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Students’ performance on missing-value word problems: a cross-national developmental study

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Abstract

This study investigates Spanish and Chinese students’ performance on both addition problems and proportion problems considering a cross-national perspective. The effect of number structure and nature of quantities was also considered. Nine hundred twenty-five 4th to 8th graders (453 Chinese, 472 Spanish) took a test which is composed of addition and proportion problems in a missing-value format. The findings showed that Chinese students held a different developmental model of the additive and proportional reasoning from Spanish students. Moreover, number structure and nature of quantities had a different impact in each country. These results indicated that students’ additive and proportional reasoning may vary from country to country due to the different cultures and educational environments. Further studies with a larger-scale sample will be needed to confirm such cross-national effects.

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Notes

  1. Details of these pairwise comparisons (including percentages and p values) for additive methods were presented in Appendix 1

  2. Details of these pairwise comparisons (including percentages and p values) for proportional methods were presented in Appendix 2

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Author information

Author notes

    Authors and Affiliations

    1. School of Psychology, Beijing Normal University, Room 1432, Haidian District, Beijing, China, 100875

      Ronghuan Jiang

    2. College of Psychology and Sociology, Shenzhen University, Room B431, Normal College, Nanshan District, Shenzhen, Guangdong, China, 518060

      Xiaodong Li

    3. Dpto. Innovación y Formación Didáctica, Universidad de Alicante, Carretera San Vicente del Raspeig s/n, 03690, Alicante, Spain

      Ceneida Fernández

    4. College of Psychology and Sociology, Shenzhen University, No. 3688 Nanhai Ave., Nanshan District, Shenzhen, Guangdong, China, 518060

      Xinchen Fu

    Authors
    1. Ronghuan Jiang
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    2. Xiaodong Li
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    3. Ceneida Fernández
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    4. Xinchen Fu
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    Corresponding author

    Correspondence to Xiaodong Li.

    Additional information

    Ronghuan Jiang. School of Psychology, Beijing Normal University, Room 1432, School of Psychology, Beijing Normal University, Haidian District, Beijing, China, 100875, Web site of institution: http://psych.bnu.edu.cn/, Email: jrh_psy@163.com

    Current themes of research:

    Mathematics learning and cognition. Inhibitory control and mathematics problem solving.

    Most relevant publications in the field of Psychology of Education:

    Li, X., Jiang, R., Qian, Y. (2014). 5∼8 graders’ overuse of proportionality on missing-value problems (Article written in Chinese). Journal of Mathematics Education [数学教育学报], 23(06), 73–77.

    Xiaodong Li. College of Psychology and Sociology, Shenzhen University, Room B431, Normal College, Shenzhen University, Nanshan District, Shenzhen, Guangdong, China, 518060, Web site of institution: http://psso.szu.edu.cn/, Email: lxd_psy@163.com

    Current themes of research:

    Mathematics thinking and learning. Inhibitory control and problem solving. Cognitive development of mathematics.

    Most relevant publications in the field of Psychology of Education:

    Li, X., Jiang, R., Qian, Y. (2014). 5∼8 graders’ overuse of proportionality on missing-value problems (Article written in Chinese). Journal of Mathematics Education [数学教育学报], 23(06), 73–77.

    Li, X., Fu, X, Lu, C. (2015). The effect of situation on college students’ word problem solving: Evidence from eye movement (Article written in Chinese). Journal of Soochow University(Educational Science Edition)[苏州大学学报(教育科学版)], 3(01), 96–104.

    Li, X., Xu, W., Li, N. (2012). The negative priming effect in Piaget-like tasks in the “Infra-logic” domain (Article written in Chinese). Journal of Psychological Science, 35(2), 358–363.

    Li, X. (2005). Academic delay of gratification of middle school students (Article written in Chinese). Acta Psychologica Sinica, 37(4), 491–496.

    Li, X., Zhang, X., Wo, J. (2002). Differences in solving compare problems: A comparison of mathematically gifted and mathematically disabled third graders of an elementary school (Article written in Chinese). Acta Psychologica Sinica, 34(4), 400–406.

    Ceneida Fernández. Dpto. Innovación y Formación Didáctica, Universidad de Alicante, Carretera San Vicente del Raspeig s/n, 03690, San Vicente del Raspeig (Alicante), Spain, Web site of institution: http://www.ua.es/, Email: ceneida.fernandez@ua.es

    Current themes of research:

    Mathematics education. Teacher training.

    Most relevant publications in the field of Psychology of Education:

    Fernández, C.; De Bock, D., Verschaffel, L., Van Dooren, W. (2014). Do students confuse dimensionality and “directionality”? Journal of Mathematical Behavior, doi:10.1016/j.jmathb.2014.07.001

    Sánchez-Matamoros, G., Fernández, C., Llinares, S. (2014). Developing pre-service teachers’ noticing of students’ understanding of the derivative concept. International Journal of Science and Mathematics Education, DOI: 10.1007/s10763-014-9544-y

    Fernández, C.; Llinares, S.; Van Dooren, W.; De Bock, D. & Verschaffel, L. (2012). The development of students’ use of additive and proportional methods along primary and secondary school. European Journal of Psychology of Education, 27, 421–438

    Fernandez, C. & Llinares, S. (2011). De la estructura aditiva a la multiplicativa: efecto de dos variables en el desarrollo del razonamiento proporcional. INFANCIA & APRENDIZAJE, 34(1), 67–80.

    Fernández, C.; Llinares, S.; Van Dooren, W.; De Bock, D., Verschaffel (2011). Effect on number structure and nature of quantities on secondary school students’ proportional reasoning. STUDIA PSYCHOLOGICA, 53(1), 69–81

    Xinchen Fu. College of Psychology and Sociology, Shenzhen University, No. 3688 Nanhai Ave., Nanshan District, Shenzhen, Guangdong, China, 518060, Web site of institution: http://psso.szu.edu.cn/, Email: fxc_psy@163.com

    Current themes of research:

    Mathematics cognition. Inhibitory control and mathematics bias.

    Most relevant publications in the field of Psychology of Education:

    Li, X., Fu, X, Lu, C. (2015). The effect of situation on college students’ word problem solving: Evidence from eye movement (Article written in Chinese). Journal of Soochow University(Educational Science Edition)[苏州大学学报(教育科学版)], 3(01), 96–104.

    Ronghuan Jiang and Xiaodong Li contributed equally to this work.

    Appendices

    Appendix 1

    Table 6 Pairwise comparisons (p values). Percentages of the use of additive methods on additive and proportional problems in China and Spain
    Full size table

    Appendix 2

    Table 7 Pairwise comparisons (p values). Percentages of the use of proportional methods on additive and proportional problems in China and Spain
    Full size table

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    Jiang, R., Li, X., Fernández, C. et al. Students’ performance on missing-value word problems: a cross-national developmental study. Eur J Psychol Educ 32, 551–570 (2017). https://doi.org/10.1007/s10212-016-0322-9

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