Abstract
Numbers and operations is widely considered the most essential domain in elementary school grades. Nevertheless, elementary students in Indonesia have consistently performed unsatisfactorily on this domain in several international mathematics assessments. This study examined 308 Indonesian sixth grade students’ current performance(s), misconception(s), and confidence level(s) on a three-tier test containing 40 number sense-related questions. The results showed that most of the students performed unsatisfactorily (indicating low number sense) with a relatively high level of confidence and exhibited considerable misconceptions. The percentage of the correct responses (i.e. answers and reasons) was approximately 46.48% for the 40 questions. Specifically, only 25 students (8.12%) had good number sense, while 60.71% of the students held either strong or moderate misconceptions. The students’ strong misconceptions were identified. In addition, other remarkable findings are presented and discussed. Furthermore, the implications of the results and the suggestions for future research are described.
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Alajmi, A., & Reys, R. (2010). Examining eighth grade Kuwaiti students’ recognition and interpretation of reasonable answer. International Journal of Science and Mathematics Education, 8(1), 117–139. https://doi.org/10.1007/s10763-009-9165-z.
Berch, D. B. (2005). Making sense of number sense: Implications for children with mathematical disabilities. Journal of Learning Disabilities, 38(4), 333–339. https://doi.org/10.1177/00222194050380040901.
Bonotto, C. (2005). How informal out-of-school mathematics can help students make sense of formal in-school mathematics: The case of multiplying by decimal numbers. Mathematical Thinking & Learning: An International Journal, 7(4), 313–344. https://doi.org/10.1207/s15327833mtl0704_3.
Burton, L. (2004). Confidence is everything–Perspectives of teachers and students on learning mathematics. Journal of Mathematics Teacher Education, 7(4), 357–381. https://doi.org/10.1007/s10857-004-3355-y.
Caleon, I., & Subramaniam, R. (2010). Development and application of a three-tier diagnostic test to assess secondary students’ understanding of waves. International Journal of Science Education, 32(7), 939–961. https://doi.org/10.1080/09500690902890130.
Cetin-Dindar, A., & Geban, O. (2011). Development of a three-tier test to assess high school students’ understanding of acids and bases. Procedia-Social and Behavioral Sciences, 15, 600–604. https://doi.org/10.1016/j.sbspro.2011.03.147.
Cheung, K. L., & Yang, D. -C. (2020). Performance of sixth graders in Hong Kong on a number sense three-tier test. Educational Studies, 46(1), 39–55. https://doi.org/10.1080/03055698.2018.1516631
Chinnappan, M. (1998). Schemas and mental models in geometry problem solving. Educational Studies in Mathematics, 36(3), 201–217. https://doi.org/10.1023/A:1003134323371.
Clarke, D. M., Clarke, D. J., & Sullivan, P. (2012). Reasoning in the Australian curriculum: Understanding its meaning and using the relevant language. Australian Primary Mathematics Classroom, 17(3), 28–32.
Devlin, K. (2017). Number sense: The most important mathematical concept in 21st century K-12 education. HUFFPOST. From https://www.huffingtonpost.com/entry/number-sense-the-most-important-mathematical-concept_us_58695887e4b068764965c2e0. Accessed 11 Mar 2019.
Eryilmaz, A. (2002). Effects of conceptual assignments and conceptual change discussions on students’ misconceptions and achievement regarding force and motion. Journal of Research in Science Teaching, 39(10), 1001–1015. https://doi.org/10.1002/tea.10054.
Facun, R. D., & Nool, N. R. (2012, May). Assessing the number sense of grade 6 pupils. Paper presented at International Conference on Education and Management Innovation, Singapore. Accessed from http://www.ipedr.com/vol30/58-ICEMI%202012-M10058.pdf
Fan, L. (2013). Textbook research as scientific research: Towards a common ground on issues and methods of research on mathematics textbooks. ZDM Mathematics Education, 45(5), 765–777. https://doi.org/10.1007/s11858-013-0530-6.
Gersten, R., Jordan, N. C., & Flojo, J. R. (2005). Early identification and intervention for students with mathematics difficulties. Journal of Learning Disabilities, 38(4), 293–304. https://doi.org/10.1177/00222194050380040301.
Gogus, A. (2013). Evaluating mental models in mathematics: A comparison of methods. Educational Technology Research and Development, 61(2), 171–195.
Green, M., Piel, J., & Flowers, C. (2008). Reversing education majors’ arithmetic misconceptions with short-term instruction using manipulatives. The Journal of Educational Research, 101(4), 234–242. https://doi.org/10.3200/JOER.101.4.234-242.
Helme, S., & Stacey, K. (2000). Can minimal support for teachers make a difference to students' understanding of decimals? Mathematics Teacher Education and Development, 2, 105–120.
Helmy, N. F., Johar, R., & Abidin, Z. (2018). Student’s understanding of numbers through the number sense strategy. Journal of Physics Conference Series, 1088, 1–6. https://doi.org/10.1088/1742-6596/1088/1/012098.
Herman. (2001, April). Strategi mental yang digunakan siswa sekolah dasar dalam berhitung [Number sense strategies used by elementary students in counting]. Paper presented at National Conference on Mathematics Education, Yogyakarta, Indonesia.
Karp, A., Dubrovsky, V. N., Bulychev, V. A., Garfunkel, S., Ovsyannikova, I., Polikarpov, S. A., . . . Wasserman, N. H. (2016). Current issues in mathematics education. Bedford, MA: COMAP.
Kuhn, J.-T., & Holling, H. (2014). Number sense or working memory? The effect of two computer-based trainings on mathematical skills in elementary school. Advances in Cognitive Psychology, 10(2), 59–67. https://doi.org/10.5709/acp-0157-2.
Lodge-Scharf, S. E. (2017). Investigating student mental models at the intersection of mathematics and physical reasoning in physics (Master’s Thesis). University of Maine, MD. From https://digitalcommons.library.umaine.edu/etd/2718.. Accessed 18 Mar 2019
Markovits, Z., & Sowder, J. T. (1994). Developing number sense: An intervention study in grade 7. Journal for Research in Mathematics Education, 25(1), 4–29. https://doi.org/10.2307/749290.
McIntosh, A., Reys, B. J., & Reys, R. E. (1992). A proposed framework for examining basic number sense. For the Learning of Mathematics, 12, 2–8.
McIntosh, A., Reys, B. J, Reys, R. E, Bana, J. & Farrel, B. (1997). Number sense in school mathematics: Student performance in four countries. Perth, Australia: Edith Cowan University.
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.
Merenluoto, K., & Lehtinen, E. (2002). Conceptual change in mathematics: Understanding the real numbers. In M. Limo’n & L. Mason (Eds.), Reconsidering conceptual change. Issues in theory and practice (pp. 233–258). Dordrecht, The Netherlands: Kluwer Academic publishers.
Merenluoto, K., & Lehtinen, E. (2004). Number concept and conceptual change: Towards a systemic model of the processes of change. Learning and Instruction, 14(5), 519–534. https://doi.org/10.1016/j.learninstruc.2004.06.016.
Ministry of Education and Culture of Indonesia. (2013). Silabus Sekolah Dasar/Madrasah Ibtidaiyah (SD/MI): Mata pelajaran Matematika [Elementary school syllabus: Mathematics]. Jakarta, Indonesia: Authors.
Mohamed, M., & Johnny, J. (2010). Investigating number sense among students. Procedia-Social and Behavioral Sciences, 8, 317–324. https://doi.org/10.1016/j.sbspro.2010.12.044.
Moseley, C., Desjean-Perrotta, B., & Utley, J. (2010). The draw-an-environment test rubric (DAET-R): Exploring pre-service teachers’ mental models of the environment. Environmental Education Research, 16(2), 189–208. https://doi.org/10.1080/13504620903548674.
Mullis, I. V. S., Martin, M. O., Foy, P., & Hooper, M. (2016). TIMSS 2015 international results in mathematics. Retrieved from Boston College, TIMSS & PIRLS International Study Center website: http://timssandpirls.bc.edu/timss2015/international-results/. Accessed 18 Mar 2019
National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston, VA: Author.
National Research Council. (2001). Adding it up: Helping children learn mathematics. In J. Kilpatrick, J. Swafford, & B. Findell (Eds.), Mathematics learning study committee, center for education, division of behavioral and social sciences and education. Washington, DC: National Academy Press.
Odom, A. L., & Barrow, L. H. (2007). High school biology students’ knowledge and certainty about diffusion and osmosis concepts. School Science and Mathematics, 107(3), 94–101. https://doi.org/10.1111/j.1949-8594.2007.tb17775.x.
Organisation for Economic Co-operation and Development [OECD]. (2010). PISA 2009 results: What students know and can do. Student performance in reading, mathematics, and science (Vol. 1). Paris, France: Author.
Organisation for Economic Co-operation and Development [OECD]. (2016). PISA 2015 results in focus. From https://www.oecd.org/pisa/pisa-2015-results-in-focus.pdf. Accessed 7 Jan 2019
Pesman, H., & Eryilmaz, A. (2010). Development of a three-tier test to assess misconceptions about simple electric circuits. The Journal of Educational Research, 103(3), 208–222. https://doi.org/10.1080/00220670903383002.
Purnomo, Y. W., Kowiyah, K., Alyani, F., & Assiti, S. S. (2014). Assessing number sense performance of Indonesian elementary school students. International Education Studies, 7(8), 74–84.
Renner, C. H., & Renner, M. J. (2001). But I thought I knew that: Using confidence estimation as a debasing technique to improve classroom performance. Applied Cognitive Psychology, 15, 23–32.
Reys, R. E., & Yang, D. C. (1998). Relationship between computational performance and number sense among sixth‐ and eighth‐grade students in Taiwan. Journal for Research in Mathematics Education, 29(2), 225–237.
Reys, R. E., Reys, B. J., McIntosh, A., Emanuelsson, G., Johansson, B., & Yang, D. C. (1999). Assessing number sense of students in Australia, Sweden, Taiwan, and the United States. School Science and Mathematics, 99(2), 61–70.
Sahdra, B., & Thagard, P. (2003). Procedural knowledge in molecular biology. Philosophical Psychology, 16(4), 477–498.
Sarwadi, H. R. H., & Shahrill, M. (2014). Understanding students’ mathematical errors and misconceptions: The case of year 11 repeating students. Mathematics Education Trends and Research, 2014, 1–10. https://doi.org/10.5899/2014/metr-00051.
Şengül, S., & Gülbağcı, H. (2012). Evaluation of number sense on the subject of decimal numbers of the secondary stage students in Turkey. International Online Journal of Educational Sciences, 4(2), 296–310.
Şengül, S., & Gülbağcı, D. H. (2014). The strategies of mathematics teachers when solving number sense problems. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 5(1), 73–88. https://doi.org/10.16949/turcomat.67936.
Stankov, L., & Crawford, J. D. (1997). Self-confidence and performance on test of cognitive abilities. Intelligence, 25(2), 93–109.
Sumarto, S. N., van Galen, F., Zulkardi, Z., & Darmawijoyo, D. (2014). Proportional reasoning: How do the 4th graders use their intuitive understanding? International Education Studies, 7(1), 69–80. https://doi.org/10.5539/ies.v7n1p69.
ten Berge, T., & van Hezewik, R. (1999). Procedural and declarative knowledge: An evolutionary perspective. Theory & Psychology, 9(5), 605–624.
Tornroos, J. (2005). Mathematics textbooks, opportunity to learn and student achievement. Studies in Educational Evaluation, 31(4), 315–327. https://doi.org/10.1016/j.stueduc.2005.11.005.
Tsai, C.-C., & Chou, C. (2002). Diagnosing students’ alternative conceptions in science. Journal of Computer Assisted Learning, 18(2), 157–165. https://doi.org/10.1046/j.0266-4909.2002.00223.x
Widjaja, W., Stacey, K., & Steinle, V. (2011). Locating negative decimals on the number line: Insights into the thinking of pre-service primary teachers. The Journal of Mathematical Behavior, 30(1), 80–90.
Wijaya, A., van den Heuvel-Panhuizen, M., & Doorman, M. (2015). Opportunity-to-learn context-based tasks provided by mathematics textbooks. Educational Studies in Mathematics, 89(1), 41–65. https://doi.org/10.1007/s10649-015-9595-1.
Xin, Y. P. (2007). Word problem solving tasks in textbooks and their relation to students’ performance. Journal of Educational Research, 100(6), 347–359. https://doi.org/10.3200/JOER.100.6.347-360.
Yang, D. C. (2019). Development of a three-tier number sense test for fifth-grade students. Educational Studies in Mathematics, 101(3), 405–424. https://doi.org/10.1007/s10649-018-9874-8
Yang, D. C., & Huang, F. Y. (2004). Relationships among computational performance, pictorial representation, symbolic representation, and number sense of sixth grade students in Taiwan. Educational Studies, 30(4), 373–389.
Yang, D. C., Li, M. N., & Lin, C. I. (2008). A study of the performance of 5th graders in number sense and its relationship to achievement in mathematics. International Journal of Science and Mathematics Education, 6(4), 789–807.
Yang, D. C., & Hsu, C. J. (2009). Teaching number sense for 6th graders in Taiwan. International Electronic Journal of Mathematics Education, 4(2), 92–109.
Yang, D. C., & Lin, Y. C. (2015). Assessing 10‐ to 11‐year‐old children's performance and misconceptions in number sense using a four‐tier diagnostic test. Educational Research, 57(4), 368–388.
Yang, D. C., & Sianturi, I. A. J. (2019a). Sixth grade students’ performance, misconceptions, and confidence when judging the reasonableness of computational results. International Journal of Science and Mathematics Education, 17(8), 1519–1540. https://doi.org/10.1007/s10763-018-09941-4
Yang, D. C., & Sianturi, I. A. J. (2019b). Assessing students’ conceptual understanding using an online three‐tier diagnostic test. Journal of Computer Assisted Learning, 35(5), 678–689. https://doi.org/10.1111/jcal.12368
Yilmaz, I., & Yalcin, N. (2012). The relationship of procedural and declarative knowledge of science teacher candidates in Newton’s laws of motion to understanding*. American International Journal of Contemporary Research, 2(3), 50–56.
Acknowledgments
This work was supported by the Ministry of Science and Technology, Taiwan, with grant no. MOST 105-2511-S-415-003-MY3. Any opinions expressed here are those of the authors and do not necessarily reflect the views of the Ministry of Science and Technology. The authors thank Cheng-Yi Chuang, M.Ed. (National Chiayi University, Taiwan), Muhammad Taqiyuddin, B.Ed. (Universitas Pendidikan Indonesia), and Erna Siregar, B.Ed. (Universitas Pelita Harapan, Indonesia) for their support in handling and collecting the data for the study.
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Yang, DC., Sianturi, I.A.J. Sixth Grade Students’ Performance, Misconception, and Confidence on a Three-Tier Number Sense Test. Int J of Sci and Math Educ 19, 355–375 (2021). https://doi.org/10.1007/s10763-020-10051-3
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DOI: https://doi.org/10.1007/s10763-020-10051-3