Education Quarterly Reviews
ISSN 2621-5799
Published: 26 July 2021
The Opinions of Mathematics Teachers about Using Mathematical Modeling in the Solution of Daily Life Problems and an Application of the Chinese Remainder Theorem
Mustafa Gök, Nihal Demir
Van Yuzuncu Yil University (Turkey), Hurriyet Middle School (Turkey)
Download Full-Text Pdf
10.31014/aior.1993.04.03.322
Pages: 100-116
Keywords: Mathematical Modeling, Daily Life Problems, Problem-Solving, Teacher Training
Abstract
The opinions of mathematics teachers about using mathematical modeling (MM) in daily life problems and their use of MM in solving a daily life problem were examined within the scope of the graduate-level MM course in this study. The research was designed as a case study. Participants are five mathematics teachers selected by the purposive sampling method. The data were obtained through a structured form containing questions about a daily life problem and using MM in a daily life problem. Teachers were given one week to answer the questions on this form. Descriptive analysis was performed on the data obtained from the teachers’ problem solving, and content analysis was carried out on the data containing the teachers’ opinions. The findings determined that although the modeling processes were generally used appropriately by the teachers in solving a daily life problem, the process of understanding the problem was quickly mentioned, the teachers had difficulties in giving the most effective solution during the evaluation stage, and the communication stage was mostly ignored. It was also found out that MM could be beneficial in many ways in solving daily life problems. On the other hand, it was indicated that there may be difficulties in terms of student-teacher-environment and that teachers give very limited space to MM in classroom practices. It can be stated that the tendency of teachers to use the approaches they are accustomed to instead of MM in the solution of daily life problems is effective in the emergence of this situation.
References
Akgün, L., Çiltaş, A., Deniz, D., Çiftçi, Z., & Işık, A. (2013). Primary school mathematics teachers’ awareness of mathematical modelling. Adiyaman University Journal of Social Sciences, (12), 1-34.https://doi.org/10.14520/adyusbd.410
Ang, K. C. (2001). Teaching mathematical modelling in Singapore schools. The mathematics educator, 6(1), 63-75. https://repository.nie.edu.sg/bitstream/10497/49/1/TME-6-1-63.pdf
Ang, K. C. (2009). Mathematical modelling and real life problem solving. In B. Kaur, Y. B. Har & M. Kapur (Eds.), Mathematical Problem Solving Yearbook 2009, Association of Mathematics Educators(pp. 159-182). Singapore: World Scientific Publishing.
Anhalt, C.O., & Cortez, R. (2016). Developing understanding of mathematical modeling in secondary teacher preparation. J Math Teacher Educ, 19, 523–545.https://doi.org/10.1007/s10857-015-9309-8
Ärlebäck, J. B. (2009). On the use of realistic fermi problems for introducing mathematical modelling in school. The Montana Mathematics Enthusiast, 6(3), 331- 364. https://scholarworks.umt.edu/cgi/viewcontent.cgi?article=1157&context=tme
Aztekin, S., & Taşpınar Şeker, Z. (2015). The content analysis of mathematical modelling studies in turkey: a meta-synthesis study. Education and Science, 40, 139-161. http://egitimvebilim.ted.org.tr/index.php/EB/article/view/4125/1006
Berenger, A. (2018). Pre-service teachers’ difficulties with problem solving. In J. Hunter, L. Darragh, & P. Perger (Eds.), Mathematics Education Research Group of Australasia(pp. 162-169). MERGA. https://files.eric.ed.gov/fulltext/ED592470.pdf
Berry, J., & Houston, K. (1995).Mathematical modelling. Bristol: J. W. Arrowsmith Ltd.
Berry, J., & Nyman, M. (1998). Introducing mathematical modelling skills to students and the use of posters in assessment. Primus,8(2), 103-115. https://doi.org/10.1080/10511979808965888
Blum, W., & Borromeo-Ferri, R. (2009). Mathematical modelling: can it be taught and learnt?. Journal of Mathematical Modelling and Application,1(1), 45-58. https://bu.furb.br/ojs/index.php/modelling/article/view/1620
Blum, W., & Leiß, D. (2007). How do students and teachers deal with modelling problems? In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.),Mathematical modelling: Education, engineering and economics (pp. 222–231). Chichester: Horwood.
Bukova-Güzel, E., Tekin-Dede, A., Hıdıroğlu, Ç. N., Kula-Ünver, S. & Özaltun-Çelik, A. (2016). Mathematical modelling in mathematics education: for researchers, educators and students. Ankara: Pegem Akademi Publishing
Christensen, L. B., Johnson, R. B., & Turner, L. A. (2015). Research methods: design and analysis(Translation Editor: Ahmet Aypay). Ankara: Anı Publishing.
Çakmak-Gürel, Z., & Işık, A. (2018). Investigation of the competences of pre-service secondary school mathematics teachers related to the mathematical modelling. E-International Journal of Educational Research, 9(3), 85-103. https://www.e-ijer.com/tr/pub/e-ijer/article/477651
Çavuş-Erdem, Z., Doğan, M. F., Gürbüz, R., & Şahin, S. (2017). The reflections of mathematical modeling in teaching tools: textbook analysis. Adıyaman University Journal of Educational Sciences, 7(1), 61-86. https://dergipark.org.tr/tr/download/article-file/320383
De Corte, E., Verschaffel, L., & Greer, B. (2000, November). Connecting mathematics problem solving to the real world. In Proceedings of the International Conference on Mathematics Education into the 21st Century: Mathematics for living (pp. 66-73). http://dipmat.math.unipa.it/~grim/Jdecorte.PDF
Demir, N., Ertem-Akbaş, E., & Gök, M. (2021). The views of lecturers about the renewed elementary mathematics teacher undergraduate program views. YYU Journal of Education Faculty, 18(1), 70-105. https://dergipark.org.tr/tr/pub/yyuefd/issue/59626/859490
Deniz, D., & Akgün, L. (2017). High school mathematic teachers’ views about mathematical modelling method and applications. Journal of Social Sciences of Mus Alparslan University, 5(1), 95-117. https://dergipark.org.tr/tr/pub/anemon/issue/27858/272677
Deniz, D., & Akgün, L. (2018). Examining prospective mathematics teachers’ abilities of mathematical modeling. Mediterranean Journal of Educational Research, 12(24), 294-312. https://doi.org/10.29329/mjer.2018.147.16
Doerr, H. M., & Pratt, D. (2008). The learning of mathematics and mathematical modelling. In M.K. Heid & G. W. Blume (Eds.), Research on technology and the teaching and learning of mathematics: Vol. 1. Research syntheses(pp. 259-286). Charlotte, NC: Information Age Press.
Doğan-Temur, Ö. (2012). Analysis of prospective classroom teachers’ teaching of mathematical modeling and problem solving. Eurasia Journal of Mathematics, Science and Technology Education, 8 (2), 83-93.https://doi.org/10.12973/eurasia.2012.822a
Doruk, B. K., & Umay, A. (2010). The effects of mathematical modeling on transferring mathematics into daily life. Hacettepe University Journal of Education, 41, 124-135. http://www.efdergi.hacettepe.edu.tr/shw_artcl-685.html
Duran, M., Doruk, M., & Kaplan, A. (2016). Mathematical modeling processes of mathematics teacher candidates: the example of tortoise paradox. Cumhuriyet International Journal of Education, 5(4), 55-71. https://dergipark.org.tr/en/download/article-file/314336
Eraslan, A., & Kant, S. (2015). Modeling processes of 4th-year middle-school students and the difficulties encountered. Educational and Sciences: Theory and Practice,15(3), 809-824. https://files.eric.ed.gov/fulltext/EJ1067424.pdf
Borromeo-Ferri, R. (2013) Mathematical modeling – the teacher’sresponsibility. In B. Dickman & A. Sanfratello (Eds.), Proceedings from the Teachers College Mathematical Modeling Oktoberfest(pp. 26-31). New York: Teachers College Columbia University.https://doi.org/10.7916/jmetc.v0i0.660
Gök, M. (2020). Mathematical mystery in a cultural game. World Journal of Education, 10(6), 64-73. https://doi.org/10.5430/wje.v10n6p64
Haines, C. R., & Crouch, R. M. (2007). Mathematical modelling and applications: Ability and competence frameworks. In W. Blum, P. L. Galbraith, H. W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education(pp. 417-424), New York, Springer.https://doi.org/10.1007/978-0-387-29822-1_46
Han, S., & Kim, H. M. (2020). Components of mathematical problem solving competence and mediation effects of instructional strategies for mathematical modeling. Education and Science, 45(202), 93-111.http://dx.doi.org/10.15390/EB.2020.7386
Hartono, Y. (2020, March). Mathematical modelling in problem solving. In Journal of Physics: Conference Series (Vol. 1480, No. 1, p. 012001). IOP Publishing.https://iopscience.iop.org/article/10.1088/1742-6596/1480/1/012001/pdf
Hıdıroğlu, Ç. N. (2012). Analysing mathematical modelling problems solving processes in the technology-aided environment: An explanation on approaches and thought processes. Master Thesis. Dokuz Eylul University, İzmir.
Hıdıroğlu, Ç. N., Tekin Dede, A., Kula, S. & Bukova Güzel, E. (2014). Examining students’ solutions regarding the comet problem in the frame of mathematical modeling process. Mehmet Akif Ersoy University Journal of Education Faculty, 1(31), 1-17.https://dergipark.org.tr/tr/pub/maeuefd/issue/19404/206140
Hıdıroğlu, Ç. N., Tekin-Dede, A., Kula-Ünver, S., & Bukova-Güzel, E. (2017). Mathematics student teachers’ modelling approaches while solving the designed eşme rug problem. EURASIA Journal of Mathematics, Science and Technology Education, 13(3), 873-892.https://doi.org/10.12973/eurasia.2017.00648a
Heymann, H. W. (2003). Why teach mathematics? A focus on general education. Dordrecht: Kluwer.
Işık, A., & Mercan, E. (2015). Analysis of the views of secondary school maths teachers on model and modeling. Kastamonu Education Journal,23(4), 1835-1850. https://dergipark.org.tr/tr/pub/kefdergi/issue/22597/241360
İncikabı, L., Ayanoğlu, P., & Uysal, R. (2020). Sixth-grade students’ procedural and conceptual understandings of division operation in a real-life context. International Electronic Journal of Elementary Education, 13(1), 35-45.https://www.iejee.com/index.php/IEJEE/article/view/1158
İncikabı, S., & Biber, A. Ç. (2020). Middle school mathematics teacher candidates’ evaluation of mathematical model eliciting activities. Medeniyet Eğitim Araştırmaları Dergisi, 4(1), 10-27. https://dergipark.org.tr/tr/pub/mead/issue/56310/741341
Kapur, J.N. (1982). The art of teaching the art of mathematical modeling.International Journal of Mathematical Education in Science and Technology,13(2), 185-192. https://doi.org/10.1080/0020739820130210
Karaci Yasa, G., & Karatas, I. (2018). Effects of the instruction with mathematical modeling on pre-service mathematics teachers’ mathematical modeling performance. Australian Journal of Teacher Education, 43(8), 1-14.http://dx.doi.org/10.14221/ajte.2018v43n8.1
Karataş, İ., & Güven, B. (2010). Examining High School Students Abilities of Solving Realistic Problems. Erzincan University Journal of Education Faculty, 12(1), 201 - 217.https://dergipark.org.tr/en/pub/erziefd/issue/5999/79996
Kertil, M. (2008). Investigating problem solving abilitiy of pre-service mathematics teachers in modeling process.Master Thesis. Marmara University, İstanbul.
Kerti̇l, M., Erbaş, A., & Çeti̇nkaya, B. (2017). Pre-service elementary mathematics teachers’ ways of thinking about rate of change in the context of a modeling activity. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 8(1), 188-217. https://dergipark.org.tr/en/pub/turkbilmat/issue/27238/304212
Kırnap Dönmez, S. M., & Dede, Y. (2020). Analysis of mathematics questions in the exams for transition to secondary education (2016, 2017 and2018 years) in terms of mathematical proficiency. Başkent University Journal of Education, 7(2), 363-374. http://buje.baskent.edu.tr/index.php/buje/article/view/327
Korkmaz, E. (2010). Middle school prospective maths and elementary school prospective teachers’ views about mathematical modelling and their mathematical modelling competency. PhD Thesis. Balıkesir University, Balıkesir.
Lesh, R. & Zawojewski, J. (2007). Problem solving and modeling. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning(pp.763-804). Charlotte, NC: Information Age Publishers.
Lincoln, Y.S., & Guba, E.G. (1985). Naturalistic inquiry. Beverly Hills, CA: Sage.
Lingefjärd, T., & Holmquist, M. (2005). To assess students’ attitudes, skills and competencies in mathematical modeling. Teaching Mathematics and Its Applications: International Journal of the IMA, 24(2-3), 123-133.https://doi.org/10.1093/teamat/hri021
Mayring, P. (2011).Introduction to Qualitative Social Research. A guide towards qualitative thinking, A. Gümüş and M. S. Durgun (Trans.), BilgeSu, Ankara.
Mason, J. (1988).Modelling: What do we really want pupils to learn? In D. Pimm (Ed.),Mathematics, Teachers and Children (pp. 201-215).London: Hodder & Stoughton.
Merriam, S. B. (2013). Qualitative case study research(Trans.: E. Karadağ). S. Turan (Ed.), in Qualitative Research: A Guide to Design and Implementation (3 ed.). Ankara: Nobel.
Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook. Thousand Oaks, CA: Sage
Milli Eğitim Bakanlığı [MEB] (2018).Mathematics curriculum (Primary and secondary school 1, 2, 3, 5, 6, 7 and 8th grades).Ankara: MoNE-Board of Education and Discipline.
Muşlu, M., & Çiltaş, A. (2016). The impact of the mathematical modeling method at teaching the subject of the process on natural numbers on the student success. Journal of Bayburt Education Faculty, 11(2).https://dergipark.org.tr/tr/pub/befdergi/issue/28762/307845
National Council of Teachers of Mathematics [NCTM] (2000). The principles and standards for school mathematics.Reston, VA: NCTM.
Özdemir, G., ve Işık, A. (2015). Teachers’ views on the instruction of area and volume concepts in solid objects with mathematical models and mathematical modeling method. Kastamonu Education Journal, 23(3), 1251- 1276.https://dergipark.org.tr/tr/pub/kefdergi/issue/22598/241407
Özer, A. Ö., & Bukova-Güzel E. (2016). Mathematical modelling problems from the viewpoint of students, prospective teachers and teachers. Manisa Celal Bayar University Journal of the Faculty of Education, 4(1), 57-73.https://dergipark.org.tr/en/pub/mcbuefd/issue/54502/742770
Peter-Koop, A. (2004). Fermi problems in primary mathematics classrooms: pupils’ interactive modelling processes.Proceedings of the 27th Annual Conference of the MERGA. Queensland, Australia. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.512.6509&rep=rep1&type=pdf
Polya, G. (1973). How to solve it: A new aspect of mathematical method(2. Baskı). Princeton, New Jersey, USA: Princeton University.
Saldaña, J. (2011).The coding manual for qualitative researchers. Thousand Oaks, CA: Sage
Schroeder, T. L., & Lester, F. K. (1989). Understanding mathematics via problem solving. In P. Trafton (Ed.), New directions for elementary school mathematics(pp. 31-42). Reston, VA: National Council of Teachers of Mathematics.
Sekerak, J. (2010). Phases of mathematical modelling and competence of high school students. The Teaching of Mathematics, 13(2), 105-112. http://teaching.math.rs/vol/tm1323.pdf
Suh, J., Matson, K., Seshaiyer, P., Jamieson, S., & Tate, H. (2021). Mathematical Modeling as A Catalyst for Equitable Mathematics Instruction: Preparing Teachers and Young Learners with 21st Century Skills. Mathematics, 9, 162. https://doi.org/10.3390/math9020162
Şahin, N., & Eraslan, A. (2019). Middle-school prospective mathematics teachers’ opinions on the use of modeling activities at the course of mathematics applications. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 10(2), 373-393.https://doi.org/10.17762/turcomat.v10i2.207
Şahin, S., Doğan, M. F., Cavus Erdem, Z., Gürbüz, R., & Temurtas, A. (2019). Prospective teachers’ criteria for evaluating mathematical modeling problems. International Journal of Research in Education and Science, 5(2), 730-743. https://www.ijres.net/index.php/ijres/article/view/680
Takaoğlu, Z. B. (2015). The effect of physics courses mathematical modelling used on prospective teachers’ interests and how they associate physics with real life and other courses. YYU Journal Of Education Faculty, 12(1), 223-263. https://dergipark.org.tr/en/pub/yyuefd/issue/25854/272581
Tanju, B. (2020). Investigation of representation and making connections skills of pre-service mathematics teachers in mathematical modeling process.Master Thesis. Hacettepe University, Ankara.
Tekin Dede, A., & Yılmaz, S. (2013). Examination of primary mathematics student teachers’ modelling competencies. Turkish Journal of Computer and Mathematics Education, 4(3).
Tekin Dede, A., & Bukova Güzel E. (2013). Mathematics teachers’ views concerning model eliciting activities, developmental process and the activities themselves. Bartın University Journal of Faculty of Education, 2(1), 300-322. https://dergipark.org.tr/tr/pub/buefad/issue/3812/51104
Türker, B., Sağlam, Y., & Umay, A. (2010). Preservice teachers’ performances at mathematical modeling process and views on mathematical modeling. Procedia-Social and Behavioral Sciences, 2(2), 4622-4628.https://doi.org/10.1016/j.sbspro.2010.03.740
Ural, A. (2014). Examining prospective mathematics teachers’ abilities of mathematical modeling.Dicle University Journal of Ziya Gökalp Faculty of Education, (23), 109-140. https://dergipark.org.tr/en/download/article-file/786765
Urhan, S., & Dost, Ş. (2016). The use of mathematical modelling activities in courses: teacher perspectives. Electronic Journal of Social Sciences, 15(59), 1279-1295.https://doi.org/10.17755/esosder.263231
Verschaffel, L., Greer, B., & De Corte, E. (2000). Making sense of word problems. Lisse, The Netherlands: Swets & Zeitlinger.
Vijayan, V., & Joshith, V. P. (2018). Reflection of problem solving skill in life and mathematics education through modeling and applying. i-manager’s Journal on Educational Psychology, 12(2), 1-6.https://doi.org/10.26634/jpsy.12.2.15141
Wilkerson, M.H., Bautista, A., Tobin, R.G., Brizuela, B. M., & Cao, Y. (2018). More than meets the eye: Patterns and shifts in middle school mathematics teachers’ descriptions of models. J Math Teacher Educ, 21, 35–61.https://doi.org/10.1007/s10857-016-9348-9
Yanagimoto, T. (2005). Teaching modelling as an alternative approach to school mathematics. Teaching Mathematics and Its Applications,24(1), 1-13. https://doi.org/10.1093/teamat/hrh011
Yanık, H. B., Bağdat, O., & Koparan, M. (2017). Investigating prospective middle-school teachers’ perspectives of mathematical modelling problems. Journal of Qualitative Research in Education (JOQRE), 5(1), 80-101.https://dx.doi.org/10.14689/issn.2148-2624.1.5c1s4m
Yu, S. Y., & Chang, C. K. (2009). What did Taiwan mathematics teachers think of model-eliciting activities and modeling? In G. Kaiser, W. Blum, R. Borromeo-Ferri ve G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling international perspectives on the teaching and learning of mathematical modelling(pp. 147-156). Springer. https://doi.org/10.1007/978-94-007-0910-2_16
Zbiek, R. M., & Conner, A. (2006). Beyond motivation: Exploring mathematical modeling as a context for deepening students’ understandings of curricular mathematics. Educational Studies in mathematics, 63(1), 89-112.https://doi.org/10.1007/s10649-005-9002-4
Zulkarnaen, R. (2018, October). Why is mathematical modeling so difficult for students?. In AIP Conference Proceedings (Vol. 2021, No. 1, p. 060026). AIP Publishing LLC.https://doi.org/10.1063/1.5062790