Geometry Teaching in Transition: An Investigation on the Importance of School Geometry in Primary Education
Abstract
Mathematics instruction in primary school has been influenced by many policy changes and empirical findings in the previous two decades. Geometry lessons, in particular, were re-evaluated due to a paradigm change and, consequently, were attributed a new meaning within the mathematics curriculum worldwide. The present paper focuses on this paradigm shift in the sense of the evaluation to what extent both the didactical potential and the practical value of geometry instruction in elementary education are currently recognised and utilised by primary grade teachers. In total, 120 primary grade teachers participated in the study. The results showed that there had been positive recognition of the didactical potential of school geometry by the teachers over the previous two decades; however, it lacked actual implementation in school practice for different reasons. The results are discussed not only with regard to the latter of these but also with regard to their theoretical and practical implications.
Downloads
References
Backe-Neuwald, D. (2000). Bedeutsame Geometrie in der Grundschule: Aus Sicht der Lehrerinnen und Lehrer, des Faches, des Bildungsauftrages und des Kindes [Meaningful geometry in primary school: From the viewpoint of the teachers, the subject, the educational mission, and the child] (Unpublished doctoral dissertation). Universität Paderborn.
Bauersfeld, H. (1992). Drei Gründe, geometrisches Denken in der Grundschule zu fördern [Three reasons to promote geometric thinking in elementary school]. In H. Schumann (Ed.), Beiträge zum Mathematikunterricht 1992 (pp. 7–33). Franzbecker Verlag.
Eichler, K.-P. (2005). Zum Geometrieunterricht in der Grundschule [On teaching geometry in the primary school]. Grundschulunterricht, 52(11), 2–6.
Franke, M., & Reinhold, S. (2016). Didaktik der Geometrie in der Grundschule [Didactics of geometry in elementary school] (3rd ed.). Springer Spektrum.
Glasnović Gracin, D., & Kuzle, A. (2018). Drawings as external representations of children’s fundamental ideas and the emotional atmosphere in geometry lessons. Center for Educational Policy Studies Journal, 8(2), 31–53. https://doi.org/10.26529/cepsj.299
Graumann, G. (1994). Geometrie im Alltag: Konzeption, Themenübersicht, Praxisberichte. Materialien für einen realitätsbezogenen Mathematikunterricht [Geometry in everyday life: Conception, topic overview, practical reports. Materials for reality-based mathematics teaching]. Franzbecker.
Graumann, G. (2009). Allgemeine Ziele, die mit Tests schwerlich erfasst werden können, erläutert an vier Beispielen aus dem Geometrieunterricht [General goals that are difficult to capture with tests, explained with four examples from the geometry classroom]. In M. Ludwig, R. Oldenburg, & J. Roth (Eds.), Argumentieren, Beweisen und Standards im Geometrieunterricht. Tagungsband des Arbeitskreises Geometrie (pp. 65–74). Franzbecker.
Hannula, M. S. (2012). Exploring new dimensions of mathematics-related affect: embodied and social theories. Research in Mathematics Education, 14(2), 137–161. https://doi.org/10.1080/14794802.2012.694281
Hattermann, M., Kadunz, G., Rezat, S., & Sträßer, R. (2015). Geometrie: Leitidee Raum und Form [Geometry: Central idea Space and Shape]. In R. Bruder, L. Hefendehl-Hebeker, B. Schmidt-Thieme, & H.-G. Weigand (Eds.), Handbuch der Mathematikdidaktik (pp. 185–219). Springer Spektrum. https://doi.org/10.1007/978-3-642-35119-8_7
Hofbauer, H. (2018). Kompetenzen und Einstellungen von Mathematiklehrkräften [Competencies and attitudes of mathematics teachers]. Springer Spektrum. https://doi.org/10.1007/978-3-658-22567-4
Jones, K. (2000). Critical issues in the design of the school geometry curriculum. In B. Barton (Eds.), Readings in mathematics education (pp. 75–90). University of Auckland.
Jones, K., & Mooney, C. (2003). Making space for geometry in primary mathematics. In I. Thompson (Ed.), Enhancing primary mathematics teaching (pp. 3–15). Open University Press.
Krauthausen, G. (2018). Einführung in die Mathematikdidaktik – Grundschule [Introduction to mathematics didactics – Elementary school]. Springer Spektrum. https://doi.org/10.1007/978-3-662-54692-5
Kultusministerkonferenz. (Eds). (2005). Bildungsstandards im Fach Mathematik für den Primarbereich [Educational standards in mathematics for the primary level]. Luchterhand.
Kuzle, A., & Bruder, R. (2016). Probleme lösen lernen im Themenfeld Geometrie [Learning to solve problems in the field of geometry]. Mathematik Lehren, 196, 2–8.
Laine, A., Ahtee, M., Näveri, L., Pehkonen, E., Koivisto, P. P., & Tuohilampi, L. (2015). Collective emotional atmosphere in mathematics lessons based on Finnish fifth graders’ drawings. LUMAT: International Journal on Math, Science and Technology Education, 3(1), 87–100. https://doi.org/10.31129/lumat.v3i1.1053
Mammana, C., & Villani, V. (Eds.). (1998). Perspectives on the teaching of geometry for the 21st century: An ICMI study. Springer.
Mayring, P. (2000). Qualitative content analysis. Forum Qualitative Sozialforschung/Forum: Qualitative Social Research, 1(2), Art. 20.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Author.
Radatz, H., & Rickmeyer, K. (1991). Handbuch für den Geometrieunterricht an Grundschulen [Handbook for teaching geometry in elementary schools]. Schroedel.
Remillard, J. T., & Heck, D. J. (2014). Conceptualizing the curriculum enactment process in mathematics education. ZDM Mathematics Education, 46(5), 705–718. https://doi.org/10.1007/s11858-014-0600-4
Senatsverwaltung für Bildung, Jugend und Wissenschaft Berlin, Ministerium für Bildung, Jugend und Sport des Landes Brandenburg. (Eds.). (2015). Rahmenlehrplan Jahrgangsstufen 1-10. Teil C, Mathematik [Framework curriculum Grades 1-10. Part C, Mathematics]. LISUM.
Simon, M. A. (2016). Explicating mathematical concept and mathematical conception as theoretical constructs for mathematics education research. Educational Studies in Mathematics, 94(2), 117–137. https://doi.org/10.1007/s10649-016-9728-1
Sinclair, N., & Bruce, C. D. (2015). New opportunities in geometry education at the primary school. ZDM Mathematics Education, 47(3), 319–329. https://doi.org/10.1007/s11858-015-0693-4
Sitter, K. (2019). Geometrische Körper an inner- und außerschulischen Lernorten: Der Einfluss des Protokollierens auf eine sichere Begriffsbildung [Geometric solids in in-school and out-of-school learning settings: the impact of logging on confident concept formation]. Springer Spektrum. https://doi.org/10.1007/978-3-658-27999-8
van den Heuvel-Panhuizen, M. (2008). Measurement and geometry in line. In Marja van der Heuvel-Panhuizen & K. Buys (Eds.), Young children learn measurement and geometry. A learning-teaching trajectory with intermediate attainment targets for the lower grades in primary school (pp. 9–14). Sense Publishers.
Wiese, I. (2016). Kognitive Anforderungen in geometrischen Aufgaben des vierten Schuljahres [Cognitive demands in geometric tasks of the fourth school year] (Doctoral dissertation). Universität Koblenz-Landau, OPUS.
Winter, H. (1976). Was soll Geometrie in der Grundschule? [What’s the purpose of geometry in primary education?]. Zentralblatt für Didaktik der Mathematik, 8(1/2), 14–18.
Wittmann, E. Ch. (1999). Konstruktion eines Geometriecurriculums ausgehend von Grundideen der Elementargeometrie [The construction of a geometry curriculum based on the fundamental ideas of elementary geometry]. In H. Henning (Ed.), Mathematik lernen durch Handeln und Erfahrung. Festschrift zum 75. Geburtstag von Heinrich Besuden (pp. 205–223). Bueltmann und Gerriets.
Wollring, B. (2007). Zur Kennzeichnung von Lernumgebungen für den Mathematikunterricht in der Grundschule [On characteristics of learning environments for teaching mathematics in elementary school]. Deutscher Bildungsserver. http://www.sinus-transfer.de/fileadmin/MaterialienIPN/Lernumgebungen_Wo_f_Erkner_070621.pdf
Authors who publish with this journal agree to the following terms:
- Authors are confirming that they are the authors of the submitted article, which will be published online in the Center for Educational Policy Studies Journal (for short: CEPS Journal) by University of Ljubljana Press (University of Ljubljana, Faculty of Education, Kardeljeva ploščad 16, 1000 Ljubljana, Slovenia). The Author’s/Authors’ name(s) will be evident in the article in the journal. All decisions regarding layout and distribution of the work are in the hands of the publisher.
- The Authors guarantee that the work is their own original creation and does not infringe any statutory or common-law copyright or any proprietary right of any third party. In case of claims by third parties, authors commit themselves to defend the interests of the publisher, and shall cover any potential costs.
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under https://creativecommons.org/licenses/by/4.0/deed.en that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.