Research article | Open Access
International Journal of Progressive Education 2022, Vol. 18(5) 269-278
An Investigation of Students' Performances in Solving Different Types of Problems
pp. 269 - 278 | DOI: https://doi.org/10.29329/ijpe.2022.467.16
Publish Date: October 01, 2022 | Single/Total View: 106/466 | Single/Total Download: 144/678
Abstract
The purpose of this study was to analyze the performances of students in solving problems presented in different forms including equations, verbal equations, stories, and stories supported by diagrams in problem-solving. A descriptive survey model was employed in the study. The study group consisted of 14 fourth-grade students. Data were collected from the students by using four different types of worksheets (equation, verbal equation, story, and story + diagram). Each worksheet consisted of 10 similar problems that require the same mathematical operations but differ in presentation. To prevent the similarity in the problems by the students, the worksheets were applied to the students face-to-face by the classroom teachers during the course hours, at two-week intervals. The obtained data were analyzed through descriptive statistics. According to the findings of the study, the students solved the equation problems more accurately than the verbal and story problems. Furthermore, it was determined that students solved diagram-supported story problems more accurately than the other problem types.
Keywords: Problem-Solving, Problem Type, Equation Problems, Story Problems, Diagram Supported Problems
APA 7th edition
Altiner, E.C. (2022). An Investigation of Students' Performances in Solving Different Types of Problems. International Journal of Progressive Education, 18(5), 269-278. https://doi.org/10.29329/ijpe.2022.467.16
Harvard
Altiner, E. (2022). An Investigation of Students' Performances in Solving Different Types of Problems. International Journal of Progressive Education, 18(5), pp. 269-278.
Chicago 16th edition
Altiner, Emel Ci̇li̇ngi̇r (2022). "An Investigation of Students' Performances in Solving Different Types of Problems". International Journal of Progressive Education 18 (5):269-278. https://doi.org/10.29329/ijpe.2022.467.16
- Ainsworth, S., & Th Loizou, A. (2003). The effects of self-explaining when learning with text or diagrams. Cognitive Science, 27(4), 669–681. https://doi.org/10.1016/S0364-0213(03)00033-8 [Google Scholar] [Crossref]
- Akay, A. (2004). İlköğretim 2. sınıf öğrencilerinin okuduğunu anlama becerilerinin matematik problemlerini çözme başarısına etkisi. (Unpublished Doctoral Thesis). Marmara University, Istanbul, Turkey. [Google Scholar]
- Berends, I. E., & van Lieshout, E. C. (2009). The effect of illustrations in arithmetic problem-solving: Effects of increased cognitive load. Learning and Instruction, 19(4), 345-353. https://doi.org/10.1016/j.learninstruc.2008.06.012 [Google Scholar] [Crossref]
- Boonen, A. J., van Wesel, F., Jolles, J., & van der Schoot, M. (2014). The role of visual representation type, spatial ability, and reading comprehension in word problem solving: An item-level analysis in elementary school children. International Journal of Educational Research, 68, 15-26. https://doi.org/10.1016/j.ijer.2014.08.001 [Google Scholar] [Crossref]
- Booth, J. L., & Koedinger, K. R. (2012). Are diagrams always helpful tools? Developmental and individual differences in the effect of presentation format on student problem solving. British Journal of Educational Psychology, 82(3), 492-511. https://doi.org/10.1111/j.2044-8279.2011.02041.x [Google Scholar] [Crossref]
- Büyüköztürk, Ş., Kılıç Çakmak, E., Akgün, Ö. E., Karadeniz, Ş., & Demirel, F. (2011). Araştırma yöntemleri [Research methods]. Ankara: Pegem Akademi. [Google Scholar]
- Carpenter, T. P., & Moser, J. M. (1984). The acquisition of addition and subtraction concepts in grades one through three. Journal for Research in Mathematics Education, 15 (3), 179–202. https://doi.org/10.5951/jresematheduc.15.3.0179 [Google Scholar] [Crossref]
- Cohen, L., Manion, L. and Morrison, (2000). Research methods in education (5th ed.). London: Routledge Falmer. [Google Scholar]
- Cooper, J. L., Sidney, P. G., & Alibali, M. W. (2018). Who benefits from diagrams and illustrations in math problems? Ability and attitudes matter. Applied Cognitive Psychology, 32(1), 24–38. https://doi.org/10.1002/acp.3371 [Google Scholar] [Crossref]
- Çilingir-Altıner, E. (2020). The reflection of the visual chunking and colouring applications on elementary school students’ geometry success. Kara Ö. T., Ulum Ö. G. (Ed.). In Studies in subject specific education (pp. 103-118), Akademisyen Yayınevi, Ankara. [Google Scholar]
- Davenport, J., Yaron, D., Klahr, D., & Koedinger, K. (2008).When do diagrams enhance learning? A framework for designing relevant representations. Proceedings of the 8th International Conference on the Learning Sciences (pp. 191–198). Mahwah, NJ: Lawrence Erlbaum Associates, Inc. [Google Scholar]
- De Corte, E., & Verschaffel, L. (1981). Children’s solution processing in elementary arithmetic problems: Analysis and improvement. Journal of Educational Psychology, 73 (6), 765– 779. https://doi.org/10.1037/0022-0663.73.6.765 [Google Scholar] [Crossref]
- Dewolf, T., Van Dooren, W., Ev Cimen, E., & Verschaffel, L. (2014). The impact of illustrations and warnings on solving mathematical word problems realistically. The Journal of Experimental Education, 82(1), 103-120. https://doi.org/10.1080/00220973.2012.745468 [Google Scholar] [Crossref]
- Dufour-Janvier, B., Bednarz, N., & Belanger, M. (1987). Pedagogical considerations concerning the problem of representation. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics. Hillsdale, NJ: LEA [Google Scholar]
- Foong, P. Y., & Koay, P. L. (1997). School word problems and stereotyped thinking. Teaching and Learning, 18(1),73-82 Retrieved from https://repository.nie.edu.sg/bitstream/10497/392/1/TL-18-1-73.pdf [Google Scholar]
- Hegarty, M., & Kozhevnikov, M. (1999). Types of visual–spatial representations and mathematical problem solving. Journal of educational psychology, 91(4), 684 –689. https://doi.org/10.1037/0022-0663.91.4.684 [Google Scholar] [Crossref]
- Hembree, R. (1992). Experiments and relational studies in problem solving: A meta-analysis. Journal for Research in Mathematics Education, 23(3), 242-273. https://doi.org/10.5951/jresematheduc.23.3.0242 [Google Scholar] [Crossref]
- Koedinger, K. R., & Nathan, M. J. (2004). The real story behind story problems: Effects of representations on quantitative reasoning. The Journal of the Learning Sciences, 13 (2), 129– 164. https://doi.org/10.1207/s15327809jls1302_1 [Google Scholar] [Crossref]
- Koedinger, K. R., Alibali, M. W., & Nathan, M. J. (2008). Trade‐offs between grounded and abstract representations: Evidence from algebra problem solving. Cognitive Science, 32(2), 366-397. https://doi.org/10.1080/03640210701863933 [Google Scholar] [Crossref]
- Lee, K., Ng, E., & Ng, S. F. (2009). The contributions of working memory and executive functioning to problem representation and solution generation in algebraic word problems. Journal of Educational Psychology, 101(2), 373–387. https://doi.org/10.1037/a0013843 [Google Scholar] [Crossref]
- Lester, F. K. (1994). Musings about mathematical problem-solving research: 1970-1994. Journal for research in mathematics education, 25(6), 660-675. https://doi.org/10.5951/jresematheduc.25.6.0660 [Google Scholar] [Crossref]
- Logan, T., & Ho, S. Y. (2013). The Classic Word Problem: The Influence of Direct Teaching. V. Steinle, L. Ball, C. Bardini (Eds.), Mathematics Education: Yesterday, Today and Tomorrow (Proceedings of the 36th Annual Conference of the Mathematics Education Research Group of Australasia (2013), pp. 743-746 [Google Scholar]
- Lowrie, T. (2020). The utility of diagrams in elementary problem solving. Cognitive Development, 55, 100921, 1-12. https://doi.org/10.1016/j.cogdev.2020.100921 [Google Scholar] [Crossref]
- Magner, U. I., Schwonke, R., Aleven, V., Popescu, O., & Renkl, A. (2014). Triggering situational interest by decorative illustrations both fosters and hinders learning in computer-based learning environments. Learning and instruction, 29, 141-152. https://doi.org/10.1016/j.learninstruc.2012.07.002 [Google Scholar] [Crossref]
- Mayer, R. (1993). Illustrations that instruct. In R. Glaser (Ed.), Advances in instructional psychology (Vol. 4, pp. 253–284). Hillsdale, NJ: LEA. [Google Scholar]
- Millî Eğitim Bakanlığı [Ministry of National Education]. (2018). Milli Eğitim Bakanlığı matematik dersi öğretim programı [Ministry of National Education mathematics course curriculum], Ankara. Retrieved from http://mufredat. meb. gov. tr/Dosyalar/201813017165445-MATEMAT% C4% B0K, 20, C3. [Google Scholar]
- Özkubat, U., Karabulut, A., & Akçayır, İ. (2020). Şemalarla matematik problemi çözme: Öğrenme güçlüğü olan öğrencilerle yürütülen şema temelli öğretim araştırmalarının incelenmesi. Ondokuz Mayıs Üniversitesi Eğitim Fakültesi Dergisi, 39(2), 327-342. DOI: 10.7822/omuefd.774137 [Google Scholar]
- Pape, S. J. (2004). Middle school children's problem-solving behavior: A cognitive analysis from a reading comprehension perspective. Journal for Research in Mathematics Education, 35(3), 187-219. https://doi.org/10.2307/30034912 [Google Scholar] [Crossref]
- Sloutsky, V. M., Kaminski, J. A., & Heckler, A. F. (2005). The advantage of simple symbols for learning and transfer. Psychonomic bulletin & review, 12(3), 508-513. https://doi.org/10.3758/BF03193796 [Google Scholar] [Crossref]
- Suwarsono, S. (1982). Visual imagery in the mathematical thinking of seventh grade students. Unpublished doctoral dissertation, Monash University, Melbourne, Australia [Google Scholar]
