| 1. |
- Bengmark, Samuel, 1965, et al.
(författare)
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Success-factors in transition to university mathematics
- 2017
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Ingår i: International Journal of Mathematical Education in Science and Technology. - : Taylor & Francis Group. - 0020-739X .- 1464-5211. ; 48:7, s. 988-1001
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Tidskriftsartikel (refereegranskat)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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| 2. |
- Bergqvist, Tomas, 1962-, et al.
(författare)
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Upper secondary students’ task reasoning
- 2008
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Ingår i: International Journal of Mathematical Education in Science and Technology. - : Informa UK Limited. - 0020-739X .- 1464-5211. ; 39:1
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Tidskriftsartikel (refereegranskat)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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| 3. |
- Asratian, Armen, et al.
(författare)
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Proper path-factors and interval edge-coloring of (3,4)-biregular bigraphs
- 2009
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Ingår i: Journal of Graph Theory. - : Wiley Periodicals Inc.. - 0364-9024 .- 1097-0118. ; 61:2, s. 88-97
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Tidskriftsartikel (refereegranskat)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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| 4. |
- Dyrvold, Anneli, 1970-
(författare)
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Difficult to read or difficult to solve? : The role of natural language and other semiotic resources in mathematics tasks
- 2016
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)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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| 5. |
- Westin, Jonas, et al.
(författare)
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Rollspelsövningar för undervisning av matematiska modeller på universitetsnivå
- 2022
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Ingår i: Högre Utbildning. - : Cappelen Damm Akademisk. - 2000-7558. ; 12:1, s. 38-46
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)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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| 6. |
- Gerken, Jan, 1991, et al.
(författare)
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Equivariance versus augmentation for spherical images
- 2022
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Ingår i: Proceedings of Machine Learning Resaerch. ; , s. 7404-7421
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Konferensbidrag (refereegranskat)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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| 7. |
- Lundow, Per Håkan, et al.
(författare)
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EXACT AND APPROXIMATE COMPRESSION OF TRANSFER MATRICES FOR GRAPH HOMOMORPHISMS
- 2008
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Ingår i: LMS Journal of Computation and Mathematics. - : Cambridge University Press. - 1461-1570. ; 11, s. 1-14
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Tidskriftsartikel (refereegranskat)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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| 8. |
- Norqvist, Mathias, 1971-
(författare)
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On Mathematical Reasoning : being told or finding out
- 2016
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- School-mathematics has been shown to mainly comprise rote-learning of procedures where the considerations of intrinsic mathematical properties are scarce. At the same time theories and syllabi emphasize competencies like problem solving and reasoning. This thesis will therefore concern how task design can influence the reasoning that students apply when solving tasks, and how the reasoning during practice is associated to students’ results, cognitive capacity, and brain activity. In studies 1-3, we examine the efficiency of different types of reasoning (i.e., algorithmic reasoning (AR) or creative mathematically founded reasoning (CMR)) in between-groups designs. We use mathematics grade, gender, and cognitive capacity as matching variables to get similar groups. We let the groups practice 14 different solution methods with tasks designed to promote either AR or CMR, and after one week the students are tested on the practiced solution methods. In study 3 the students did the test in and fMRI-scanner to study if the differing practice would yield any lasting differences in brain activation. Study 4 had a different approach and focused details in students’ reasoning when working on teacher constructed tasks in an ordinary classroom environment. Here we utilized audio-recordings of students’ solving tasks, together with interviews with teachers and students to unravel the reasoning sequences that students embark on. The turning points where the students switch subtask and the reasoning between these points were characterized and visualized. The behavioral results suggest that CMR is more efficient than AR, and also less dependent on cognitive capacity during the test. The latter is confirmed by fMRI, which showed that AR had higher activation than CMR in areas connected to memory retrieval and working memory. The behavioral result also suggested that CMR is more beneficial for cognitively less proficient students than for the high achievers. Also, task design is essential for both students’ choice of reasoning and task progression. The findings suggest that: 1) since CMR is more efficient than AR, students need to encounter more CMR, both during task solving and in teacher presentation, 2) cognitive capacity is important but depending on task design, cognitive strain will be more or less high during test situations, 3) although AR-tasks does not prohibit the use of CMR they make it less likely to occur. Since CMR-tasks can emphasize important mathematical properties, are more efficient than AR- tasks, and more beneficial for less cognitively proficient students, promoting CMR can be essential if we want students to become mathematically literate.
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| 9. |
- Pilotto, Francesca, et al.
(författare)
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Late Holocene anthropogenic landscape change in northwestern Europe impacted insect biodiversity as much as climate change did after the last Ice Age
- 2022
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Ingår i: Proceedings of the Royal Society of London. Biological Sciences. - : Royal Society Publishing. - 0962-8452 .- 1471-2954. ; 289:1977
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Tidskriftsartikel (refereegranskat)abstract
- Since the last Ice Age (ca 115 000–11 700 years ago), the geographical ranges of most plants and animals have shifted, expanded or contracted. Understanding the timing, geographical patterns and drivers of past changes in insect communities is essential for evaluating the biodiversity implications of future climate changes, yet our knowledge of long-term patterns is limited. We applied a network modelling approach to the recent fossil record of northwestern European beetles to investigate how their taxonomic and trait composition changed during the past 16 000 years. We found two major changes in beetle faunas 4000–3500 and 10 000–9500 years ago, coinciding with periods of human population growth in the Late Holocene and climate warming in the Early Holocene. Our results demonstrate that humans have affected insect biodiversity since at least the introduction of agropastoralism, with landscape-scale effects that can be observed at sites away from areas of direct human impact.
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| 10. |
- Brandell, Gerd, et al.
(författare)
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Gender and Mathematics: recent development from a Swedish perspective
- 2007
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Ingår i: ZDM. - : Springer Science and Business Media LLC. - 1863-9690 .- 1863-9704. ; 39:3, s. 235-250
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Tidskriftsartikel (refereegranskat)abstract
- A fairly large study of attitudes towards mathematics among Swedish students at secondary level was conducted during 2001–2004. A newly developed instrument was used that was designed to capture gender stereotyped attitudes among students related to various aspects of mathematics in education and future life. The new scale and its development are described with reference to the original Australian studies. The scale builds on the Fennema–Sherman attitude scale “Mathematics as a male domain” but allows mathematics to be viewed as female, male or gender neutral, reflecting a different societal and educational situation than in the seventies when attitudes towards mathematics as a male domain were first investigated. The Swedish study shows that mathematics is perceived as gendered, mostly as a male domain, by large minorities of students at secondary level. However, the results are complex, with clear differences in responses from female and male students. Furthermore, mathematics is also viewed as female in some aspects. A comparison with Australian data shows that Swedish students are less inclined to view mathematics as a female domain than Australian students of the same age. The relevance of the study is related to the lack of equity in mathematics in education and as a professional field in the Swedish society, documented by earlier research.
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