Original article | Journal of Innovative Research in Teacher Education 2023, Vol. 4(2) 167-183
Cecilia Sveider, Joakim Samuelsson, Anja Thorsten & Marcus Samuelsson
pp. 167 - 183 | DOI: https://doi.org/10.29329/jirte.2023.572.1 | Manu. Number: MANU-2302-17-0002.R2
Published online: September 26, 2023 | Number of Views: 74 | Number of Download: 370
Abstract
The present study aimed to investigate pre-service teachers’ mathematics teaching when responding to virtual pupils’ unexpected mathematical questions concerning how to sort fractions. The research was conducted with 102 pre-service teachers participating in a teacher education program specializing in upper elementary school mathematics. The main data collection strategy took the form of video recordings of teaching sessions involving semi-virtual simulations. The recordings were analyzed through a qualitative explorative analysis process involving three phases, focusing on the object of learning and how the pre-service teachers handled the mathematics content pertaining to comparing fractions. The simulated teaching activity, together with the large sample, allowed us to discover patterns concerning how PSTs teach when they are asked unexpected questions related to fractions. The results show qualitatively different ways of teaching. PSTs draw pupils’ attention to different learning objects by using different representations and more or less correct mathematics. This study offers teacher educators knowledge about how PSTs teach when confronted by students with unexpected questions concerning fractions and can therefore support teacher educators in interpreting students’ mathematics instruction and help them decide how best to support PSTs’ teaching instruction.
Keywords: Preservice teacher, Fraction teaching, Simulation, Variation theory
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Badiee, F., & Kaufman, D. (2015). Design evaluation of a simulation for teacher education. SAGE Open, 5(2). https://doi.org/10.1177/2158244015592454 Barbieri, C. A., Rodrigues, J., Dyson, N., & Jordan, N. C. (2020). Improving fraction understanding in sixth graders with mathematics difficulties: Effects of a number line approach combined with cognitive learning strategies. Journal of Educational Psychology, 112(3), 628–648. https://doi.org/10.1037/edu0000384 Baumert, J., Kunter, M., Blum, W., Brunner, M., Voss, T., Jordan, A., Klusmann, U., Krauss, S., Neubrand, M., & Tsai, Y. M. (2010). Teachers’ mathematical knowledge, cognitive activation in the classroom, and student progress. American Educational Research Journal, 47(1), 133–180. https://doi.org/10.3102/0002831209345157 Blömeke, S., & Kaiser, G. (2017). Understanding the development of teachers' professional competencies as personally, situationally, and socially determined. In D. J. Clandinin and J. Husu (Ed.). The Sage handbook of research on teacher education pp. 783–802 SAGE Publications India. Blömeke, S., & Jentsch, A., & Ross, N., & Kaiser, G., & König, J. (2022). Opening up the black box: Teacher competence, instructional quality, and students’ learning progress. Learning and Instruction, 79. https://doi.org/10.1016/j.learninstruc.2022.101600 Blömeke, S., Olsen, R.V., Suhl, U. (2016). Relation of student achievement to the quality of their teachers and instructional quality. In: Nilsen, T., Gustafsson, JE. (Eds) Teacher quality, instructional quality and student outcomes. IEA Research for Education (pp.21–50). Springer, Cham. https://doi.org/10.1007/978-3-319-41252-8_2 Bryman, A. (2018). Samhällsvetenskapliga metoder (3ed.). Liber Clarke, D., & Roche, A. (2009). Students’ fraction comparison strategies as a window into robust understanding and possible pointers for instruction. Educational Studies in Mathematics, 72, 127–138. https://doi.org/10.1007/s10649-009-9198-9. Cochran-Smith, M., & Maria V, A. (2015). Studying teacher preparation: The questions that drive research. European Educational Research Journal, 14(5), 379–394. https://doi.org/10.1177/1474904115590211 Cramer, K., & Post, T., & delMas, R. (2002). Initial fraction learning by fourth- and fifth-grade students: A comparison of the effects of using commercial curricula with the effects of using the rational number project curriculum. Journal for Research in Mathematics Education, 33(2). https://doi.org/10.2307/749646 DeWolf, M., & Vosniadou, S. (2015). The representation of fraction magnitudes and the whole number bias reconsidered. Learning and Instruction, 37, 39–49. https://doi.org/10.1016/j.learninstruc.2014.07.002 Dieker, L., & Rodriguez, J., & Lignugaris-Kraft, B., & Hynes, M., & Hughes, C. (2014). The potential of simulated environments in teacher education: Current and future possibilities. Teacher education and special education. The Journal of the Teacher Education Division of the Council for Exceptional Children, 37(1), 21–33. https://doi.org/10.1177/088840641351268310.1177/0888406413512683. Doyle, W. (2006). Ecological approaches to classroom management. In C. M. Evertson & C. S. Weinstein (Eds.), Handbook of classroom management: Research, practice, and contemporary issues (pp. 97–125). Lawrence Erlbaum Associates Publishers. Ersozlu, Z., Ledger, S., Ersozlu, A., Mayne, F., & Wildy, H. (2021). Mixed-reality learning environments in teacher education: An analysis of TeachLivE™ research. SAGE Open, 11(3). https://doi.org/10.1177/21582440211032155 Fazio, L. K., DeWolf, M., & Siegler, R. S. (2016). Strategy use and strategy choice in fraction magnitude comparison. Journal of Experimental Psychology: Learning, Memory, and Cognition, 42, 1-16. doi: 10.1037/xlm0000153 Goldin, G., & Shteingold, N. (2001). Systems of representation and the development of mathematical concepts. In A. A. Cuoca & F. R. Curcio (Red.), The roles of representation in school mathematics (pp. 1–23). NCTM. Kaufman, D., & Ireland, A. (2016). Enhancing teacher education with simulations. TechTrends, 60(3), 260–267. https://doi.org/10.1007/s11528-016-0049-0 Kieren, T. E. (1980). Five faces of mathematical knowledge building. Department of Secondary Education, University of Alberta. Kilpatrick, J., & Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. Washington DC: National Academy Press. Lakoff, G. (1987). Cognitive models and prototype theory. In U. Neisser (Ed.), Concepts and conceptual development: Ecological and intellectual factors in categorization (pp. 63–100). Cambridge University Press. Lortie-Forgues, H., Tian, J., & Siegler, R. S. (2015). Why is learning fraction and decimal arithmetic so difficult? Developmental Review, 38, 201–221. https://doi.org/10.1016/j.dr.2015.07.008 Mack, N. K. (1990). Learning fractions with understanding: Building on informal knowledge. Journal for Research in Mathematics Education, 21(1), 16–32. http://doi.org/10.2307/749454 Malinowski, B. (1922). Ethnology and the study of society. Economica, 6, 208–219. https://doi.org/10.2307/2548314 Marton, F., & Booth, S. A. (1997). Learning and awareness. Lawrence Erlbaum Associates Publishers. Marton, F. (2015). Necessary conditions of learning. Routledge. Marton, F., & Pang, M. F. (2013). Meanings are acquired from experiencing differences against a background of sameness, rather than from experiencing sameness against a background of difference: Putting a conjecture to the test by embedding it in a pedagogical tool. Frontline Learning Research, 1(1), 24–41. https://doi.org/1. 10.14786/flr.v1i1.16 Maxwell, J. (1992). Understanding and validity in qualitative research. Harvard Educational Review, 62. 279–300. McMullen, J., Hannula-Sormunen, M.M., & Lehtinen, E. (2014). Spontaneous focusing on quantitative relations in the development of children's fraction knowledge. Cognition and Instruction, 32. 198–218. https://doi.org/10.1080/07370008.2014.887085 Mitchell, A., & Horne, M. (2010). Gap thinking in fraction pair comparisons is not whole number thinking: Is this what early equivalence thinking sounds like. Shaping the Future of Mathematics Education, 414–421. http://www.merga.net.au/publications/counter.php?pub=pub_conf&id=881 Ni, Y. J., & Zhou, Y. D. (2005). Teaching and learning fraction and rational numbers: The origins and implications of whole number bias. Educational Psychologist, 40(1), 27–52. https://doi.org/10.1207/s15326985ep4001_3 Pearn, C., & Stephens, M. (2004). Why you have to probe to discover what year 8 students really think about fractions. In I. Putt, R. Faragher, & M. McLean (Eds.), Proceedings of the 27th Annual Conference of the Mathematics Education Research Group of Australasia 2004 (pp. 430–437). MERGA. Pedersen, P., & Bjerre, M. (2021). Two conceptions of fraction equivalence. Educational Studies in Mathematics, 107(1), 135-157. https://doi.org/10.1007/s10649-021-10030-7 Post, T., Lappan, G., & Cramer, K. (1987). Research into practice: Children's strategies in ordering rational numbers. The Arithmetic Teacher, 35(2), 33–35. Rau, M. A., & Matthews, P. G. (2017). How to make ‘more’ better? Principles for effective use of multiple representations to enhance students’ learning about fractions. ZDM - Mathematics Education, 49(4), 531–544. https://doi.org/10.1007/s11858-017-0846-8 Resnick, I., Jordan, N. C., Hansen, N., Rajan, V., Rodrigues, J., Siegler, R. S., & Fuchs, L. S. (2016). Developmental growth trajectories in understanding of fraction magnitude from fourth through sixth grade. Developmental Psychology, 52(5), 746–757. https://doi.org/10.1037/dev0000102 Schlesinger, L., Jentsch, A., Kaiser, G., König, J., & Blömeke, S. (2018). Subject-specific characteristics of instructional quality in mathematics education. ZDM: The International Journal on Mathematics Education, 50(3), 475–490. https://doi.org/10.1007/s11858-018-0917-5 Schneider, M., & Siegler, R. S. (2010). Representations of the magnitudes of fractions. Journal of Experimental Psychology: Human Perception and Performance, 36(5), 1227–1238. https://doi.org/10.1037/a0018170 Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational researcher, 15(2), 4–14. https://doi.org/10.3102/0013189X015002004 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), 346–351. https://doi.org/10.1177/0963721417700129 Siegler, R. S., Thompson, C. A., & Schneider, M. (2011). An integrated theory of whole number and fractions development. Cognitive Psychology, 62(4), 273–296. https://doi.org/10.1016/j.cogpsych.2011.03.001 Sveider, C. (2021). Representationer av tal I bråkform: En studie om matematikundervisning på mellanstadiet. (Doctoral dissertation). Linköping: Linköping University Electronic Press, https://doi.org/10.3384/diss.diva-178048 Swedish Research Council. (2017). Good research practice. Vetenskapsrådet. Szendrei, J. (1996). Concrete materials in the classroom. In A. Bishop (Red.), International handbook of mathematics education (pp. 411–434). Kluwer. Tatto, M. T., Schwille, J., Senk, S., Ingvarson, L., Peck, R., & Rowley, G. (2008). Teacher Education and Development Study in Mathematics (TEDS-M): Policy, practice, and readiness to teach primary and secondary mathematics. Conceptual framework. East Lansing, MI: Teacher Education and Development International Study Center, College of Education, Yang, D., & Lai, M. L. (2013). Teaching benchmark strategy for fifth graders in Taiwan. Journal of Education and Learning, 2(2), 69–77. https://doi.org/10.5539/jel.v2n2p69 |