<p>Denna rapport handlar om hur man som lärare kan variera undervisningen i matematik med en fokusering på laborativ matematik. Den riktar sig främst mot gymnasiet men är även aktuell för både för yngre och äldre åldrar. Rapporten behandlar lärares och elevers syn på undervisning samt ger konkreta förslag på hur sådan undervisning kan gå till. Syftet med rapporten är att undersöka vad det finns för alternativ till traditionell undervisning och presentera dessa. Metoden som använts är intervjuer där jag tagit kontakt med lärare som är kända för att använda alternativa undervisningsmetoder och laborativ matematik. Totalt fem intervjuer.</p><p> </p><p>Resultatet visar på att undervisningen i matematik är enformig och att den bör varieras för att bli lärorik och intressant. Rapporten ger konkreta förslag på hur sådan undervisning kan gå till. Flera lärare vill testa alternativ undervisning men tvekar eftersom de inte vet att den fungerar eller anser att det inte finns tid till sådan arbetsmetod. En varierad, laborativ undervisning verkar ge goda resultat men det finns inga vetenskapliga undersökningar som bevisar detta.</p> / <p>This report investigates various ways of diversifying mathematics teaching, especially elaborative mathematics. Primarily it focuses upper secondary school, but the results should have an impact on lower and higher levels as well. From an account of teacher and student views the report provides some concrete suggestions for improvement. The purpose of the report is to investigate alternatives for the traditional ways of teaching. Five teachers known for their experience on alternative teaching methods and on laboratory mathematics have been interviewed.</p><p> </p><p>The result shows that mathematics teaching is uniform and that it needs to be diversified. The report presents a sample of ideas for such teaching. Many teachers are willing to try this type of teaching but hesitate since there are no proofs of positive results or because there is too little time for such methods. A diversified, laboratory teaching seems to contribute good results but this has not been proved.</p>

Understanding the processes that govern mating behaviors is a fundamental goal of evolutionary biology and behavioral ecology. Population-level patterns of mate acquisition and offspring production, otherwise known as the genetic mating system, play a central role in the sexual selection on morphological and behavioral traits and may facilitate speciation. The central hypothesis of this research is that variation in environmental conditions, such as temperature, turbidity, and habitat, and demographic influences such as population density, sex ratios and temporal availability of mates, may limit mating and reproductive success in a predictive manner. Therefore the goal of this dissertation is to examine the contributions of geographic and temporal variation on the plasticity of the genetic mating system in two species of pipefish. The first study examined whether meaningful variation in the genetic mating system exists between two natural populations of the dusky pipefish, Syngnathus floridae. Results of this investigation provide evidence that the genetic mating system differs among different geographic locations. The second study considered the relative contributions of environmental conditions and population demographics on differences in the genetic mating system of dusky pipefish from five natural populations. The results of this investigation show strong trends for demographic and environmental factors to strongly influence the genetic mating system between populations. The third study considered how variation in the number of available mates predicts the outcome of sexual selection during the course of a breeding season in the broad-nosed pipefish, Sygnathus typhle. The results of this study indicate a strong influence of the operational sex ratio on the genetic mating system. In addition to these studies, a study was conducted to investigate whether phylogeographic relationships may be responsible for geographic variation in the genetic mating system of the dusky pipefish of pipefish. Mitochondrial DNA analysis does not substantiate subspecies designations for this species and microsatellite analysis show a clear pattern of isolation by distance. Taken together, these studies significantly enhance the understanding of how mating systems are organized over broad environmental gradients and temporal/spatial scales and to the evolution of sexual selection on the whole.

Syftet med denna kvalitativa studie, utifrån en fenomenografisk ansats, var att beskriva lärares uppfattningar av vad elevers tilltro till eget tänkande och egen förmåga att lära matematik innebär och hur de gör för att främja detta. Datainsamlingen bestod av intervjuer med lärare från förskoleklass till och med år sex. Lärares uppfattningar beskrevs i att eleven visar lust, mod, stolthet och ansvar, särskilt när eleven vågat ta sig igenom en utmaning som den först inte trott sig klara. En förutsättning för tilltro var ett tryggt gruppklimat. I främjandet av tilltro tog lärarna utgångspunkt i elevers erfarenheter med positiva förväntningar på eleverna i en lustfylld och kommunikativ undervisning. Uppmuntran och utmaningar på adekvat nivå, som skapar förståelse är kännetecknande för att eleven ska känna att den lyckas. Det omgivande samhället har stor betydelse för elevers tilltro. Lärarens engagemang, nyfikenhet och uppmärksamhet på elevers tillägnade kunskaper för att erövra nytt matematiskt kunnande var av vikt för tilltron. Det framkom att eleverna bör uppmärksammas på att matematiska kunskaper och beräkningar ligger bakom de produkter som finns i vår omgivning. / The purpose of this qualitative study, based on a phenomenographical approach, was to describe teachers' perceptions of what the students' confidence in their own thinking and their own ability to teach mathematics and how they are doing to promote this. Data collection consisted of interviews with teachers from pre until year six. Teacher perceptions were described in the student show desire, courage, pride and responsibility, especially when they dared to get through a challenge as the first not thought to cope. A prerequisite for faith was a safe group environment. The promotion of confidence took the teachers based on students' experiences with positive expectations for students in a luscious and communicative teaching. Encouragement and challenges at the appropriate level, which creates understanding is characteristic for the student to feel that they succeed. The surrounding community is very important for the students' confidence. The teacher's dedication, curiosity and attention devoted to the pupils' knowledge to conquer new mathematical literacy was important for confidence. It appeared that the students should be aware of the mathematical knowledge and calculations behind the products that are in our surroundings.

Denna rapport handlar om hur man som lärare kan variera undervisningen i matematik med en fokusering på laborativ matematik. Den riktar sig främst mot gymnasiet men är även aktuell för både för yngre och äldre åldrar. Rapporten behandlar lärares och elevers syn på undervisning samt ger konkreta förslag på hur sådan undervisning kan gå till. Syftet med rapporten är att undersöka vad det finns för alternativ till traditionell undervisning och presentera dessa. Metoden som använts är intervjuer där jag tagit kontakt med lärare som är kända för att använda alternativa undervisningsmetoder och laborativ matematik. Totalt fem intervjuer.   Resultatet visar på att undervisningen i matematik är enformig och att den bör varieras för att bli lärorik och intressant. Rapporten ger konkreta förslag på hur sådan undervisning kan gå till. Flera lärare vill testa alternativ undervisning men tvekar eftersom de inte vet att den fungerar eller anser att det inte finns tid till sådan arbetsmetod. En varierad, laborativ undervisning verkar ge goda resultat men det finns inga vetenskapliga undersökningar som bevisar detta. / This report investigates various ways of diversifying mathematics teaching, especially elaborative mathematics. Primarily it focuses upper secondary school, but the results should have an impact on lower and higher levels as well. From an account of teacher and student views the report provides some concrete suggestions for improvement. The purpose of the report is to investigate alternatives for the traditional ways of teaching. Five teachers known for their experience on alternative teaching methods and on laboratory mathematics have been interviewed.   The result shows that mathematics teaching is uniform and that it needs to be diversified. The report presents a sample of ideas for such teaching. Many teachers are willing to try this type of teaching but hesitate since there are no proofs of positive results or because there is too little time for such methods. A diversified, laboratory teaching seems to contribute good results but this has not been proved.

This thesis is devoted to the study of different generalizations of the classical conception of a function of bounded variation. First, we study the functions of bounded p-variation introduced by Wiener in 1924. We obtain estimates of the total p-variation (1&lt;p&lt;∞) and other related functionals for a periodic function f in Lp([0,1]) in terms of its Lp-modulus of continuity ω(f;δ)p. These estimates are sharp for any rate of decay of ω(f;δ)p. Moreover, the constant coefficients in them depend on parameters in an optimal way. Inspired by these results, we consider the relationship between the Riesz type generalized variation vp,α(f) (1&lt;p&lt;∞, 0≤α≤1-1/p) and the modulus of p-continuity  ω1-1/p(f;δ). These functionals generate scales of spaces that connect the space of functions of bounded p-variation and the Sobolev space Wp1. We prove sharp estimates of vp,α(f) in terms of ω1-1/p(f;δ). In the same direction, we study relations between moduli of p-continuity and q-continuity for 1&lt;p&lt;q&lt;∞. We prove an inequality that estimates ω1-1/p(f;δ) in terms of ω1-1/q(f;δ). The inequality is sharp for any order of decay of ω1-1/q(f;δ). Next, we study another generalization of bounded variation: the so-called bounded Λ-variation, introduced by Waterman in 1972. We investigate relations between the space ΛBV of functions of bounded Λ-variation, and classes of functions defined via integral smoothness properties. In particular, we obtain the necessary and sufficient condition for the embedding of the class Lip(α;p) into ΛBV. This solves a problem of Wang (2009). We consider also functions of two variables. Applying our one-dimensional result, we obtain sharp estimates of the Hardy-Vitali type p-variation of a bivariate function in terms of its mixed modulus of continuity in Lp([0,1]2). Further, we investigate Fubini-type properties of the space Hp(2) of functions of bounded Hardy-Vitali p-variation. This leads us to consider the symmetric mixed norm space Vp[Vp]sym of functions of bounded iterated p-variation. For p&gt;1, we prove that Hp(2) is not embedded into Vp[Vp]sym, and that Vp[Vp]sym is not embedded into Hp(2). In other words, Fubini-type properties completely fail in the class of functions of bounded Hardy-Vitali type p-variation for p&gt;1. / Baksidestext The classical concept of the total variation of a function has been extended in several directions. Such extensions find many applications in different areas of mathematics. Consequently, the study of notions of generalized bounded variation forms an important direction in the field of mathematical analysis. This thesis is devoted to the investigation of various properties of functions of generalized bounded variation.  In particular, we obtain the following results: sharp relations between spaces of generalized bounded variation and spaces of functions  defined by integral smoothness conditions  (e.g., Sobolev and Besov spaces); optimal properties of certain scales of function spaces of frac- tional smoothness generated by functionals of variational type; sharp embeddings within  the scale of spaces of functions of bounded p-variation; results concerning bivariate functions of bounded p-variation, in particular sharp estimates of total variation in terms of the mixed Lp-modulus of continuity, and Fubini-type properties.

In traditional trade theories, foreign trade plays the role of filling the gap of products not produced within the country. However, in the early 1960s increasing exchange of similar products, intra-industry trade, in the world trade have been observed by trade theorists. After the realization of the fact that intra-industry trade has become a very important part of world trade, more comprehensive studies on intra-industry trade have been conducted. At the end of the 1970s, trade theorists started to analyze intra-industry trade between developed countries (horizontal intra-industry trade) and intra-industry trade between developed and developing countries (vertical intra-industry trade) separately, because their characteristics were different. Horizontal intra-industry models were characterized by attribute variation between products while vertical intra-industry models were characterized by quality variation. This study investigates the issue of measurement of horizontal and vertical intra-industry trade for Turkish manufacturing industry. We address the questions of whether the intra-industry trade in Turkish manufacturing sector is more of the horizontal or the vertical type and whether the vertical industries dominates horizontal industries in number at the 3- digit industry level. Empirical analyses shows that the majority of intra-industry trade in Turkish manufacturing sector is of the vertical nature / Turkish manufacturing sector exports lower quality varieties in exchange for higher quality varieties. Also, our empirical analyses indicate that a large percent of 3- digit industries considered as primarily involved in intra-industry trade are vertical industries.

This study is based on an interest in trying to understand what is needed to ensure that students actually learn in a learning object, in this study equations. Algebra is an area of mathematics in several studies proved to be a stumbling block for many students. Using letters in mathematis is difficult for most students according to research reports and it is also consistent with my own experince as a teacher. The purpose of this study was to seek answers to what in the lesson content and also during the interview that allowed the students to learn more about the learning object. Based on students' prior knowledge and the difficulties students might have with the learning object and the offer of learning, I try to get an answer to what might have contribut the students to developed knowledge of the learning object. This qualitative study is based on a variation theory perspective. The two students who participated in the study attended the same class in high school. By using the theory of variation patterns, it made it possible for me to describe how students learn new things about the learning object, equations. To gain insight into how the students solved the data and developed new knowledge, I had the lesson content and their statements in the interviews to help me understand the difficulties in solving the equtionatask and what in the lessons that have contributed to new knowledge. The results show that pupils' understanding and difficulties in learning objects are relevant to how they can perceive, discern and assimilate new knowledge. One student was able to experience learning from their prior knowledge and assimilate what he had to develop in the variety in the offer of learning. The offered learning did not give the second student the same opportunity. The results indicates that the knowledge of students' prior knowledge, the difficulties the learning object can create and students' own narrative, I argue on the basis of the study'sresults, it is important knowledge for every teacher to be aware of befor the presentation of the lesson if it will give every student opportunities to learn.

The seasonal and diurnal concentrations of atmospheric carbonyls were measured by the LpDNPH-Cartridge and the microcomputer air sampling device at Nan-Chie and Hsiung-Kong sites in Kaohsiung area. Then, factor analysis and absolute principal component analysis were also used to determine the source apportionment in Kaohsiung area. Total concentrations of carbonyls were higher in Summer than in winter at Nan-Chie and Hsiung-Kong sites. Measurements showed that the highest carbonyls were formaldehyde and acetaldehyde, due to the fact that photochemical activities are stronger in summer than in winter. The concentrations of total carbonyls, formaldehyde, acetaldehyde were showed similar diurnal variations, that highest concentrations were found in the morning and noon, then drop down at afternoon and increased at night. Due to the fact that photochemical activities and vehicle exhausts. C1-C3 ratio indicated the local participation of anthropogenic hydrocarbons was important in the production of carbonyls in the Kaohsiung area. C1/C2 was highest in the summer than in the winter, that photochemical activities cause highest concentrations of formaldehyde, especially in the summer noon. The results of factor analysis and absolute principal component analysis showed that the primary pollution sources at Nan-Chie were traffic exhausts (diesel and gasoline vehicle) and stationary sources (petrochemical and food industry) and restaurant emissions, and the primary pollution sources at Hsiung-Kong were traffic exhausts (diesel and gasoline vehicle), stationary emissions (metal assembly and petrochemical industry) and restaurant emissions.

Understanding the processes that govern mating behaviors is a fundamental goal of evolutionary biology and behavioral ecology. Population-level patterns of mate acquisition and offspring production, otherwise known as the genetic mating system, play a central role in the sexual selection on morphological and behavioral traits and may facilitate speciation. The central hypothesis of this research is that variation in environmental conditions, such as temperature, turbidity, and habitat, and demographic influences such as population density, sex ratios and temporal availability of mates, may limit mating and reproductive success in a predictive manner. Therefore the goal of this dissertation is to examine the contributions of geographic and temporal variation on the plasticity of the genetic mating system in two species of pipefish. The first study examined whether meaningful variation in the genetic mating system exists between two natural populations of the dusky pipefish, Syngnathus floridae. Results of this investigation provide evidence that the genetic mating system differs among different geographic locations. The second study considered the relative contributions of environmental conditions and population demographics on differences in the genetic mating system of dusky pipefish from five natural populations. The results of this investigation show strong trends for demographic and environmental factors to strongly influence the genetic mating system between populations. The third study considered how variation in the number of available mates predicts the outcome of sexual selection during the course of a breeding season in the broad-nosed pipefish, Sygnathus typhle. The results of this study indicate a strong influence of the operational sex ratio on the genetic mating system. In addition to these studies, a study was conducted to investigate whether phylogeographic relationships may be responsible for geographic variation in the genetic mating system of the dusky pipefish of pipefish. Mitochondrial DNA analysis does not substantiate subspecies designations for this species and microsatellite analysis show a clear pattern of isolation by distance. Taken together, these studies significantly enhance the understanding of how mating systems are organized over broad environmental gradients and temporal/spatial scales and to the evolution of sexual selection on the whole.

This study is aiming to investigate the distribution of epibenthic shrimp communities in relation to the environmental factors of their habitats in the coastal sandy bottom of southwestern Taiwan. Shrimp samples were collected from April 2002 to July 2003, with a beam trawl operated at seven stations along the coasts. Simultaneously, water temperature, salinity, dissolved oxygen were measured and sediments were collected. Particle size and organic matter of the sediments were then analyzed in the laboratory. The results of PCA analyses on these environmental factors revealed that the observations could be segregated into two groups along the PC1, representing rainy season with high temperature, low salinity and dry season with low temperature, high salinity, respectively. The observations with coarse particle (>0.125 mm), representing samples from north sites, were found to distribute in the upper part of the PC2; while those with fine particle (<0.125 mm), representing samples from south sites, distributed in the lower part. In total, 15,591 individuals of shrimp were collected, including 20 genus, 39 species. Metapenaeopsis palmensis (88.2%), Trachysalambria curvirostris (3.6%), M. barbata (3.5%) and Parapenaeopsis cornuta (1.4%) were the four dominant species. Significant differences in the spatial distribution were due to the different composition of the dominant species. Although M. palmensis was the most abundant species in most stations, its percentage abundance was the lowest at Fangliao and Jiading, where the dominant species were T. curvirostris for the former and M. barbata and P. cornuta for the latter. Species preferences for various combinations of environmental variables are responsible for shifts in the structure and overall abundance of assemblages and dictated some patterns. Higher abundances of T. curvirostris, Trachypenaeus granulosus, and Solenocera koelbeli were associated with the appearance of high temperature, low salinity and very fine sand, representing the environmental features of Fangliao and Linbian during the rainy season. Stenopus hispidus, Metapenaeus moyebi, Metapenaeus ensis and M. palmensis were abundant coinciding with low temperature, high salinity and high silt and clay that reflecting the dry season of Linyuan and Linbian waters. Metapenaeopsis dalei and M. barbata appeared in large numbers at habitats with high temperature, low salinity and coarse sand, which mainly occurred in Zouying to Jhongjhou during the rainy season. Moreover, Scyllarus rugosus and Parapenaeopsis cornuta seemed to prefer coarse sandy bottom mainly distributed from Jiading to Linyuan. Temporal fluctuations were associated with the population dynamic of the dominant species. The abundance was reduced while the M. palmensis migrated to open sea in late summer and early autumn. As the juveniles of M. palmensis and M. barbata back to the inshore waters, the abundance were increased and reached the peak in spring. Because of the limited distribution, T. curvirostris and P. cornuta were not influence the overall temporal fluctuations but the local fluctuations. Overall, temporal fluctuations act more at a specific level even structural one, and may be linked to some particular stages of the benthic shrimp life cycle, but do not significantly influence the spatial organization.