Ir al contenido

Documat


Mathematical problems in and out of school: The impact of considering mathematical operations and reality on real-life solutions

  • Autores: Andrea Wisenöcker, Sarah Binder, Manuel Holzer, Anna Valentic, Celina Wally, Cornelia S. Große
  • Localización: European Journal of Psychology of Education, ISSN-e 1878-5174, ISSN 0256-2928, Vol. 39, Nº 2, 2024, págs. 767-783
  • Idioma: inglés
  • DOI: 10.1007/s10212-023-00718-0
  • Enlaces
  • Resumen
    • In this study, effects of asking participants to make different types of considerations when solving a realistic word problem were investigated. A two-factorial experiment with the factors “addressing realistic considerations” (with vs. without) and “addressing mathematical operations” (with vs. without) was conducted. It was assumed that reality-based considerations would lead to reality-based problem-solving strategies, thus fostering real-life solutions, while considering mathematical operations would lead to problem-solving strategies usually promoted in school, which were expected to impair realistic solutions. Analyses are based on N = 165 participants. The results showed that being asked to make reality-based considerations did not significantly affect realistic solutions (F(1, 161) = 2.43, p = 0.121, ηp2 = 0.015), while being asked to consider appropriate mathematical operations significantly impaired realistic solutions (F(1, 161) = 8.54, p = 0.004, ηp2 = 0.050). These findings suggest that inducing typical school problem-solving strategies may be detrimental when it comes to solving mathematical problems in a realistic way.

  • Referencias bibliográficas
    • Blum, W. (2011). Can modelling be taught and learnt? Some answers from empirical research. In G. Kaiser, W. Blum, R. Borromeo Ferri, &...
    • Blum, W., & Borromeo Ferri, R. (2009). Mathematical modelling: Can it be taught and learnt? Journal of Mathematical Modelling and Application,...
    • Bonotto, C. (2001). How to connect school mathematics with students’ out-of-school knowledge. ZDM Mathematics Education, 33(3), 75–84.
    • Carpenter, T. P., Lindquist, M. M., Matthews, W., & Silver, E. A. (1983). Results of the third NAEP mathematics assessment: Secondary...
    • Cevikbas, M., Kaiser, G., & Schukajlow, S. (2022). A systematic literature review of the current discussion on mathematical modelling...
    • Cooper, B., & Harries, T. (2002). Children’s responses to contrasting “realistic” mathematics problems: Just how realistic are children...
    • Depaepe, F., De Corte, E., & Verschaffel, L. (2009). Analysis of the realistic nature of word problems in upper elementary mathematics...
    • Dewolf, T., Van Dooren, W., EvCimen, E., & Verschaffel, L. (2014). The impact of illustrations and warnings on solving mathematical word...
    • Dewolf, T., Van Dooren, W., Hermens, F., & Verschaffel, L. (2015). Do students attend to representational illustrations of non-standard...
    • Dewolf, T., Van Dooren, W., & Verschaffel, L. (2017). Can visual aids in representational illustrations help pupils to solve mathematical...
    • Faul, F., Erdfelder, E., Buchner, A., & Lang, A.-G. (2009). Statistical power analyses using G*Power 3.1: Tests for correlation and regression...
    • Fitzpatrick, C. L., Hallett, D., Morrissey, K. R., Yıldız, N. R., Wynes, R., & Ayesu, F. (2019). Response sentences, examples, and authenticity...
    • Gravemeijer, K. (1997). Solving word problems: A case of modelling? Learning and Instruction, 7(4), 389–397.
    • Greer, B. (1997). Modelling reality in mathematics classrooms: The case of word problems. Learning and Instruction, 7(4), 293–307.
    • Große, C. S. (2014). Learning to solve story problems - Supporting transitions between reality and mathematics. European Journal of Psychology...
    • Große, C. S. (2015). Fostering modeling competencies: Benefits of worked examples, problems to be solved, and fading procedures. European...
    • Große, C. S. (2017). Effects of multiple choice options in mathematics learning. European Journal of Science and Mathematics Education, 5(2),...
    • Große, C. S. (2018). “Copying allowed - but be careful, errors included!” – Effects of copying correct and incorrect solutions on learning...
    • Große, C. S. (2022). Multiple solutions in dyads or alone–Fostering the acquisition of modeling competencies in mathematics. Learning and...
    • Hagena, M., Leiss, D., & Schwippert, K. (2017). Using reading strategy training to foster students’ mathematical modelling competencies:...
    • Jiménez, L., & Verschaffel, L. (2014). El desarrollo de las soluciones infantiles en la resolución de problemas aritméticos no estándar...
    • Kinda, S. (2012). Generating multiple answers for a word problem with insufficient information. Instructional Science, 40(6), 1021–1031.
    • Krawitz, J., Chang, Y. P., Yang, K. L., & Schukajlow, S. (2022). The role of reading comprehension in mathematical modelling: Improving...
    • Masingila, J. O., Muthwii, S. M., & Kimani, P. M. (2011). Understanding students’ out-of-school mathematics and science practice. International...
    • Mason, L., & Scrivani, L. (2004). Enhancing students’ mathematical beliefs: An intervention study. Learning and Instruction, 14(2), 153–176.
    • Mevarech, Z. R., Terkieltaub, S., Vinberger, T., & Nevet, V. (2010). The effects of metacognitive instruction on third and sixth graders...
    • Niss, M., Blum, W., & Galbraith, P. (2007). Introduction. In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and...
    • Palm, T. (2008). Impact of authenticity on sense making in word problem solving. Educational Studies in Mathematics, 67(1), 37–58.
    • Reusser, K., & Stebler, R. (1997). Every word problem has a solution – The social rationality of mathematical modeling in schools. Learning...
    • Schukajlow, S., & Blum, W. (2011). Zum Einfluss der Klassengröße auf Modellierungskompetenz, Selbst- und Unterrichtswahrnehmungen von...
    • Schukajlow, S., Krug, A., & Rakoczy, K. (2015). Effects of prompting multiple solutions for modelling problems on students’ performance....
    • Schukajlow, S., Kaiser, G., & Stillman, G. (2018). Empirical research on teaching and learning of mathematical modelling: A survey on...
    • Van Dooren, W., Lem, S., De Wortelaer, H., & Verschaffel, L. (2019). Improving realistic word problem solving by using humor. The Journal...
    • Verschaffel, L., De Corte, E., & Lasure, S. (1994). Realistic considerations in mathematical modeling of school arithmetic word problems....
    • Verschaffel, L., De Corte, E., & Borghart, I. (1997). Pre-service teachers’ conceptions and beliefs about the role of real-world knowledge...
    • Verschaffel, L., De Corte, E., & Vierstraete, H. (1999). Upper elementary school pupils’ difficulties in modeling and solving nonstandard...
    • Verschaffel, L., Greer, B., & De Corte, E. (2000). Making sense of word problems. Swets & Zeitlinger.
    • Verschaffel, L., Van Dooren, W., Greer, B., & Mukhopadhyay, S. (2010). Reconceptualising word problems as exercises in mathematical modelling....
    • Verschaffel, L., Schukajlow, S., Star, J., & Van Dooren, W. (2020). Word problems in mathematics education: A survey. ZDM Mathematics...
    • Weyns, A., Van Dooren, W., Dewolf, T., & Verschaffel, L. (2017). The effect of emphasising the realistic modelling complexity in the text...
    • Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics...
    • Yerushalmy, M. (1997). Mathematizing verbal descriptions of situations: A language to support modeling. Cognition and Instruction, 15, 207–264.
    • Zöttl, L., Ufer, S., & Reiss, K. (2010). Modelling with heuristic worked examples in the KOMMA learning environment. Journal für Mathematik-Didaktik,...

Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno