Didactic Transposition of Rational Numbers: a Case From a Textbook Analysis and Prospective Elementary Teachers’ Mathematical and Didactic Knowledge
Povzetek
Didaktični prenos racionalnih števil: primer iz analize učbenika ter matematično in didaktično znanje bodočih učiteljev razrednega pouka. Namen študije je predstaviti podrobno analizo didaktičnega prenosa racionalnih števil iz predvidenega znanja v poučevanje znanja, ki poteka v instituciji za izobraževanje učiteljev. Znanje racionalnih števil, ki naj bi se poučevalo, analiziramo po učbeniku matematike in ga pri predmetu matematika uporabljajo bodoči učitelji razrednega pouka. Analiza se osredinja na matematične prakseologije, zlasti na tip nalog in tehnik. Posredovano znanje nato proučujemo po sodelovalnih delih 32 bodočih učiteljev na temo dveh hipotetičnih nalog učiteljev (HNU), povezanih z operacijami z racionalnimi števili.
Prenosi
Literatura
Alajmi, A. H. (2012). How do elementary textbooks address fractions? A review of mathematics textbooks in the USA, Japan, and Kuwait. Educational Studies in Mathematics, 79(2), pp. 239–261. https://doi.org/10.1007/s10649-011-9342-1
Alenazi, A. (2016). Examining middle school pre-service teachers’ knowledge of fraction division interpretations. International Journal of Mathematical Education in Science and Technology, 47(5), pp. 696–716. https://doi.org/10.1080/0020739X.2015.1083127
Austin, P., Carbone, R. E., & Webb, P. (2011). Prospective primary school teachers’ attempts to pose acceptable word problems on the addition of fractions: Some insights from South Africa and the United States of America. African Journal of Research in Mathematics, Science and Technology Education, 15(2), pp. 168–178. https://doi.o–rg/10.1–080/10288457.2011.10740710
Bosch, M., & Gascón, J. (2006). Twenty-Five Years of the Didactic Transposition. ICMI Bulletin, 58, pp. 51–65.
Brousseau, G. (2002). Theory of Didactical Situations in Mathematics. New York: Kluwer Academic Publisher.
Charalambous, C. Y., & Pitta-Pantazi, D. (2007). Drawing on a theoretical model to study students’ understandings of fractions. Educational Studies in Mathematics, 64(3), pp. 293–316. https://doi.org/10.1007/s10649-006-9036-2
Chevallard, Y. (1985). La transposition didactique. Grenoble: La pensée sauvage.
Chevallard, Y. (2006). Steps towards a new epistemology in mathematics education. In M. Bosch (Ed.), Proceedings of the IV Congress of the European Society for Research in Mathematics Education (pp. 21–30). Grenoble: La Pensée Sauvage.
Chevallard, Y. (2007). Readjusting Didactics to a Changing Epistemology. European Educational Research Journal, 6(2), pp. 131–134. https://doi.org/10.2304/eerj.200–7.6.2.131
Chevallard, Y., & Bosch, M. (2014). Didactic transposition in mathematics education. In Encyclopedia of Mathematics Education (pp. 170–174). Springer Netherlands.
Depaepe, F., Torbeyns, J., Vermeersch, N., Janssens, D., Janssen, R., Kelchtermans, G., … Van Dooren, W. (2015). Teachers’ content and pedagogical content knowledge on rational numbers: A comparison of prospective elementary and lower secondary school teachers. Teaching and Teacher Education, 47, pp. 82–92. https://doi.o–rg/10.1016/j.tate.2014.12.009
Freudenthal, H. (1991). Revisiting Mathematics Education: China lecturers. Dordrecht: Kluwer Academic Publishers.
Graeber, A. O., & Tirosh, D. (1988). Multiplication and division involving decimals: Preservice elementary teachers’ performance and beliefs. The Journal of Mathematical Behavior, 7(3), pp. 263–288.
Graeber, A. O., Tirosh, D., & Golver, R. (1989). Preservice teachers’ misconceptions in solving verbal problems in multiplication and division. Journal for Reseach in Mathematics Education, 20(1), pp. 95–102.
Hill, H. C., Schilling, S. G., & Ball, D. L. (2004). Developing Measures of Teachers’ Mathematics Knowledge for Teaching. The Elementary School Journal, 105(1), pp. 11–30. https://doi.org/10.1086/428763
Isiksal, M., & Cakiroglu, E. (2011). The nature of prospective mathematics teachers’ pedagogical content knowledge: The case of multiplication of fractions. Journal of Mathematics Teacher Education, 14(3), pp. 213–230. https://doi.org/10.1007/s10857-010-9160-x
Johar, R., Patahuddin, S. M., & Widjaja, W. (2017). Linking pre-service teachers’ questioning and students’ strategies in solving contextual problems: A case study in Indonesia and the Netherlands. The Mathematics Enthusiast, 14(1–3), pp. 101–128. https://do–i.org/10.1242/dmm.009688
Kara, F., & İncikabı, L. (2018). Sixth grade students’ preferences on multiple representations used in fraction operations and their performance in their preferences. Elementary Education Online, 17(4), pp. 2136–2150. https://doi.org/10.17051/ilkonline.20–19.506984
Kastberg, S., & Morton, C. (2014). Mathematical content knowledge for teaching elementary mathematics: A focus on decimals. The Mathematics Enthusiast, 11(2), pp. 311–332.
Li, H. C. (2014). A comparative analysis of British and Taiwanese students’ conceptual and procedural knowledge of fraction addition. International Journal of Mathematical Education in Science and Technology, 45(7), pp. 968–979. https://doi.org/10.108–0/0020739X.2014.892163
Lundberg, A. L. V., & Kilhamn, C. (2018). Transposition of Knowledge: Encountering Proportionality in an Algebra Task. International Journal of Science and Mathematics Education, 16(3), pp. 559–579. https://doi.org/10.1007/s10763-016-9781-3
Ma, L. (1999). Knowing and Teaching Elementary Mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ.: Lawrence Erlbaum Associates.
Newton, K. J. (2008). An Extensive Analysis of Preservice Elementary Teachers’ Knowledge of Fractions. American Educational Research Journal, 45(4), pp. 1080–1110. https://doi.org/10.3102/0002831208320851
Pansell, A., & Boistrup, L. B. (2018). Mathematics teachers’ teaching practices in relation to textbooks: Exploring praxeologies. The Mathematics Enthusiast, 15(3), pp. 541–562.
Putra, Z. H. (2014). Pendidikan matematika SD kelas tinggi [Mathematics education for upper grade elementary school]. Pekanbaru: Unpublished textbook.
Putra, Z. H. (2016). Pengetahuan mahasiswa pedidikan guru sekolah dasar dalam merepresentasikan operasi pecahan dengan model persegi panjang [Prospective elementary teachers' knowledge in representing operation of fraction using rectangular models]. Jurnal Elemen, 2(1), pp. 1–13. https://doi.org/10.2940–8/jel.v2i1.174
Putra, Z. H. (2018). A praxeological analysis of pre-service elementary teachers’ knowledge of rational numbers. Recherches En Didactique Des Mathematiques, 38(3), pp. 315–364.
Putra, Z. H. (2019a). Elementary teachers’ knowledge on fraction multiplication: An anthropological theory of the didactic approach. Journal of Teaching and Learning in Elementary Education, 2(1), pp. 47–52. https://doi.org/http://dx.doi.org/10.3–3578/jtlee.v2i1.6964
Putra, Z. H. (2019b). Praxeological change and the density of rational numbers: The case of pre-service teachers in Denmark and Indonesia. Eurasia Journal of Mathematics, Science and Technology Education, 15(5), pp. 1–15. https://doi.org/10.29333/ejmste/105867
Putra, Z. H. H., & Winsløw, C. (2018). Teachers’ collective knowledge: The case of equivalent fractions. Journal of Physics: Conference Series, 1088(1), pp. 1–6. https://doi.org/10.1088/1742-6596/1088/1/012003
Sembiring, R. K., Hadi, S., & Dolk, M. (2008). Reforming mathematics learning in Indonesian classrooms through RME, 40, pp. 927–939. https://doi.org/10.1–007/s11858-008-0125-9
Senk, S. L., Tatto, M. T., Reckase, M., Rowley, G., Peck, R., & Bankov, K. (2012). Knowledge of future primary teachers for teaching mathematics: An international comparative study. ZDM - International Journal on Mathematics Education, 44(3), pp. 307–324. https://doi.org/10.1007/s11858-012-0400-7
Siegler, R. S., & Lortie-Forgues, H. (2017). Hard Lessons: Why Rational Number Arithmetic Is So Difficult for So Many People. Current Directions in Psychological Science, 26(4), pp. 346–351. https://doi.org/10.1177/0963721417700129
Tirosh, D., & Graeber, A. O. (1989). Elementary teachers’ explicit beliefs about multiplication and division. Educational Studies in Mathematics, 20(1), pp. 79–96.
van Steenbrugge, H., Lesage, E., Valcke, M., Desoete, A., Steenbrugge, H. Van, Lesage, E., Desoete, A. (2014). Preservice elementary school teachers’ knowledge of fractions: A mirror of students’ knowledge? Journal of Curriculum Studies, 46(1), pp. 138–161. https://doi.org/10.1080/00220272.2013.839003
Widjaja, W., Stacey, K., & Steinle, V. (2008). Misconceptions about density of decimals: Insights from Indonesian pre-service teachers’ work. Journal for Science and Mathematics for Education in Southeast Asia, 31(2), pp. 117–131.
Wijaya, A., van den Heuvel-Panhuizen, M., & Doorman, M. (2015). Opportunity-to-learn context based tasks provided by mathematics textbooks. Educational Studies in Mathematics, 89, pp. 41–65. https://doi.org/10.1007/s10649-015-9595-1
Wijayanti, D., & Winsløw, C. (2017). Mathematical practice in textbooks analysis: Praxeological reference models, the case of proportion. Journal of Research in Mathematics Education, 6(3), pp. 307–330. https://doi.org/10.17583/redi–mat.2017.2078
Copyright (c) 2020 Jerneja Herzog
To delo je licencirano pod Creative Commons Priznanje avtorstva 4.0 mednarodno licenco.