Using Concept Cartoons to investigate future primary school teachers’ pedagogical content knowledge on addition
DOI:
https://doi.org/10.48489/quadrante.23011Keywords:
Concept Cartoons, future teachers, mathematics education, pedagogical content knowledge, pupils' misconceptions, written addition algorithmAbstract
This paper introduces an exploratory empirical qualitative study that has been carried out with two diverse groups of future primary school teachers (before vs after the attendance of a course on didactics of mathematics). The study uses an educational tool called Concept Cartoons accompanied by a set of six indicative questions as a means of collecting data on pedagogical content knowledge (PCK) in mathematics. In particular, the study focuses on future teachers’ written responses to virtual pupils’ opinions in a virtual classroom situation related to the algorithm of written addition of natural numbers. The findings reveal ten different code categories of displays of PCK related to knowledge of pupils (three categories), knowledge of tasks (one category) and knowledge of instruction (six categories), some of them related to strong PCK, others to weak PCK. According to the findings, all the categories related to knowledge of pupils occurred in the post-didactic group only, all the categories that appeared only in the pre-didactic group are connected to weak PCK, and all the categories that occurred only in the post-didactic group are connected to strong PCK.
References
Anghileri, J. (2007). Developing number sense. London: Bloomsbury Continuum.
Ashlock, R. B. (2010). Error patterns in computation. Using error patterns to help each student learn. Boston: Allyn & Bacon.
Atasoy, S., & Ergin, S. (2017). The effect of concept cartoon-embedded worksheets on grade 9 students’ conceptual understanding of Newton’s Laws of Motion. Research in Science & Technological Education, 35(1), 58-73. https://doi.org/10.1080/02635143.2016.1248926
Ball, D. L., Lubienski, S. T., & Mewborn, D. S. (2001). Research on teaching mathematics: The unsolved problem of teachers’ mathematical knowledge. In V. Richardson (Ed.), Handbook of research on teaching (pp. 433–456). New York: Macmillan.
Buchbinder, O., & Kuntze, S. (Eds.) (2018). Mathematics teachers engaging with representations of practice. Cham: Springer. https://doi.org/10.1007/978-3-319-70594-1
Chin, C., & Teou, L. Y. (2009). Using concept cartoons in formative assessment: Scaffolding students’ argumentation. International Journal of Science Education, 31(10), 1307-1332. https://doi.org/10.1080/09500690801953179
Dabell, J., Keogh, B., & Naylor, S. (2008). Concept Cartoons in Mathematics Education [CD-ROM]. Sandbach: Millgate House Education.
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, 82-92. https://doi.org/10.1016/j.tate.2014.12.009
Depaepe, F., Van Roy, P., Torbeyns, J., Kleickmann, T., Van Dooren, W., & Verschaffel, L. (2018). Stimulating pre-service teachers’ content and pedagogical content knowledge on rational numbers. Educational Studies in Mathematics, 99(2), 197-216. https://doi.org/10.1007/s10649-018-9822-7
Depaepe, F., Verschaffel, L., & Kelchtermans, G. (2013). Pedagogical content knowledge: A systematic review of the way in which the concept has pervaded mathematics educational research. Teaching and Teacher Education, 34, 12-25. https://doi.org/10.1016/j.tate.2013.03.001
Grossman, P., Compton, C., Igra, D., Ronfeldt, M., Shahan, E., & Williamson, P. (2009). Teaching practice: A cross-professional perspective. Teachers College Record, 111(9), 2055-2100.
Hansen, A. (2013). Children’s errors in mathematics. Understanding common misconceptions in primary schools. London: SAGE.
Keogh, B., & Naylor, S. (1993). Learning in science: Another way in. Primary Science Review, 26, 22-23.
Keogh B., Naylor S., de Boo M., & Feasey R. (2001). Formative assessment using Concept Cartoons: Initial teacher training in the UK. In H. Behrendt et al. (Eds.), Research in Science Education - Past, Present, and Future (pp. 137-142). Springer, Dordrecht. https://doi.org/10.1007/0-306-47639-8_18
Kleickmann, T., Richter, D., Kunter, M., Elsner, J., Besser, M., Krauss, S., & Baumert, J. (2013). Teachers’ content and pedagogical content knowledge: the role of structural differences in teacher education. Journal of Teacher Education, 64, 90-106. https://doi.org/10.1177/0022487112460398
Ma, L. (1999). Knowing and teaching elementary mathematics. Mahwah: Erlbaum. https://doi.org/10.4324/9781410602589
McClain, K. (2003). Supporting preservice teachers’ understanding of place value and multidigit arithmetic. Mathematical Thinking and Learning, 5(4), 281-306. https://doi.org/10.1207/s15327833mtl0504_03
McIntosh, A. (2002). Common errors in mental computation of students in grades 3 - 10. In B. Barton, K. C. Irwin, M. Pfannkuch, & M. O. J. Thomas (Eds.), Mathematics Education in the South Pacific (pp. 457-464). Sydney: MERGA.
Miles, M. B., Huberman, A. M., & Saldaña, J. (2014). Qualitative data analysis. A methods sourcebook. Thousand Oaks, CA: SAGE.
Naylor, S., & Keogh, B. (2000). Science Concept Cartoons. Sandbach: Millgate House.
Naylor, S., & Keogh, B. (2013). Concept Cartoons: What have we learnt? Journal of Turkish Science Education, 10(1), 3-11.
Naylor, S., Keogh, B., & Downing, B. (2007). Argumentation and primary science. Research in Science Education, 37, 17-39. https://doi.org/10.1007/s11165-005-9002-5
Ormanci, U., & Sasmaz-Oren, F. (2011). Assessment of concept cartoons: An exemplary study on scoring. Procedia Social and Behavioral Sciences, 15, 3582-3589. https://doi.org/10.1016/j.sbspro.2011.04.339
Pekel, F. O. (2019). Effectiveness of argumentation-based concept cartoons on teaching global warming, ozone layer depletion, and acid rains. Journal of Environmental Protection and Ecology, 20(2), 945-953.
Reyes-Roncancio, J. D., Romero-Osma, G. P. & Bustos-Velazco, E. H. (2019). Teaching physics through contextualised concept cartoons. Revista Científica, 36(3), 323-337. https://doi.org/10.14483/23448350.15156
Ryan, J., & Williams, J. (2011). Children’s mathematics 4-15. Learning from errors and misconceptions. New York: McGraw-Hill Education.
Samková, L. (2018). Concept Cartoons as a representation of practice. In O. Buchbinder, & S. Kuntze (Eds.), Mathematics teachers engaging with representations of practice (pp. 71-93). Cham, Switzerland: Springer. https://doi.org/10.1007/978-3-319-70594-1_5
Schleppegrell, M. J. (2007). The linguistic challenges of mathematics teaching and learning: A research review. Reading & Writing Quarterly: Overcoming Learning Difficulties, 23(2), 139-159. https://doi.org/10.1080/10573560601158461
Selter, C. (2001). Addition and subtraction of three-digit numbers: German elementary children’s success, methods and strategies. Educational Studies in Mathematics, 47, 145-173.
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14. https://doi.org/10.3102/0013189x015002004
Shulman, L. S. (1987). Knowledge and teaching. Foundations of the new reform. Harvard Educational Review, 57(1), 1-22. https://doi.org/10.17763/haer.57.1.j463w79r56455411
Temel, S., & Sen, S. (2019). Comprehension levels of prospective teachers related to the heat and temperature concepts. In B. Akkuş et al. (Eds.), Turkish Physical Society 35th International Physics Congress (TPS35) (no. 030066). Melville, NY: American Institute of Physics. https://doi.org/10.1063/1.5135464
Thanheiser, E. (2009). Preservice elementary school teachers’ conceptions of multidigit whole numbers. Journal for Research in Mathematics Education, 40(3), 251-281.
Thompson, I. (1994). Young children’s idiosyncratic written algorithms for addition. Educational Studies in Mathematics, 26, 323-345. https://doi.org/10.1007/bf01279519
Turner, J., Smith, C., Keogh, B., & Naylor, S. (2013). English Concept Cartoons. Sandbach: Millgate House Publishers.
van der Berg, E. (2013). The PCK of laboratory teaching: Turning manipulation of equipment into manipulation of ideas. Scientia in Educatione, 4(2), 74-92. https://doi.org/10.14712/18047106.86
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