Háskóli Íslands
Varanleg URI fyrir þennan undirflokkhttps://hdl.handle.net/20.500.11815/6086
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Verk The drying of fish and utilization of geothermal energy : the Icelandic experience(2003) Arason, Sigurjón; Faculty of Food Science and NutritionDrying is an ancient method for preservation of foods, the main purpose of which is to prolong the preservation time. In order to dry food, an external source of energy is needed to extract water from it. The use of geothermal energy in fish processing to replace oil and electricity offers great potential. In the fishing industry, geothermal energy has mainly been applied to indoor drying of salted fish, codheads, small fish, stockfish and other products. In this paper an emphasis is placed on drying fish and associated processes, and how geothermal energy can be used to substitute oil or electricity. The Icelandic Fisheries Laboratories have been experimenting with different methods of drying and several drying stations have been designed for indoor drying of fish products. Today there are around twenty companies in Iceland, which are drying fish indoors using electricity and/or geothermal energy. There are unexplored possibilities in utilization of geothermal energy in regions where good harbors are located in geothermal areas.Verk Mathematics Teacher Knowledge in Iceland. Historical and Contemporary Perspective(2008) Bjarnadóttir, Kristín; EducationVerk Good Mathematics Teaching and Classroom Norms : – Views of Secondary School Students –(St Patricks College, 2011) Bjarnadóttir, Kristín; Dooley, Therese; Corcoran, Dolores; Ryan, Miriam; EducationThis article describes a research on students’ views of what constitutes good mathematics teaching. A questionnaire with open ended questions was given to 106 students in six different mathematics classes, with five different teachers, in four different upper secondary schools in Iceland. The questions were designed to get at students concerns and opinions of what constitutes good mathematics teaching and where the strengths of their particular teacher lie. The students of all the teachers considered ‘clear explanations of the content’ as the teachers’ main advantages as well as thorough mathematical knowledge and incisive teaching, while they also appreciated highly personal qualities such as patience, cheerfulness, and care for their students’ progress. Remarks on the characteristics of good teaching witnessed different societal norms in the groups as well as different beliefs about students’ own roles, the roles of others, teachers included, and the general nature of mathematical activity in school.Verk Geometry Teaching in Iceland in the Late 1800s and the Van Hiele Theory(Institut National de Recherche Pedagogique, 2009) Bjarnadóttir, Kristín; Durant-Guerrier, Viviane; Soury-Lavergne, Sophy; Arzarello, Ferdinando; MenntavísindasviðThe first Icelandic textbook in geometry was published in 1889. Its declared aim was to avoid formal proofs. Concurrently geometry instruction was being debated in Europe; whether it should be taught as purely deductive science, or built on experiments and intuitive thinking. The policy of Icelandic intellectuals was to enhance strategies to lead their country towards independence and technical progress, which partly coincided with foreign didactic currents. The discussion on geometry teaching is connected to the van Hiele theory of the 1950s on geometric thinking.Verk Implementing ‘modern math’ in Iceland – : Informing parents and the public(Publishing Office of the University of Rzeszow, 2011) Bjarnadóttir, Kristín; Pytlak, Marta; Rowland, Tim; Swoboda, Ewa; Education‘Modern math’ was implemented in Icelandic schools at all levels in the 1960s. It was introduced to parents at meetings and by media articles, interviews and a television programme in 17 episodes. It is argued that the information was presented by unrealistic convictions of the quality of the ‘modern math’ programme, that the timing of the presentations was not optimal, and that more information was needed when the programme had reached the majority of pupils at the primary level.Verk 18th Century Mathematics Education : Effects of Enlightenment in Iceland(2012) Bjarnadóttir, Kristín; EducationLiving conditions in Iceland worsened in the period 1600–1800, and the greatest lava flow on earth in historical times in 1783–84 was accompanied with severe earthquakes and famine. Concurrently, the Enlightenment movement, channelled from Germany through Denmark, had considerable influence in Iceland from 1770 onwards. People, interested in progress in Iceland, established a society which advanced the Enlightenment by publishing a journal and books on various practical matters. Among them were philosopher Ó. Olavius and lawyer Ó. Stephensen, later Governor of Iceland, both educated in Copenhagen. The Enlightenment movement produced in the 1780s substantial arithmetic textbooks deliberately intended to raise the educational standards of Icelanders. One of them was by Olavius in 1780, modelled on Danish and German textbooks. The other arithmetic textbook published in 1785 by Stephensen, was accompanied with introduction to algebra, modelled on lectures at the University of Copenhagen. It was immediately sanctioned as a textbook at the two Latin schools, where, however, mathematics education was at its nadir until 1822. These two books, in addition to a book of arithmetic tables, remained the only arithmetics textbooks available in Icelandic until the 1840s. Both were good representatives of the typical European arithmetic textbook of the practica type. Their influence in the aftermath of the disastrous events will be explored as well as their roots in German arithmetic education tradition in the Enlightenment period.Verk The Norse treatise Algorismus : Preserved in manuscript GKS 1812 4to(Oslo Metropolitan University, 2019) Bjarnadóttir, Kristín; Halldórsson, Bjarni Vilhjálmur; Barbin, Evelyn; Janquist, Uffe Thomas; Kjeldsen, T.H.; Smestad, Björn; Tzanakis, C.; EducationThe treatise Algorismus is a complete prose translation of the Latin hexameter Carmen de Algorismo into the medieval Old Norse language. Carmen is dated in 1202, written by the French canon Alexander de Villa-Dei. The treatise explains for the first time the Hindu-Arabic decimal place value numeral notation and calculation methods to the Norse people, Icelanders and Norwegians. Algorismus also relates the four Elements: Earth, Water, Air and Fire to cubic numbers and ratios. The treatise exists in four manuscripts, one of them only a fragment. The four manuscripts are compared by digital methods to show that the two oldest of them are quite similar and possibly copies of the same copy of the original translation. This paper focuses on the version in Ms GKS 1812 4to. It is a pedogogical study of the algorithms presented in the treatise, contrasting them with current day methods and the presentation in Carmen.Verk The 1877 Regulation for the Learned School in Iceland(2004) Bjarnadóttir, Kristín; Furinghetti, Fulvia; Kajser, Sten; Tzanakis, Constantinos; MenntavísindasviðIn the 19th century, only one learned school existed in Iceland, where the population was 47,000 in 1801 and 72,000 in 1880. Considering the circumstances, the Learned School enjoyed excellent mathematics teaching in the period 1822–1862, when the school was served by Björn Gunnlaugsson, a gold medallist in mathematics from the University of Copenhagen. In the 1860s, discussions about teaching modern languages intensified in Denmark and other Nordic countries. In 1871, Denmark’s learned schools were divided into two streams, specializing in languages and history on one side and mathematics and natural sciences on the other side. Regulations were prepared for the sole Icelandic learned school in 1876, suggesting that the Icelandic school would continue as a onestream school, while Hebrew would be eliminated and Greek reduced to make room for the modern languages, French and English. German and Danish had previously been taught during the first four years. Mathematics would continue throughout the school as previously. Immediately after the proposals for the new regulation were introduced, the governor of Iceland sent them to the Minister of Iceland in Copenhagen along with a long letter, containing his own proposals, suggesting a clear language-history stream in the Icelandic school, as it would overload the pupils to study Latin and mathematics at the same time. He proposed that mathematics be reduced. The Minister for Iceland forwarded the original proposals to King Christian IX, suggesting that Danish and exegetics replaced mathematics in the last two years of the school. This became the conclusion of the matter and the mathematics-science stream was first established in 1919. Over the next couple of years the teachers of the school tried to influence this decision, while it seems that the headmaster, who was a philologist, had lobbied his way through the official system with his emphasis on languages. Letters from the governor, the minister and the teachers are preserved at the National Archives in Iceland. They reveal interesting arguments for and against mathematics education, all of which harmonise in one way or another with the Mogens Niss’s analysis of fundamental reasons for mathematics education from historical and contemporary perspectives, published in the International Handbook of Mathematics Education (1996).Verk Development of the Mathematics Education System in Iceland in the 1960s in Comparison to Three Neighbouring Countries(University of Cyprus and ERME, 2007) Bjarnadóttir, Kristín; Pitta-Pantazi, D.; Philippou, C.; MenntavísindasviðMathematics education in Iceland was behind that of its neighbouring countries up to the 1960s, when radical ideas of implementing logic and set theory into school mathematics reached Iceland, mainly from Denmark. Introduction of ‘modern’ mathematics in Icelandic schools is compared to its parallels in Denmark, Norway and England. Similarities are found in expectations of social and economic progress, promoted by the OECD, expectations of increased clarity and improved understanding of mathematics, a clash between different cultures of teacher education and egalitarian trends in providing ‘education for all,’ with the implication ‘mathematics for all’. The differences lie mainly in different societal structure, characterized by Iceland’s recent independence from Denmark, its sparse population and underdeveloped decision-making structure.Verk 17th and 18th century European arithmetic in an 18th century Icelandic manuscript(TU WIEN Technische Universität Wien, 2011) Bjarnadóttir, Kristín; Barbin, Evelyne; Kronfellner, Manfred; Tzanakis, Constantinos; EducationIcelandic arithmetic books from the 18th century, printed and in manuscripts, adhered to the European structure of practical arithmetic textbooks, formed in the late Middle Ages: The number concept, numeration, the four operations in whole numbers and fractions, monetary and measuring units, extraction of roots, ratio, progressions and proportions. A manuscript textbook, Arithmetica – That is reckoning art, dated in 1721, deviates from the general model in that it does not treat monetary and measuring units but includes theoretical sections on the number concept and common notions on arithmetic. No specific model for the manuscript has been spotted, while similarities to works by authors as Ramus, Stevin, Suevus, Meichsner and Euler were found.Verk Arithmetic Textbooks and 19th Century Values(2013) Bjarnadóttir, Kristín; Janquist, Uffe Thomas; EducationIn this paper two nineteenth century Icelandic arithmetic textbooks are investigated, both written according to the late medieval tradition of libri di abbaco, practical textbooks. The authors were influenced by the German Protestant tradition that arithmetic education was to serve ethic education, as well as by the Enlightenment. Above all, they worked for the autonomy of Iceland from Denmark. Their textbooks served the purpose of teaching young people wise allocation and yield of their resources with the overall goal of individual as well as national prosperity and financial independence.Verk New-Math Influences in Iceland : Selective Entrance Examinations into High Schools(IREM de Montpellier, 2016) Bjarnadóttir, Kristín; Radford, Luis; Furinghetti, Fulvia; Hausberger, Thomas; EducationThe New Math was implemented in Iceland with the intention to facilitate understanding in the midst of increased demands for education for all. The article contains an analysis and comparison of typical papers in a selective entrance examination into high schools before and after the implementation period of the New Math during 1966–1968, and a discussion on the understanding it was expected to facilitate.Verk Was Euclid in Iceland when he was supposed to go?.(2016) Bjarnadóttir, Kristín; Krainer, Konrad; Vondrova, Nada; MenntavísindasviðIn a seminar on new thinking in school mathematics, held in Royaumont, France, in 1959, one of the main speakers, Jean Dieudonné, summarized the new schoolmathematics programme he had in mind in the sentence: Down with Euclid. The purpose of the article is to analyse the context in which this quote was expressed and connect it to geometry teaching in Iceland where Euclidean geometry instruction seldom had a firm ground. Euclidean geometry in an amended version gained new interest in Iceland by the introduction of the New Math in the 1960s.Verk Menntun stærðfræðikennara í ljósi sögunnar(Rannsóknarstofnun Kennaraháskóla Íslands, 2005) Bjarnadóttir, Kristín; MenntavísindasviðÍ greininni er fjallað um stærðfræðimenntun við Kennaraskóla Íslands, fræðslulögin 1946 og lög um menntun kennara frá 1947 og árangur nemenda á landsprófi í völdum skólum borinn saman við aðstæður og menntun kennara þeirra og menntun stærðfræðikennara í framhaldsskólum. Þessi atriði eru skoðuð með tilliti til ummæla um biðtíma í menntakerfinu á fundi um menntaáætlunargerð árið 1965. Rætt er um bil á milli grunnskóla og framhaldsskóla á sviði stærðfræði og stærðfræðikennslu og hvernig megi brúa það bil. Að lokum er rætt um núverandi stöðu mála, viðbrögð við námskrá framhaldsskóla frá 1999 og hugmyndum um styttingu framhaldsskóla með tillti til stærðfræðikennslu og hlutverk Kennaraháskóla Íslands í því samhengi.Verk The Concept of Understanding in Mathematics Textbooks in Iceland(Tapir Academic Press, 2007) Bjarnadóttir, Kristín; Bergsten, Christer; Grevholm, Barbro; Strømskag Måsøval, Heidi; EducationThe importance of understanding concepts and procedures is emphasized in most mathematics textbooks written in Iceland, from the earliest writings in Icelandic up to present day. Simultaneously, assertions are found at regular intervals that the emphasis on understanding is a novelty, not promoted in earlier times. In order to analyze what lies behind these statements, the literary meaning of the Icelandic word “skilja”, usually translated as “understand”, will be compared to the corresponding words in Danish, English and Latin, and related to the modern sense of understanding in mathematics.Verk Regula de Tri, its origin and presentations in Icelandic textbooks(Sense Publisher, 2009) Bjarnadóttir, Kristín; Winslow, Carl; EducationRegula de Tri, the Rule of Three, is in its simplest form a way of computing the fourth proportional in an equation of two ratios. It was an indispensable topic in Iceland from the first textbooks in arithmetic in the 18th century until the 1970s. Instruction in the Rule of Three in compulsory education developed into a ritual procedure for exercises of certain types and content, often without relevance to contemporary life or reference to ratios and proportions. It was subjected to severe criticism at times of changes in compulsory education, in the early 20th century and at the introduction of the “New Math” in the 1960s. At that time the Rule of Three was quashed once and for all, and attention was turned to the plain concepts of ratio and proportions.Verk Icelandic Ethno-Mathematics : Íslensk þjóðháttastærðfræði(2018) Bjarnadóttir, Kristín; EducationDuring the centuries, ordinary people in Iceland had few opportunities to study mathematics and few reasons to apply it. Instead, Icelanders have composed verses since medieval times, adhering to complex rules of rhymes and alliteration. They have preserved the ancient Germanic rules of prosody in the popular pastime of composing and reciting Icelandic ballads, ríma, exercised by young and old, men and women. This artistic puzzle, to compose a meaningful text within the complex constraints of length of words, length of lines, rhymes and alliteration, is a mathematical and artistic activity meeting Ubiratan d’Ambrosio’s definition of ethnomathematics as intersections of culture, historical traditions, sociocultural roots, and mathematics. No material is needed, only a skilful mind and the memory to rehearse the product in the dark winter evenings and long summer nights at work.Verk Ritgerðin Algorismus – samanburður handrita(Hið íslenska bókmenntafélag, 2010) Bjarnadóttir, Kristín; Halldórsson, Bjarni Vilhjálmur; Guðmundsson, Einar H.; Brynjarsdóttir, Eyja Margrét; Karlsson, Gunnar; Vésteinsson, Orri; Jakobsson, Sverrir; MenntavísindasviðVerk Arithmetica - Það er reikningslist. Rætur í menningu mótmælenda(Hið íslenska bókmenntafélag, 2017) Bjarnadóttir, Kristín; Hugason, Hjalti; Guttormsson, Loftur; Eggertsdóttir, Margrét; MenntavísindasviðArithmetic textbooks, which appeared in Iceland in the eighteenth century in print and in manuscripts, adhered to the pattern of European practical textbooks, originating among Italian merchants in the late Middle Ages. Their content was numeration, the four arithmetic operations and relevant methods, measuring units and currency, extraction of roots, sequences, ratio and proportions. The Icelandic manuscript Arithmetica — það er reikningslist [Arithmetica — That is arithmetic art] from 1721 deviates from this pattern in that it does not contain measurements and currency. It treats thoroughly the number concepts and common notions, which are usually only found in theoretical textbooks on arithmetic. The manuscript does not refer to the Icelandic context in any respect. No particular model for it has been found. There are, however, similarities with textbooks written in German by the authors Suevus and Meichsner, both titled Arithmetica Historica, published in protestant towns and written with respect to the Holy Script and good history books. Furthermore, the manuscript bears some resemblance to textbooks by Euler, the French philosopher and Huguenot Ramus, and the Dutch mathematician and Calvinist Stevin. The sixteenth century Protestant movements seem to have been a fertile ground for new thinking in educational matters. The chapter concludes with a discussion on two possible authors of Arithmetica — það er reikningslist: Bishop Jón Árnason and naval officer Magnús Arason Thorkelin. The arithmetic problems relate to European content and the world of educated people. The unknown author must have been well acquainted with European cultural currents and heritage, such as Euclid’s Elements.Verk Ratios and Proportions in Iceland 1716–2016(Instituto de Matemática, Universidade Federal do Rio de Janeiro, 2018) Bjarnadóttir, Kristín; Schubring, Gert; Fan, Lianghuo; Geraldo, Victor; EducationThe topics of ratios and proportions are investigated in the oldest Icelandic arithmetic textbook, Arithmetica Islandica of 1716, preserved in the manuscript Lbs. 1694 8vo. The conjecture that it is a translation of the printed Danish Arithmetica Danica of 1649 is rejected, while there may be some transmissions of ideas. In continuation, the history of teaching ratio and proportions from Arithmetica Danica until the latest textbook in Icelandic, Skali of 2016, is investigated and related to recent research on obstacles in proportional reasoning.