107 research outputs found
Mathematical education in Iceland in a historical context:socio-economic demands and influences
Verbal Syntax in an Electronic Bilingual Icelandic Dictionary: A Preliminary Study
Denne artikkelen handler om verbbeskrivelsen i en elektronisk utgave av denenspråklige islandske standardordboken, Íslensk or›abók (2000), og hvordan den kanutnyttes i tospråklig sammenheng. Hovedforskjellen mellom en trykt og en elektroniskordbok ligger i de ulike presentasjonsmåtene, i et bokformat er det tekstens omfangsom bestemmer utformingen av beskrivelsen men i en elektronisk framstillingmå det tas hensyn til hvor mye tekst det kan vises på skjermen. Teksten må delesopp i passe store enheter. For å få det til i den elekroniske utgaven av Íslenskor›abók føres verbale konstruksjoner opp som sublemmaer under de enkelteverbene. Dette betyr at den syntagmatiske beskrivelse blir mer utførlig og systematiskenn i de eldre utgaver av ordboken. I artikkelen blir verdien av denne framstillingenvurdert, spesielt med hensyn til en tospråklig ordboksbeskrivelse
Breaking away from tradition: Linking a database of inflection to an electronic dictionary
Icelandic inflection is complex and there is an abundance of variant forms, which are very often changeable according to time and style. The choice of variants within a paradigm in some cases depends on meaning and context. The tradition in Icelandic dictionaries is to give the principal parts of words, as indicators of inflectional classes. These, however, contain insufficient information for the remainder of the paradigm to be predictable. In an online dictionary this problem can be solved by a link to a database of inflection, such as the Database of Modern Icelandic Inflection (DMII). This is the method chosen in ISLEX, the Icelandic-Scandinavian online dictionary, and as a result the information provided far exceeds the tradition in Icelandic dictionaries. Both projects are under construction at The Árni Magnússon Institute for Icelandic Studies. The breakaway from tradition also takes place in the actual production of the paradigms for the DMII. Icelandic textbooks and handbooks on morphology describe the system as a whole, i.e., they are constructed ‘top-down’, with a limited number of examples for each inflectional class. The production of DMII is, in contrast, ‘bottom-up’, as it is based on research on individual words, not inflectional classes. The aim is to provide enough information for the user to make an educated choice by himself
New-math influences in Iceland. Selective entrance examinations into High Schools
The 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
The Case for Normalization: Linking Lexicographic Resources for Icelandic
The topic of this paper is the linking of two major lexicographic resources on Icelandic, the Dictionary of Old Norse Prose (ONP) in Copenhagen, and the Written Language Archive (WLA) at the Árni Magnússon Insti-tute for Icelandic Studies in Reykjavík. The resources would be linked by normalizing the headwords from the ONP to the standard used for Modern Icelandic spelling by the use of a spellchecker originally de-signed for use on Modern Icelandic. This is possible, as the major differ-ences in word forms between the two sources are mostly a matter of changes in spelling, whereas the morphology of Icelandic has been rela-tively unchanged through the centuries. Future work would consist of normalizing the citation collections themselves, thus creating a valuable resource linking variant word forms to their headwords or lemmas
Lexicalization and the Selection of Compounds for a Bilingual Icelandic Dictionary Base
Artikkelen handler om de problemer som hefter ved lemmatisering av sammensetninger i en tospraklig ordbok der islandsk er kildespraket. Fordi enkelte ord kan vise varierende ordformer som førsteledd i sammensetninger, vil lemmaseleksjonen ikke utelukkende gjenspeile semantisk leksikalisering. Det må også tas hensyn til at leksikaliseringen i mange tilfeller er begrenset til en bestemt formvariant. Dette forholdet kompliseres ytterligere ved at sammensetninger som viser et produktivt ordlagingsmønster, kan inneholde polyseme ordledd, eller ved at ordleddene star i en flertydig relasjon til hverandre
Landspróf miðskóla 1946-1976. Áhrif nýju stærðfræðinnar.
Landspróf miðskóla sem inntökupróf í menntaskóla og kennaraskóla og síðar fleiri skóla
var haldið á árunum 1946–1976. Prófað var í átta námsgreinum þar sem íslenska vó tvöfalt.
Landsprófið var upphaflega grundvallað á reglugerð nr. 3/1937 um námsefni til prófs upp
úr öðrum bekk Menntaskólans í Reykjavík. Landsprófið í stærðfræði hélst að miklu leyti
óbreytt á árunum 1947–1965. Prófað var í lesnum dæmum sem nemendur höfðu lært áður
og í ólesnum dæmum. Frá árinu 1966 breyttist prófgerðin: lesin dæmi voru felld niður,
prófið var stytt og tekið var að prófa úr svokallaðri nýrri stærðfræði. Þar var lögð aukin
áhersla á tölur og eiginleika þeirra en einnig á mengi ásamt tilheyrandi rithætti og aðgerðum samkvæmt Drögum að námsskrá í landsprófsdeildum miðskóla frá árinu 1968. Markmiðið með innleiðingu nýju stærðfræðinnar var að auka skilning nemenda í stærðfræði.
Fjögur landsprófsverkefni í stærðfræði frá árunum 1953, 1966, 1971 og 1975 voru greind
með tilliti til inntaks og færnikrafna samkvæmt greiningarlykli TIMSS. Greiningin sýnir
að inntak prófverkefnanna breyttist í samræmi við Drög að námsskrá en um leið styttust
dæmin, orðadæmum fækkaði og jafnframt fjölgaði innbyrðis óskyldum prófatriðum. Færnikröfur færðust frá lausnaleit yfir í aukna beitingu rútínuaðferða en dæmum með flóknum
samsettum aðferðum fækkaði.
Gögn sýna að meðaleinkunn í stærðfræði, sem áður hafði verið lægri en meðaleinkunn
allra átta námsgreinanna á landsprófi, færðist nær heildarmeðaleinkunn og nemendum
gekk hlutfallslega betur en áður. Vonir höfðu staðið til þess að innleiðing mengjafræði yki
skýrleik og skilning. Vart var þó hægt að búast við því. Nemendur þurftu á sama tíma að
kynnast venjulegri algebru sem mörgum hefur reynst torskilin og námsefnið studdi samhengið milli mengjafræði og algebru aðeins að litlu leyti. Eftir sitja spurningar um hvort
glíma við sundurlaus atriði stuðli fremur að vélrænum skilningi en lengri samsett dæmi, og
hvort lesin dæmi eigi rétt á sér.The goal of new education legislation in Iceland in 1946 was to create a uniform
education system, with eight-year compulsory education and equal access to college
preparatory education. Previously, the two schools, which may be considered parallel to British grammar schools, had selected their students under strict admission
control and their own entrance examinations. As a compromise, regulations for the
Reykjavík Grammar School, dating from 1937, were chosen as a basis for a national entrance examination in eight school subjects, to be run in all larger towns and rural
boarding schools. The examination was intended to ensure a certain and standardized minimum knowledge in a number of subjects; the selection of the fittest with
respect to certain attributes considered necessary for studies in a grammar school
and a university or other establishments of higher education; and to offer all students
and their relatives a certain assurance of an assessment of the examination papers
by impartial persons.
In the national examination’s first year it became clear that examining in Euclidian
geometry did not work as teachers at lower levels had no such training. The mathematics examination was divided into two parts with equal weight, seen problems
and unseen problems, tested two days in a row. The content of the unseen examination became typically 6–8 problems; 4–6 story problems on area, volume and proportions, some to be solved by setting up equations; and two rather complicated fractions with algebraic denominators. The story problems either described situations in
contemporary daily life, or were versions of old problems.
By the mid-1960s, the examination, originally intended to provide equal opportunities
to education, became considered as a hindrance on young people’s path to preparation for life. Initially, a constant rate of 20% of the cohort attempted the examination
and 13-14% reached grammar school admission. By 1969 the rate had risen to 34%
vs. 21%. The seen problems were dropped, the examination was shortened considerably and the number of problems rose to 50 small and often unrelated items to ease
grading but also to help the less able students to show basic competences.
In the midst of this demand for education for all, New Math was implemented for the
purpose of facilitating understanding. The paper contains an analysis and comparison of typical examination papers before and after the implementation of New Math.
The analysis was made according to TIMSS Monograph no. 1: Curriculum framework
for mathematics and science by Robitaille et al. (1993).
The results of an analysis of examination papers from 1953, 1966, 1971 and 1975 indicate that the content swayed towards using set-theoretical notation and number notation to various number bases and back again. The proportion of simplifying algebraic
expressions and solving equations stayed around 50% with a slight increase, while
new topics were introduced to statistics and probability. Performance expectations
became less oriented towards independent development of notation, vocabulary,
and algorithms. The expectations developed away from using complex procedures
towards routine procedures, and investigating and problem solving was reduced. In
general, the examination developed into a host of incoherent details of diffused focus. However, data show that the average mathematics grade, which had been about
0.5 lower on the 0–10 scale than the average grade in all eight subjects during the
1950s and 1960s, had reached other subjects in 1972 during this process of increased
number of simpler problems.
Some questions remain as to what kinds of syllabi and examinations enhance mathematical thinking and understanding. Richard Skemp (1978) expressed concerns that
the backwash effect of examinations and overburdened syllabi promoted superficial
instrumental understanding at the cost of deeper relational understanding. George
Polya (1973) suggested that students think of a familiar problem in devising a plan for
solving problems. Could the seen problems enhance understanding on that ground?
Could multi-step word problems provide opportunities for teachers, together with
their students, to delve into mathematical processes and thus create lattices of acts
of understanding, as proposed by Anna Sierpinska (1994)?Publishers versio
New-math influences in Iceland. Selective entrance examinations into High Schools
The 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
Online Data on Icelandic Inflection. Descriptive or Prescriptive: “Why, for whom, by whom” and how?
Mismunandi gengi nemenda í PISA 2012 í stærðfræði eftir stærð skóla: Hefur menntun og starfsreynsla kennara áhrif?
Publishers versionAthugun á niðurstöðum í stærðfræði í PISA-rannsókninni 2003 sýndi að árangur
nemenda í tveimur stærstu skólunum var marktækt betri en í minni skólum. Sérstaklega var árangurinn slakur í skólum með 11–25 þátttakendur. Athugun á árangri
í dönskum skólum í sömu PISA-rannsókn sýndi einnig betra gengi í stórum skólum
en litlum. Þegar niðurstöður PISA 2012 á Íslandi voru komnar fram var Námsmatsstofnun beðin að flokka skólana í fjóra flokka eftir fjölda þátttakenda í PISA-rannsókninni. Árangur í flokki stærstu skólanna reyndist marktækt betri en í minni
skólum. Til að grafast fyrir um hugsanlegar ástæður þessa var gerð könnun meðal
stærðfræðikennara valinna skóla. Kennarar voru spurðir um menntun þeirra, starfshlutfall við stærðfræðikennslu, reynslu af stærðfræðikennslu á unglingastigi og
námsefni í stærðfræði. Niðurstöður benda til þess að hátt starfshlutfall við stærðfræðikennslu, löng starfsreynsla og sér í lagi samfella í kennslu, það er reynsla kennara af að kenna sama hópi og sama námsefni yfir lengra tímabil en eitt skólaár, stuðli
að góðum árangri nemenda.Peer Reviewe
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