- 1432-1807. ; 379, s. 347-76
-
Journal article (peer-reviewed)abstract
- We obtain asymptotics for sums of the form Sigma(p)(n=1) e(alpha(k) n(k) + alpha(1)n), involving lower order main terms. As an application, we show that for almost all alpha(2) is an element of [0, 1) one has sup(alpha 1 is an element of[0,1)) | Sigma(1 <= n <= P) e(alpha(1)(n(3) + n) + alpha(2)n(3))| << P3/4+epsilon, and that in a suitable sense this is best possible. This allows us to improve bounds for the fractal dimension of solutions to the Schrodinger and Airy equations.
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| 39. |
- Liu, Yang, 1960-
(author)
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Syllogistic Analysis and Cunning of Reason in Mathematics Education
- 2013
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Doctoral thesis (other academic/artistic)abstract
- This essay explores the issue of organizing mathematics education by means of syllogism. Two aspects turn out to be particularly significant. One is the syllogistic analysis while the other is the cunning of reason. Thus the exploration is directed towards gathering evidence of their existence and showing by examples their usefulness within mathematics education.The syllogistic analysis and the cunning of reason shed also new light on Chevallard's theory of didactic transposition. According to the latter, each piece of mathematical knowledge used inside school is a didactic transposition of some other knowledge produced outside school, but the theory itself does not indicate any way of transposing, and this empty space can be filled with the former.A weak prototype of syllogism considered here is Freudenthal's change of perspective. Some of the major difficulties in mathematics learning are connected with the inability of performing change of perspective. Consequently, to ease the difficulties becomes a significant issue in mathematics teaching. The syllogistic analysis and the cunning of reason developed in this essay are the contributions to the said issue.
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| 40. |
- Wang, Siyang, et al.
(author)
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CONVERGENCE OF FINITE DIFFERENCE METHODS FOR THE WAVE EQUATION IN TWO SPACE DIMENSIONS
- 2018
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In: Mathematics of Computation. - : American Mathematical Society (AMS). - 0025-5718 .- 1088-6842. ; 87:314, s. 2737-2763
-
Journal article (peer-reviewed)abstract
- When using a finite difference method to solve an initial-boundary-value problem, the truncation error is often of lower order at a few grid points near boundaries than in the interior. Normal mode analysis is a powerful tool to analyze the effect of the large truncation error near boundaries on the overall convergence rate, and has been used in many research works for different equations. However, existing work only concerns problems in one space dimension. In this paper, we extend the analysis to problems in two space dimensions. The two dimensional analysis is based on a diagonalization procedure that decomposes a two dimensional problem to many one dimensional problems of the same type. We present a general framework of analyzing convergence for such one dimensional problems, and explain how to obtain the result for the corresponding two dimensional problem. In particular, we consider two kinds of truncation errors in two space dimensions: the truncation error along an entire boundary, and the truncation error localized at a few grid points close to a corner of the computational domain. The accuracy analysis is in a general framework, here applied to the second order wave equation. Numerical experiments corroborate our accuracy analysis.
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| 41. |
-
Discrete Geometry and Mathematical Morphology : First International Joint Conference, DGMM 2021, Uppsala, Sweden, May 24–27, 2021, Proceedings
- 2021
-
Editorial collection (peer-reviewed)abstract
- This book constitutes the proceedings of the First IAPR International Conference on Discrete Geometry and Mathematical Morphology, DGMM 2021, which was held during May 24-27, 2021, in Uppsala, Sweden.The conference was created by joining the International Conference on Discrete Geometry for computer Imagery, DGCI, with the International Symposium on Mathematical Morphology, ISMM.The 36 papers included in this volume were carefully reviewed and selected from 59 submissions. They were organized in topical sections as follows: applications in image processing, computer vision, and pattern recognition; discrete and combinatorial topology; discrete geometry - models, transforms, visualization; discrete tomography and inverse problems; hierarchical and graph-based models, analysis and segmentation; learning-based approaches to mathematical morphology; multivariate and PDE-based mathematical morphology, morphological filtering.The book also contains 3 invited keynote papers.
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| 42. |
- Hammar Chiriac, Eva, 1961-
(author)
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Group work is not one, but a great many processes – Understanding group work dynamics
- 2012
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In: Encyclopedia of Mathematics Research. - New York : Nova Science Publishers, Inc. - 9781613242285 ; , s. 153-167
-
Book chapter (other academic/artistic)abstract
- This book discusses current research developments in the field of mathematics. Topics presented include exceptional groups, symmetric spaces and applications; LIE group analysis; graph groupoids and corresponding representations; fuzzy logic in molecular computing; closed-loop optimal fuzzy reasoning; nozzle design optimisation; a branch-and-price algorithm for the stochastic generalised assignment problem; parametric dual regularisation in a linear-convex mathematical programming and fast multilevel algorithms for diverse application in computational biology and bioinformatics.
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| 43. |
- Ni, Ying, 1976-
(author)
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Nonlinearly Perturbed Renewal Equation with Perturbations of a Non-polynomial Type
- 2010
-
In: Proceedings of the International Symposium on Stochastic Models in Reliability Engineering, Life Science and Operations Management, Beer Sheva, 2010.. - Beer Sheva : SCE - Shamoon College of Engineering. ; , s. 754-763
-
Conference paper (peer-reviewed)abstract
- The object of study is a model of nonlinearly perturbed continuous-time renewal equation with multivariate non-polynomial perturbations. The characteristics of the distribution generating the renewal equation are assumed to have expansions in the perturbation parameter with respect to a non-polynomial asymptotic scale which can be considered as a generalization of the standard polynomial scale. Exponential asymptotics for such a model are obtained and applications are given.
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| 44. |
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| 45. |
- Eriksson, Kimmo, et al.
(author)
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Bentley’s conjecture on popularity toplist turnover under random copying
- 2010
-
In: The Ramanujan journal. - : Springer Science and Business Media LLC. - 1382-4090 .- 1572-9303. ; 23, s. 371-396
-
Journal article (peer-reviewed)abstract
- Bentley et al studied the turnover rate in popularity toplists in a ’random copying’ model of cultural evolution. Based on simulations of a model with population size N, list length ℓ and invention rate μ, they conjectured a remarkably simple formula for the turnover rate: ℓ√μ. Here we study an overlapping generations version of the random copying model, which can be interpreted as a random walk on the integer partitions of the population size. In this model we show that the conjectured formula, after a slight correction, holds asymptotically.
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| 46. |
- Gerken, Jan, 1991, et al.
(author)
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Equivariance versus augmentation for spherical images
- 2022
-
In: Proceedings of Machine Learning Resaerch. ; , s. 7404-7421
-
Conference paper (peer-reviewed)abstract
- We analyze the role of rotational equivariance in convolutional neural networks (CNNs) applied to spherical images. We compare the performance of the group equivariant networks known as S2CNNs and standard non-equivariant CNNs trained with an increasing amount of data augmentation. The chosen architectures can be considered baseline references for the respective design paradigms. Our models are trained and evaluated on single or multiple items from the MNIST- or FashionMNIST dataset projected onto the sphere. For the task of image classification, which is inherently rotationally invariant, we find that by considerably increasing the amount of data augmentation and the size of the networks, it is possible for the standard CNNs to reach at least the same performance as the equivariant network. In contrast, for the inherently equivariant task of semantic segmentation, the non-equivariant networks are consistently outperformed by the equivariant networks with significantly fewer parameters. We also analyze and compare the inference latency and training times of the different networks, enabling detailed tradeoff considerations between equivariant architectures and data augmentation for practical problems.
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| 47. |
- Liljekvist, Yvonne, 1967-, et al.
(author)
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Multi-theoretical approach when researching mathematics teachers’ professional development in self-organized online groups
- 2019
-
In: Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education (CERME11) ⟨hal-02418200⟩.
-
Conference paper (peer-reviewed)abstract
- Teachers worldwide are using social media as a professional development resource. In studying social media as ‘a place’ for teachers’ professional development, we investigated large Facebook groups with themes connected to teaching and learning in compulsory schools. The interaction in these groups was analysed within the framework of systemic functional grammar. In order to reveal knowledge known and shared by teachers as a community, we have also used Shulman’s (1987) framework. Most posts received responses and this response is in line with the expected response pattern. The speech functions ‘Questions’ and ‘Offers’ were most common. Further, most posts addressed subject specific knowledge. The multi-theoretical approach used when researching mathematics teachers’ professional development in self-organized online groups showed that these large Facebook groups facilitated professional learning.
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| 48. |
- Lundow, Per Håkan, et al.
(author)
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EXACT AND APPROXIMATE COMPRESSION OF TRANSFER MATRICES FOR GRAPH HOMOMORPHISMS
- 2008
-
In: LMS Journal of Computation and Mathematics. - : Cambridge University Press. - 1461-1570. ; 11, s. 1-14
-
Journal article (peer-reviewed)abstract
- The aim of this paper is to extend the previous work on transfer matrix compression in the case of graph homomorphisms. For H-homomorphisms of lattice-like graphs we demonstrate how the automorphisms of H, as well as those of the underlying lattice, can be used to reduce the size of the relevant transfer matrices. As applications of this method we give currently best known bounds for the number of 4- and 5-colourings of the square grid, and the number of 3- and 4-colourings of the three-dimensional cubic lattice. Finally, we also discuss approximate compression of transfer matrices.
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| 49. |
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| 50. |
- Sterner, Görel, 1949, et al.
(author)
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Reasoning about Representations: Effects of an Early Math Intervention
- 2020
-
In: Scandinavian Journal of Educational Research. - : Informa UK Limited. - 0031-3831 .- 1470-1170. ; 64:5, s. 782-800
-
Journal article (peer-reviewed)abstract
- The outcomes of a longitudinal randomized number sense intervention including pre-, post- and follow-up tests are reported. The intervention was conducted in Grade 0 when children were six years old. Using Concrete-Representational-Abstract principles, a structured explicit 10-week program focusing on numbers and collective reasoning about representations was conducted by the classroom teachers. In addition to their regular mathematics teaching, a trained control group received an equally structured and explicit intervention program but without the critical mathematics component. The children in the experimental group outperformed the children in the control group on number sense growth between the pre- and the post-test. There was also a sustained effect of the intervention nine months later when children were assessed in Grade 1.
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