An Analysis of Students’ Error in Learning Mathematical Problem Solving: The Perspective of David Kolb’s Theory

Abstract

Schoenfeld and Sloane argued that the main task of mathematics education is to explain students’ thought processes in order to improve the quality of mathematics learning. Many students make errors in answering maths tests. It turns out that various types of errors depend on students’ learning styles. The focus of this research was to analyze students’ errors in solving mathematics problems based on differences in students’ learning styles according to David Kolb’s theory of experiential learning. The study was conducted at Vocational Middle School in Cirebon-Indonesia. The research used a qualitative research case study approach. The instrument used in this study was the Kolb Learning Style Inventory (KLSI version 3.1), and math tests. For data analysis, this study used triangulation techniques. The four categories of learning orientations were found among 24 students who participated in this study, namely converging, accommodating, assimilating, and diverging. The difference with other studies is that this study focuses on discussing student errors based on learning styles. Each type of learning style was associated with its unique errors. Errors made by divergers were procedural errors and misunderstandings; the assimilators’ types of error were procedural and conceptual errors; the convergers’ error type was a procedural error; the type of error made by accommodators was a theoretical error. Conceptual errors were caused by a misunderstanding of existing concepts, leading the students to make errors in the answer to math tests. Strategy errors can be encountered by students when they were stuck in the answer to a math test. A procedural error occurred when students used a non-systematic method in completing the test.

Keywords

• Students’ error
• Learning styles
• Problem-solving
• Mathematics

Kaynakça

1. Archer, L., DeWitt, J., & Dillon, J. (2014). ‘It didn’t really change my opinion’: exploring what works, what doesn’t and why in a school science, technology, engineering and mathematics careers intervention. Research in Science & Technological Education, 32(1), 35-55. https://doi.org/10.1080/02635143.2013.865601
2. Bloom, B. S. (1956). Taxonomy of educational objectives. McKay.
3. Cawley, J., Parmar, R., Foley, T. E., Salmon, S., & Roy, S. (2001). Arithmetic performance of students: Implications for standards and programming. Exceptional Children, 67(3), 311-328. https://doi.org/10.1177/001440290106700302
4. Chinn, S. (2020). More trouble with maths: A complete manual to identifying and diagnosing mathematical difficulties. Routledge.
5. Creswell, J. W., & Creswell, J. D. (2017). Research design: Qualitative, quantitative, and mixed methods approaches. Sage.
6. Etikan, I., & Bala, K. (2017). Sampling and sampling methods. Biometrics & Biostatistics International Journal, 5(6), 00149. http://dx.doi.org/10.15406/bbij.2017.05.00149
7. Geiger, M. A. (1992). Learning styles of introductory accounting students: An extension to course performance and satisfaction. The Accounting Educators' Journal, 4(1), 22-39.
8. Geist, E. A., & King, M. (2008). Different, not better: Gender differences in mathematics learning and achievement. Journal of Instructional Psychology, 35(1), 43–52.

9. Granberg, C. (2016). Discovering and addressing errors during mathematics problem-solving—A productive struggle?. The Journal of Mathematical Behavior, 42, 33-48. https://doi.org/10.1016/j.jmathb.2016.02.002
10. Hannover, B., & Kessels, U. (2004). Self-to-prototype matching as a strategy for making academic choices. Why high school students do not like math and science. Learning and Instruction, 14(1), 51–67. https://doi.org/10.1016/j.learninstruc.2003.10.002
11. Hansen, A., Drews, D., Dudgeon, J., Lawton, F., & Surtees, L. (2020). Children's errors in mathematics. Learning Matters.
12. Herholdt, R., & Sapire, I. (2014). An error analysis in the early grades mathematics-A learning opportunity?. South African Journal of Childhood Education, 4(1), 43-60. https://doi.org/10.4102/sajce.v4i1.46
13. Hidayat, R., & Iksan, Z. H. (2015). The Effect of Realistic Mathematic Education on Students’ Conceptual Understanding of Linear Progamming. Creative Education, 6(22), 2438-2445. http://dx.doi.org/10.4236/ce.2015.622251
14. Hiebert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics 2 (pp. 1–27). Routledge. https://doi.org/10.4324/9780203063538
15. Jaber, M. Y., Givi, Z. S., & Neumann, W. P. (2013). Incorporating human fatigue and recovery into the learning–forgetting process. Applied Mathematical Modelling, 37(12-13), 7287-7299. https://doi.org/10.1016/j.apm.2013.02.028
16. Jordan, N. C., & Montani, T. O. (1997). Cognitive arithmetic and problem solving: A comparison of children with specific and general mathematics difficulties. Journal of Learning Disabilities, 30(6), 624–634. https://doi.org/10.1177/002221949703000606
17. Junaedi, I., M., Suyitno, A., M., Endang Sugiharti, I. U., & Eng, C. K. (2015). Disclosure Causes of Students Error in Resolving Discrete Mathematics Problems Based on NEA as A Means of Enhancing Creativity. International Journal of Education, 7(5), 31-42. https://doi.org/10.5296/ije.v7i4.8462
18. Kolb, D. A. (1976). Learning style inventory technical manual. McBer.
19. Kolb, D. A. (1981). Learning styles and disciplinary differences. In A. W. Chickering (Ed.), The modern American college (pp. 232–255). The Modern American College.
20. Kolb, D. A. (1984). Experience as the source of learning and development. Upper Sadle River: Prentice Hall.
21. Kolb, D. A., Boyatzis, R. E., & Mainemelis, C. (2001). Experiential learning theory: Previous research and new directions. Perspectives on thinking, learning, and cognitive styles, 1(8), 227-247. https://doi.org/10.4324/9781410605986-9
22. Leech, N. L., & Onwuegbuzie, A. J. (2007). An array of qualitative data analysis tools: A call for data analysis triangulation. School Psychology Quarterly, 22(4), 557–584. https://doi.org/10.1037/1045-3830.22.4.557
23. Lim, D. H., & Morris, M. L. (2009). Learner and instructional factors influencing learning outcomes within a blended learning environment. Journal of Educational Technology & Society, 12(4), 282–293. Retrieved from https://www.jstor.org/stable/jeductechsoci.12.4.282
24. Manolis, C., Burns, D. J., Assudani, R., & Chinta, R. (2013). Assessing experiential learning styles: A methodological reconstruction and validation of the Kolb Learning Style Inventory. Learning and Individual Differences, 23(1), 44–52. https://doi.org/10.1016/j.lindif.2012.10.009
25. Mercer, C. D., & Mercer, A. R. (2019). Teaching students with learning problems. University of Toronto Press.
26. Mohamad, M. M., Sulaiman, N. L., Sern, L. C., & Salleh, K. M. (2015). Measuring the validity and reliability of research instruments. Procedia-Social and Behavioral Sciences, 204, 164–171. https://doi.org/10.1016/j.sbspro.2015.08.129
27. Montague, M., Warger, C., & Morgan, T. H. (2000). Solve it! Strategy instruction to improve mathematical problem solving. Learning Disabilities Research & Practice, 15(2), 110-116. https://doi.org/10.1207/sldrp1502_7
28. Neef, N. A., Nelles, D. E., Iwata, B. A., & Page, T. J. (2003). Analysis of precurrent skills in solving mathematics story problems. Journal of Applied Behavior Analysis, 36(1), 21-33. https://doi.org/10.1901/jaba.2003.36-21
29. O'Connell, A. A. (1999). Understanding the nature of errors in probability problem-solving. Educational Research and Evaluation, 5(1), 1-21. https://doi.org/10.1076/edre.5.1.1.3887
30. Orhun, N. (2007). An investigation into the mathematics achievement and attitude towards mathematics with respect to learning style according to gender. International Journal of Mathematical Education in Science and Technology, 38(3), 321-333. https://doi.org/10.1080/00207390601116060
31. Peker, M. (2009). Pre-Service teachers' teaching anxiety about mathematics and their learning styles. Eurasia Journal of Mathematics, Science & Technology Education, 5(4). 335-345. https://doi.org/10.12973/ejmste/75284
32. Peker, M., & Mirasyedioğlu, Ş. (2008). Pre-service elementary school teachers’ learning styles and attitudes towards mathematics. Eurasia Journal of Mathematics, Science & Technology Education, 4(1), 21-26. https://doi.org/10.12973/ejmste/75302
33. Pugalee, D. K. (2004). A comparison of verbal and written descriptions of students' problem solving processes. Educational Studies in mathematics, 55(1-3), 27-47. https://doi.org/10.1023/b:educ.0000017666.11367.c7
34. Quilter, D., & Harper, E. (1988). Why we didn't like mathematics, and why we can't do it. Educational research, 30(2), 121-134. https://doi.org/10.1080/0013188880300206
35. Papadopoulos, I. (2020). Using tasks to bring challenge in mathematics classroom. Journal of Pedagogical Research, 4(3), 375-386.
36. Radatz, H. (1980). Students’ errors in the mathematical learning process: A survey. For the Learning of Mathematics, 1(1), 16–20. https://www.jstor.org/stable/40247696
37. Riccomini, P. J. (2005). Identification and remediation of systematic error patterns in subtraction. Learning Disability Quarterly, 28(3), 233–242. https://doi.org/10.2307/1593661
38. Riding, R., & Rayner, S. (2013). Cognitive styles and learning strategies: Understanding style differences in learning and behavior. David Fulton.
39. Rittle-Johnson, B., & Alibali, M. W. (1999). Conceptual and procedural knowledge of mathematics: Does one lead to the other? Journal of Educational Psychology, 91(1), 175–189. https://doi.org/10.1037/0022-0663.91.1.175
40. Rofalina, F. (2015). Infografik: Pelajaran paling disukai dan dibenci siswa Indonesia. https://www.zenius.net/blog/7657/pelajaran-disukai-dibenci-siswa
41. Ryan, J., & Williams, J. (2007). Children’s mathematics 4–5: Learning from errors and misconceptions. McGraw-Hill Education.
42. Sari, D. P., Darhim, D., & Rosjanuardi, R. (2018). Errors of students learning with react strategy in solving the problems of mathematical representation ability. Journal on Mathematics Education, 9(1), 121-128. https://doi.org/10.22342/jme.9.1.4378.121-128
43. Schmeck, R. R. (2013). Learning strategies and learning styles. Springer Science & Business Media.
44. Schoenfeld, A. H. (2016). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. Journal of Education, 196(2), 1–38. https://doi.org/10.1177/002205741619600202
45. Schoenfeld, A. H., & Sloane, A. H. (2016). Mathematical thinking and problem solving. Routledge.
46. Stacey, K. (2015). The international assessment of mathematical literacy: PISA 2012 framework and items. In S. J. Cho (Ed.), The 12th International Congress on Mathematical Education (pp. 771–790). Springer. https://doi.org/10.1007/978-3-319-17187-6_43
47. Suyitno, A., & Suyitno, H. (2015). Learning therapy for students in mathematics communication correctly based-on application of Newman procedure (a case of Indonesian student). International Journal of Education and Research, 3(1), 529-538.
48. Taylor, N., Clay-Williams, R., Hogden, E., Braithwaite, J., & Groene, O. (2015). High performing hospitals: A qualitative systematic review of associated factors and practical strategies for improvement. BMC Health Services Research, 15(1), 244. https://doi.org/10.1186/s12913-015-0879-z
49. Taylor, S. J., Bogdan, R., & DeVault, M. (1999). Introduction to qualitative research methods: A guidebook and resource. The Journal of Nervous & Mental Disease, 187(9), 587. https://doi.org/10.1097/00005053-199909000-00011
50. Tirta Gondoseputro, T. (1999). The cross-cultural perspective of teachers’ beliefs and their influence on teaching practices: A case study of two teachers teaching secondary mathematics in Australia and Indonesia. In J. M. Truran & K. M. Truran (Eds.), Making the difference: Proceedings of the twenty-second annual conference of the mathematics education research group of Australasia incorporated (pp. 494–501). The Mathematics Education Research Group of Australasia Incorporated.
51. Tuyen, N. H. (2018). The Process of Approaching and Implementing Experiential Learning for Teaching Maths to Junior Secondary School Students in Viet Nam. American Journal of Educational Research, 6(6), 877-882. https://doi.org/10.12691/education-6-6-42
52. Voigt, J. (2013). Negotiation of mathematical meaning in classroom processes: Social interaction and learning mathematics. In L. P. Steffe, P. Nesher, P. Cobb, B. Sriraman, B. Greer (Eds.), Theories of mathematical learning (pp. 33–62). Routledge. https://doi.org/10.1007/978-94-017-2057-1_6
53. Warshauer, H. K. (2015). Productive struggle in middle school mathematics classrooms. Journal of Mathematics Teacher Education, 18(4), 375-400. https://doi.org/10.1007/s10857-014-9286-3
54. Watson, I. (1980). Investigating errors of beginning mathematicians. Educational Studies in Mathematics, 11(3), 319–329. https://doi.org/10.1007/BF00697743