Impact of Order of Data in Word Problems on Division of a Whole into Unequal Parts

  • Jarmila Novotná Univerzita Karlova v Praze, Pedagogická fakulta M.D. Rettigové 4 116 39 Praha 1
  • Martin Chvál Univerzita Karlova, Pedagogická fakulta
Keywords: Context, “if-clause” formulation, mathematics, order of numerical data, word problems

Abstract

The paper investigates how the order of numerical data in word problems on division of a whole into unequal parts affects achievement and reasoning of 14-16-year old pupils. The variable was altered in two word problems, in one of which also the context was changed (psychological variable) and in the latter “if-clause” is or is not used (linguistic variable). 182 pupils were involved in the experiment. The solutions were analysed quantitatively using Item Response Theory as well as qualitatively. The data suggest that pupils’ success is affected by the order of numerical data in the statement in an unfamiliar context. The presence of “if-clause” in the statement was studied in a two-level problem. The order of numerical data played its role in case of formulations without “if”. The results of the experiment are of interest for mathematics education as well as for construction of tests. The paper is an extended version of the paper by Novotná (2018).  

Author Biography

Martin Chvál, Univerzita Karlova, Pedagogická fakulta

References


  • Daroczy, G., Wolska, M., Meurers, W. D. and Nuerk, H. C. (2015) ‘Word problems: a review of linguistic and numerical factors contributing to their difficulty’, Frontiers in Psychology, vol. 6, no. 348, pp. 22–34. http://dx.doi.org/10.3389/fpsyg.2015.00348

  • Downton. A. and Sullivan, P. (2017) ‘Posing complex problems requiring multiplicative thinking prompts students to use sophisticated strategies and build mathematical connections’, Educational Studies in Mathematics, vol. 95, no. 3, pp. 303-328. http://doi.org/10.1007/s10649-017-9751-x

  • Gelfman, E. and Kholodnaya, M. (1999) ‘The role of ways of information coding in student’s intellectual development’, Proceedings of the First Conference on the European Society for Research in Mathematics Education, vol. 2, pp. 38-48, [Online], Available:  http://www.mathematik.uni-dortmund.de/~erme/doc/cerme1/cerme1_proceedings_part2.pdf. [15 Nov 2018].

  • Hembree, R. (1992) ‘Experiments and relational studies in problem solving: A meta-analysis’, Journal for Research in Mathematics Education, vol. 23, no. 3, pp. 242-273. http://dx.doi.org/10.2307/749120

  • Lord, F. M. (1980) Applications of item response theory to practical testing problems, Hillsdale, N.J.: Lawrence Erlbaum Associates.

  • Mason, J. (2018) ‘Structuring structural awareness: A commentary’, Building the foundation: Whole Numbers in the Primary Grades, Cham: Springer International Publishing, pp. 323-340.

  • Nesher, P., Hershkovitz, S. and Novotná, J. (2003) ‘Situation model, text base and what else? Factors affecting problem solving’, Educational Studies in Mathematics, vol. 52, no. 2, pp. 151-176. https://doi.org/10.1023/A:1024028430965

  • Novotná, J. (2010) Study of solving word problems in teaching of mathematics. From atomic analysis to the analysis of situations, Saarbrücken: LAP LAMBERT Academic Publishing.

  • Novotná, J. (2018) ‘Impact of order of data in word problems on division of a whole into unequal parts’, ERIE 2018, Prague: CULS, pp. 257-264.

  • Novotná, J., Eisenmann, P., Přibyl, J., Ondrušová, J. and Břehovský, J. (2013) ‘Heuristic strategies in problem solving in school mathematics’, ERIE 2013, Prague: CULS, pp. 461-468.

  • Novotná, J. and Vondrová, N. (2017) ‘Pupils’ strategies for missing value proportional problems’, Proceedings of ERIE 2017, Prague: CULS, pp. 279-286.

  • Přibyl, J. and Eisenmann, P. (2014) ‘Properties of problem solving strategies’, Proceedings of ERIE 2014, Prague: CULS, pp. 623-630.

  • Riley, M. S. and J. G. Greeno (1988) ‘Developmental Analysis of Understanding Language about Quantities and of Solving Problems’, Cognition and Instruction, vol. 5, no. 1, pp. 49-101. http://dx.doi.org/10.1207/s1532690xci0501_2

  • Searle, B.W., Lorton, P. Jr. and Suppes, P. (1974) ‘Structural variables affecting CAI performance on arithmetic word problems of disadvantaged and deaf students’, Educational Studies in Mathematics, vol. 5, pp. 371-384, http://dx.doi.org/10.1007/BF01424555

  • Soneira, C., González-Calero, J.A. and Arnau D. (2018) ‘An assessment of the sources of the reversal error through classic and new variables’, Educational Studies in Mathematics, vol. 99, no. 1, pp. 43-56. https://doi.org/10.1007/s10649-018-9828-1

  • Van der Linden, W.J. and Hambleton, R.K. (1997) Handbook of Modern Item Response Theory, New York: Springer, http://dx.doi.org/10.1007/978-1-4757-2691-6

  • Vicente, S., Orrantia, J. and Verschaffel, L. (2008) ‘Influence of situational and mathematical information on situationally difficult word problems’, Studia Psychologica, vol. 50, no. 4, pp. 337-356.

  • Vondrová, N., Novotná, J. and Havlíčková, R. (2019) ‘The influence of solving and situational information on pupils’ achievement in additive word problems with several states and transformations’, ZDM Mathematics Education, pp. 1-15, https://doi.org/10.1007/s11858-018-0991-8

  • Wijaya, A., van den Heuvel-Panhuizen, M. And Doorman, M. (2015) ‘Opportunity-to-learn context-based tasks provided by mathematics textbooks’, Educational Studies in Mathematics, vol. 89, no. 1, pp. 41-65. https://doi.org/10.1007/s10649-015-9595-1

  • Zohar, A. and Gershikov, A. (2008) ‘Gender and Performance in Mathematical Tasks: Does the Context Make a Difference?’, International Journal of Science and Mathematics Education, vol. 6, no. 4, pp. 677-693, http://dx.doi.org/10.1007/s10763-007-9086-7

Published
2019-01-09
How to Cite
Novotná, J. and Chvál, M. (2019) ’Impact of Order of Data in Word Problems on Division of a Whole into Unequal Parts’, Journal on Efficiency and Responsibility in Education and Science, vol. 11, no. 4, pp. 85-92. https://doi.org/10.7160/eriesj.2018.110403
Section
Research Paper