Student Misconceptions in Elementary School When Solving Problems on Mathematical-Literacy-Based Question Types

Firstlyta Bulan Aulya Ahmad; Alifatul Hidayah; Zaenal Abidin

doi:10.26740/jrpd.v11n3.p373-388

Authors

Firstlyta Bulan Aulya Ahmad State University of Surabaya
Alifatul Hidayah State University of Surabaya
Zaenal Abidin State University of Surabaya

DOI:

https://doi.org/10.26740/jrpd.v11n3.p373-388

Keywords:

Mathematical Literacy, Misconception, Plane Figures, Fractions, Problem-Based Learning

Abstract

Existing studies have examined context-based mathematical errors and topic-specific misconceptions, while less attention has been given to their distribution across mathematical literacy processes and their persistence over time. This study examines misconceptions among 15 Grade 5 students when solving mathematical literacy problems involving plane figures and fractions. A descriptive qualitative design was employed using two written tests administered approximately one month apart and probing questions during problem solving. Students’ responses were classified according to the formulating, employing, and interpreting processes. Eight types of misconceptions were identified. Half of the identified errors occurred in the employing process, while the formulating and interpreting processes each accounted for one quarter. In the second test, approximately half of the students answered correctly, while the remaining students displayed misconceptions consistent with those identified previously. The findings highlight the need for explicit instruction on shape properties, formula selection, keyword interpretation, and result verification. A structured, context-first learning sequence incorporating Problem-Based Learning warrants further empirical investigation.

References

Blum, W., & Niss, M. (1991). Applied mathematical problem solving, modelling, applications, and links to other subjects: State, trends and issues in mathematics instruction. Educational Studies in Mathematics, 22(1), 37–68. https://doi.org/10.1007/BF00302716

Braithwaite, D. W., Leib, E. R., Siegler, R. S., & McMullen, J. (2019). Individual differences in fraction arithmetic learning. Cognitive Psychology, 112, 81–98. https://doi.org/10.1016/j.cogpsych.2019.04.002

Dochy, F., Segers, M., Van den Bossche, P., & Gijbels, D. (2003). Effects of problem-based learning: A meta-analysis. Learning and Instruction, 13(5), 533–568. https://doi.org/10.1016/S0959-4752(02)00025-7

Fox, M. C., Ericsson, K. A., & Best, R. (2011). Do procedures for verbal reporting of thinking have to be reactive? A meta-analysis and recommendations for best reporting methods. Psychological Bulletin, 137(2), 316–344. https://doi.org/10.1037/a0021663

Fujita, T. (2012). Learners’ level of understanding of the inclusion relations of quadrilaterals and prototype phenomenon. The Journal of Mathematical Behavior, 31(1), 60–72. https://doi.org/10.1016/j.jmathb.2011.08.003

Hegarty, M., Mayer, R. E., & Monk, C. A. (1995). Comprehension of arithmetic word problems: A comparison of successful and unsuccessful problem solvers. Journal of Educational Psychology, 87(1), 18–32. https://doi.org/10.1037/0022-0663.87.1.18

Hmelo-Silver, C. E. (2004). Problem-based learning: What and how do students learn? Educational Psychology Review, 16(3), 235–266. https://doi.org/10.1023/B:EDPR.0000034022.16470.f3

McNeil, N. M., & Alibali, M. W. (2005). Why won’t you change your mind? Knowledge of operational patterns hinders learning and performance on equations. Child Development, 76(4), 883–899. https://doi.org/10.1111/j.1467-8624.2005.00884.x

Ni, Y., & Zhou, Y.-D. (2005). Teaching and learning fraction and rational numbers: The origins and implications of whole number bias. Educational Psychologist, 40(1), 27–52. https://doi.org/10.1207/s15326985ep4001_3

Rittle-Johnson, B., Siegler, R. S., & Alibali, M. W. (2001). Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of Educational Psychology, 93(2), 346–362. https://doi.org/10.1037/0022-0663.93.2.346

Sandelowski, M. (2000). Whatever happened to qualitative description? Research in Nursing & Health, 23(4), 334–340. https://doi.org/10.1002/1098-240X(200008)23:4<334::AID-NUR9>3.0.CO;2-G

Siegler, R. S., & Pyke, A. A. (2013). Developmental and individual differences in understanding of fractions. Developmental Psychology, 49(10), 1994–2004. https://doi.org/10.1037/a0031200

Smith, J. P., III, diSessa, A. A., & Roschelle, J. (1994). Misconceptions reconceived: A constructivist analysis of knowledge in transition. The Journal of the Learning Sciences, 3(2), 115–163. https://doi.org/10.1207/s15327809jls0302_1

Stacey, K. (2011). The PISA view of mathematical literacy in Indonesia. Journal on Mathematics Education, 2(2), 95–126. https://doi.org/10.22342/jme.2.2.746.95-126

Tan Şişman, G., & Aksu, M. (2016). A study on sixth grade students’ misconceptions and errors in spatial measurement: Length, area, and volume. International Journal of Science and Mathematics Education, 14(7), 1293–1319. https://doi.org/10.1007/s10763-015-9642-5

Veenman, M. V. J., Van Hout-Wolters, B. H. A. M., & Afflerbach, P. (2006). Metacognition and learning: Conceptual and methodological considerations. Metacognition and Learning, 1(1), 3–14. https://doi.org/10.1007/s11409-006-6893-0

Verschaffel, L., Schukajlow, S., Star, J., & Van Dooren, W. (2020). Word problems in mathematics education: A survey. ZDM Mathematics Education, 52(1), 1–16. https://doi.org/10.1007/s11858-020-01130-4

Vilenius-Tuohimaa, P. M., Aunola, K., & Nurmi, J.-E. (2008). The association between mathematical word problems and reading comprehension. Educational Psychology, 28(4), 409–426. https://doi.org/10.1080/01443410701708228

Vosniadou, S., & Verschaffel, L. (2004). Extending the conceptual change approach to mathematics learning and teaching. Learning and Instruction, 14(5), 445–451. https://doi.org/10.1016/j.learninstruc.2004.06.014

Wijaya, A., van den Heuvel-Panhuizen, M., Doorman, M., & Robitzsch, A. (2014). Difficulties in solving context-based PISA mathematics tasks: An analysis of students’ errors. The Mathematics Enthusiast, 11(3), 555–584. https://doi.org/10.54870/1551-3440.1317

Wijaya, T. T., Hidayat, W., Hermita, N., Alim, J. A., & Talib, C. A. (2024). Exploring contributing factors to PISA 2022 mathematics achievement: Insights from Indonesian teachers. Infinity Journal, 13(1), 139–156. https://doi.org/10.22460/infinity.v13i1.p139-156