Search results for "41"
showing 10 items of 3365 documents
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…
Reproducing pairs of measurable functions and partial inner product spaces
2016
We continue the analysis of reproducing pairs of weakly measurable functions, which generalize continuous frames. More precisely, we examine the case where the defining measurable functions take their values in a partial inner product space (PIP spaces). Several examples, both discrete and continuous, are presented.
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…
Mapping properties for the Bargmann transform on modulation spaces
2010
We investigate mapping properties for the Bargmann transform and prove that this transform is isometric and bijective from modulation spaces to convenient Banach spaces of analytic functions.
Teaching and learning for mathematical literacy
2020
This dissertation reports from research that investigates the nature of teaching and learning for mathematical literacy in three lower secondary schools in Norway. Mathematical literacy is a notion used to denote the competences required to meet the mathematical demands of life in modern society. The importance of education for mathematical literacy is emphasised by The Organisation for Economic Cooperation and Development (OECD), and mathematical literacy has become increasingly prominent in national curricula around the world. In the Norwegian curriculum, mathematical literacy is considered a basic skill that should be developed across school subjects. This study of teaching and learning …
Effect of Different Green Extraction Methods and Solvents on Bioactive Components of Chamomile (Matricaria chamomilla L.) Flowers
2020
Chamomile (Matricaria chamomilla L.) dried flowers contain a group of interesting biologically active compounds such as sesquiterpenes, flavonoids, coumarins, vitamins, phenolic acids and glucosides. Therefore, the aim of the present study was to characterize the composition in bioactive compounds (specialized metabolites) present in water and ethanol extracts of chamomile flowers, together with monitoring the impact of different extraction techniques (conventional vs. ultrasound-assisted extraction (UAE)) on the parameters under investigation. UAE treatment significantly decreased the extraction time of bioactive compounds from herbal material. Polyphenolic compounds content and antioxidan…