An Examination of Fourth-Grade Elementary School Students’ Number Sense in Context-Based and Non-Context-Based Problems

  • Derya CanEmail author
  • İ. Elif Yetkin Özdemir


Research on number sense presents contradictory arguments and results regarding the effects of context-based tasks and activities on students’ number sense. The aim of this study was to examine fourth-grade elementary school students’ number sense as they solve context-based (CB) and non-context-based (NCB) items. A survey design was employed and data collected using CB and NCB tests for this purpose. The results showed that students were more successful on NCB test compared to the CB test. Students performed best on the problems related to the “using a reference point” component of number sense, while they performed worst on the “understanding of the number size” component. The majority of students used rule-based strategies (RBSs) for both CB and NCB tests. Interviews with students who solved CB items using RBSs showed that students were able to recognize and use number sense-based strategies (NSBSs) to some degree when they were asked for alternative solution methods. The variability found in students’ recognition and use of number sense seem to depend on such factors as the lack of number sense, preference to RBS, task structure (e.g. involving visual representations and easy numbers), and task requirements (e.g. asking for estimation or comparison vs. exact answer, requiring additional adjustments on reference points).


Context-based and non-context-based problems Elementary school mathematics Fourth-grade students Number sense Number sense-based strategies Rule-based strategies 


  1. Almedia, R., & Bruno, A. (2017). Establishing profiles on the use of number sense. REDIMAT, 6(1), 56–84.CrossRefGoogle Scholar
  2. Anghileri, J. (2000). Teaching number sense. London: Cromwell Press.Google Scholar
  3. Antell, S. E., & Keating, D. P. (1983). Perceptions of numerical invariance in neonates. Child Development, 54, 695–701.CrossRefGoogle Scholar
  4. Barwell, R. (2001). Difficulties with mathematical word problems. Proceedings of the British Society for Research in Learning Mathematics, 21(2), 63–74.Google Scholar
  5. Berch, D. B. (2005). Making sense of number sense: Implications for children with mathematical disabilities. Journal of Learning Disabilities, 38(4), 333–339.CrossRefGoogle Scholar
  6. Can, D. (2017). İlkokul dördüncü sınıf öğrencilerinin sayı duyularının bağlam temelli ve bağlam temelli olmayan problem durumlarında incelenmesi, [Examination of fourth grade elementary school students' number sense in context-based and noncontext-based problems] (Unpublished doctoral dissertation). Hacettepe Üniversitesi, Eğitim Bilimleri Enstitüsü, Ankara.Google Scholar
  7. Cramer, K. A., Post, T. R., & del Mas, R. C. (2002). Initial fraction learning by fourth- and fifth-grade students: A comparison of the effects of using commercial curricula with the effects of using the rational number project curriculum. Journal for Research in Mathematics Education, 33(2), 111–144.CrossRefGoogle Scholar
  8. Cummins, D. D., Kintsch, W., Reusser, K., & Weimer, R. (1988). The role of understanding in solving word problems. Cognitive Psychology, 20, 405–438.CrossRefGoogle Scholar
  9. Çekirdekci, S., Şengül, S., & Doğan, M. C. (2016). Examining the relationship between number sense and mathematics achievement of the 4th grade students. Qualitative Studies (NWSAQS), 11(4), 48–66.Google Scholar
  10. Gersten, R., & Chard, D. (1999). Number sense: Rethinking arithmetic instruction for students with mathematical disabilities. The Journal of Special Education, 33(1), 18–28.CrossRefGoogle Scholar
  11. Gersten, R., Jordan, N. C., & Flojo, J. R. (2005). Early identification and interventions for students with mathematics difficulties. Journal of Learning Disabilities, 38, 293–304.CrossRefGoogle Scholar
  12. Gravemeijer, K. (1997). Commentary. Solving word problems: A case of modelling? Learning and Instruction, 7, 389–397.CrossRefGoogle Scholar
  13. Gülbağcı Dede, H. (2015). İlköğretim ve ortaöğretim matematik öğretmen adaylarının sayı hissinin incelenmesi [An investigation of pre-service elementary and secondary mathematics teachers’ number sense] (Unpublished doctoral dissertation). Eğitim Bilimleri Enstitüsü, Marmara Üniversitesi, İstanbul.Google Scholar
  14. Hiebert, J. (1999). Relationships between research and the NCTM Standards. Journal for Research in Mathematics Education, 30, 3–19.CrossRefGoogle Scholar
  15. Hope, J. (1989). Promoting number sense in school. Arithmetic Teacher, 36(6), 12–16.Google Scholar
  16. Irwin, K. C. (2001). Using everyday knowledge of decimals to enhance understanding. Journal for Research in Mathematics Education, 32(4), 399–420.CrossRefGoogle Scholar
  17. İymen, E. (2012). 8. sınıf öğrencilerinin üslü ifadelerle ilgili sayı duyularının sayı duyusu bileşenleri bakımından incelenmesi. [Analysis of 8 grade students’ number sense on exponents in terms of number sense components] (Unpublished master dissertation). Fen Bilimleri Enstitüsü, Pamukkale Üniversitesi, Denizli.Google Scholar
  18. Jordan, N. C., Kaplan, D., Olah, L. N., & Locuniak, M. N. (2006). Number sense growth in kindergarten: A longitudinal investigation of children at risk for mathematics difficulties. Child Development, 77, 153–175.CrossRefGoogle Scholar
  19. Kayhan Altay, M. (2010). İlköğretim ikinci kademe öğrencilerinin sayı duyularının; sınıf düzeyine, cinsiyete ve sayı duyusu bileşenlerine göre incelenmesi, [An investigation of middle grade students’ number sense in terms of grade level, gender, and components of number sense] (Unpublished doctoral dissertation). Eğitim Bilimleri Enstitüsü, Hacettepe Üniversitesi, Ankara.Google Scholar
  20. Kelley, T. L. (1939). The selection of upper and lower groups for the validation of test items. Journal of Educational Psychology, 30(1), 17–24.CrossRefGoogle Scholar
  21. Kerslake, D. (1986). Fractions: Children’s strategies and errors: A report of the strategies and errors in secondary mathematics project. England: NFER-Nelson Publishing Company.Google Scholar
  22. Kintsch, W., & Greeno, J. G. (1985). Understanding and solving word arithmetic problems. Psychological Review, 92, 109–129.CrossRefGoogle Scholar
  23. 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, 366–397.CrossRefGoogle Scholar
  24. 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, 129–164.CrossRefGoogle Scholar
  25. Lago, R., & DiPerna, J. (2010). Number sense in kindergarten: A factor-analytic study of the construct. School Psychology Review, 39, 164–180.Google Scholar
  26. Lan, Y. J., Sung, Y. T., Tan, N. C., Lin, C. P., & Chang, K. E. (2010). Mobile-device-supported problem-based computational estimation instruction for elementary school students. Educational Technology & Society, 13(3), 55–69.Google Scholar
  27. Li, M. N. F., & Yang, D. C. (2010). Development and validation of a computer-administered number sense scale for fifth-grade children in Taiwan. School Science and Mathematics, 110(4), 220–230.CrossRefGoogle Scholar
  28. Louange, J. E. G. (2007). An examination of the relationships between teaching and learning styles, and the number sense and problem solving ability of Year 7 students (Unpublished doctoral dissertation). Perth, Australia: Edith Cowan University.Google Scholar
  29. Markovits, Z., & Sowder, J. (1994). Developing number sense: An intervention study in grade 7. Journal for Research in Mathematics Education, 25(1), 4–29.CrossRefGoogle Scholar
  30. McIntosh, A., Reys, B. J., & Reys, R. E. (1992). A proposed framework for examining basic number sense. For the Learning of Mathematics, 12(3), 2–9.Google Scholar
  31. McIntosh, A., Reys, R. E., & Reys, B. J. (1997). Mental computation in the middle grades: The importance of thinking strategies. Mathematics Teaching in the Middle School, 2, 322–327.Google Scholar
  32. Ministry of National Education. (2009). Elementary School Curricula: Mathematics Curricula for Grades 1–5. Ankara: Milli Eğitim Basımevi.Google Scholar
  33. Phipps, M. C. (2008). A phenomenological investigation on eighth graders’ number sense of fractions (Unpublished doctoral dissertation). University of Northern Colorado, Greeley, CO.Google Scholar
  34. Pollitt, A., Marriott, C., & Ahmed, A. (2000). Language, contextual and cultural constraints on examination performance. Paper presented at International Association for Educational Assessment, Jerusalem, Israel.Google Scholar
  35. Reys, R., Reys, B., 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.CrossRefGoogle Scholar
  36. 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.CrossRefGoogle Scholar
  37. Tsao, Y. L. (2005). The number sense of preservice elementary teachers. College Student Journal, 39(4), 647–679.Google Scholar
  38. Wynn, K. (1992). Addition and subtraction by human infants. Nature, 358(27), 749–750.CrossRefGoogle Scholar
  39. Yang, D. C. (1995). Number sense performance and strategies possessed by sixth and eighth grade students in Taiwan (Unpublished doctoral dissertation). University of Missouri, Columbia, MO.Google Scholar
  40. Yang, D. C. (2003). Developing number sense through realistic settings. APMC, 8(3), 12–17.Google Scholar
  41. Yang, D. C. (2005). Number sense strategies used by sixth grade students in Taiwan. Educational Studies, 31(3), 317–334.CrossRefGoogle Scholar
  42. Yang, D.C. (2019). Performance of fourth graders when judging the reasonableness of a computational result. International Journal of Science and Mathematics Education, 17(1), 197–215.CrossRefGoogle Scholar
  43. 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.CrossRefGoogle Scholar
  44. Yang, D. C., & Li, M. F. (2008). An investigation of 3rd-grade Taiwanese students’ performance in number sense. Educational Studies, 34(5), 443–455.CrossRefGoogle Scholar
  45. Yang, D. C., Li, M. F., & Li, W. J. (2008a). Development of a computerized number sense scale for 3rd graders: Reliability and validity analysis. International Electronic Journal of Mathematics Education, 3(2), 110–124.Google Scholar
  46. Yang, D. C., Li, M. N., & Lin, C. I. (2008b). 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, 789–807.CrossRefGoogle Scholar
  47. Yang, D. C., & Liu, Y. F. (2013). Examining the differences on comparing fraction size for 5th graders between contextual and numerical problems. Asian Journal of Education and e-Learning, 1(2), 112–117.Google Scholar
  48. Yang, D. C., Reys, R. E., & Wu, L. L. (2010). Comparing how fractions were developed in textbooks used by the 5th- and 6th-graders in Singapore, Taiwan, and the U.S.A. School Science and Mathematics, 110(3), 118–127.CrossRefGoogle Scholar
  49. Yang, D. C., & Wu, W. R. (2010). The study of number sense: Realistic activities integrated into third-grade math classes in Taiwan. The Journal of Educational Research, 103, 379–392.CrossRefGoogle Scholar
  50. Yang, D. C., & Wu, S. S. (2012). Examining the differences of 8th graders’ estimation performance between contextual and numerical problems. US-China Educational Review, 12, 1061–1067.Google Scholar
  51. Yapıcı, A. (2013). 5, 6 ve 7. sınıf öğrencilerinin yüzdeler konusunda sayı duyularının incelenmesi [An investigation of 5, 6 and 7th grade students’ number sense related to percentages] (Unpublished master’s dissertation). Hacettepe University, Ankara.Google Scholar
  52. Zanzali, N. A., & Ghazali, M. (2002). Assessment of school children’s number sense. Available at

Copyright information

© Ministry of Science and Technology, Taiwan 2019

Authors and Affiliations

  1. 1.Faculty of EducationMehmet Akif Ersoy UniversityBurdurTurkey
  2. 2.Faculty of EducationAnkaraTurkey

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