Students’ Misconceptions about Locating Integers and Decimals on Number Line
Abstract
This paper explores misconceptions about locating integers and decimals on horizontal and vertical number lines as revealed by the students’ responses enrolled at Federal Government Secondary Schools in Islamabad. The instrument was a test based on 4 parts containing integers and decimals placing on horizontal and vertical number lines. 368 students were the sample of the study. The analysis of students’ incorrect responses ranged from 4% to 62%. The analyses of students’ incorrect responses helped for the investigation of students’ misconceptions. Four misconceptions leading to incorrect placement of integers and decimals were identified. The opposite sign misconception appeared when students placed positive integers in negative region and negative integers in positive region of number line. The other two misconceptions Translating Positive Interval (TPI) and Translating Negative Interval (TNI) appeared by creating the positive and negative part of the number line which emerged through the negative and positive intervals. The ‘decimal-point-ignored’ misconception was identified when students ignored decimal point and considered the remaining part as whole numbers on horizontal and vertical number lines. The implication for the students and teachers is that, teaching of integers and decimals should not be confined to conceptual understanding only but also through the visual description on number lines which must be focused during teaching.
References
Diezmann, C. M. & Lowrie, T. (2006). Primary students’ knowledge of and errors on number lines. In Grootenboer, P. and Zevenbergen, R. and Chinnapan, M. (Eds.). Proceedings 29th Annual Conference of the Mathematics Education Research Group of Australasia, (pp. 171-178). Canberra.
Fuadiah, N. F., Suryadi, D. & Turmudi. (2017). Some difficulties in understanding negative numbers faced by students; A qualitative study applied at secondary schools in Indonesia. International Education Studies, 10(1), 24-38.
Hannula, M. S. (2003). Locating fractions on a number line. In N.A. Pateman, B. J. Dougherty, & J. T. Zilliox (Eds.), Proceedings of the 27th conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 17-24). Honolulu, HI: Psychology of Mathematics Education.
Irwin, K. (1995). Students’ images of decimal fractions. In L. Meira, & D. Carraher (Eds.), Proceedings of the 19th conference of the International Group for the Psychology of Mathematics Education (pp. 50–59). Reclife, Brazil: PME.
Mackinlay, J. (1999). Automating the design of graphical presentations of relational information. In S. K. Card, J. D. Mackinlay, & B. Schneiderman (Eds.), Readings in information visualization: Using vision to think, (pp. 66-81). San Francisco, CA: Morgan Kaufmann.
Mclntosh, J., Stacey, K., Tromp, C., & Lightfoot, D. (2000). Designing constructivist computer games for teaching about decimal numbers. In J. Bana, & A. Chapman (Eds.), Mathematics education beyond 2000. Proceedings of the 23rd annual conference of the Mathematics Education Research Group of Australasia (pp. 409–416). Fremantle, Western Australia: MERGA.
Michaelidou, N., Gagatsis, A., & Pitta-Pantazi, D. (2004). The number line as a representation of decimal numbers: A research with sixth grade students. In M. J. Hoines, & A. B. Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, (pp. 305–312). Bergen, Norway: PME.
Peled, I., & Carraher, D. (2008). Signed numbers and algebraic thinking. In J. J. Kaput, D. W. Carraher, & M. L. Blanton (Eds.), Algebra in the early grades, (pp. 303–328). New York: NCTM.
Putt, I. J. (1995). Pre-service teacher ordering of decimal numbers: When more is smaller and less is larger!. Focus on Learning Problems in Mathematics, 17(3), 1–15.
Schindler, M. & Hußmann, S. (2013). About students’ individual concepts of negative integer- in terms of the order relation. Proceedings of the Eighth Conference of the European Society for Research in Mathematics Education (CERME). Working Group 2, 373-382.
Schindler, M., Hußmann, S., Nilsson, P., & Bakker, A. (2017). Sixth-grade students’ reasoning on the order relation of integers as influenced by prior experience: an inferentialist analysis. Mathematics Education Research Journal, 29, 471-492.
Stacy, K. (2005). Travelling the road to expertise: A longitudinal study of learning. In Chick, H. L. & Vincent, J. L. (Eds.). Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education (pp. 19-36). Melbourne: PME.
Stacey, K., Helme, S., Steinle, V., Baturo, A., Irwin, K., & Bana, J. (2001). Pre-service teachers’ knowledge of difficulties in decimal numeration. Journal of Mathematics Teacher Education, 4(3), 205–225.
Steinle, V. (2004). Changes with age in students’ misconceptions of decimal numbers (PhD thesis, University of Melbourne, Melbourne, Australia). Retrieved from http://repository.unimelb.edu.au/10187/686.
Steinle, V., & Stacey, K. (1998). The incidence of misconceptions of decimal notation amongst students in Grades 5 to 10. In C. Kanes, M. Goos, & E. Warren (Eds.), Teaching Mathematics in New Times. Proceedings of the 21st annual conference of the Mathematics Education Research Group of Australasia (pp. 548-555). Gold Coast, Australia: MERGA.
Steinle, V., & Stacey, K. (2004). Persistence of decimal misconceptions and readiness to move to expertise. In M. J. Hoines, & A. B. Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (pp. 225–232). Bergen, Norway: Bergen University College.
Swan, M. (1983). Teaching Decimal Place Value: A Comparative Study of "Conflict" and "Positive Only" Approaches. Nottingham: Shell Centre for Mathematical Education.
Widjaja, W., Stacy, K. and Steinle, V. (2011). Locating negative decimals on the number line: Insights in to the thinking of pre-service primary teachers. Journal of Mathematical Behavior, 30, 80-91.
All articles published in IJITL are open-access articles published and distributed under the Creative Commons Attribution-NonCommercial 4.0 International License which allows reproduction, distribution, derives and non-commercial use, provided the original work is cited and authors and publisher are properly identified.
IJITL allows the authors to retain copyright under the CC BY NC license.
