Teacher and Student Opinions on Teaching Four Operations with Integer Numbers in 7th Grade with Counting Stamps

Year 2024, , 142 - 156, 30.07.2024

Ahmet Burak Süzen , Tayfun Tutak , Aziz İlhan , Büşra Nayıroğlu

https://doi.org/10.31458/iejes.1343835

Abstract

The study examines the views of middle school mathematics teachers and 7th-grade students on using counting stamps to teach four operations with integers. The study was conducted with ten mathematics teachers with different professional seniority and ten 7th-grade students studying in these schools. The teachers were asked six open-ended opinion form questions, and the students were simultaneously asked five open-ended opinion form questions. In this qualitative study, the interview technique was used to analyze the views of teachers and students. A structured interview form was preferred as a data collection tool. A qualitative research method was adopted in collecting, analyzing, and interpreting the data of this study. Content analysis was used to analyze and interpret the data. According to the study results, it was determined that teachers and students did not find counting stamps functional and that they needed to be more adequate in operations with integers. Therefore, there is a need for new models that can replace counting stamps.

Keywords

Mathematics teaching, integers, four operations, counting stamps, modelling

References

• Altıparmak, K., & Özdoğan, E. (2010). A study on the teaching of the concept of negative numbers. International Journal of Mathematical Education in Science and Technology, 41(1), 31-47. https://doi.org/10.1080/00207390903189179
• Battista, M. T. (1983). A complete model for operations on integers. The Arithmetic Teacher, 30(9), 26-31. Berry, J. S. & Houston, S. K. (1995). Mathematical modelling. Edward Arnold.
• Bikić, N., Burgić, D., & Kurtić, V. (2021). The effects of mathematical modeling in teaching mathematics of linear, quadratic and logarithmic functions. European Journal of Mathematics and Science Education, 2(2), 129-144. https://doi.org/10.12973/ejmse.2.2.129
• Bilgili, S., Özkaya, M., Çiltaş, A. & Konyalı, A. C. (2020). Examining secondary school mathematics teachers’ error approaches to modeling. Anemon Muş Alparslan University Journal of Social Sciences, 8(3), 871882. https://doi.org/10.18506/anemon.637049
• Büyükadıgüzel, Z. (2019). The effect of mathematical modeling activities on the achievement of 7th grade students and examination of student opinions. [Master's Thesis], Bolu Abant İzzet Baysal University Institute of Educational Sciences.
• Büyüköztürk, Ş. Kilic, C. E. Akgün, Ö. E. Karadeniz, Ş. & Demirel. F. (2012). Scientific research methods (13th ed.). Pegem A.
• Bosse, M. J., Lynch-Davis, K., Adu-Gyamfi, K., & Chandler, K. (2016). Using integer manipulatives: Representational determinism. International Journal for Mathematics Teaching and Learning, 17(3), 1-20. https://doi.org/10.4256/ijmtl.v17i3.37
• Bozkurt, A, & Kuran, K. (2016). Teachers' views on implementing and designing activities in mathematics textbooks. Ege Education Journal, 17(2), 377-398. https://doi.org/10.12984/egeefd.280750
• Bozkurt, A., & Polat, M. (2011). Teachers' views on the effect of modeling with counters on learning integers. Gaziantep University Journal of Social Sciences, 10(2), 787-801.
• Çakmak-Gürel, Z., &. Işık, A. (2016). Examination of primary school mathematics teacher candidates' competencies regarding mathematical modeling, E-International Journal of Educational Research, 9(3), 85-103. https://doi.org/10.19160/ijer.477651
• Cemen, P. B. (1993). Adding and subtracting integers on the number line. Arithmetic Teacher, 40(7), 388-389. https://doi.org/10.24106/kefdergi.833879
• Cunningham, A. W. (2009). Using the number line to teach signed numbers for remedial community college mathematics. Math Teaching Research Journal Online, 3(4), 1-40.
• Coşkun, R., Altunışık, R., & Yıldırım, E. (2019). Research methods in social sciences: SPSS applied. Sakarya Publishing.
• Çetin, H. (2016). The effect of integer teaching supported by multiple representations with an inquiry learning approach on the achievements, model preferences and transition skills between representations of 6th grade students. [Doctoral Thesis]. Necmettin Erbakan University, Institute of Educational Sciences.
• Durmaz, B. (2017). Achievements of mathematics teachers and candidates in modeling four operations with integers with counting stamps. Ahi Evran University Kırşehir Faculty of Education Journal, 18(3), 171-192.
• Ekiz, D. (2003). Introduction to research methods and methods in education. Anı Publishing.
• Erdem, E., Başıbüyük, K., Gökkurt, B., Şahin, Ö., & Soylu, Y. (2015). Difficulties in teaching whole numbers and suggested solutions. Journal of Education Faculty, 17(1), 97-117. https://doi.org/10.17556/jef.53497
• Erdem, E. (2015). The effect of enriched learning environment on mathematical reasoning and attitude [Doctoral thesis]. Atatürk University, Institute of Educational Sciences.
• Gallardo, A. (2002). The extension of the natural-number domain to the integers in the transition from arithmetic to algebra. Educational Studies in Mathematics, 49(1), 171-192.
• Hacısalihoğlu-Karadeniz, M. & Hodancı, A. N. (2022). Determining sixth grade students' misconceptions about integers. Journal of Computer and Educational Research, 10(20), 358-370. https://doi.org/10.18009/jcer.1087195
• Hattie, J. (2009). Visible learning: A synthesis of over 800 meta-analyses relating to achievement. Routledge.
• Işıksal-Bostan, M. (2009). Difficulties regarding negative numbers, misconceptions and suggestions to eliminate these misconceptions. In E. Bingölbali & M. F. Özmantar (Eds.), Mathematical difficulties encountered in primary education and solution suggestions (p. 155-184). Pegem Academy.
• İşgüden, E. (2008). Difficulties encountered by 7th and 8th grade students regarding integers.  Master’s Thesis. Osmangazi University, Institute of Science and Technology.
• Kandemir, M. A. (2011). Examining the effects of modeling activities on students' affective characteristics, problem solving and technology-related thoughts. [Master’s Thesis], Balıkesir University, Institute of Educational Sciences.
• Kapur, J. N. (1998). Mathematical modeling. New age international Publishers.
• Karataş, Z. (2017). Paradigm transformation in social sciences research: Rise of qualitative approach. Turkish Journal of Social Work Research, 1(1), 68-86.
• Kilhamn, C. (2011). Making sense of negative numbers. [Doctoral Dissertation]. University of Gotenburg, Faculty of Education.
• Kutluca, T. & Akın, M. F. (2013). Somut materyallerle matematik öğretimi: Dört kefeli cebir terazisi kullanımı üzerine nitel bir çalışma. Turkish Journal of Computer and Mathematics Education, 4(1), 48-65.
• Kutluca, T., & Kaya, D. (2023). Mathematical modelling: A retrospective overview. Journal of Computer and Education Research, 11 (21), 240-274. https://doi.org/10.18009/jcer.1242785
• Lesh, R. A. & Doerr, H. (2003). Foundations of model and modelling perspectives on mathematic teaching and learning. In R. A. Lesh & H. Doerr (Eds.), Beyond constructivism: A models and modelling perspectives on mathematics teaching, learning and problem solving (pp. 3-33). Lawrance Erlbauum.
• Mayer, R. C., Dawis, J. H., & Schoorman, F. D. (1995). An integrative model of organizational trust. Academy of Management Review, 20(1), 709-734. https://doi.org/10.5465/amr.1995.9508080335
• Miles, M, B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded Sourcebook. (2nd ed). Sage Publication.
• Ministry of National Education [MoNE]. (2018). Secondary school mathematics course (5th, 6th, 7th and 8th grades) curriculum. Board of Education and Discipline.
• Ministry of National Education [MoNE]. (2019). Secondary school mathematics course book for 7th graders. Board of Education and Discipline.
• Ministry of National Education [MoNE] (2024). Maths mobilisation. Accessed at 06.04.2024 from https://www.meb.gov.tr/matematik-seferberligi-basladi/haber/26241/tr
• Niss, M. (1998). Aspects of the nature and state of research in mathematics education. Educational Studies in Mathematics 40(1), 1-24.
• Özdemir, E. (2021). Performing basic operations with integers using a number line and counting scales. International Journal of Educational Studies in Mathematics, 8(1), 44-58. https://doi.org/10.17278/ijesim.838672
• Patton, Q. M. (2014). Qualitative research and evaluation methods (Whole, M. & Demir, S. B, Trans.). Pegem Academy.
• Punch, K. F. (2005). Introduction to social research (Trans. D. Bayrak, H. B. Arslan & Z. Akyüz). Siyasal Publishing.
• Saban, A. (2008). Metaphors about school. Educational Administration: Theory and Practice, 14(3), 459-496. Saka, E. (2016). The role of technology in the process of solving mathematical modeling problems of teacher candidates. Doctoral Thesis], Karadeniz Technical University, Institute of Educational Sciences.
• Sevecan, F. & Çilingiroğlu, N. (2007). Qualitative data collection methods used in research in the field of health. Community Medicine Bulletin, 26(1), 1-6.
• Soydaş Çakır, H. & Akyazı, E. (2021). Interaction increasing factors: Research on e-learning content design. International e-Journal of Educational Studies, 5(9), 25-40. https://doi.org/10.31458/iejes.786457
• Sriraman, B. (2005, February). Conceptualizing the notion of model eliciting. Paper presented at the Fourth Congress of the European Society or Research in Mathematics Education, Sant Feliu de Guíxols.
• Tavşancıl, E., & Aslan, E. (2001). Content analysis and application examples for verbal, written and other materials. Epsilon Publication.
• Tutak, T., Süzen, A. B., & İnan, İ. E. (2019). Determining the mistakes of secondary school mathematics teachers on operation priority. Participatory Educational Research, 7(1), 16-29. http://dx.doi.org/10.17275/per.20.2.7.1
• Türnüklü, A. (2000). A qualitative research technique that can be used effectively in educational research: Interview. Educational Administration in Theory and Practice, 24(1), 543-559.
• Yıldırım, A. & Şimşek, H. (2008). Qualitative research methods in the social sciences. Seckin Publishing.
• Zwaneveld, G., Perrenet, J., Van Overveld, K., & Borghuis, T. (2017). Mathematical modeling in dutch textbooks is it real mathematical modeling? In G. A. Stillman, W. Blum, & G. Kaiser (Eds.), Mathematical modeling and applications: Crossing and researching boundaries in mathematics education (1 ed., pp. 503–514). Springer International Publishing AG. Advanced online broadcasting. https://doi.org/10.1007/978-3-319-62968-1_42