Primal-Dual Algorithms for Semidefinit Optimization Problems based on generalized trigonometric barrier function

Recently, M. Bouafoa, et al. (Journal of optimization Theory and Applications, August, 2016), investigated a new kernel function which differs from the self-regular kernel functions. The kernel function has a trigonometric Barrier Term. In this paper we generalize the analysis presented in the above paper for Semidefinit Optimization Problems (SDO). It is shown that the interior-point methods based on this function for large-update methods, the iteration bound is improved significantly. For small-update interior point methods the iteration bound is the best currently known bound for primal-dual interior point methods. The analysis for SDO deviates significantly from the analysis for linear optimization. Several new tools and techniques are derived in this paper.publishedVersio

Recontextualisation of knowledge in the new Norwegian curriculum: Epistemic and non-epistemic design in learning objectives for social studies

The recent Norwegian curriculum reform for schools, called “The subject renewal”, is part of an international trend regarding knowledge-based curricula. The Norwegian curriculum, which places decisive emphasis on subjects and subject concepts, aims to bring in-depth learning and knowledge back to schools. This paper is based on Rata’s theory, referred to as the curriculum design coherence (CDC) model, and examines the curriculum for social studies. The analysis reveals significant differences in the curriculum’s goal formulations, with designs that lack connections between subject concepts and content knowledge, which sheds light on how the transition to a knowledge-based curriculum is accompanied by several unresolved issues. The paper explains why curricula with coherent designs and epistemically structured knowledge are a prerequisite for in-depth learning and cumulative knowledge building in schools.publishedVersio

The Icarus Effect Rephrased : Range of Semantic Gravity and Forms of Knowledge in New Norwegian Teacher Education

In the 2000s, several major education reforms have been implemented in Norway. The reform in the teacher education is heavily inspired by the Finnish model, with introduction of a new research-based content, with the aim of developing a new type of professional knowledge, as a basis for teachers’ professional practice. Drawing on Maton’s Legitimation Code Theory, this paper explores the tensions in the new Norwegian teacher education, between knowledge and ways of knowing, by examining students’ practices, expressed in students’ research and development papers in the new teacher education. The paper refutes a one-dimensional concept of experience-based practical knowledge in the teacher education and argues that professional knowledge is based on practices that are informed by specialized and theoretical knowledge.publishedVersio

Epistemic and Nonepistemic Design in Textbooks in Social Studies for Lower Secondary School: Do the Textbooks Facilitate Knowledge Building and In-Depth Learning?

e subject renewal, the new Norwegian curriculum for the school, is part of an international trend with a shift towards more knowledge-based curricula, to bring knowledge and in-depth learning back to the school. Against this background, this study examines new Norwegian textbooks in social studies for schools. e analysis is based on a social realist framework, which combines semantics and content analysis and reveals major di erences in the design of the textbooks. A distinction is made between epistemic and nonepistemic design, and this study shows that the absence of an epistemic structure is a problem that haunts new textbooks in social studies. When textbooks lack a design that connects subject concepts, content, and competencies, students will not get access to epistemic knowledge, something which creates barriers to in-depth learning and cumulative knowledge building in the subject.Epistemic and Nonepistemic Design in Textbooks in Social Studies for Lower Secondary School: Do the Textbooks Facilitate Knowledge Building and In-Depth Learning?publishedVersio

The Janus Face of Professional Knowledge : What Organizational Principles Are behind the Students’ Perceptions of Professional Knowledge in New Norwegian Teacher Education?

Integration of theory and practice is the key element in the research on teachers’ professional knowledge. Traditionally, this topic has created a polarization between practical and theoretical knowledge. The reform in the new Norwegian teacher education has introduced a new and watered-down concept of knowledge and research-based knowledge in education. With the reform, conflicting perceptions have arisen of what we can understand with professional knowledge in teacher education. Based on Maton’s Legitimation Code Theory, and with examples from a study of students’ R&D papers, this paper sheds light on the conflicting concept of professional knowledge in new Norwegian teacher education. The paper refutes a generic concept of knowledge and argues that teachers’ professional knowledge is based on practices that are informed by specialized forms of knowledge in the subject area.publishedVersio

Interior-point methods for P∗(κ)-linear complementarity problem based on generalized trigonometric barrier function

Recently, M.~Bouafoa, et al. investigated a new kernel function which differs from the self-regular kernel functions. The kernel function has a trigonometric Barrier Term. In this paper we generalize the analysis presented in the above paper for $P_{*}(\kappa)$ Linear Complementarity Problems (LCPs). It is shown that the iteration bound for primal-dual large-update and small-update interior-point methods based on this function is as good as the currently best known iteration bounds for these type methods. The analysis for LCPs deviates significantly from the analysis for linear optimization. Several new tools and techniques are derived in this paper.publishedVersio

Technology and knowledge. In what way are knowledge and teachers’ knowledge practices in subject areas crucial for the integration of technology in education?

In recent decades, education has undergone a digital transformation. In Norway, the government’s digitalization strat-egy for education includes ambitious goals and plans, with expectations of new forms of teaching and learning, betterlearning, and improved learning outcomes. Despite the increased availability of technology in Norwegian schools,there is still a significant gap between available technology in the classroom and teachers’ use of this technology foreducational purposes. This paper is based on Legitimation Code Theory (LCT) and explores teachers’ understandingof subject-area knowledge practices. Drawing on an empirical survey of a number of schools in northern Norway,completed in 2018/19, this paper uses one dimension of LCT to explore and compare the organized principles under-lying teachers’ knowledge practices in the key subjects of mathematics and Norwegian. An analysis suggests a code‘clash’ with mathematics and a code ‘match’ with Norwegian, which may help explain their different patterns of tech-nology integration. This research provides new perspectives on the integration of technology in education and sug-gests that different forms of subject-area knowledge have varying effects on teachers’ knowledge practices with theuse of technology in schools. This insight, which reveals the importance of knowledge and knowledge practices, willhave an impact on strategies for integrating technology in schools and on measures that can promote better learningin subjects using technology in education,publishedVersio

A polynomial-time algorithm for LO based on generalized logarithmic barrier functions

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The effect of level-marked mathematics tasks on students’ self-efficacy : An experimental study

This study investigates whether and to what extent students’ self-efficacy in mathematics is affected by level-marked mathematics tasks. An online survey with an experimental design was used to collect data from lower secondary school students in Norway (n = 436). The effect of level-marked mathematics tasks was measured by comparing students’ responses to tasks with no level marking with their responses to the same tasks marked as being easy, medium or difficult. The study’s design was set up carefully, featuring experimental and control groups. A Wilcoxon test showed a significant gap in students’ self-efficacy when approaching the same tasks without level marking and with difficult-level marking. In addition, a Friedman test showed that the gap between students’ self-efficacy when encountering the same task with and without level marking expanded significantly with increasing difficulty markings. This result has implications for students in terms of their mathematics learning and for mathematics teachers in terms of their future differentiation initiatives.publishedVersio

Radical visible pedagogy and cumulative knowledge-building in education

Twenty-first century learning revolves around a pedagogical discourse based on simplistic dichotomies, favoring a student-centered approach. This direction claims that such a learning model will lead to in-depth learning in education. This paper refutes this claim and argues that curricula based on twenty-first century learning promotes a social and context-dependent form of knowledge. To examine the problem of 21st century learning, and to develop an alternative, this paper introduces Bernstein’s pedagogical modalities, which are investigated using the terms “semantic gravity” and “semantic density.” These concepts are used to analyze teachers’ pedagogical practices in three different subjects, considering the further effects of these practices on learning and knowledge-building, as expressed in submitted student papers. The analysis suggests that practices that create long semantic waves, where knowledge is transformed between decontextualized meanings and contextualized meanings, are a condition for in-depth learning and cumulative knowledge-building. The paper argues that this form of knowledge-building is a result of a radical visible pedagogy, which includes practices that are based on different forms of knowledge, making visible how these forms of knowledge can be connected and transformed in education.publishedVersio