| 1. |
- Johansson, Helena, 1971-
(författare)
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Mathematical Reasoning : In physics and real-life context
- 2015
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis is a compilation of four papers in which mathematical reasoning is examined in various contexts, in which mathematics is an integral part. It is known from previous studies that a focus on rote learning and procedural mathematical reasoning hamper students’ learning of mathematics. The aims of this thesis are to explore how mathematical reasoning affects upper secondary students’ possibilities to master the physics curricula, and how real-life contexts in mathematics affect students’ mathematical reasoning. This is done by analysing the mathematical reasoning requirements in Swedish national physics tests; as well as by examining how mathematical reasoning affects students’ success on the tests/tasks. Furthermore, the possible effect of the presence of real-life contexts in Swedish national mathematics tasks on students’ success is explored; as well as if the effect differs when account is taken to mathematical reasoning requirements. The framework that is used for categorising mathematical reasoning, distinguishes between imitative and creative mathematical reasoning, where the latter, in particular, involves reasoning based on intrinsic properties. Data consisted of ten Swedish national physics tests for upper secondary school, with additional student data for eight of the tests; and six Swedish national mathematics tests for upper secondary school, with additional student data. Both qualitative and quantitative methods were used in the analyses. The qualitative analysis consisted of structured comparisons between representative student solutions and the students’ educational history. Furthermore, various descriptive statistics and significance tests were used. The main results are that a majority of the physics tasks require mathematical reasoning, and particularly that creative mathematical reasoning is required to fully master the physics curricula. Moreover, the ability to reason mathematically creatively seems to have a positive effect on students’ success on physics tasks. The results indicate additionally, that there is an advantage of the presence of real-life context in mathematics tasks when creative mathematical reasoning is required. This advantage seems to be particularly notable for students with lower grades.
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| 2. |
- Johansson, Helena, 1971-
(författare)
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Mathematical Reasoning in Physics Tests : Requirements, Relations, Dependence
- 2013
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- By analysing and expanding upon mathematical reasoning requirements in physics tests, this licentiate thesis aims to contribute to the research studying how students’ knowledge in mathematics influence their learning of physics. A sample of physics tests from the Swedish National Test Bank in Physics was used as data, together with information of upper secondary students’ scores and grades on the tests. First it was decided whether the tasks in the tests required mathematical reasoning at all and if they did, that reasoning was characterised. Further, the relation between students’ grades and mathematical reasoning requirements was examined. Another aim in this thesis is to try out if the Mantel-Haenszel procedure is an appropriate statistical method to answer questions about if there is a dependence between students’ success on different physics tasks requiring different kinds of mathematical reasoning. The results show that 75% of the tasks in the physics tests require mathematical reasoning and that it is impossible to pass six out of eight tests without mathematical reasoning. It is also revealed that it is uncommon that a student gets a higher grade than Pass without solving tasks that require the student to come up with not already familiar solutions. It is concluded that the Mantel-Haenszel procedure is sensitive to the number of students each teacher accounts for. If there are not too few students, the procedure can be used. The outcome indicates that there is a dependence between success on tasks requiring different kinds of reasoning. It is more likely that a student manages to solve a task that requires the produce of new reasoning if the student has solved a task that is familiar from before.
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| 3. |
- Menegon, Aurelio
(författare)
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Thom property and Milnor-Le fibration for analytic maps
- 2023
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Ingår i: Mathematische Nachrichten. - : John Wiley & Sons. - 0025-584X .- 1522-2616. ; 296:8, s. 3481-3491
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Tidskriftsartikel (refereegranskat)abstract
- Let (X, 0) be the germ of either a subanalytic set X subset of Rn$X \subset {\mathbb {R}}<^>n$ or a complex analytic space X subset of Cn$X \subset {\mathbb {C}}<^>n$, and let f:(X,0)->(Kk,0)$f: (X,0) \rightarrow ({\mathbb {K}}<^>k, 0)$ be a K${\mathbb {K}}$-analytic map-germ, with K=R${\mathbb {K}}={\mathbb {R}}$ or C${\mathbb {C}}$, respectively. When k=1$k=1$, there is a well-known topological locally trivial fibration associated with f, called the Milnor-Le fibration of f, which is one of the main pillars in the study of singularities of maps and spaces. However, when k>1$k>1$ that is not always the case. In this paper, we give conditions which guarantee that the image of f is well-defined as a set-germ, and that f admits a Milnor-Le fibration. We also give conditions for f to have the Thom property. Finally, we apply our results to mixed function-germs of type fg over bar :(X,0)->(C,0)$f \bar{g}: (X,0) \rightarrow ({\mathbb {C}},0)$ on a complex analytic surface X subset of Cn$X \subset {\mathbb {C}}<^>n$ with arbitrary singularity.
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| 4. |
- Nyström, Peter, 1959, et al.
(författare)
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Hur samstämmiga är svenska styrdokument och nationella prov med ramverk och uppgifter i TIMSS Advanced 2015?
- 2016
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- TIMSS Advanced (Trends in Mathematics and Science Study ) är en internationell studie som undersöker gymnasieelevers kunskaper i avancerad matematik och fysik. TIMSS Advanced har genomförts tre gånger, 1995, 2008 och 2015, och Sverige har deltagit varje gång. I 2015 års studie deltog svenska elever i årskurs 3 på naturvetenskaps- och teknikprogrammet som slutfört eller håller på att slutföra kursen matematik 4 respektive fysik 2. Studien ger möjlighet att analysera förändringar i motsvarande elevgruppers kunskaper över tid inom dessa områden, men också möjlighet att jämföra svenska resultat med resultat från andra länder. TIMSS Advanced 2015 har genomförts av Skolverket i samarbete med Nationellt Centrum för Matematikutbildning (NCM) vid Göteborgs universitet. Skolverket har sammanställt en nationell huvudrapport med resultaten från TIMSS Advanced 2015. En viktig utgångspunkt för tolkning och analys av resultaten är att veta i vilken utsträckning svenska elever fått möjlighet att lära sig det som prövas i TIMSS Advanced. I denna rapport analyseras därför samstämmigheten mellan TIMSS Advanced 2015 och svenska ämnesplaner, nationella prov och bedömningsstöd. Mot bakgrund av ämnenas kopplingar mellan varandra genomförs också en analys som särskilt fokuserar på inslaget av matematik i fysikuppgifterna.
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| 5. |
- Bergqvist, Ewa, 1971-, et al.
(författare)
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A theoretical model of the connection between the process of reading and the process of solving mathematical tasks
- 2010
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Ingår i: Mathematics and mathematics education. - Linköping, Sweden : Svensk förening för matematikdidaktisk forskning, SMDF. - 9197393460 ; , s. 47-57
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Konferensbidrag (refereegranskat)abstract
- In this paper we suggest a theoretical model of the connection between the process of reading and the process of solving mathematical tasks. The model takes into consideration different types of previous research about the relationship between reading and solving mathematical tasks, including research about traits of mathematical tasks (a linguistic perspective), about the reading process (a psychological perspective), and about behavior and reasoning when solving tasks (a mathematics education perspective). In contrast to other models, our model is not linear but cyclic, and considers behavior such as re-reading the task.
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| 6. |
- Bergqvist, Ewa, 1971-, et al.
(författare)
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Communicating mathematics or mathematical communication? : An analysis of competence frameworks
- 2012
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Ingår i: Proceedings of the 36th Conference of the International Group for the Psychology of Mathematics Education. ; , s. 67-74
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Konferensbidrag (refereegranskat)abstract
- In this study we analyse the communication competence included in two different frameworks of mathematical knowledge. The main purpose is to find out if mathematical communication is primarily described as communication of or about mathematics or if it is (also) described as a special type of communication. The results show that aspects of mathematics are mostly included as the content of communication in the frameworks but the use of different forms of representation is highlighted both in the frameworks and also in prior research as a potential cause for characterising mathematical communication differently than "ordinary" communication.
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| 7. |
- Bergqvist, Ewa, 1971-, et al.
(författare)
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Relating vocabulary in mathematical tasks to aspects of reading and solving
- 2012
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Ingår i: Evaluation and comparison of mathematical achievement: Dimensions and perspectives. - Linköping : Svensk Förening för MatematikDidaktisk Forskning. ; , s. 61-70, s. 61-70
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Konferensbidrag (refereegranskat)abstract
- This paper focuses on relationships between vocabulary in mathematical tasks and aspects of reading and solving these tasks. The paper contains a framework that highlights a number of different aspects of word difficulty as well as many issues to consider when planning and implementing empirical studies concerning vocabulary in tasks, where the aspect of common/uncommon words is one important part. The paper also presents an empirical method where corpora are used to investigate issues of vocabulary in mathematical tasks. The results from the empirical study show that there are connections between different types of vocabulary and task difficulty, but that they seem to be mainly an effect of the total number of words in a task.
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| 8. |
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| 9. |
- Bergqvist, Ewa, 1971-, et al.
(författare)
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Språkbrukets roll i matematikundervisningen
- 2014
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Ingår i: Nämnaren. - 0348-2723. ; 2014:1, s. 27-31
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Tidskriftsartikel (populärvet., debatt m.m.)abstract
- Det språk vi använder oss av i matematikklassrummet kan fokuseras på många olika sätt. Språket är också nödvändigt att förhålla sig till vid utvecklingen av sitt matematiska tänkande. Författarna diskuterar här relationer mellan språk och lärande.
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| 10. |
- Bergqvist, Ewa, Docent, 1971-, et al.
(författare)
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The role of implicit theoretical assumptions in empirical research
- 2023
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Ingår i: Proceedings of the 46th Conference of the International Group for the Psychology of Mathematics Education. - Haifa : University of Haifa. - 9789659311224 ; , s. 107-114
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Konferensbidrag (refereegranskat)abstract
- There is much research on the role of theory in mathematics education research, at least from more overarching or theoretical perspectives. Micro analyses of the role of theory in particular research studies are rarer. We contribute by analysing one empirical study to allow for in-depth analyses and discussions around the role of theory in a specific case, concerning relationships between mathematics and reading. Our results show that studies that do not use an explicit theoretical model can still be strongly influenced by implicit theoretical assumptions. We conclude that it is important to identify existing theoretical assumptions in an empirical research study and try to convey them as clearly as possible, and we discuss specific issues concerning research on relationships between mathematics and reading.
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