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Titill: 
  • Stærðfræðimenntun á tuttugustu öld : áhrif Ólafs Daníelssonar
Útgáfa: 
  • September 2013
Útdráttur: 
  • Ólafur Dan Daníelsson (1877–1957) lauk Mag.Scient.-prófi í stærðfræði frá Kaup-mannahafnarháskóla árið 1904. Næstu ár ritaði hann fyrstu útgáfu Reikningsbókar sinnar, sem út kom árið 1906 og lauk við doktorsritgerð á sviði rúmfræði árið 1909, fyrstur Íslendinga. Meðal kennara hans var Julius Petersen, kunnur kennslubóka-höfundur. Ólafur réðst að Kennaraskóla Íslands við stofnun hans 1908 og mótaði stærðfræðiskilning fyrstu 160 kennaraefnanna sem brautskráðust þaðan. Hann vann ötullega að stofnun stærðfræðideildar við Menntaskólann í Reykjavík árið 1919 og var ráðinn til að móta hana. Ólafur samdi fjórar kennslubækur í stærð-fræði, Reikningsbók, Um flatarmyndir, Kennslubók í hornafræði og Kennslubók í algebru. Kennsla hans og kennslubækur, sér í lagi í reikningi og algebru, mótuðu stærðfræðimenntun á Íslandi fram á miðjan áttunda áratug tuttugustu aldar , þar sem þær voru námsefni til landsprófs, strangs inntökuprófs í menntaskóla og kennaraskóla. Reikningsbók Ólafs var einnig fyrirmynd reikningsbókar fyrir börn sem valin var til útgáfu hjá Ríkisútgáfu námsbóka. Afstaða Ólafs til stærðfræði og stærðfræðikennslu var strangfræðileg, hann taldi stærðfræði fullkomnustu vísinda-grein sem til væri og markmið hans var að leiða nemendur inn í vinnusal vísind-anna. Hann vildi skýra stærðfræðina frá rótum ef hann taldi það mögulegt, ella geymdi hann rökstuðning þar til hann taldi sig geta undirbyggt hann nægilega vel á fræðilegan hátt.

  • Útdráttur er á ensku

    The first Icelandic mathematician to complete a doctoral degree was Ólafur Dan-íelsson (1877–1957). He first completed a Mag. Scient. degree at the University of Copenhagen to be eligible to teach in the Danish high school system. His univer-sity professors were two well-known geometers: Hieronymus Georg Zeuthen and Julius Petersen, a textbook writer. However, he was not hired as the mathematics teacher at the sole Icelandic high school when he returned home in 1904; the position went to an engineer. Daníelsson then began to prepare his doctoral thesis, which he defended in 1911: Nogle Bemærkninger om algebraiske Flader der kunne bringes til at svare entydigt til en Plan Punkt for Punkt /Several re-marks on algebraic surfaces which could have one-to-one correspondence to a plane. The thesis was an extension of earlier works by professor Zeuthen and other well-known scientists of the time: Clebsch, Castelnuevo and Cremona. Meanwhile, to support his growing family, Daníelsson taught pupils privately and composed a little arithmetic textbook, Reikningsbók/Arithmetic, published in 1906. Daníelsson was appointed as the first mathematics teacher at the Iceland Teacher College at its establishment in 1908. The students were mature people who may have been teaching for a number of years but who had not enjoyed schooling themselves. Daníelsson revised his textbook Arithmetic for their needs, republishing it in 1914. In 1919, a mathematics stream was established at Reykjavík High School following Daníelsson’s and his friends’ initiative. Daníels-son was appointed to develop it, aiming for students to become eligible to attend the Polytechnic College in Copenhagen and to take university studies in the sciences. Before that, students had to spend an extra year abroad. At that time Daníelsson began his mission to create high school mathematics textbooks. He wrote four textbooks in the 1920s, out of which two, the third version of Arithmetic and Algebra, became very influential through the mid-twentieth century and shaped the mathematics education of generations. Eventually they were replaced in the 1970s by “New Math” textbooks. His two geometry text-books, however, proved to be too ambitious for his students who had little pre-vious experience with geometric concepts. Daníelsson’s approach to school mathematics was strictly academic. His teach-ing inspired his students, at least if they showed talent and commitment. One of them said, “What especially influenced us was his enthusiasm and respect for mathematics.” He explained mathematics in an intelligible way, supported by proofs if he thought it would be useful, but allowed space for initiative and crea-tivity only in his verbal exercises. Daníelsson’s extensive influence may be attributed to several factors. His strong personality and firm belief in mathematics as a superb science made him an ex-cellent champion of mathematics education. Moreover, he was the mathematics teacher of the first 167 primary school teachers in Iceland. His former students propagated Daníelsson’s vision and interpretation of school mathematics, and one of them, E. Bjarnason, published a primary school arithmetic textbook in 1927–1929 which has been deemed to be a simplified version of Daníelsson’s own Arithmetic for adolescents. Bjarnason’s textbook was chosen as the sole arithmetic textbook during the 1940s to 1970s when a state monopoly publishing house ensured the provision of free textbooks for all children. Bjarnason’s text-book may have been considered as the most suitable preparation for high school freshmen due to its compatibility with Daníelsson’s Arithmetic. Another factor was that Reykjavík High School was the only school of its kind. When another school became established in 1930, Daníelsson became protector of its mathematics and science stream. Admission to Reykjavík High School became restricted in 1929, which created strong competition. Following this, new lower secondary schools were established around the country in the 1930s for the common people who had not had the opportunity to attend school after age 14. Daníelsson’s Arithmetic was taken up in more and more of these schools to enable their most promising students to transfer to one of the upper grades of the six-year Reykjavík High School. In 1946, the six-year high schools were reduced to four-year upper secondary schools, and a national entrance examination was implemented in a number of lower secondary schools as a precondition for admission to these upper sec-ondary schools. In deference to the hitherto dominant Reykjavík High School, the mathematics syllabus for the entrance examination was taken from the former second grade of this school, which included Daníelsson’s Arithmetic and Algebra textbooks. The syllabus and its exam remained in place from 1946 to 1976, al-though alternatives to Daníelsson’s textbooks were gradually brought in, espe-cially after 1968 when the “New Math” was introduced in Iceland.

Birtist í: 
  • Netla
ISSN: 
  • 1670-0244
Samþykkt: 
  • 4.11.2013
URI: 
  • http://hdl.handle.net/1946/16834


Skrár
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