| 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.
|
|
| 12. |
- Eriksson, Urban, Lektor i fysik med inriktning mot fysikdidaktik, 1968-
(author)
-
Disciplinary discernment : reading the sky in astronomy education
- 2019
-
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.
|
|
| 13. |
- Lundberg, Anna L.V. 1967
(author)
-
Encountering Proportional Reasoning During a Single Algebra Lesson: A Microgenetic Analysis
- 2022
-
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.
|
|
| 14. |
- Asratian, Armen, et al.
(author)
-
Proper path-factors and interval edge-coloring of (3,4)-biregular bigraphs
- 2009
-
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.
|
|
| 15. |
- Lindahl, Karl-Olof, 1975-
(author)
-
Applied Algebraic Dynamics
- 2010
-
In: P-Adic Numbers, Ultrametric Analysis, and Applications. - : Pleiades Publishing, Ltd.. - 2070-0466 .- 2070-0474. ; 2:4, s. 360-362
-
Journal article (peer-reviewed)
|
|
| 16. |
- Sorooshian, Shahryar, 1980, et al.
(author)
-
Performance of the decision-making trial and evaluation laboratory
- 2023
-
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.
|
|
| 17. |
- Pejlare, Johanna, 1976, et al.
(author)
-
Programming to learn mathematics - exploring student teachers' instrumental genesis
- 2022
-
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.
|
|
| 18. |
- Borg, Andreas, et al.
(author)
-
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.
|
|
| 19. |
- Dyrvold, Anneli, 1970-
(author)
-
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.
|
|
| 20. |
- Viirman, Olov, et al.
(author)
-
Different views – some Swedish mathematics students’ concept images of the function concept
- 2010
-
In: Nordisk matematikkdidaktikk. - Göteborg : NCM. - 1104-2176. ; 15:4, s. 5-24
-
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.
|
|
