Mistakes Made by Students While Posing Problems for Equations Containing Algebraic Fractional Expressions
Mistakes students make while posing problems
Abstract views: 94 / PDF downloads: 97 / PDF downloads: 85
Keywords:Algebraic fractions, verbal problems, problem posing, mistakes
Conceptual and procedural knowledge has historically been one of the most discussed subjects in mathematics. In this study, errors in equations including algebraic fractional expressions were examined to determine where ninth-grade students in their comprehension of these expressions. The study employed a holistic multiple-case strategy, and the gathered data were evaluated using content analysis. The results indicate that students made the most mistakes with the definitions of quotient and fraction-whole. Certain sorts of errors in the job are applicable to all fraction interpretations, while others appear to be fraction-specific. Depending on the type of fraction, the mistake circumstances varies.
Acar, N. (2010). Kesir Çubuklarının İlköğretim 6. Sınıf öğrencilerinin Kesirlerde Toplama ve Çıkarma İşlemlerindeki Başarılarına Etkisi. Yayınlanmış Yüksek Lisans Tezi. Selçuk Üniversitesi, Fen Bilimleri Enstitüsü, KONYA.
Akçay, A. O., & Ardıç, F. (2020). Sınıf öğretmeni adaylarının kesirlerde problem kurma becerilerinin incelenmesi. The Journal of International Education Science, 25(7), 108-119. DOI: http://dx.doi.org/10.29228/INESJOURNAL.47919
Alibali, Martha W., Mitchell J. Nathan, Matthew S. Wolfgram , R. Breckinridge Church, Steven A. Jacobs, Chelsea Johnson Martinez & Eric J. Knuth (2014) How Teachers Link Ideas in Mathematics Instruction Using Speech and Gesture: A Corpus Analysis, Cognition and Instruction, 32:1, 65-100, DOI: 10.1080/07370008.2013.858161
Ayllón, M.F. (2005). Invención de Problemas con Números Naturales, Enteros Negativos y Racionales: Tarea para Profesores de Educación Primariaen Formación; Trabajo de investigación tutelada, Universidad de Granada: Granada, Spain
An, S., Kulm, G., & Wu, Z. (2004). The pedagogical content knowledge of middle school mathematics teachers in China and the U.S. Journal of MathematicsTeacherEducation, 7(2), 145–172.
Aydogdu Iskenderoglu, T. (2018). Fraction multiplication and division word problems posed by different years of pre-service elementary mathematics teachers. European Journal of Educational Research, 7(2), 373-385.
Barlow, A.T.; Cates, J.M. (2006). The impact of problem posing on elementary teachers’ beliefs about mathematics and mathematics teaching. Sch. Sci. Math. 106, 64–73.
Basturk, S. (2016). Primary student teachers' perspectives of the teaching of fractions. Acta Didactica Napocensia, 9(1), 35-44.
Birgin, O. ve Gürbüz, R.(2009). İlköğretim II. Kademe Öğrencilerinin Rasyonel Sayılar konusundaki İşlemsel ve Kavramsal Bilgi Düzeylerinin İncelenmesi. Eğitim Fakültesi Dergisi, XXII (2), 2009, 529-550
Bossé, M. J., Adu-Gyamfi, K. and Cheetham, M. (2011). Translations among mathematical representations: Teacher beliefs and practices. International Journal of Mathematics Teaching and Learning, 15(6), 1–23.
Brown, S. I., & Walter, M. I. (2005). The art of problem posing (3rd ed.). Lawrence Erlbaum Associates.
Brownell, W. (1935). Psychological considerations in the learning and teaching of arithmetic. In The teaching of arithmetic (Tenth yearbook of the National Council of Teachers of Mathematics) (pp. 1–31). New York: Bureau of Publications, Teachers College.
Bunar, N. (2011). Altıncı sınıf öğrencilerinin kümeler, kesirler ve dört işlem konularında problem kurma ve çözme becerileri. Yüksek Lisans Tezi. Afyon Kocatepe Üniversitesi. AFYON.
Byrnes, J. (1992). The conceptual basis of procedural learning. Cognitive Development, 7, 235-257.
Byrnes, J., & Wasik, B. (2009). Factors predictive o f mathematics achievement in kindergarten, first and second grades: An opportunity-propensity analysis. Contemporary Educational Psychology, 34, 167-183.
Christou, C.; Mousoulides, N.; Pittalis, M.; Pitta-Pantazi, D.; Sriraman, B. (2005). An empirical taxonomy of problem posing processes. ZDM 2005, 37, 149–158.
Cai, J., Hwang, S., Jiang, C., & Silber, S. (2015). Problem-posing research in mathematics education: Some answered and unanswered questions. In F. Singer, N. Ellerton & J. Cai (Eds.), Mathematical problem posing (pp. 3-34). Springer. https://doi.org/10.1007/978-1-4614-6258-3
Chae, J. (2005). Middle school students’ sense-making of algebraic symbols and construction of mathematical concepts using symbols. PhD Thesis. Indiana University, Graduate Faculty of The University of Georgia in Partial.
Crooks, N. M. & Alibali, M. W. (2014). Defining and measuring conceptual knowledge of mathematics. Developmental Review. doi: 10.1016/j.dr.2014.10.001
De Jong, T., & Ferguson-Hessler, M. G. M. (1996). Types and qualities of knowledge. Educational Psychologist, 31(2), 105–113.
Dogan-Coskun, S. (2019). The Analysis of the Problems Posed by Pre-service Elementary Teachers for the Addition of Fractions. International Journal of Instruction, 12(1), 1517-1532.
Empson, S. B. (1995). Equal sharing and shared meaning: The development of fraction concepts in a first grade classroom. Paper presented at the American Educational Research Association, San Francisco, CA.
English, L. D. (1997). The development of fifth-grade children's problem-posing abilities. Educational Studies in Mathematics, 34(3), 183-217.
Eroğlu, D., Camcı, F. ve Tanışlı, D. (2019). Altıncı sınıf öğrencilerinin kesirler ve kesirlerdeki toplamaçıkarma konusundan bilgilerinin yapılandırılmasına ilişkin tahmini öğrenme yol haritası.Pamukkale Üniversitesi Eğitim Fakültesi Dergisi, 45, 116-143.
Garofalo, J. and Lester, F.K., Jr.: (1985). 'Metacognition, cognitive monitoring, and mathematical performance', Journal for Research in Mathematics Education 16
Ghasempour, Z., Bakar, N., & Jahanshahloo, G. R. (2013). Innovation in teaching and learning through problem posing tasks and metacognitive strategies. International Journal of Pedagogical Innovations, 1(1), 53-62.
Gonzales, N. A. (1994). Problem posing: A neglected component in mathematics courses for prospective elementary and middle school teachers. School Science and Mathematics, 94(2), 78–84. https://doi.org/10.1111/j.1949-8594.1994.tb12295.x
Greeno, J. G. (1978). Understanding and procedural knowledge in mathematics instruction. Journal Educational Psychologist Volume 12, 1978
Harwood, T. G. and Garry, T., (2003). An overview of content analysis. The Marketing Review, Volume 3, Number 4, 1 December 2003, pp. 479-498(20). Westburn Publishers Ltd. DOI: https://doi.org/10.1362/146934703771910080
Hiebert, J.,& Carpenter, T. P. (1992). Learning and teaching with understanding. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 65-97). New York: Mcmillan.
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 (pp. 1-27). Hillsdale, NJ: Lawrence Erlbaum Associates.
Işık, C., & Kar, T. (2012a). The analysis of the problems posed by the pre- service teachers about equations. Australian Journal of Teacher Education, 37(9), 93-113
Izsak, A. (2008). Mathematical knowledge for teaching fraction multiplication. Cognition and Instruction, 26(1), 95–143.
Jääskeläinen, R. (2010). Think-aloud protocol. In Y. Gambier & L. van Doorslaer (Eds.), Handbook of translation studies (Volume 1) (pp. 371-373). John Benjamins Publishing Company. https://doi.org/10.1075/hts.1
Kavuncu, T. & Yenilmez, K. (2021). Beşinci sınıf öğrencilerinin kesir modellerine uygun problem kurma ve çözme becerilerinin incelenmesi. Eskişehir Osmangazi Üniversitesi Türk Dünyası Uygulama ve Araştırma Merkezi (ESTÜDAM) Eğitim Dergisi, 6 (2), 201-218.
Kieren, T.E. (1993). Rational and fractional numbers: From quotient fields to recursive understanding. In Rational Numbers: An Integration of Research; Carpenter, T.P., Fennema, E., Romberg, T.A., Eds.; Erlbaum: Hillsdale, NJ, USA, pp. 49–84.
Koichu, B., Harel, G., & Manaster, A. (2013). Ways of thinking associated with mathematics teachers’ problem posing in the context of division of fractions. Instructional Science, 41(4), 681-698.
Kojima, K., Miwa, K., & Matsui, T. (2009). Study on support of learning from examples in problem posing as a production task. In S.C. Kong et all. (Eds.). Proceedings of the 17th International Conference on Computers in Education [CDROM]. Asia-Pacific Society for Computers in Education.
Kopparla, M., Bicer, A., Vela, K., Lee, Y., Bevan, D., Kwon, H., ... & Capraro, R. M. (2019). The effects of problem-posing intervention types on elementary students’ problem-solving. Educational Studies, 45(6), 708-725. https://doi.org/10.1080/03055698.2018.1509785
Lamon, S.J. (2001). Presenting and representing: From fractions to rational numbers. In The Roles of Representation in School Mathematics; National Council of Teachers of Mathematics: Reston, VA, USA; pp. 146–165
Liu, C.,Xin, Z., and Li, X. (2011). The Development of Chinesestudents’ understanding of theconcept of fractions from fifth to eighth grade. Journal of Mathematics Education, 4(2), 17-34.
Lesh, R. and Doerr, H. M. (2003). Foundations of models and modelling perspective on mathematics teaching, learning, and problem solving. R. Lesh and H. M. Doerr (Eds.), Beyond constructivism: Models and modelling perspectives on mathematics problem solving, learning, and teaching in (pp. 3–33). Mahwah: Laurence Erlbaum.
Martinez, S.; Blanco, V. (2021). Analysis of Problem Posing Using Different Fractions Meanings. Educ. Sci. 2021, 11, 65. https://doi.org/ 10.3390/educsci11020065
Merriam, S. B., & Tisdell, E. J. (2016). Qualitative research: A guide to design and implementation (4th ed.). John Wiley & Sons.
Öksüz, C. (2004). Children understanding of algebric fraction as quotients. (Unpublished doctoral dissertation). University of Arizona, Arizona
Panasuk, R. M.,& Beyranevand, M. L. (2010). Algebra students’ ability to recognize multiple representations and achievement. International Journal for Mathematics Teaching and Learning, 1–21.
Pardhan, H. & Mohammad, R.F., (2005). Teaching Science and Mathematics For Conceptual Understanding? A Rising Issue Eurasia J. Math. Sci. & Tech. Ed., 1(1), 1-20.
Perera, P.B.; Valdemoros, M.E. (2007). Propuesta didáctica para la enseñanza de las fracciones en cuarto grado de educación primaria. In Investigación en Educación Matemática XI; SEIEM: San Cristóbal de la Laguna, Tenerife, pp. 209–218.
Pirie, S. E. B. (2002). Problem posing: What can it tell us aboutstudents’ mathmatical understanding. In Proceedings of the 24th Annual Meeting North American Chapter of the International group for the Psychology of Mathematics Educatio (pp. 925-958). GA, Athens.
Ploger, D., & Hecht, S. (2009). Enhancing children's conceptual understanding of mathematics through Chartworld software. . Journal of Research in Childhood Education, 23(3), 267-277.
Robinson, K. M., & Dubé, A. K. (2009a). Children’s understanding of addition and subtraction concepts. Journal of Experimental Child Psychology, 103, 532–545.
Roth,K, Jones,B, Idol,L, (1990). Developing meaningful conceptual understanding in science. Dimensions of thinking and cognitive instruction1990Hilldale, NJErlbaum139175
Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19–28.
Stephens, M. (2003). Regulating the entry of teachers of mathematics into the profession: challenges, new models, and glimpses into the future. Second International Handbook of Mathematics Education pp. 767-793
Star, J. R. (2001). Re-conceptualizing procedural knowledge: Innovation and flexibility in equation solving. Unpublished doctoral dissertation, University of Michigan, Ann Arbor.
Stoyanova, E. (1998). Problem posing in Mathematics Classrooms. In Research in Mathematics Education: A Contemporary Perspective; McIntosh, A., Ellerton, N., Eds.; Edith Cowan University, MASTEC: Perth, WA, USA; pp. 164–185.
Taştepe, M. & Yanık, H. B. (2021). “Kavramsal Bilginin Gelişiminin İncelenmesi: Cebirsel Kesirli İfadeleri İçeren Denklemler Bağlamında". Uluslararası Sosyal ve Eğitim Bilimleri Dergisi, 16: 83-103.
Toluk, Z.(2001). Eşit paylaşım ortamlarının kesir öğretiminde kullanımı. Kuram ve Uygulamada Eğitim Bilimleri. 1 (1)
Van de Walle, J.A. Karp, K.S. ve Bay-Williams, J.M. (2012). İlkokul ve ortaokul matematiği: Gelişimsel yaklaşımla öğretim. (Çev. Editörü: Soner Durmuş). Ankara: Nobel Yayın Dağıtım. 7. Basımdan Çeviri.
Yıldırım, A. & Şimşek, H. (2013). Sosyal bilimlerde nitel araştırma yöntemleri. (9. Baskı). Ankara:SeçkinYayıncılık.
Yin, R. K. (2018). Case study research and applications: Design and methods (6th ed.). Sage Publications.
How to Cite
Copyright (c) 2023 Journal of Qualitative Research in Education
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.