Document Type : Original Research Paper

Authors

1 mathematics department (responsible author), Shahid Rajaee Teacher Training Universit. Tehran. Iran

2 psychology Department , Shahid Rajaee Teacher Training University. Tehran. Iran

3 Department of mathematics education, Shahid Rajaee Teacher Training University. Tehran. Iran

Abstract

Understanding negative numbers and doing operations on them is one of the fundamental subjects in mathematics that students face many problems when they encounter them at school. One of the problems that leads to very serious learning difficulties in mathematics is those misconceptions students may have from previous inadequate teaching, informal thinking, or poor remembrance. Recognition of misconception and the origins that create them in the fields and at different levels of education, can improve learning.  Misunderstanding in this study is incomplete or incorrect interpretation of a concept that cause systematic errors in the performance. This study investigates the student’s understanding and misconception of negative numbers. Descriptive statistics, survey, is used as a method of this study. The population of the study is all second level students of guidance school in the academic year 1391-92 and all the seventh level students of Darmian town in the academic year 1392-93. 443 students in second level of guidance school and 55 students in seventh level were chosen as a sample of the study based on cluster random sampling. A self-designed questionnaire by the researcher is used as the instrument for the study, the questionnaire was based on “Bofferding” and “Kilhamn” questionnaire. Results showed that most of the students don’t have a true understanding of negative numbers in school and face problems in applying their knowledge to solve mathematical problems. Also the results of the current study showed that some of the students consider "-" as a reducing operator and some consider "+" as an increasing operator.

Keywords

Main Subjects

[1] Kilhamn, C., Making Sense of Negative Numbers, Doctoral Thesis, University of Gothenburg, (2011), Available online at: https://gupea.ub.gu.se/handle/2077/24 151 (Accessed 10 August 2012), pp.1- 288. [2] Cathcart, W. G., Pothier, Y. M., Vance, J. H., and Bezuk, N. S., Learning mathematics in elementary and middle schools, (Third Edition.), Upper Saddle River, NJ: Prentice, (2003). [3] Ball, D. L., With an eye on the mathematical horizon: Dilemmas of teaching elementary mathematics., Elementary School Journal, Vol. 93, No. 4, (1993), pp. 373-397. [4] Davidson, P. M., Precursors of nonpositive integer concepts, Retrieved from ERIC database, (ED356146), (1992). [5] Gullick, M. M., Wolford, G., and Temple, E., Understanding less than nothing: Neural distance effects for negative numbers, available at http://www.science direct.com. NeuroImage, Vol. 62, No.1, (2012), pp. 542-554. [6] Schliemann, A. D., Carraher, D. W., Brizuela, B. M., Earnest, D., Goodrow, A., Lara-Roth. S. and Peled, I., Algebra in elementary school. In N. Pateman , B. Dougherty, & J. Zilliox (Eds.), Proceedings of the 2003 Joint Meeting of PME and PMENA, CRDG, College of Education, University of Hawai'i: Honolulu , HI, Vol. 4, (2003), pp. 127-134. [7] Bofferding, L., Negative integer understanding: Characterizing first graders' mental models, Journal for Research in Mathematics Education, Vol. 45, No. 2, (2014), pp. 194-245. [8] Beery, J., Cochell, G., Dolezal, C., Sauk, A., and Shuey, L, Negative numbers. In V. Katz, J. & K. D. Michalowics (Eds.), Historical Modules Project (CD-ROM). Mathematical Association of America, (2004). [9] Carraher, D. W., Schliemann, A. D., Brizuela, B. M., & Ernest, D., Arithmetic and algebra in early mathematics education. Journal for Research in Mathematics Education, Vol. 37, No. 2, (2006), pp. 87-115. [10] Bishop, J. P., Lamb, L. L. C., Philipp. R. A., Schappelle, B. P., and Whitacre, I., An investigation of negative-number reasoning: The case of Violet. Presentation at the meeting of Annual Meeting of the American Educational Research Association, New Orleans, LA. (National), (2011). [11] Lemonidis, Ch., and Polytidis, D., The implementation of an electronic model in teaching negative numbers and their operations, 13 th International Conference ICT in the education of the Balkan countries Varna, June 17 - 19, (2010) Balkan Society for Pedagogy and Education. [12] Pourazima, Z., A Study on Impact of 5th Grade Teacher Training on their Knowledge of Student’s Decimal Misconceptions, A thesis submitted to the Graduate Studies Office in partial fulfilment of the requirements for the degree of Master in Mathematics Education, Shahid Rajaee Teacher Training University ,Faculty of Science, January (2013), pp. 1-96. [13] Bakhshalizade, S. H., Identify common Misconceptions of fourth grade students in mathematics content, Research and Education Organization, (2014), PP. 1- 381. [14] Allen, G. D., Misconceptions in mathematics, Department of Mathematics ,Texas A & M University, College Station, (2007). [15] Smith, J. P, diSessa, A., A. and Roschelle, J., Misconceptions reconceived:A constructivist analysis of knowledge in transition, The Journal of the Learning Sciences , Vol. 3, No. 2, 1993-(1994), pp. 115-163. [16] Erdogan, M. Ö., Misconceptions in radicals in high school mathematics, Procedia Social and Behavioral Sciences Vol. 15, (2011), pp. 120-127. [17] Swan, M., Dealing with misconceptions in mathematics. in Gates, ed, (2001), pp. 65-147. [18] Donald, G. A., Student Thinking Lesson 1. Misconceptions in mathematics Texas A&M University College Station, TX 77843-3368 Department of Mathematics, (2007). [19] Vlassis, J., Making sense of the minus sign or becoming flexible in `negativity´. Learning and Instruction, Vol. 14, No. 5, (2004), pp. 469-484. [20] Vlassis, J., The balance model: Hindrance or support for the solving بررسی فهم و درک دانشآموزان از عدد منفی و .... نشریه علمی پژوهشی فناوری آموزش، جلد 01 ،شماره 2 ،زمستان 0931 027 of linear equations with one unknown. Educational Studies in Mathematics, Vol. 49, No. 3, (2002), pp. 341-359. [21] Lamb, L. L., Bishop, J. P., Phillip, R. A., Schappelle, B. P., Whitacre, I., & Lewis, M. L., eveloping symbol sense for the minus sign, Mathematics Teaching in the Middle School Retrieved from http://www.jstor.org/stable/10.5951/m athteacmiddscho.18.1.0005, Vol. 18, No. 1, (2012), pp 5-9. [22] Vlassis, J., The role of mathematical symbols in the development of number conceptualization, The case of the minus sign, Philosophical Psychology, Vol. 21, No. 4, (2008), pp. 555-570. [23] Vlassis, J., What do students say about the role of the minus sign inpolynomials ?In M. Tzekaki, M. Kaldrimidou & H. Sakonidis (Eds.), Proceedings of the 33rdconference of the international group for the psychology of mathematics education, Thessaloniki, Greece: PME, Vol. 5, (2009), pp. 289-296 [24] Bofferding , L., Grappling with negative numbers: Uncertainty is progress, Paper presented at the annual meeting of the American Educational Research Association, Denver, CO, April/May (2010), Journal of Research in Mathematics Education, pp.1 -12. [25] Peled, I., Mukhopadhyay, S., and Resnick, L. B., Formal and informal sources of mental models for negative numbers, In G. Vergnaud, J. Rogalski & M. Artique (Eds.), The 13th International Conference for the Psychology of Mathematics Education ,Paris, France: PME, Vol. 3, (1989), pp. 108-112. [26] Schwarz, B. B., Kohn, A. S., and Resnick, L. B., Positives about negatives: A case study of an intermediate model for signed numbers, The Journal of the Learning Sciences, doi:10.1207/s15327809 jls 0301_2, Vol. 3, No. 1, (1998), pp. 37- 92. [27] Behrend, J. L., and Mohs, L. C., From simple questions to powerful connections: A two-year conversation about negative numbers. Teaching Children Mathematics , Vol. 12, No. 5, (2006), pp. 260-264. [28] Gallardo, A., The extension of the natural number domain to the integers in the transition from arithmetic to algebra, Educational Studies in Mathematics, Kluwer Academic publishers, Printed in the Netherlands, Vol. 49, (2002), pp. 171-192. [29] Gallardo, A., & Hernández, A., Zero and negativity on the number line, In J. H .Woo, H. C. Lew, K. S. Park & D. Y. Seo (Eds.), Proceedings of the 31st inter-national conference of the international group for the psychology of mathematics education , Seoul, South Korea: PME, Vol. 1, (2007), pp. 220. [30] Stacey, K., Helme, S., & Steinle, V., Confusions between decimals, fractions and negative numbers: A consequence of the mirror as a conceptual metaphor in three different ways, In M. van den HeuvelPanhuizen (Ed.), The 25thinternational conference for the psychology of mathematics education, Utrecht, the Netherlands: PME , Vol. 4, (2001), pp. 217-224. [31] Nazri, M. J., Investigating the Root causes of 1th Grade Secondary Students of Negative Numbers, A thesis submitted to the Graduate Studies Office in partial fulfilment of the requirements for the degree of Master in Mathematics Education, Shahid Beheshti University ,Faculty of Science, (2013), pp. 1-96. [32] Rashedi, F., A Study on negative numbers Conception of 7th mistakes grade students and their, A thesis submitted to the Graduate Studies Office in partial fulfilment of the requirements for the degree of Master in Mathematics Education, Shahid Rajaee Teacher Training University ,Faculty of Science, sep. (2013), pp 1- 150. [33] Iranmanesh, A., Naini, K., Shavarani, A., Davoodi, KH., Reyhani, E., Rastegar, A., Eslahpazir, B., Bijanzadeh, M. H., Alamiyan, V., The junior high school math courses, Office of Planning and writing textbooks, (2013). [34] Farzan,M., Bahemat Shirvaneh, S., Dibayi, M. T., Farhoodi Moghadam, P., Second Guidance Math, Office of Planning and writing textbooks, (2005).
CAPTCHA Image