Assessing Future Teachres' Knowledge on Fractions: Written Tests vs Concept Cartoons

Authors

  • Libuše Samková Faculty of Education University of South Bohemia Jeronýmova 10 České Budějovice

DOI:

https://doi.org/10.7160/eriesj.2018.110301

Keywords:

Concept Cartoons; fractions; future primary school teachers; problem solving; word problems

Abstract

The contribution investigates opportunities that an educational tool called Concept Cartoons can offer in future teachers' education, namely in comparison with word problems in standard written tests. The referred empirical study was conducted in two separated consecutive stages, with two groups of future primary school teachers (the first one from the Czech Republic, and the second one from Slovakia). The participants of the first stage solved four word problems (T1, T2, T3, T4) with increasing difficulty within the written test, and a problem with a similar structure and difficulty as T3 but in the Concept Cartoon form. The second stage of the study served as a complementary stage, its participants solved only the word problem T3 and the Concept Cartoon. In both stages, the comparison of results and solution procedures revealed many participants who mastered the word problem(s) but displayed a fundamental misconception when working with the Concept Cartoon. Two thirds of the participants presented non-corresponding responses to these two corresponding tasks: they solved one of them correctly and the other one incorrectly. All of the problems in the study were based on the part-whole interpretation of fractions, the revealed misconception consisted of incorrect determination of the whole.

References

  • Behr, M., Lesh, R., Post, T. and Silver, E. (1983) ‘Rational number concepts’, in Acquisition of mathematics concepts and processes, New York: Academic Press, pp. 91-125.

  • Cramer, K. and Lesh, R. (1988) ‘Rational number knowledge of preservice elementary education teachers’, in Proceedings of PME 88, DeKalb, Il: PME, pp. 425-431.

  • Dabell, J., Keogh, B. and Naylor, S. (2008) Concept Cartoons in Mathematics Education, Sandbach: Millgate House Education.

  • Depaepe, F., Torbeyns, J., Vermeersch, N., Janssens, D., Janssen, R., Kelchtermans, G., Verschaffel, L. and 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, vol. 47, pp. 82-92. http://dx.doi.org/10.1016/j.tate.2014.12.009

  • Grossman, P., Compton, C., Igra, D., Ronfeldt, M., Shanan, E. and Williamson, P. (2009) ‘Teaching practice: A cross-professional perspective’, Teachers College Record, vol. 111, no. 9, pp. 2055-2100.

  • Herbst, P. and Chazan, D. (2011) ‘On creating and using representation of mathematics teaching in research and teacher development’, ZDM Mathematics Education, vol. 43, pp. 1-5. http://doi.org/10.1007/s11858-011-0306-9

  • Hošpesová, A., Tichá, M. (2015) ‘Problem posing in primary school teacher training’, in Singer, F.M., Ellerton, N.F. and Cai, J. (ed.) Mathematical problem posing, New York: Springer, pp. 433-447. http://doi.org/10.1007/978-1-4614-6258-3_21

  • Ingram, J., Pitt, A. and Baldry, F. (2015) ‘Handling errors as they arise in whole-class interactions’, Research in Mathematics Education, vol. 17, pp. 183-197. http://doi.org/10.1080/14794802.2015.1098562

  • Kazemi, E. and Stipek, D. (2001) ‘Promoting conceptual thinking in four upper-elementary mathematics classrooms’, Elementary School Journal, vol. 102, pp. 59-80. http://doi.org/10.1086/499693

  • Lamon, S.J. (1999) Teaching fractions and ratios for understanding, Mahwah, NJ: LEA.

  • Ma, L. (1999) Knowing and teaching elementary mathematics, Mahwah, NJ: Erlbaum.

  • Národní ústav pro vzdělávání (NÚV), (2015) Rámcový vzdělávací program pro základní vzdělávání, Praha: MŠMT, [Online], Available: http://www.msmt.cz/file/37052/ [5 Sep 2018].

  • Nesher, P. (1987) ‘Towards an instructional theory: the role of student's misconceptions’, For the Learning of Mathematics, vol. 7, no. 3, pp. 33-40.

  • Novotná, J. and Vondrová, N. (2017) ‘Pupils' strategies for missing value proportional problems’, in Proceedings of ERIE 2017, Prague, pp. 279-286, [Online], Available: http://erie.v2.czu.cz/en/r-13628-proceedings-2017 [5 Sep 2018].

  • Pavlovičová, G. and Švecová, V. (2017) ‘Some misconceptions in understanding of fractions’, in Proceedings of EDULEARN17 Conference, Barcelona, pp. 5463-5470. http://doi.org/10.21125/edulearn.2017.2246

  • Ryan, J. and Williams, J. (2011) Children's mathematics 4-15. Learning from errors and misconceptions, Berkshire: Open University Press.

  • Samková, L. (2018a) ‘Concept Cartoons as a representation of practice’, in Mathematics Teachers Engaging with Representations of Practice. ICME-13 Monograph, New York: Springer. http://doi.org/10.1007/978-3-319-70594-1_5

  • Samková, L. (2018b) ‘Written tests vs Concept Cartoons: the case of future teachers and fractions’, in Proceedings of ERIE 2018, Prague, pp. 314-321, [Online], Available: http://erie.v2.czu.cz/en/r-13780-proceedings-2018 [5 Sep 2018].

  • Samková, L. and Tichá, M. (2015) ‘Investigating future primary teachers' grasping of situations related to unequal partition word problems’, Quaderni di Ricerca in Didattica (Mathematics), vol. 25, no. 2, pp. 295-303.

  • Samková, L. and Tichá, M. (2016a) ‘Developing open approach to mathematics in future primary school teachers’, in Proceedings of ERIE 2016, Prague, pp. 494-501, [Online], Available: http://erie.v2.czu.cz/en/r-13629-proceedings-2016 [5 Sep 2018].

  • Samková, L. and Tichá, M. (2016b) ‘On the way to develop open approach to mathematics in future primary school teachers’, ERIES Journal, vol. 9, no. 2, pp. 37-44. http://doi.org/10.7160/eriesj.2016.090202

  • Samková, L. and Tichá, M. (2017a) ‘Observing how future primary school teachers reason about fractions’, in Proceedings of ERIE 2017, Prague, pp. 363-371, [Online], Available: http://erie.v2.czu.cz/en/r-13628-proceedings-2017 [5 Sep 2018].

  • Samková, L. and Tichá, M. (2017b) ‘On the way to observe how future primary school teachers reason about fractions’, ERIES Journal, vol. 10, no. 4, pp. 93-100. http://doi.org/10.7160/eriesj.2017.100401

  • Schleppenbach, M., Flevares, L.M., Sims, L.M. and Perry, M. (2007) ‘Teachers' responses to student mistakes in Chinese and U.S. mathematics classrooms’, Elementary School Journal, vol. 108, pp. 131-147. http://doi.org/10.1086/525551

  • Singer, F.M., Ellerton, N.F. and Cai, J. (2015) Mathematical problem posing, New York: Springer. http://doi.org/10.1007/978-1-4614-6258-3

  • Star, J.R. and Strickland, S.K. (2008) ‘Learning to observe: using video to improve preservice mathematics teachers' ability to notice’, Journal of Mathematics Teacher Education, vol. 11, pp. 107-125. http://doi.org/10.1007/s10857-007-9063-7  

  • Steffe, L. and Olive, J. (2010) Children's fractional knowledge, New York: Springer. http://doi.org/10.1007/978-1-4614-6258-3

  • Švecová, V., Pavlovičová, G., Rybanský, Ľ. and Klimentová, L. (2017) Reifikácia zlomkov vo vzťahu k osobnej potrebe štruktúry, Praha: Wolters Kluwer.

  • Tichá, M. and Macháčková, J. (2006) Rozvoj pojmu zlomek ve vyučování matematice, Praha: JČMF.

  • Uličná, K. (2017) ‘Professional vision: focus on knowledge-based reasoning’, in Proceedings of ERIE 2017, Prague, pp. 482-489, [Online], Available: http://erie.v2.czu.cz/en/r-13628-proceedings-2017 [5 Sep 2018].

  • van Es, E.A. and Sherin, M.G. (2002) ‘Learning to notice: scaffolding new teachers' interpretations of classroom interactions’, Journal of Technology and Teacher Education, vol. 10, pp. 571-596.

  • Vondrová, N. and Žalská, J. (2015) ‘Ability to notice mathematics specific phenomena: what exactly do student teachers attend to?’, Orbis Scholae, vol. 9, no. 2, pp. 77-101. http://doi.org/10.14712/23363177.2015.81

    • Additional Files

    Published

    2018-10-01

    How to Cite

    Samková, L. (2018) ’Assessing Future Teachres’ Knowledge on Fractions: Written Tests vs Concept Cartoons’, Journal on Efficiency and Responsibility in Education and Science, vol. 11, no. 3, pp. 45–52. https://doi.org/10.7160/eriesj.2018.110301

    Issue

    Vol. 11 No. 3 (2018)

    Section

    Research Paper

    License

    Authors declare with this manuscript intended for publication to ERIES Journal that:

    • all co-authors agree with the publication of the manuscript even after amendments arising from peer review;
    • all co-authors agree with the posting of the full text of this work on the web page of ERIES Journal and to the inclusion of references in databases accessible on the internet;
    • no results of other researchers were used in the submitted manuscript without their consent, proper citation, or acknowledgement of their cooperation or material provided;
    • the results (or any part of them) used in the manuscript have not been sent for publication to any other journal nor have they already been published (or if so, that the relevant works are cited in this manuscript);
    • submission of the manuscript for publication was completed in accordance with the publishing regulations pertaining to place of work;
    • experiments performed comply with current laws and written consent of the Scientific Ethics Committee / National Animal Care Authority (as is mentioned in the manuscript submitted);
    • grant holders confirm that they have been informed of the submitted manuscript and they agree to its publication.

    Authors retain copyright and grant ERIES Journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the published work with an acknowledgement of its initial publication in ERIES Journal. Moreover, authors are able to post the published work in an institutional repository with an acknowledgement of its initial publication in ERIES Journal. In addition, authors are permitted and encouraged to post the published work online (e.g. institutional repositories or on their website) as it can lead to productive exchanges, as well as earlier and greater citation of published work.