Tölur og mengi – Numbers and sets. A New Math textbook in Iceland in the 1960s
Abstract
Only few mathematics textbooks were developed in Icelandic during 1930–1966, and the model textbooks in use were originally developed in the 1920s. In 1966, Iceland was hit by an international school-mathematics reform movement, the New Math. The learning material, which was introduced at the arrival of the movement until the 1970s, was all of foreign origin except one textbook. The author of that textbook, denoted Tölur og mengi [Numbers and sets], was main actor in the introduction of the New Math, Guðmundur Arnlaugsson, duly supported by his colleague, Björn Bjarnason. In the paper, their way of introducing the new ideas and the methods they used will be described. Among their tools is the textbook which later influenced other mathematics textbooks for adolescents after the peak of the New Math wave.
References
Allendoerfer, C. B. & Oakley, C. O. (1963). Principles of mathematics (second edition). New York: McGraw-Hill Book Company.
Arnlaugsson, G. (1961). Danski menntaskólinn í deiglunni [The Danish high school in a crucible]. Menntamál, 34 (1), 71-75.
Arnlaugsson, G. (1966). Tölur og mengi [Numbers and sets]. Reykjavík: Ríkisútgáfa námsbóka.
Arnlaugsson, G. (1967). Ný viðhorf í reikningskennslu [New perspectives in mathematics teaching]. Menntamál, 40 (1), 40-51.
Arnlaugsson, G. (1971). Stærðfræði [Mathematics]. In M. Jónasson (Ed.), Nám og kennsla [Learning and teaching] (pp. 296-320). Reykjavík: Heimskringla.
Bjarnadóttir, K. (1979). Talnaspegill [Number mirror]. Reykjavík: Ríkisútgáfa námsbóka.
Bjarnadóttir, K. (2007). Mathematical education in Iceland in historical context - socio-economic demands and influences (Ph.D. dissertation nr. 456-2007). Roskilde University. Retrieved from http://rudar.ruc.dk/handle/1800/2914
Bjarnadóttir, K. (2011). Implementing 'modern math' in Iceland - informing parents and the public. In M. Pytlak, T. Rowland & E. Swoboda (Eds.), Proceedings of the seventh congress of the European Society for Research in Mathematics Education, 9th-13th February, 2011 Rzeszów, Poland (pp. 1670- 1679. University of Rzeszów. Retrieved fromt http://www.cerme7.¬univ.rzeszow.pl/-WG/12/CERME7_WG12_Bjarnadottir.pdf
Bjarnadóttir, K. (2014). History of teaching arithmetic. In A. Karp & G. Schubring (Eds.), Handbook on the history of mathematics education (pp. 431-458). New York: Springer. https://doi.org/10.1007/978-1-4614-9155-2_21
Bjarnason, E. (1939-1941). Reikningsbók Elíasar Bjarnasonar [Elías Bjarnason's arithmetic] (Vol. 1-4, second edition. First published in 1927-1929). Reykjavík: Ríkisútgáfa námsbóka.
Bruner, J. S. (1960). The process of education. New York: Vintage Books. https://doi.org/10.4159/9780674028999
Bundgaard, A. (1969-1972). Stærðfræði. Reikningur [Mathematics. Arithmetic] (Vol. 3a-6). Reykjavík: Ríkisútgáfa námsbóka.
Bundgaard, A. and E. Kyttä (1967-1968). Stærðfræði. Reikningur. [Mathematics. Arithmetic] (Vol. 1-2b). Reykjavík: Ríkisútgáfa námsbóka.
Daníelsson, Ó. (1920). Reikningsbók [Arithmetic]. Reykjavík: Arinbjörn Sveinbjarnarson.
Daníelsson, Ó. (1927). Kenslubók í algebru [A textbook in algebra]. Akureyri: Bókaverslun Þorsteins M. Jónssonar.
Dansk biografisk leksikon in Den store danske Gyldendals åbne encyclopædi. Retrieved from http://www.denstoredanske.dk
Furinghetti, F., Menghini, M., Arzarello, F. & Giacardi, L. (2008). ICMI renaissance: the emergence of new issues in mathematics education. In M. Menghini, F. Furinghetti, L. Giacardi & F. Arzarello (Eds.), The first century of the International Commission on Mathematics Instruction (1908-2008). Reflecting and shaping the world of mathematics education (pp. 131-147). Rome: Instituto della Enciclopedia Italiana.
Gíslason, S. Á. (1911-1914). Reikningsbók [Arithmetic] (Vol. 1-6). Reykjavík: Bókaverslun Sigfúsar Eymundssonar.
Gjone, G. (1983). "Moderne matematikk" i skolen. Internasjonale reformbestrebelser og nasjonalt læreplanarbeid (Vol. 1-8). Oslo: Universitetsforlaget.
Hvítbók um umbætur í menntun [A white-book on reforms in education] (2014). Reykjavík: Mennta- og menningarmálaráðuneytið.
Kilpatrick, J. (1992). A history of research in mathematics education. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 3-38). New York: Macmillan.
Kristjánsson, Ó. Þ. (1958-1965). Kennaratal. [Teachers' biographical lexicon]. Reykjavík: Oddi.
Kristjánsson, Ó. & Harðardóttir, S. (1985-88). Kennaratal. [Teachers' biographical lexicon]. Reykjavík: Oddi.
Lárusson, H. (1974-1975). Stærðfræði handa 7., 8. og 9. bekk grunnskóla [Mathematics for grades 7, 8 and 9 of the basic school]. Reykjavík: Ríkisútgáfa námsbóka.
Lög um fræðslu barna [Law on primary education], no. 34/1946.
Lög um gagnfræðanám [Law on middle-school education], no. 48/1946.
Lög um grunnskóla [Law on compulsory school], no. 63/1974.
Lög um menntaskóla [Law on high schools], no. 58/1946.
Lög um skólakerfi og fræðsluskyldu [Law on a school system and educational requirements], no. 22/1946.
Menntamálaráðuneytið (1968). Drög að námskrá í landsprófsdeildum miðskóla [A draft curriculum for the national examination]. Reykjavík: Höfundur.
Menntamálaráðuneytið (1974). Drög að námskrá handa 7., 8. og 9. bekk grunnskóla [A draft curriculum for grades 7, 8 and 9 of the basic school]. Reykjavík: Höfundur.
Nordisk råd (1967a). New school mathematics in the Nordic countries. Stockholm: Nordisk råd.
Nordisk råd (1967b). Nordisk skolmatematik [Nordic school mathematics]. Stockholm: Nordisk råd.
OEEC (1961). New thinking in school mathematics (second edition). Paris: OEEC.
Pálsson, J. & Ólafsson, H. (1961). Athuganir á landsprófi miðskóla. Skírnir, 135, 195-210.
Piaget, J. (1973). Comments on mathematical education. In A. G. Howson (Ed.), Developments in mathematical education. Cambridge University Press. https://doi.org/10.1017/CBO9781139013536.004
Piene, K. (1960a). Kronikk, OEEC seminar i matematikk. Nordisk matematisk tidskrift, 8 (1), 53-62.
Piene, K. (1960b). Nye vejer i skolematematikken. Nordisk matematisk tidskrift, 8(2), 65-71.
Reglugerð fyrir Menntaskólann í Reykjavík [Regulations for Reykjavík high school], no. 3/1937.
Sawyer, W. W. (1964a). Mathematician's delight (First published in 1943). Middlesex: Penguin Books.
Sawyer, W. W. (1964b). Vision in elementary mathematics. Introducing mathematics 1. Middlesex: Penguin Books.
Schaaf, W. L. (1965). Basic concepts of elementary mathematics. New York: John Wiley and Sons.
Schubring, G. (2014). The road not taken - the failure of experimental pedagogy at the Royaumont seminar 1959. Journal für Mathematik Didaktik, 35 (1), 159-171. https://doi.org/10.1007/s13138-013-0058-x
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