https://www.mdu.se/

We study Hilbert functions, Lefschetz properties, and Jordan type of Artinian Gorenstein algebras associated to Perazzo hypersurfaces in projective space. The main focus lies on Perazzo threefolds, for which we prove that the Hilbert functions are always unimodal. Further we prove that the Hilbert function determines whether the algebra is weak Lefschetz, and we characterize those Hilbert functions for which the weak Lefschetz property holds. By example, we verify that the Hilbert functions of Perazzo fourfolds are not always unimodal. In the particular case of Perazzo threefolds with the smallest possible Hilbert function, we give a description of the possible Jordan types for multiplication by any linear form.

We show that, having a Hom-Lie algebra and an element of its dual vector space that satisfies certain conditions, one can construct a ternary totally skew-symmetric bracket and prove that this ternary bracket satisfies the Hom-Filippov-Jacobi identity, i.e. this ternary bracket determines the structure of 3-Hom-Lie algebra on the vector space of a Hom-Lie algebra. Then we apply this construction to two Hom-Lie algebras constructed on an associative, commutative algebra using σ-derivation and involution, and we obtain two 3-Hom-Lie algebras.

This paper presents a quadrature method for evaluating layer potentials in two dimensions close to periodic boundaries, discretized using the trapezoidal rule. It is an extension of the method of singularity swap quadrature, which recently was introduced for boundaries discretized using composite Gauss–Legendre quadrature. The original method builds on swapping the target singularity for its preimage in the complexified space of the curve parametrization, where the source panel is flat. This allows the integral to be efficiently evaluated using an interpolatory quadrature with a monomial basis. In this extension, we use the target preimage to swap the singularity to a point close to the unit circle. This allows us to evaluate the integral using an interpolatory quadrature with complex exponential basis functions. This is well-conditioned, and can be efficiently evaluated using the fast Fourier transform. The resulting method has exponential convergence, and can be used to accurately evaluate layer potentials close to the source geometry. We report experimental results on a simple test geometry, and provide a baseline Julia implementation that can be used for further experimentation.

We present a spectrally accurate method for the rapid evaluation of free-space Stokes potentials, i.e., sums involving a large number of free space Green’s functions. We consider sums involving stokeslets, stresslets and rotlets that appear in boundary integral methods and potential methods for solving Stokes equations. The method combines the framework of the Spectral Ewald method for periodic problems (Lindbo and Tornberg in J Comput Phys 229(23):8994–9010, 2010. doi: 10.1016/j.jcp.2010.08.026 ), with a very recent approach to solving the free-space harmonic and biharmonic equations using fast Fourier transforms (FFTs) on a uniform grid (Vico et al. in J Comput Phys 323:191–203, 2016. doi: 10.1016/j.jcp.2016.07.028 ). Convolution with a truncated Gaussian function is used to place point sources on a grid. With precomputation of a scalar grid quantity that does not depend on these sources, the amount of oversampling of the grids with Gaussians can be kept at a factor of two, the minimum for aperiodic convolutions by FFTs. The resulting algorithm has a computational complexity of $$O(N \log N)$$ O ( N log N ) for problems with N sources and targets. Comparison is made with a fast multipole method to show that the performance of the new method is competitive.

We study the double-mean-reverting model by Gatheral. Our previous results concerning the asymptotic expansion of the implied volatility of a European call option, are improved up to order 3, that is, the error of the approximation is ultimately smaller that the 1.5th power of time to maturity plus the cube of the absolute value of the difference between the logarithmic security price and the logarithmic strike price.

The double-mean-reverting model by Gatheral [1] is motivated by empirical dynamics of the variance of the stock price. No closed-form solution for European option exists in the above model. We study the behaviour of the implied volatility with respect to the logarithmic strike price and maturity near expiry and at-the- money. Using the method by Pagliarani and Pascucci [6], we calculate explicitly the first few terms of the asymptotic expansion of the implied volatility within a parabolic region.

The double-mean-reverting model by Gatheral is motivated by empirical dynamics of the variance of the stock price. No closed-form solution for European option exists in the above model. We study the behaviour of the implied volatility with respect to the logarithmic strike price and maturity near expiry and at-the-money. Using the method by Pagliarani and Pascucci, we calculate explicitly the first few terms of the asymptotic expansion of the implied volatility within a parabolic region.

The Gatheral double stochastic volatility model is a three-factor model with mean-reverting stochastic volatility that reverts to a stochastic long-run mean. Our previous paper investigated the performance of the first and second-order implied volatilities expansions under this model. Moreover, a simple partial calibration method has been proposed. This paper reviews and extends previous results to the third-order implied volatility expansions under the same model. Using Monte-Carlo simulation as the benchmark method, extensive numerical studies are conducted to investigate the accuracy and properties of the third-order expansion. 

For the space of (σ,τ)-derivations of the group algebra C[G] of a discrete countable group G, the decomposition theorem for the space of (σ,τ)-derivations, generalising the corresponding theorem on ordinary derivations on group algebras, is established in an algebraic context using groupoids and characters. Several corollaries and examples describing when all (σ,τ)-derivations are inner are obtained. Considered in details are cases of (σ,τ)-nilpotent groups and (σ,τ)-FC groups.

Emissions from oil wells and refineries are sources of air pollutants depending on their composition and amounts. The current study focuses on investigation and detecting of thermal anomalies and active hotspots in oil pipelines and refineries locations in Iraq, along with the spatial distribution of the ultraviolet aerosol (UV Aerosol) index. The goal is to assign the most polluted cities that can assist in evaluating the consequences of the air pollution on human and the environmental risk as well. We carried out the analysis of the products obtained from Terra/ MODIS data derived from channels 21 (4 µm) and 31 (11 µm), and the Sentinel-5P products/ Level 2 for the UV Aerosol index in the atmosphere, and found a number of active thermal signals in different geographic areas in Iraq, especially in southeastern and northeastern parts of the country, where the most of Iraq's petroleum resources are located there. The study shows a good correlation between the observed thermal anomalies and the UV emissions, and the results proved that the aerosol emission changes is significantly affected by emissions from oil wells and refineries. We also used fires reports obtained from the department of safety and fires in Basra to validate the outcomes and to investigate the final interpretation of the obtained results that were consist with the documented reports. As well as the results also shows a significant spatio-temporal variations in values of UV index among different parts of Iraq, and the larger amount of UV index has been seen in southern Iraq in Basra.

Understanding the intricacies of teaching is a fundamental pursuit within the realm of educational research. As we chart the trajectory of research in this field, we find that the earliest conception of teaching was premised on a set of ideologies and beliefs that were formulated through observation and emulation of an established sage of a stage or gleaned from philosophical treatises that aim to theorise about the nature of teaching (Markee Citation1995). Propelled by Conversation Analysis (CA) is the treatment of teaching as a set of locally enacted practices that are accomplished through the detailed orchestration of verbal and non-verbal resources and that can be studied through rigorous analysis of naturally occurring interactions in the classrooms. The Practical Nature of L2 Teaching delves into the practical nature of teaching from a conversation-analytic perspective in order to offer a fine-tuned understanding of how teaching unfolds in real-world language classrooms. While intended for varied audiences, this book holds particular value for novice CA researchers looking for a repository of CA findings to refer to as they work on their data, novice teachers seeking to further their expertise, and teacher educators working towards integrating a practice-based approach into their existing teacher preparation programmes. I will revisit this later in detail, but for now, let us acquaint ourselves with the structure and content of the book. It is worth mentioning that while I will provide a general overview of the book, my aim is not to exhaust this limited space by providing an extensive chapter-by-chapter analysis. Instead, I will focus more on showing who can benefit from it, suggesting various ways to harness its insights, and offering pathways to build upon it.

This study investigates how shared understanding is established during a rarely researched instructional and interactional context, namely teacher-student interactions during between-desk instructions (BDIs). Specifically, the authors focus on instructional interactions initiated by students during project-based language teaching in an upper-secondary Swedish classroom and probe into how students' formulations of understanding of a teacher's prior responses shape the subsequent interactional trajectories. Their conversation analytic investigation reveals that the teacher produces either confirming or disconfirming actions following students' formulations of understanding. These response types accomplish two distinct forms of interactional work: (a) when the teacher confirms the students' formulations, she expands the sequence with instruction-related elaborations; and (b) when the teacher does not confirm the formulations, she accounts for that, prompting students to reformulate their understanding. Overall, this study contributes to the body of research on BDIs as a recurring yet under-investigated lesson practice during project work.

In Sweden, the Compulsory School for Students with Intellectual Disabilites (CSSID) is currently experiencing political change, as this type of school is being renamed and is undergoing organisational changes. The inclusion of children with intellectual disabilities (ID) in schooling, and in general society, has been challenged and debated for decades; such debates are at the heart of some of these changes. In this study, we have systematically investigated the policy work (e.g. government reports and statements) preceding and governing the changes. Hence, the purpose of the study is to contribute knowledge on how policy documents inscribe meaning to the inclusion of children with ID. Results show that discourses on inclusion are connected to neoliberal values and practices, such as assessment, global comparison, and accountability. It has been suggested that this may have a profound and long-term effect on how children with ID are fabricated and hence, how the child with ID and their education can be understood in terms of being included in the idea of ‘all students’ in policy, and in addition, in practice.

When someone violates a social norm, others may think that some sanction would be appropriate. We examine how the experience of emotions like anger and disgust relate to the judged appropriateness of sanctions, in a pre-registered analysis of data from a large-scale study in 56 societies. Across the world, we find that individuals who experience anger and disgust over a norm violation are more likely to endorse confrontation, ostracism and, to a smaller extent, gossip. Moreover, we find that the experience of anger is consistently the strongest predictor of judgments of confrontation, compared to other emotions. Although the link between state-based emotions and judgments may seem universal, its strength varies across countries. Aligned with theoretical predictions, this link is stronger in societies, and among individuals, that place higher value on individual autonomy. Thus, autonomy values may increase the role that emotions play in guiding judgments of social sanctions.

In this study we are interested in how learners of geometrical optics express disciplinary relevant aspects multimodally in an inquiry-based learning with support of a computer simulation. Students' discussions and work with the simulation were filmed, transcribed, and we analysed some parts of the transcript where the students show signs of disciplinary relevant aspects by a method based in conversation analysis. We found evidence that the students use multiple semiotic resources for expressing disciplinary relevant aspects about the tasks, especially gestures. The letter are by their visual nature well suited for communication in physics, and are used by the students to transduct semiotic information.

Recent research at the cross between cognitive and social sciences is investigating the cognitive mechanisms behind cooperative decisions. One debated question is whether cooperative decisions are made faster than non-cooperative ones. Yet empirical evidence is still mixed. In this paper we explore the implications of individual heterogeneity in social value orientation for the effect of response time on cooperation. We conduct a meta-analysis of available experimental studies (n=8; treatments=16; 5,232 subjects). We report two main results: (i) the relation between response time and cooperation is moderated by social value orientation, such that it is positive for individualist subjects and negative for prosocial subjects; (ii) the relation between response time and cooperation is partly mediated by extremity of choice. These results suggest that highly prosocial subjects are fast to cooperate, highly individualist subjects are fast to defect, and subjects with weaker preferences make slower and less extreme decisions. We explain these results in terms of decision-conflict theory.

The emergence of COVID-19 dramatically changed social behavior across societies and contexts. Here we study whether social norms also changed. Specifically, we study this question for cultural tightness (the degree to which societies generally have strong norms), specific social norms (e.g. stealing, hand washing), and norms about enforcement, using survey data from 30,431 respondents in 43 countries recorded before and in the early stages following the emergence of COVID-19. Using variation in disease intensity, we shed light on the mechanisms predicting changes in social norm measures. We find evidence that, after the emergence of the COVID-19 pandemic, hand washing norms increased while tightness and punishing frequency slightly decreased but observe no evidence for a robust change in most other norms. Thus, at least in the short term, our findings suggest that cultures are largely stable to pandemic threats except in those norms, hand washing in this case, that are perceived to be directly relevant to dealing with the collective threat. Tightness-looseness theory predicts that social norms strengthen following threat. Here the authors test this and find that, after the emergence of the COVID-19 pandemic, hand washing norms increased, but no evidence was observed for a robust change in most other norms.

Social norms have been investigated across many disciplines for many years, but until recently, studies mainly provided indirect, implicit and correlational support for the role of social norms in driving behaviour. To understand how social norms, and in particular social norm change, can generate a large-scale behavioural change to deal with some of the most pressing challenges of our current societies, such as climate change and vaccine hesitancy, we discuss and review several recent advances in social norm research that enable a more precise underpinning of the role of social norms: how to identify their existence, how to establish their causal effect on behaviour and when norm change may pass tipping points. We advocate future research on social norms to study norm change through a mechanism-based approach that integrates experimental and computational methods in theory-driven, empirically calibrated agent-based models. As such, social norm research may move beyond unequivocal praising of social norms as the missing link between self-interested behaviour and observed cooperation or as the explanation for (the lack of) social tipping. It provides the toolkit to understand explicitly where, when and how social norms can be a solution to solve large-scale problems, but also to recognize their limits.This article is part of the theme issue 'Emergent phenomena in complex physical and socio-technical systems: from cells to societies'.

In graph theory, centrality measures are very crucial in ranking vertices of the graph in order of their importance. Alpha and eigenvector centralities are some of the highly placed centrality measures applied especially in social network analysis, disease diffusion networks and mechanical infrastructural developments. In this study we focus on recalculating alpha and eigenvector centralities using graph partitioning techniques. We write an algorithm for partitioning, sorting and efficiently computing these centralities for a graph. We then numerically demonstrate the technique on some sample small-sized networks to recalculate the two centrality measures

Several recent results concerning Hom-Leibniz algebra are reviewed, the notion of symmetric Hom-Leibniz superalgebra is introduced and some properties are obtained. Classification of 2-dimensional Hom-Leibniz algebras is provided. Centroids and derivations of multiplicative Hom-Leibniz algebras are considered including the detailed study of 2-dimensional Hom-Leibniz algebras.

An inverse problem of finding an unknown heat source for a class of linear parabolic equations is considered. Such problems can typically be converted to a direct problem with non-local conditions in time instead of an initial value problem. Standard ways of solving these non-local problems include direct temporal and spatial discretization as well as the shooting method, which may be computationally expensive in higher dimensions. In the present article, we present approaches based on low-rank approximation via Arnoldi algorithm to bypass the computational limitations of the mentioned classical methods. Regardless of the dimension of the problem, we prove that the Arnoldi approach can be effectively used to turn the inverse problem into a simple initial value problem at the cost of only computing one-dimensional matrix functions while still retaining the same accuracy as the classical approaches. Numerical results in dimensions d=1,2,3 are provided to validate the theoretical findings and to demonstrate the efficiency of the method for growing dimensions.

One of the main ingredients of existing multiscale numerical methods for homogenization problems is an accurate description of the coarse scale quantities, e.g., the homogenized coefficient via local microscopic computations. Typical multiscale frameworks use local problems that suffer from the so-called resonance or cell-boundary error, dominating the all other errors in multiscale computations. Previously, the second order wave equation was used as a local problem to eliminate such an error. Although this approach eliminates the resonance error totally, the computational cost of the method is known to increase with increasing wave speed. In this paper, the possibility of integrating perfectly matched layers to the local wave equation is explored. In particular, questions in relation with accuracy and reduced computational costs are addressed. Numerical simulations are provided in a simplified one-dimensional setting to illustrate the ideas.

In this paper, the representations of color hom-Lie algebras have been reviewed and the existence of a series of coboundary operators is demonstrated. Moreover, the notion of a color omni-hom-Lie algebra associated to a linear space and an even invertible linear map have been introduced. In addition, characterization method for regular color hom-Lie algebra structures on a linear space is examined and it is shown that the underlying algebraic structure of the color omni-hom-Lie algebra is a color hom-Leibniz a algebra.

In this paper, we study (non-Abelian) extensions of a given hom-Lie color algebra and provide a geometrical interpretation of extensions. In particular, we characterize an extension of a hom-Lie color algebra g by another hom-Lie color algebra h and discuss the case where h has no center. We also deal with the setting of covariant exterior derivatives, Chevalley derivative, curvature and the Bianchi identity for possible extensions in differential geometry. Moreover, we find a cohomological obstruction to the existence of extensions of hom-Lie color algebras, i.e., we show that in order to have an extendible hom-Lie color algebra, there should exist a trivial member of the third cohomology.

All children have the right to become equal citizens of the society. Children with intellectual disabilities have difficulties in learning and may need support to reach that equality, and some extra resources may be needed. Compared to children with typical development, children with intellectual disabilities have problems in three cognitive areas that are essential for learning activities: Abstract thinking. Understanding/using abstract symbols (text, numbers, money, and time) and imagining non-experienced things and situations. Several-steps thinking. Understanding multiple-level instructions and connections between cause and effect. Simultaneous handling of information. Nuanced considerations/comparisons, risk considerations and problem solving that manifest in complex social situations.

Endorsing an interactive bio-psycho-social understanding of intellectual disabilities implies that learning limitations are the discrepancy between abilities and the level and/or quality of support, and according to this an inclusive approach to learning should be based on knowledge about abilities rather than dis-abilities. Two inclusive classroom strategies for learning are presented and discussed in this chapter. These strategies seek ways of providing universal, inclusive learning situations where children with intellectual disability can interact with any children and the most important role for a teacher is to find ways to support the children in that interaction.

Using the Rabinowitsch trick, we prove an explicit version of the central quaternionic Nullstellensatz formulated and proved by Alon and Paran. (c) 2024 The Author. Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons .org /licenses /by /4 .0/).

The product formula for evaluating products of skew polynomials is used to construct a class of rings. As an application, we present a method of evaluating quotients of skew polynomials.

We introduce and study flipped non-associative polynomial rings. In particular, we show that all Cayley–Dickson algebras naturally appear as quotients of a certain type of such rings; this extends the classical construction of the complex numbers (and quaternions) as a quotient of a (skew) polynomial ring to the octonions, and beyond. We also extend some classical results on algebraic properties of Cayley–Dickson algebras by McCrimmon to a class of flipped non-associative polynomial rings.

In the present paper, we study the first and second order of accuracy difference schemes for the approximate solution of the inverse problem for hyperbolic–parabolic equations with unknown time-independent source term. The unique solvability of constructed difference schemes and the stability estimates for their solutions are obtained. The proofs are based on the spectral representation of the self-adjoint positive definite operator in a Hilbert space.

In this paper, we study some equivalent conditions for a color hom-Lie algebra to be a complete color hom-Lie algebra. In particular, we discuss the relationship between decomposition and completness for a color hom-Lie algebra. Moreover, we check some conditions that the set of αs -derivations of a color hom-Lie algebra to be complete and simply complete. Finally, we find some conditions in which the decomposition into hom-ideals of the complete multiplicative color hom-Lie algebras is unique up to order of hom-algebra.

The purpose of the study is to contribute with knowledge about what mothers describe doing to support their children in grade 1. The research questions are as follows: What do the mothers do to support their children’s education on a general level? What do the mothers do to specifically support their children’s reading and writing development? Eleven parents (all mothers) participated. Interviews were analysed thematically, whereby six themes addressing their support were identified: 1) Talk with children about school; 2) Handle school-related problems; 3) Have a positive attitude towards school; 4) Guide children’s reading and writing; 5) Coach specific training; and 6) Collaborate with school staff about children’s reading homework. The bioecological model for human development constitutes a theoretical frame and an understanding of what influences children’s development, for example, parents’ support to children’s reading and writing development. It provided useful concepts (e.g., microsystem, proximal processes, mesosystem, and chronosystem) for a discussion of the themes. The study is relevant for prospective and professional teachers in early grades, special needs teachers, other school staff, principals, policymakers, and parents.

The worldwide need and request for a workforce equipped with thorough high qualitativeknowledge but also a capability to use it in complex situations, has become the entrance ticketfor entrepreneurial skills entering the Swedish compulsory education. Thus, schools play an important role providing a space for individuals practicing these skills, being for instance able to see opportunities and make something from them, being initiative, self-confident, risktaking, creative and problem solving. With the aim to increase the knowledge of how entrepreneurial skills unfolds as part of the education at earlier ages, this mainly qualitative study follows a novel attempt to build a common thread of entrepreneurial skills from preschool to grade nine, in a small mid-Swedish municipality during 2018. Focusing on initial challenges, the findings show the teachers struggle with both content, methods and progression. Related to the curricula’s formulation arena, there is a discrepancy between this and the teachers’ transformation and realisation arena. This suggests theydo not always do what the curricula stipulate or they themselves classify as most important,they generally seem to struggle to link their subjects to entrepreneurial skills and there is a lack of progression between grades and in transitions between school levels.

Estimates of tree heartwood and sapwood profiles are important in the pulp industry and for dynamic vegetation models, in which they determine tree biomechanical stability and hydraulic conductivity. Several phenomenological models of stem profiles have been developed for this purpose, based on assumptions on how tree crown and foliage distributions change over time. Here, we derive estimates of tree profiles by synthesizing a simple pipe model theory of plant form with a recently developed theory of branch thinning that from simple assumptions quantifies discarded branches and leaves. This allows us to develop a new trunk model of tree profiles from breast height up to the top of the tree. We postulate that leaves that are currently on the tree are connected by sapwood pipes, while pipes that previously connected discarded leaves or branches form the heartwood. By assuming that a fixed fraction of all pipes remain on the trunk after a branching event, as the trunk is traversed from the root system to the tips, this allows us to quantify trunk heartwood and sapwood profiles. We test the trunk model performance on empirical data from five tree species across three continents. We find that the trunk model accurately describes heartwood and sapwood profiles of all tested tree species (calibration; R-2: 84-99%). Furthermore, once calibrated to a tree species, the trunk model predicts heartwood and sapwood profiles of conspecific trees in similar growing environments based only on the age and height of a tree (cross-validation/prediction; R-2: 68-98%). The fewer and often contrasting parameters needed for the trunk model make it a potentially useful complementary tool for biologists and foresters.

The Escalator Boxcar Train (EBT) is a commonly used method for solving physiologically structured population models. The main goal of this paper is to overcome computational disadvantages of the EBT method. We prove convergence, for a general class of EBT models in which we modify the original EBT formulation, allowing merging of cohorts. We show that this modified EBT method induces a bounded number of cohorts, independent of the number of time steps. This in turn, improves the numerical algorithm from polynomial to linear time. An EBT simulation of the Daphnia model is used as an illustration of these findings.

The Escalator Boxcar Train (EBT) is one of the most popular numerical

methods used to study the dynamics of physiologically structured population models.

The original EBT model accumulates an increasing system of ODEs to solve for each

time step. In this project, we propose a merging procedure to overcome computational

disadvantageous of the EBT method, the merging is done as an automatic feature.

In particular we apply the model including merging to a colony of Daphnia Pulex.

The classical pipe model theory introduced by Shinozaki, Yoda, Hozumi,

and Kira (1964a,b) is used to estimate tree sapwood area. It rests on the

conceptual idea that leaves are supported by pipes, serving as vascular

passages. The simple pipe model of plant form does not predict the heart

wood area and is thus not suitable for stem diameter estimates below the

tree crown. For this reason, Shinozaki, Yoda, Hozumi, and Kira (1964a)

verbally described an extended pipe model theory of tree form that in

principle accounts for the accumulation of disused pipes from discarded

branches and leaves. However, this pipe model theory of tree form is difficult

to apply in practice as lost branches and leaves are rarely known.

 Here, we synthesize the pipe model theory of plant form with a recently

developed theory of branch thinning that quantify discarded branches and

leaves. This allows us to develop a new stem model of tree profiles from

breast height up to the top of the tree. We test the stem model perfor

mance on empirical data from four tree species across three continents.

We find that the stem model accurately describes heartwood and sapwood

profiles of all tested tree species (calibration; R2: 84-99 %). Furthermore,

once calibrated to a tree species, the stem model predicts heartwood and

sapwood profiles of conspecific trees in similar growing environments based

only on the age and height of a tree (cross-validation / prediction; R2:

62-98 %).

Modelling population dynamics in ecological systems reveals properties that are difficult to find by empirical means, such as the probability that a population will go extinct when it is exposed to harvesting. To study these properties, we use an aquatic ecological system containing one fish species and an underlying resource as our models. In particular, we study a class of stage-structured population systems with and without starvation. In these models, we study the resilience, the recovery potential, and the probability of extinction and show how these properties are affected by different harvesting rates, both in a deterministic and stochastic setting. In the stochastic setting, we develop methods for deriving estimates of these properties. We estimate the expected outcome of emergent population properties in our models, as well as measures of dispersion. In particular, two different approaches for estimating the probability of extinction are developed. We also construct a method to determine the recovery potential of a species that is introduced in a virgin environment.

This study investigated the affordances of a mobile video observation and tagging tool used to evaluate presentation skills in English language classrooms. The data consists of 35 video-recorded presentations in a higher education setting. Using a digital evaluation grid, the students received feedback based on visual analytics generated by the mobile app. The students then were asked to reflect on their performances, and were also asked to comment on the affordances and limitations of the method and the tool. Qualitative data that came from (1) students’ written self-evaluations and reflections and (2) their reported perceptions of the affordances of the tool were analyzed using the Constant Comparison Method. Analyses of reflective writings indicated the dominance of negative self-evaluations of language use, while affective factors were also a strong theme. The video-tagging tool was found to be very beneficial by the learners, mainly in enabling them to notice their strengths and weaknesses in presenting in English and facilitating effective feedback. The results show that this data-led reflective presentation model can be beneficial for learners as they can identify points of development.

Keywords: Teachers´ leadership, parents-teachers ‘conference, primary school, didactic, hermeneutic, lifeworld phenomenology

This thesis aims to explain what importance teachers´ leadership is given and how teachers' leadership appears in the parents-teacher conferences. The theoretical frame is lifeworld phenomenology, which means that the world is a social, intersubjective, and historical world where people experience, act, and intertwine in a private and a shared world. The study is inspired by a lifeworld approach and the data was analyzed to consider people's context, their experiences and the challenges involved in leading parent-teacher conferences. The empirical work is based on observations of parent-teacher conferences and interviews with teachers and students. The analyses are made with the support of the life-world phenomenological concepts of hållning, seeing-as and pedagogical tact. The concept hållning has a duality and loses its meaning in translation. Hållning means a bodily approach and is an intertwining between the teacher's attitude and her body posture. All three concepts include verbal and bodily communicative expressions and sensitive and intuitive actions, their meanings will be highlighted and explained. 

The results show that teachers' leadership in parent-teacher conferences includes both preparatory and subsequent work and forms part of the teaching. Leadership both shapes the parent-teacher conference and is shaped in the same and given importance when teachers show consideration for the student, the relationship between teacher and student and the situation, balance challenges with time and sensitive topics, choose to take notes in the parent-teacher conferences in favor of presence in the conversation itself and document afterwards. Teachers' leadership in parent-teacher conferences shape the conversation through teachers' willingness to involve the students, flexibility, and ability to structure. Teachers' leadership in parent-teacher conferences are shaped by teachers' responsiveness, compliance, presence, attention, ability to improvise and playfulness.

The study's life-world phenomenological approach has made it possible to see that the parent-teacher conference requires a didactic knowledge related to the student as a person, to the content and to the structure that surrounds the conversation. This has been made visible in teachers' intuitive actions and bodily expressions as well as unreflected and reflected experiences. The study's starting points have made it possible to broaden the didactic understanding of the teachers' leadership in parent-teacher conferences by highlighting the clear intertwining of these conferences with other teaching

The purpose of this paper is to introduce Hom-prealternative superalgebras and their bimodules. Some constructions of Hom-prealternative superalgebras and Hom-alternative superalgebras are given, and their connection with Hom-alternative superalgebras are studied. Bimodules over Hom-prealternative superalgebras are introduced, relations between bimodules over Hom-prealternative superalgebras and the bimodules of the corresponding Hom-alternative superalgebras are considered, and construction of bimodules over Hom-prealternative superalgebras by twisting is described.

Background: Inclusive learning environments are considered as crucial for children’s engagement with learning and participation in school. Partnering for change (P4C) is a collaborative school-based service delivery model where services are provided at three levels of intensity based on children’s needs (class, group-, individual interventions). Interventions in P4C are provided universally to support all children with learning, not only children with special education needs (SEN), and as such are expected to be health-promoting. Aim: The aim of the study is to evaluate the effectiveness and cost-effectiveness of P4C as well as school staff members’ and children’s experiences after P4C. Methods: In a parallel, non-randomised controlled intervention design, 400 children, aged 6–12 years, and their teachers, will be recruited to either intervention classes, working according to the P4C, or to control classes (allocation ratio 1:1). Data will be collected at baseline, post-intervention (4 months), and 11 months follow-up post baseline. The primary outcome is children’s engagement with learning in school. Secondary outcomes include for example children’s health-related quality of life and wellbeing, occupational performance in school, attendance, and special educational needs. The difference-in-differences method using regression modelling will be applied to evaluate any potential changes following P4C. Focus group interviews focusing on children, and professionals’ experiences will be performed after P4C. A health economic evaluation of P4C will be performed, both in the short term (post intervention) and the long term (11-month follow-up). This study will provide knowledge about the effectiveness of P4C on children’s engagement with learning, mental health, and wellbeing, when creating inclusive learning environments using a combination of class-, group- and individual-level interventions. Trial registration number: NCT05435937. 

This chapter looks at the discourse of multilingualism in the Irish education sector with a specific focus on teacher educators. The research was conducted among primary and second level teacher educators and the results highlight the need to address English as an Additional Language more directly in teacher education in order to improve classroom practice.

The overall aim of this thesis is to use a curriculum theoretical perspective to contrib­ute knowledge about the impact of recent reforms on teachers’/preschool teachers’ teaching, with a special focus on mathematics. The thesis takes its starting point in a licentiate thesis that was completed in 2014. The further doctoral studies are based on two articles. These articles answer specific research questions. Substudy 1 was a systematic literature review that focused on the role of the preschool teacher in teaching mathematics in preschool. Substudy 2 explored how preschool teachers in­terpret their teaching mission based on the curriculum’s directives and how they describe the meaning of the concept of preschool teaching. The data from Substudy 1 consisted of 68 research articles, and Substudy 2 was based on 50 preschool teachers’ reflection texts. The theoretical underpinnings of the thesis are two theoretical perspec­tives: curriculum theory and Bernstein’s theory of pedagogic practice. The results from the two substudies show the importance of preschool teachers having both sub­ject knowledge and didactic competence to carry out teaching in spontaneous situa­tions and planned activities. The results from Substudy 1 show two different roles that pre­school teachers adopt when teaching mathematics in preschool education guided by social pedagogical or pre-primary curriculum traditions; these are the role of instructor and the role of an interactor. In the research studies, preschool teachers provide instruction with planned subject content or interact with the children’s play and other everyday situations to promote children’s mathematics learning. The results from Substudy 2 show an education that is guided by invisible pedagogy within the social pedagogical curriculum tradition. The preschool teachers describe teaching taking place spontaneously in play and other everyday situations based on children’s own interests and needs. The preschool teachers also have a purpose with the teaching, and they plan activities together with the children. These reveal teaching governed by visible pedagogy, which is characteristic of the pre-primary curriculum tradition. Further­more, there are indications that a new curriculum tradition is emerging bearing some sim­ilarities to previous traditions, an approach that is both play-based and goal-oriented. Children’s participation and influence are central in the teaching, which means that the teaching conforms to the children’s interests, and that goals from the curriculum are woven into the everyday work. The preschool teacher consciously shapes the envi­ronment in the preschool and uses materials to promote children’s learning, and the teaching has more distinct subject content. Together with the licentiate study, the two substudies show that teachers and preschool teachers have difficulty transforming a new curriculum text into practically applicable form. The curricula leave room for interpretation, and the uncertainty that arises in the transformation arena shows that they need support to realize the curriculum’s new guidelines.

The purpose of the study is to contribute knowledge about how teaching in preschool can be understood in relation to how teaching is described by preschool teachers. The following research questions were posed:How do preschool teachers describe teaching and its meaning in preschool? and What didactic questions appear in preschool teachers’ descriptions of teaching in preschool? The empirical data consist of reflective texts that were analysed through content analysis with the help of Bernstein’s concepts: classification and framing, and visible and invisible pedagogy. The results show that the preschool teachers in the study perceived the introduction of the concept of teaching in preschool as an opportunity, which allowed them to become more aware of their actions in different learning situations. That the preschool teachers described teaching taking place through play and in everyday situations based on children's interests and needs hints at an organization with invisible pedagogy, weak classification and weak framing. Strong classification and strong framing, on the other hand, became manifest when the preschool teachers described that they plan what they do with the children and use materials, organize children’s groups and design environments to promote children’s learning. Furthermore, the preschool teachers focused mainly on the didactic questions of how and why, while the what-question received less attention.

The aim of the study is to find similarities and differences concerning the new formulations on teaching in revised curriculum in Swedish preschool and international research in early childhood education, Teaching is more clarified in the revised curriculum. Swedish preschool education is moving towards a more formalized approach where teaching is more visible (Helenius, 2018). There is a consensus that early mathematics is important in policy and research but there is no agreement on how mathematics education should be implemented. There are differences between and within countries, a clear difference is the relation between play and teaching (Palmér & Björklund, 2016). The concepts of classification and framing are used to discuss the visibility of pedagogics in the formalization of teaching mathematics in preschool (Bernstein, 2000). This is a literature review regarding research on teaching mathematics in early childhood education. It draws from a number of scholarly research article conducted between 2014 and 2019. The data collection is in progress. Qualitative and quantitative content analysis will compare emerged codes. The expected results will consist of empirical research. Ethical consideration is met by showing respect and responsiveness to other researchers work. This literature review is based on peer-reviewed articles. Preliminary findings indicate differences in how teaching mathematics in preschool is described. Preschool in Sweden has a tradition of a play-based pedagogy and no formal assessment of children as many other countries. Perhaps, the change may push teaching to become more visible and formal (Helenius, 2018). Implications for policy and practice will be discussed.