Lessons from a Small-scale Observational Study - An Example of the Teaching of Fractions

The aim of this paper is to demonstrate what a small-scale project can tell about features of teaching and learning in two different cultures. We argue that some features, which may not be easily observed within one culture, can become more visible in the contrast in order to get a better understanding of the teaching practice per se, even from a small scale project. We have studied the mathematics teaching in one classroom in Hong Kong and four in Sweden. Based on the assumption, that how the content is taught has an important implication on what students may possibly learn, we compared how the teaching of the same topic (fraction) may differ between the two places. Some profound differences regarding how the same topic was dealt with in the two countries were found. In the Hong Kong data several things were handled in one lesson at the same time whereas in the Swedish data this happened in a sequence of lessons spreading over a substantial period.published_or_final_versio

Different possibilities to learn from the same task

In this paper we focus on variation of the design and the implementation of a specific task during three mathematics lessons in the 8th grade in a learning study (Marton & Tsui, 2004; Runesson, 2008). The theme of the lesson was division, with a denominator between 0 and 1. The teachers wanted their students to understand that when dividing with a denominator less than 1, the quotient is larger than the numerator. Four teachers collaboratively planned, analyzed and revised three lessons in a cyclic process. The study shows that the implementation of the task changed between the lessons. Although the same task was used in the lessons, the way it was enacted provided different possibilities to learn

On the variationally consistent computational homogenization of elasticity in the incompressible limit

Background Computational homogenization is a well-established approach in material modeling with the purpose to account for strong micro-heterogeneity in an approximate fashion without excessive computational cost. However, the case of macroscopically incompressible response is still unresolved. Methods The computational framework for Variationally Consistent Homogenization (VCH) of (near) incompressible solids is discussed. A canonical formulation of the subscale problem, pertinent to a Representative Volume Element (RVE), is established, whereby complete macroscale incompressibility is obtained as the limit situation when all constituents are incompressible. Results Numerical results for single RVEs demonstrate the seamless character of the computational algorithm at the fully incompressible limit. Conclusions The suggested framework can seamlessly handle the transition from (macroscopically) compressible to incompressible response. The framework allows for the classical boundary conditions on the RVE as well as the generalized situation of weakly periodic boundary conditions

Mesoscale modelling of crack-induced diffusivity in concrete

Cracks have large impact on the diffusivity of concrete since they provide low-resistance pathways for moisture and chloride ions to migrate through the material. In this work, crack-induced diffusivity in concrete is modelled on the heterogeneous mesoscale and computationally homogenized to obtain macroscale diffusivity properties. Computations are carried out using the finite element method (FEM) on three-dimensional Statistical Volume Elements (SVEs) comprising the mesoscale constituents in terms of cement paste, aggregates and the Interfacial Transition Zone (ITZ). The SVEs are subjected to uni-axial tension loading and cracks are simulated by use of an isotropic damage model. In a damaged finite element, the crack plane is assumed to be perpendicular to the largest principle strain, and diffusivity properties are assigned to the element only in the in-plane direction of the crack by anisotropic constitutive modelling. The numerical results show that the macroscale diffusivity of concrete can be correlated to the applied mechanical straining of the SVE and that the macroscale diffusivity increases mainly in the transversal direction relative to the axis of imposed mechanical straining

Compilation of life cycle assessments of cultivated blue mussels

With a growing world population there is an increased demand of sustainable and nutritious food. There is not much more land to farm on whether for food or for feed for livestock. Aquaculture increases more than any other production method, however there is still often a need for feed. Mussels are low trophic species that grow without input of feed, additives and antibiotics. They are filter feeding organisms consuming planktonic particles. Therefore, when harvested, nutrients are removed from the environment, reducing eutrophication. Life cycle assessment is a standardised method of calculating environmental impact. The goals of this thesis were to compile life cycle assessments about cultivated blue mussels through a literature review and to recalculate the carbon footprint and the marine eutrophication potential. The inventory assessments of six published mussel LCA studies and one dataset were analysed. Harmonization of methodologies was performed and a uniform functional unit of one tonne of Blue mussels produced was chosen. The recalculation resulted in a mean of 0,95 kg CO2-equivalents/kg mussel with shells at harvest and 5 mg N-equivalents/kg produced of mussels with shells at harvest. Hotspots identified were production of material used in cultivation, followed by energy and fuel use. Even though mussels have a low environmental impact, using more energy efficient boats or farmers sharing vessels could further reduce the emissions. Mussels have a high nutritional value and are relatively sustainable, making them an interesting future food product or ingredient in new products

Total carbon sequestration during an entire rotation period of oil palm in northern Borneo

Considerable amounts of carbon (C) has been lost from tropical forests as a result of continuous conversion of tropical forests into oil palm plantations. Therefore, a better understanding of the C budget and potential sequestration rate in oil palm plantations and how it compares to natural forests is needed. Which is crucial in order to provide a more reasonable C credit payment to limit the widespread land conversion of tropical forests to oil palm plantations. In this thesis, I quantified the amount of C in both above- and belowground pools, which included: aboveground oil palms, stumps, senesced fawns, fine litter, coarse woody debris, roots and soil over an entire rotation period of oil palm. I established 12 plots of similar conditions within a chrono sequence of oil palm, spanning from recently planted plantations <1 year old to a 22 year old plantation. Using this approach, I was able to calculate the carbon sequestration rate during an entire rotation period of oil palm as well as assess changes in different carbon pools. I estimated that 160-ton C ha-1 is lost when converting a secondary forest in Sabah Borneo to oil palm plantations. However, I found that rate of C sequestration (ton C ha-1 yr-1) in oil palm is considerably higher than C sequestration in primary and secondary tropical forests. Aboveground oil palm and soil C are the two major C pools in oil palm plantation, yet it is changes in aboveground oil palm during the rotation period that is responsible for the high C sequestration rate. I also estimated an economic profit of 37,333 USD during a rotation period based on data from the production of fresh fruit bodies. Comparing the profit to the difference in C sequestration between natural forests and oil palm plantation I calculated a C credit payment of 54-96 USD ton-1 CO2 that would be need to conserve carbon in tropical forests while at the same time provide the same economic revenue as oil palm production , which is considerably higher than the current price for C. Thus, if we want to limit the conversion of tropical forest to oil palm plantations the current C credit payment is not enough and addition payments for other ecosystem services (i..,e biodiversity and water quality) are needed.En betydande mängd kol har försvunnit från tropiska skogar som ett resultat av kontinuerlig konvertering av tropiska skogar till oljepalmsplantage. På grund av detta behövs en bättre förståelse för kollager och potentiell kolbindning i oljepalmsplantage samt hur det skiljer sig från naturlig skog. Vilket är väsentlig för att skapa ett mer resonabelt pris på kolkrediter för att begränsa konverteringen av skog till oljepalmsplantage. I denna uppsatts har jag kvantifierat mängden kollager i både ovan och under mark, vilket inkluderade oljepalmer, stubbar, avskurna oljepalmslöv, förna, död ved, rötter och jord under en hel rotation av första generations oljepalm. Jag etablerade 12 ytor med likande förhållanden med en krono sekvens av oljepalm, från nyligen planterat <1 år till 22år gammal plantage. Med hjälp av detta kunde jag räkna ut kolbindningen under en hel rotation av oljepalm samt uppskatta förändringar i de olika kollagren. Jag uppskattar att 160-ton kol ha-1 försvinner när en sekundär skog i Sabah Borneo konverteras till oljepalmsplantage. Dock så fann jag att kolbindningen i oljepalmsplantage är betydligt högre än i primär och sekundär skog. Kol i oljepalmerna och jorden är de två största kollagren i oljepalmsplantage, men det är förändringar i oljepalmerna som driver kolbindningen. Jag uppskattar en ekonomisk vinst på 37,333 USD under en rotationsperiod baserat på fruktproduktionen. Genom att jämföra vinsten emot skillnaden i kolbindning och lager för sekundär samt primär skog så uppskattar jag att priset på kolkrediter ska vara 54-96 USD ton-1 CO2 för att bevara kollagren i tropisk skog men ge samma ekonomiska vinst som oljepalmsplantage, vilket är betydligt högre än det nuvarande priset. Således om vi vill begränsa konverteringen av tropiska skogar till oljepalmsplantage så räcker inte det med de nuvarande kolkrediterna, utan ytterligare betalning för andra ekosystemstjänster (ex. biodiversitet och vattenkvalitet) behövs

A collective enquiry into critical aspects of teaching the concept of angles

This paper describes an approach to teaching that enhances pupils’ learning in mathematics. The model described – Learning study – involves teachers and researchers cooperating in an iterative process, gathering data about teaching and pupils’ learning, analysing the data, planning and revising their teaching. A particular theoretical framework was used as a guiding principle when designing and analysing learning. The goal was to identify aspects critical for learning the angle concept. It is demonstrated how the teachers were able to identify the critical aspects and change the teaching in a way that promoted pupils’ learning. What these critical aspects may entail and what teachers and researchers can learn from a Learning study is discussed

A 3D/2D comparison between heterogeneous mesoscale models of concrete

A model for 3D Statistical Volume Elements (SVEs) of mesoscale concrete is presented and employed in the context of computational homogenization. The model is based on voxelization where the SVE is subdivided into a number of voxels (cubes) which are treated as solid finite elements. The homogenized response is compared between 3D and 2D SVEs to study how the third spatial dimension influence the over-all results. The computational results show that the effective diffusivity of the 3D model is about 1.4 times that of the 2D model

The puzzle and politics of historical reconstruction: The case of the rise and development of Christianity and Judaism

This essay focuses on the topic of the emergence of Christianity and Judaism as related but distinct religious traditions, as an example of a process of religious and cultural change, which has had an enormous impact on Western and other societies around the world. At the heart of this question lies what appear to be contradictions between normative practices in antiquity and those we know of today, leading us to consider the historical and hermeneutical issue of continuity and change over time; its how, when and why. Rejecting the idea that theological differences between Judaism and Christianity necessitated a ‘parting of ways’ between them, it is argued that social, political and colonial decision-making was essential to this process, and that, furthermore, a historical focus on institutional realities in the ancient Mediterranean world, including in Jewish society, will challenge many long-held assumptions about the origins not only of Christianity but also of Judaism. The general historical reconstruction offered is then applied to a specific archaeological site, Capernaum, showing how traces of the larger pattern of development from the first to the fifth century CE may be seen in the histories of two buildings in this town