| 1. |
- Helenius, Ola, 1970, et al.
(författare)
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Measuring temperature within the didactic space of preschool
- 2016
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Ingår i: Nordisk matematikkdidaktikk, NOMAD. - : Nationellt centrum för matematikutbildning (NCM). - 1104-2176. ; 21:4, s. 155-176
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Tidskriftsartikel (refereegranskat)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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| 2. |
- Johansson, Maria, et al.
(författare)
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Young children’s multimodal mathematical explanations
- 2014
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Ingår i: ZDM - the International Journal on Mathematics Education. - : Springer. - 1863-9690 .- 1863-9704. ; 46:6, s. 895-909
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Tidskriftsartikel (refereegranskat)abstract
- This paper investigates how three children provided mathematical explanations whilst playing with a set of glass jars in a Swedish preschool. Using the idea of semiotic bundles combined with the work on multimodal interactions, the different semiotic resources used individually and in combinations by the children are described. Given that the children were developing their verbal fluency, it was not surprising to find that they also included physical arrangements of the jars and actions to support their explanations. Hence, to produce their explanations of different attributes such as thin and sameness, the children drew on each other’s gestures and actions with the jars. This research has implications for how the relationship between verbal language and gestures can be viewed in regard to young children’s explanations.
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| 3. |
- Roos, Helena, 1974-
(författare)
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Students’ voices of inclusion in mathematics education
- 2023
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Ingår i: Educational Studies in Mathematics. - : Springer. - 0013-1954 .- 1573-0816. ; 113:2, s. 229-249
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Tidskriftsartikel (refereegranskat)abstract
- This study foregrounds three students who are regarded by their teachers as being in special educational needs in mathematics (SEM) and these same students voicing what inclusion in mathematics education means to them. In this study, inclusion is defined as processes of participation. Discourse analysis was applied when analysing these students’ voices of inclusion in mathematics education in two inclusive mathematics classrooms, with both classes aiming to include every student in the mathematics education. The three main Discourses which were identified were the Discourse of assessment, the Discourse of being in a mathematics classroom setting, and the Discourse of accessibility in mathematics education. The analysis of the Discourses indicates that they were affected by wider sociopolitical discourses. Furthermore, when inclusion is regarded as processes of participation in mathematics education, the results indicate that participation becomes more complex. Therefore, in this process, both ideological and societal issues, as well as individual and subject-specific issues, must be considered in the educational endeavour.
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| 4. |
- Roos, Helena, 1974-
(författare)
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The meaning(s) of inclusion in mathematics in student talk : Inclusion as a topic when students talk about learning and teaching in mathematics
- 2019
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis contributes to research and practice within the field of special education in mathematics with more knowledge about, and an understanding of, students´ meaning(s) of inclusion in mathematics education. Three research questions guide the study: What meaning(s) is/are ascribed, and how is inclusion used, in mathematics education research? What meaning(s) do the students ascribe to inclusion in mathematics learning and teaching? And what frames students´ meaning(s) of inclusion in mathematics learning and teaching?The first part of this study began with a systematic literature review on the notion of inclusion in mathematics education research, and the search resulted in 1,296 research studies. Of these, 76 studies were retained after the criteria for time span and peer-reviewed research were applied and 19 duplicates had been removed. The second part of the study involves a case study of three students and their meaning(s) of inclusion in mathematics education. The selected school was a lower secondary school in an urban area of Sweden. The school had set out to work inclusively, meaning their aims were to include all students in the ordinary classroom teaching in every subject and to incorporate special education into the ordinary teaching with no fixed special education groups. Three students were chosen for this part of the study: one in Grade 7 and two in Grade 8. Edward, one of the students in Grade 8, was chosen because he was thought to be a student in access to mathematics education. The other two students were chosen because they were thought to be struggling to gain access to mathematics education: Veronica in Grade 7 and Ronaldo in Grade 8 (the same class as Edward). In this study, the object of the study is the meaning(s) of inclusion in student talk. This study is an instrumental and collective case (Stake, 1995), as it involves several students’ meaning(s) aimed at developing a more general understanding of inclusion in mathematics education. The case is also an information-rich case (Patton, 2002), with contributions from students in mathematics education at an inclusive school. Applying Flyvbjerg’s (2006; 2011) notions, one can also call this kind of selection “information-oriented”, and the case is an extreme one – a choice made in order to get “a best case scenario”. An extreme case is a case used to “obtain information on unusual cases which can be especially problematic or especially good in a more closely defined sense” (Flyvbjerg, 2011, p. 307). The data in this study consists of both observations and interviews conducted during the spring semester 2016. The observations took place in a Grade 7 and Grade 8 classroom at the same school where the interviewed students were enrolled. At least one mathematics lesson each month for each class was observed, and student interviews followed each observation. The observations were used to provide a context for the interviews and to support the analysis. In this study, discourse analysis (DA) as described by Gee (2014a; 2014b) was chosen as both the theoretical frame and as an analytical tool because of its explanatory view on discourse, with description foregrounded. With the help of DA, this study describes both the meaning(s) and the use of the notion of inclusion in mathematics education research. It also describes students’ meaning(s) of inclusion in mathematics education as well as framing issues in student talk of inclusion in mathematics education. From Gee´s point of view, DA encompasses all forms of interaction, both spoken and written, and he provides a toolkit for analysing such interaction by posing questions to the text. Gee distinguishes two theoretical notions, big and small discourses, henceforth referred to as Discourse (D) and discourse (d). Discourse represents a wider context, both social and political, and is constructed upon ways of saying, doing, and being: “If you put language, action, interaction, values, beliefs, symbols, objects, tools, and places together in such a way that other recognize you as a particular type of who (identity) engaged in a particular type of what (activity), here and now, then you have pulled of a Discourse” (Gee, 2014 a, p. 52, Gee’s italics). When looking at discourse (with a small d), it focuses on language in use – the “stretches of language” we can see in the conversations we investigate (Gee, 2014a, 2014b), meaning the relations between words and sentences and how these relations visualize the themes within the conversations. These small discourses can inform on how the language is used, what typical words and themes are visible, and how the speakers or writers design the language. According to Gee (2015), big Discourse sets a larger context for the analysis of small discourse. The results of the first part of the study answer to the research question, What meaning(s) is ascribed, and how is inclusion used in mathematics education research? They show that research on inclusion in mathematics education use the term inclusion when both referring to an ideology and a way of teaching, although these two uses are usually treated separately and independently of each other. The results of the second part of the study answer to the following research questions: What meaning(s) do the students ascribe to inclusion in mathematics learning and teaching? And what frames students´ meaning(s) of inclusion in mathematics learning and teaching? These questions show how meaning(s) of inclusion in student talk can be described by three overarching Discourses: the Discourse of mathematics classroom setting, of assessment, and of accessibility in mathematics education. Within these Discourses, smaller discourses make issues of meanings of inclusion for the students visible in terms of: testing, grades, tasks, the importance of the teacher, (not) being valued, the dislike of mathematics, the classroom organization, and being in a small group. This study shows the complexities and challenges of teaching mathematics, all while simultaneously handling students’ diversity and promoting the mathematical development of each student. To enhance students’ participation and access demands that the teacher knows her or his students, is flexible, has a pedagogical stance and tactfulness, and is knowledgeable in mathematics and mathematics education. It also demands that the teacher is able to take a critical stance and resist the prevailing discourse of assessment that can sometimes overshadow the mathematics education, and in a sense, almost become mathematics for the students. Furthermore, this study also shows how complex and challenging it is to be a mathematics student: they are required to relate to, understand, and participate in many Discourses existing at the same time in a single mathematics classroom. These Discourses interrelate and are embedded in power relations between students and teachers and institutions. This demands that the students are alert and able to use various symbols and objects as well as recognize patterns, and then act accordingly. Hence, to be able to fully participate, you have to be able to talk the talk and walk the walk (Gee, 2014a). This means that not only do you have to use the language correctly, but also you have to act properly at the right time and place.
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| 5. |
- Björklund, Camilla, 1977, et al.
(författare)
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Sharpening the Focus on Numbers and Counting: Preschool Educators Differentiating Aspects of Mathematical Knowledge for Teaching
- 2017
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Ingår i: Mathematics Teacher Education and Development. - : Mathematics Education Research Group of Australasia. - 1442-3901. ; 19:3, s. 117-134
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Tidskriftsartikel (refereegranskat)abstract
- This article reports a study of educators differentiating aspects of mathematical knowledge for teaching in preschool as part of a further-education programme. Eight Swedish preschool educators participated in focus group discussions about documentations from their own practice during a school year, to enhance their awareness of their mathematics education practice. The object of learning for the participants is more specifically how numbers and counting are made content for learning in preschool practice. The educators’ authentic documentations are reflected upon in focus group meetings and further analysed by the researchers to find out what aspects the educators differentiate during the programme. Results show that educators’ learning about content for children’s learning in preschool is a complex process. This process involves several aspects necessary to discern for a professional development to occur, but the collaborative approach seems prosperous in that new aspects are brought to the fore, influencing their reflective practice.
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| 6. |
- Helenius, Ola, et al.
(författare)
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Mathematical exclusion with the every day
- 2015
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Ingår i: Proceedings of the Ninth Conference of the European Society for Research in Mathematics Education (CERME9). - : Charles University, Faculty of Education. ; , s. 1584-1590
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Konferensbidrag (refereegranskat)abstract
- Problem solving can involve using mathematics to solve everyday problems. In this study, we examine an interaction between a teacher and a class of six-year olds in Sweden around an open-ended problem, from an everyday context. Using Bernstein's ideas about vertical and horizontal discourse, a mixture of everyday and mathematics understandings is identified in the interaction. This mixture seems to result in confusion for both the teacher and the children over what should be the focus. This paper raises issues about how the connection to the everyday in problem solving could reduce children's opportunities to learn mathematics.
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| 7. |
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| 8. |
- Lindström, Torsten, et al.
(författare)
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Uniqueness of limit cycles for a limiting case of the chemostat : does it justify the use of logistic growth rates?
- 2015
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Ingår i: Electronic Journal of Qualitative Theory of Differential Equations. - : University of Szeged. - 1417-3875. ; :47, s. 1-14
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Tidskriftsartikel (refereegranskat)abstract
- On infinitesimally short time intervals various processes contributing to population change tend to operate independently so that we can simply add their contributions (Metz and Diekmann, The dynamics of physiologically structured populations, 1986, p. 3). This is one of the cornerstones for differential equations modeling in general. Complicated models for processes interacting in a complex manner may be built up, and not only in population dynamics. The principle holds as long as the various contributions are taken into account exactly. In this paper we discuss commonly used approximations that may lead to non-removable dependency terms potentially affecting the long run qualitative behavior of the involved equations. We prove that these terms do not produce such effects in the simplest and most interesting biological case, but the general case is left open. Our main result is a rather complete analysis of an important limiting case. Once complete knowledge of the qualitative properties of simple models is obtained, it greatly facilitates further studies of more complex models. A consequence of our analysis is that standard methods can be applied. However, the application of those methods is far from straightforward and require non-trivial estimates in order to make them valid for all values of the parameters. We focus on making these proofs as elementary as possible.
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| 9. |
- Argatov, Ivan I
(författare)
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A scalar prototype problem of deep abrasive drilling with an infinite free boundary : an asymptotic modeling study
- 2019
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Ingår i: Journal of Engineering Mathematics. - : Springer. - 0022-0833 .- 1573-2703. ; 118:1, s. 29-41
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Tidskriftsartikel (refereegranskat)abstract
- A vanishing at infinity solution of the three-dimensional Laplace equation is sought in an a priori unknown domain with overdetermined boundary conditions, the right-hand sides of which depend on the unit normal to the free boundary. A perturbation analysis of the nonstandard free boundary problem that models deep abrasive drilling has been performed under the assumption that the free boundary is close to the surface of a given semi-infinite cylinder, the longitudinal position of which depends on the boundary data, and the leading-order asymptotic solution has been developed.
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| 10. |
- Klonowska, Kamilla, et al.
(författare)
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Comparing the optimal performance of parallel architectures
- 2004
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Ingår i: Computer journal. - Oxford : Oxford University Press. - 0010-4620 .- 1460-2067. ; 47:5, s. 527-544
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Tidskriftsartikel (refereegranskat)abstract
- Consider a parallel program with n processes and a synchronization granularity z. Consider also two parallel architectures: an SMP with q processors and run-time reallocation of processes to processors, and a distributed system (or cluster) with k processors and no run-time reallocation. There is an inter-processor communication delay of t time units for the system with no run-time reallocation. In this paper we define a function H(n,k,q,t,z) such that the minimum completion time for all programs with n processes and a granularity z is at most H(n,k,q,t,z) times longer using the system with no reallocation and k processors compared to using the system with q processors and run-time reallocation. We assume optimal allocation and scheduling of processes to processors. The function H(n,k,q,t,z)is optimal in the sense that there is at least one program, with n processes and a granularity z, such that the ratio is exactly H(n,k,q,t,z). We also validate our results using measurements on distributed and multiprocessor Sun/Solaris environments. The function H(n,k,q,t,z) provides important insights regarding the performance implications of the fundamental design decision of whether to allow run-time reallocation of processes or not. These insights can be used when doing the proper cost/benefit trade-offs when designing parallel execution platforms.
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