Search results for "VDP::Matematikk og naturvitenskap: 400::Matematikk: 410"
showing 10 items of 136 documents
Tiendeklassingers problemløsningsstrategier i matematikk : En studie av et utvalg tiendeklassingers strategibruk under arbeid med tre problemløsnings…
2017
Masteroppgave matematikkdidaktikk MA502 – Universitetet i Agder 2017 In this study I have looked at a sample of tenth graders and the types of strategies they apply while attempting to solve three problem solving tasks in mathematics. According to the national Norwegian mathematics curriculum, students are supposed to be able to apply problem solving strategies flexibly and efficiently by the time they finish grade 10. My impression is that mathematics teachers in general tend to put more emphasis on other goals and learning outcomes, the ones that will be tested in particular. With that as a backdrop, I wanted to investigate how students undertake different kinds of problem solving tasks; …
Motivasjon ved bruk av digitale verktøy : Hvordan kan bruk av digitale verktøy påvirke motivasjonen til elevene i matematikk?
2017
Masteroppgave matematikkdidaktikk MA502 – Universitetet i Agder 2017 The theme for this master study is motivation related to the use of digital tools. In this thesis, motivation is about what motives lie behind the pupils’ behaviour, and what influences the pupils to act a certain way The aim with this study is to see if the pupils’ motivation is influenced by using digital tool in mathematics education. My research question is: How can the use of digital tools influence the pupils’ motivation in mathematics? In order to answer this, I have looked at the following questions: 1. Is there a connection between the pupils’ understanding of mathematical concepts and the pupils’ motivation in ma…
On the existence of solutions to the higher order : Korteweg de Vries-Burgers equation
2019
Master's thesis Mathematics MA503 - University of Agder 2019 Vi studerer eksistensen av løsninger til den høyere ordens Korteweg deVries-Burgers likningenut+ 2uux−uxx+uxxxxx= 0. Ved ̊a jobbe medestimater i Sobolev rom finner vi at det eksisterer unik løsning i SobolevrommetHsfors >1/2. Ved ̊a bruke det relativt modderne Bourgainrommet klarer vi ̊a redusere denne verdien betraktelig, og vi viser at deteksisterer løsninger iHsfors >−2.
The sine anecdote in Kovalevskaya’s memoirs; British Journal for the History of Mathematics
2022
In Sofya Vasilyevna Kovalevskaya’s memoirs there is a rather ambiguous story about how she came to understand trigonometric functions on her own as a teenager by reading the chapter on optics in Tyrtov’s elementary physics textbook. Furthermore, she claims that in so doing, she happened to follow ‘the same road that had been taken historically: that is, instead of a sine I used a chord’. We examine Tyrtov’s textbook in search of sources for such inspiration and quote hitherto unknown critical reactions to her autobiographical reflections by Kovalevskaya’s teacher I I Malevich. We conclude that Kovalevskaya’s memoirs may well be marred by personal interests and/or faltering memory. By adding…
Another look at the two Egyptian pyramid volume ‘formulas’ of 1850 BCE
2022
Paid Open Access
A collaboratively-derived research agenda for e-assessment in undergraduate mathematics
2022
AbstractThis paper describes the collaborative development of an agenda for research on e-assessment in undergraduate mathematics. We built on an established approach to develop the agenda from the contributions of 22 mathematics education researchers, university teachers and learning technologists interested in this topic. The resulting set of 55 research questions are grouped into 5 broad themes: errors and feedback, student interactions with e-assessment, design and implementation choices, affordances offered by e-assessment tools, and mathematical skills. This agenda gives a framework for a programme of research aligned with practical concerns that will contribute to both theoretical an…
The Limit Notion at Three Educational Levels in Three Countries
2022
AbstractThis paper documents how the limit concept is treated in high school, at a university and in teacher education in England, France and Sweden. To this end we make use of vignettes, data-grounded accounts of the situation at the three levels in the three countries. These are analysed using the Anthropological Theory of the Didactic (ATD). While university praxeologies are relatively similar across the three countries, greater differences manifest themselves in high school and teacher education. For instance, at the high school level, in France a local praxeology on the limits of sequences is taught, which is not the case in England or Sweden. Results from the analysis of limits are ex…
Asymptotic geometry and Delta-points
2022
We study Daugavet- and $\Delta$-points in Banach spaces. A norm one element $x$ is a Daugavet-point (respectively a $\Delta$-point) if in every slice of the unit ball (respectively in every slice of the unit ball containing $x$) you can find another element of distance as close to $2$ from $x$ as desired. In this paper we look for criteria and properties ensuring that a norm one element is not a Daugavet- or $\Delta$-point. We show that asymptotically uniformly smooth spaces and reflexive asymptotically uniformly convex spaces do not contain $\Delta$-points. We also show that the same conclusion holds true for the James tree space as well as for its predual. Finally we prove that there exis…
How are proof and proving conceptualized in mathematics curriculum documents in the USA and Japan?
2022
Only a few international comparative studies have reported on proof and proving in curriculum documents. This report proposes a method of comparing the meaning of proof-related words in two specific countries’ curriculum documents (the USA and Japan) through quantitative and interpretative analyses. Using a text mining approach to explore text data, we found that the co-occurrence network of the words “proof” and “prove” in curriculum documents from the two countries is quite different. In the USA, the word “proof” is concerned with justification and “prove” is used as a general process, while in Japan “proof” is more related to discovery and “prove” is more associated with specific theorem…
Isometric factorization of vector measures and applications to spaces of integrable functions
2022
Let $X$ be a Banach space, $\Sigma$ be a $\sigma$-algebra, and $m:\Sigma\to X$ be a (countably additive) vector measure. It is a well known consequence of the Davis-Figiel-Johnson-Pelczýnski factorization procedure that there exist a reflexive Banach space $Y$, a vector measure $\tilde{m}:\Sigma \to Y$ and an injective operator $J:Y \to X$ such that $m$ factors as $m=J\circ \tilde{m}$. We elaborate some theory of factoring vector measures and their integration operators with the help of the isometric version of the Davis-Figiel-Johnson-Pelczýnski factorization procedure. Along this way, we sharpen a result of Okada and Ricker that if the integration operator on $L_1(m)$ is weakly compact, t…