Hållpunkter för lärande : småbarns möten

Developed from human activities, mathematical knowledge is bound to the world and cultures that men and women experience. One can say that mathematics is rooted in humans’ everyday life, an environment where people reach agreement regarding certain “laws” and principles in mathematics. Through interaction with worldly phenomena and people, children will always gain experience that they can then in turn use to understand future situations. Consequently, the environment in which a child grows up plays an important role in what that child experiences and what possibilities for learning that child has. Variation theory, a branch of phenomenographical research, defines human learning as changes in understanding and acting towards a specific phenomenon. Variation theory implies a focus on that which it is possible to learn in a specific learning situation, since only a limited number of critical aspects of a phenomenon can be simultaneously discerned and focused on. The aim of this study is to discern how toddlers experience and learn mathematics in a daycare environment. The study focuses on what toddlers experience, how their learning experience is formed, and how toddlers use their understanding to master their environment. Twenty-three children were observed videographically during everyday activities. The videographic methodology aims to describe and interpret human actions in natural settings. The children are aged from 1 year, 1 month to 3 years, 9 months. Descriptions of the toddlers’ actions and communication with other children and adults are analyzed phenomenographically in order to discover how the children come to understand the different aspects of mathematics they encounter. The study’s analysis reveals that toddlers encounter various mathematical concepts, similarities and differences, and the relationship between parts and whole. Children form their understanding of such aspects in interaction with other children and adults in their everyday life. The results also show that for a certain type of learning to occur, some critical conditions must exist. Variation, simultaneity, reasonableness and fixed points are critical conditions of learning that appear to be important for toddlers’ learning. These four critical conditions are integral parts of the learning process. How children understand mathematics influences how they use mathematics as a tool to master their surrounding world. The results of the study’s analysis of how children use their understanding of mathematics shows that children use mathematics to uphold societal rules, to describe their surrounding world, and as a tool for problem solving. Accordingly, mathematics can be considered a very important phenomenon that children should come into contact with in different ways and which needs to be recognized as a necessary part of children’s everyday life. Adults working with young children play an important role in setting perimeters for children’s experiences and possibilities to explore mathematical concepts and phenomena. Therefore, this study is significant as regards understanding how children learn mathematics through everyday activities.

Matematiskt gestaltande i förskolan

The purpose of the thesis is to study how mathematics is experienced and used in preschool children’s activities and how preschool teachers frame their teaching of mathematical content. The studies include analyses of children’s actions in different activities from a mathematical perspective and preschool teachers’ intentions with and their teaching of mathematics. Preschool teachers’ understanding of the knowledge required in this area is also scrutinised. The theoretical points of departure are variation theory and sociocultural theory. With variation theory the focus is directed towards how mathematical content is dealt with in teaching situations where preschool teachers have chosen the learning objects. The sociocultural perspective has been chosen because children’s mathematical learning in play often takes place in interactions with others and in the encounter with culturally mediated concepts. The theoretical framework also includes didactical points of departure. The study is qualitative, with videography and phenomenography as metholological research approaches. In the study, video observations and interviews with preschool teachers have been used as data collection methods. The results show that in children’s play mathematics consists of volume, geometrical shapes, gravity, quantity and positioning. The situations also include size, patterns, proportions, counting and the creation of pairs. The preschool teachers’ intentions, planning and staging of their goal-oriented work are that all children should be given the opportunity to discern a mathematical content. This also includes making learning objects visible in here-and-now-situations. Variation and a clear focus on the mathematical content are important in this context. One of the study’s knowledge contributions concerns the didactics of mathematics in the preschool. This relates to the teaching of mathematics and includes the knowledge that preschool teachers regard as essential for their teaching. This includes theoretical and practical knowledge about children and children’s learning and didactical issues and strategies. The conclusion is that preschool teachers need to have a basic knowledge of mathematics and the didactics of mathematics.

Statistical variation of weld profiles and their expected influence on fatigue strength

The general objective of this study was to conduct astatistical analysis on the variation of the weld profiles and their influence on the fatigue strength of the joint. Weld quality with respect to its fatigue strength is of importance which is the main concept behind this thesis. The intention of this study was to establish the influence of weld geometric parameters on the weld quality and fatigue strength. The effect of local geometrical variations of non-load carrying cruciform fillet welded joint under tensile loading wasstudied in this thesis work. Linear Elastic Fracture Mechanics was used to calculate fatigue strength of the cruciform fillet welded joints in as-welded condition and under cyclic tensile loading, for a range of weld geometries. With extreme value statistical analysis and LEFM, an attempt was made to relate the variation of the cruciform weld profiles such as weld angle and weld toe radius to respective FAT classes.

Macroalgal Defenses Against Herbivory: Causes and Consequences of Intraspecific Variation

In marine benthic communities, herbivores consume a considerable proportion of primary producer biomass and, thus, generate selection for the evolution of resistance traits. According to the theory of plant defenses, resistance traits are costly to produce and, consequently, inducible resistance traits are adaptive in conditions of variable herbivory, while in conditions of constant/strong herbivory constitutive resistance traits are selected for. The evolution of resistance plasticity may be constrained by the costs of resistance or lack of genetic variation in resistance. Furthermore, resource allocation to induced resistance may be affected by higher trophic levels preying on herbivores. I studied the resistance to herbivory of a foundation species, the brown alga Fucus vesiculosus. By using factorial field experiments, I explored the effects of herbivores and fish predators on growth and resistance of the alga in two seasons. I explored genetic variation in and allocation costs of resistance traits as well as their chemical basis and their effects on herbivore performance. Using a field experiment I tested if induced resistance spreads via water-borne cues from one individual to another in relevant ecological conditions. I found that in the northern Baltic Sea F. vesiculosus communities, strength of three trophic interactions strongly vary among seasons. The highly synchronized summer reproduction of herbivores promoted their escape from the top-down control of fish predators in autumn. This resulted into large grazing losses in algal stands. In spring, herbivore densities were low and regulated by fish, which, thus,enhanced algal growth. The resistance of algae to herbivory increased with an increase in constitutive phlorotannin content. Furthermore, individuals adopted induced resistance when grazed and when exposed to water-borne cues originating from grazing of conspecific algae both in the laboratory and in field conditions. Induced resistance was adopted to a lesser extent in the presence of fish predators. The results in this thesis indicate that inducible resistance in F. vesiculosus is an adaptation to varying herbivory in the northern Baltic Sea. The costs of resistance and strong seasonality of herbivory have likely contributed to the evolution of this defense strategy. My findings also show that fish predators have positive cascading effects on F. vesiculosus which arise via reduced herbivory but possibly also through reduced resource allocation to resistance. I further found evidence that the spread of resistance via water-borne cues also occurs in ecologically realistic conditions in natural marine sublittoral. Thus, water-borne induction may enable macroalgae to cope with the strong grazing pressure characteristic of marine benthic communities. The results presented here show that seasonality can have pronounced effects on the biotic interactions in marine benthic communities and thereafter influence the evolution of resistance traits in primary producers.