Research Article
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Implications from a Modelling based Flipped Mathematics Course

Year 2023, Volume: 7 Issue: 15, 465 - 483, 21.10.2023
https://doi.org/10.31458/iejes.1286927

Abstract

The present study investigated the effect of the flipped classroom model, which was practiced in an undergraduate mathematics class, on pre-service primary school teachers’ ability to solve problems related to real life and modelling. This study was designed as an action research study exploring the implementation of a new teaching technique. The participants were 16 pre-service teachers who voluntarily took part in the study. The implementation period, which lasted for five weeks, included the following topics: ordered pairs, Cartesian product, relation and its characteristics, the concept of function, types of functions, and linear relation. The data in this study consisted of worksheets that had problem-solving processes, video records of classroom practices, participant journals, and field notes taken by the researcher. The data were analyzed through content analysis. It was observed that the flipped classroom model in the study enabled students to develop their mathematics language, conceptual knowledge, and the use of multiple representations by providing them with an opportunity to work on modelling and real-life problems. This model allowed students to take responsibility for their learning and also provided the teacher with an opportunity to prevent mistakes and misconceptions of students. In addition, it was observed in the data collected from classroom practices and student journals that student–student and student–teacher interactions developed as a result of the classes taught in the flipped classroom model.

Ethical Statement

Ethical approval and written permission for this study were obtained from the Adnan Menderes University with the decision dated 10/03/2017 and numbered 15428.

References

  • Anderson, L., & Brennan, J. P. (2015). An experiment in “flipped” teaching in freshman calculus. PRIMUS, 25(9-10), 861-875. https://doi.org/10.1080/10511970.2015.1059916
  • Aydın, M., Ökmen, B., Şahin, S., & Kılıç, A. (2021). The meta-analysis of the studies about the effects of flipped learning on students’ achievement. Turkish Online Journal of Distance Education, 22(1), 33–51.
  • Ball, D. L. (1990). The mathematical understandings that prospective teacher bring to teacher education. Elementary School Journal. 90, 449–466.
  • Bergmann, J., & Sams, A. (2012). Flip your classroom: Reach every student in every class every day. Washington DC: International Society for Technology in Education (ISTE).
  • Bhagat, K. K., Chang, C. N., & Chang, C. Y. (2016). The impact of the flipped classroom on mathematics concept learning in high school. Educational Technology & Society, 19 (3), 134-142.
  • Bredow, C. A., Roehling, P. V., Knorp, A. J., & Sweet, A. M. (2021). To Flip or Not to Flip? A Meta-Analysis of the Efficacy of Flipped Learning in Higher Education. Review of Educational Research, 91(6), 878–918. https://doi.org/10.3102/00346543211019122
  • Bukova-Güzel, E. (2016). Matematik eğitiminde matematiksel modelleme [Mathematical modeling in mathematics education]. Ankara: Pegem Akademi.
  • Cohen, L., Manion, L., & Morrison, K. (2007). Research methods in education (6th ed.). New York, NY: Routledge.
  • Cronhjort, M., Filipsson, L., & Weurlander, M. (2017). Improved engagement and learning in flipped-classroom calculus. Teaching Mathematics and its Applications: An International Journal of the IMA, 37(3), 113-121. https://doi.org/10.1093/teamat/hrx007
  • Foldnes, N. (2016). The flipped classroom and cooperative learning: Evidence from a randomised experiment. Active Learning in Higher Education, 17(1), 39-49. https://doi.org/10.1177/1469787415616726
  • Geiger, V., & Kaiser, G. (2014, July). Initial thoughts on the instructional perspective. In Proceedings of the 2014 PME Conference (Vol. 1, pp. 159-162). Vancouver: Simon Fraser University.
  • Gravemeijer, K., & Doorman, M. (1999). Context problems in realistic mathematics education: A calculus course as an example. Educational Studies in Mathematics, 39(1-3), 111-129.
  • Guerrero, S., Beal, M., Lamb, C., Sonderegger, D., & Baumgartel, D. (2015). Flipping undergraduate finite mathematics: findings and implications, PRIMUS, 25(9-10), 814-832. https://doi.org/10.1080/10511970.2015.1046003
  • Heuett, W. J. (2017). Flipping the math classroom for non-math majors to enrich their learning experience, PRIMUS. https://doi.org/10.1080/10511970.2016.1256925
  • Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students’ learning. Second handbook of research on mathematics teaching and learning, 1, 371-404.
  • Jungić, V., Kaur, H., Mulholland, J., & Xin, C. (2015). On flipping the classroom in large first year calculus courses. International Journal of Mathematical Education in Science and Technology, 46(4), 508-520. https://doi.org/10.1080/0020739X.2014.990529
  • Kensington-Miller, B., Novak, J., & Evans, T. (2016). Just do it: flipped lecture, determinants and debate, International Journal of Mathematical Education in Science and Technology, 47(6), 853-862, https://doi.org/10.1080/0020739X.2015.1129075
  • Kirvan, R., Rakes, C. R., & Zamora, R. (2015). Flipping an algebra classroom: analyzing, modeling, and solving systems of linear equations, Computers in the Schools, 32(3-4), 201-223. https://doi.org/10.1080/07380569.2015.1093902
  • Lesh, R.A., & Doerr, H. M. (2003). Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching. Mahwah, NJ: Lawrence Erlbaum.
  • Lesh, R., Yoon, C., & Zawojewski, J. (2007). John Dewey revisited-making mathematics practical versus making practice mathematical. In R. Lesh, E. Hamilton & J. Kaput (Eds.), Foundations for the future in mathematics education (pp. 315-348). Mahwah, NJ: Lawrence Erlbaum.
  • Lesseig, K., & Krouss, P. (2017). Implementing a flipped instructional model in college algebra: profiles of student activity, International Journal of Mathematical Education in Science and Technology, 48(2), 202-214. https://doi.org/10.1080/0020739X.2016.1233586
  • Lewin, K. (1948). Resolving social conflicts; selected papers on group dynamics. New York, NY: Harper & Row.
  • McGivney-Burelle, J., & Xue, F. (2013). Flipping calculus. Primus, 23(5), 477-486.
  • Murphy, J., Chang, J-M., & Suaray, K. (2016). Student performance and attitudes in a collaborative and flipped linear algebra course, International Journal of Mathematical Education in Science and Technology, 47(5), 653-673. https://doi.org/10.1080/0020739X.2015.1102979
  • Naccarato, E., & Karakok, G. (2015). Expectations and implementations of the flipped classroom model in undergraduate mathematics courses. International Journal of Mathematical Education in Science and Technology, 46(7), 968-978.
  • Niss, M. (1999). Aspects of the nature and state of research in mathematics education. Educational Studies in Mathematics, 40(1), 1-24.
  • Novak, J., Kensington-Miller, B., & Evans, T. (2016). Flip or flop? Students’ perspectives of a flipped lecture in mathematics, International Journal of Mathematical Education in Science and Technology, https://doi.org/10.1080/0020739X.2016.1267810
  • OECD, (2010), PISA 2012 Field trial problem solving framework: draft subject to possible revision after the field trial, Available online at: 18.09.2018 http://www.oecd.org/pisa/pisaproducts/46962005.pdf Petrillo, J. (2016). On flipping first-semester calculus: A case study. International Journal of Mathematical Education in Science and Technology, 47(4), 573-582.
  • Schroeder, L.B., McGivney-Burelle, J., & Xue, F. (2015). To flip or not to flip? An exploratory study comparing student performance in calculus I, PRIMUS, 25(9-10), 876-885.
  • Sherrow, T., Lang, B., & Corbett, R. (2016). The flipped class: Experience in a university business communication course. Business and Professional Communication Quarterly, 79(2), 207-216. https://doi.org/10.1177/2329490615614840
  • Siller, H-S., Cevikbas, M., Geiger, V., & Greefrath, G. (2022, July). The role of digital resources in mathematical modelling research. In Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 152-155). Alicante: University of Alicante.
  • Sopamena, P., Sangadji, K., Riaddin, D., Kaliky, S., & Assgaf, G. (2023). Effectiveness of flipped classroom model on mathematics achievement at the university level: A meta-analysis study. International Journal of Instruction, 16(1), 767-780.
  • Stralan, P., Osborn, A., & Palmer, E. (2020). The flipped classroom: A meta-analysis of effects on student performance across disciplines and education levels. Educational Research Review,. 30, 100314. http://doi.org/10.1016/j.edurev.2020.100314
  • Strayer, J. (2007). The effects of the classroom flip on the learning environment: A comparison of learning activity in a traditional classroom and a flip classroom that used an intelligent tutoring system (Doctoral dissertation, The Ohio State University).
  • Şen, E-O. (2022). Thematic analysis of articles on flipped learning in Mathematics education. Turkish Online Journal of Distance Education-TOJDE, 23(2), 202-222.
  • Van Sickle, J. (2015). Adventures in flipping college algebra. PRIMUS, 25(8), 600-613. https://doi.org/10.1080/10511970.2015.1031299
  • Witt, C. M., Trivedi, C., & Aminalroayae, F. (2021). Using flipped instruction in a technology-enhanced learning environment: the case for scaffolding. Issues in Information Systems, 22(2), 52-62. https://doi.org/10.48009/2_iis_2021_52_62
  • Wright, S. E. (2015) Linear algebra and the experiences of a “Flipper”. PRIMUS, 25(8), 627-640. https://doi.org/10.1080/10511970.2015.1031304
  • Yıldırım, A. & Şimşek, H. (2005). Sosyal Bilimlerde Nitel Araştırma Yöntemleri [Qualitative Research Methods in Social Sciences]. Ankara: Seçkin Yayınları.
  • Yoon, C., Dreyfus, T., & Thomas, M. (2010). How high is the tramping track? Mathematising and applying in a calculus model-eliciting activity. Mathematics Education Research Journal, Australia, 22(1), 141-157.
  • Zainuddin, Z. (2017). First-year college students’ experiences in the EFL flipped classroom: A case study in Indonesia, International Journal of Instruction, 10(1), 133-150.
  • Zawojewski, J. S., Lesh, R., ve English, L. D. (2003). A models and modelling perspective on the role of small group learning. In R. A. Lesh & H. Doerr (Eds.), Beyond constructivism: models and modeling perspectives on mathematics problem solving, learning and teaching, (pp. 337- 358). Mahwah, NJ: Lawrence Erlbaum.

Implications from a Modelling based Flipped Mathematics Course

Year 2023, Volume: 7 Issue: 15, 465 - 483, 21.10.2023
https://doi.org/10.31458/iejes.1286927

Abstract

The present study investigated the effect of the flipped classroom model, which was practiced in an undergraduate mathematics class, on pre-service primary school teachers’ ability to solve problems related to real life and modelling. This study was designed as an action research study exploring the implementation of a new teaching technique. The participants were 16 pre-service teachers who voluntarily took part in the study. The implementation period, which lasted for five weeks, included the following topics: ordered pairs, Cartesian product, relation and its characteristics, the concept of function, types of functions, and linear relation. The data in this study consisted of worksheets that had problem-solving processes, video records of classroom practices, participant journals, and field notes taken by the researcher. The data were analyzed through content analysis. It was observed that the flipped classroom model in the study enabled students to develop their mathematics language, conceptual knowledge, and the use of multiple representations by providing them with an opportunity to work on modelling and real-life problems. This model allowed students to take responsibility for their learning and also provided the teacher with an opportunity to prevent mistakes and misconceptions of students. In addition, it was observed in the data collected from classroom practices and student journals that student–student and student–teacher interactions developed as a result of the classes taught in the flipped classroom model.

References

  • Anderson, L., & Brennan, J. P. (2015). An experiment in “flipped” teaching in freshman calculus. PRIMUS, 25(9-10), 861-875. https://doi.org/10.1080/10511970.2015.1059916
  • Aydın, M., Ökmen, B., Şahin, S., & Kılıç, A. (2021). The meta-analysis of the studies about the effects of flipped learning on students’ achievement. Turkish Online Journal of Distance Education, 22(1), 33–51.
  • Ball, D. L. (1990). The mathematical understandings that prospective teacher bring to teacher education. Elementary School Journal. 90, 449–466.
  • Bergmann, J., & Sams, A. (2012). Flip your classroom: Reach every student in every class every day. Washington DC: International Society for Technology in Education (ISTE).
  • Bhagat, K. K., Chang, C. N., & Chang, C. Y. (2016). The impact of the flipped classroom on mathematics concept learning in high school. Educational Technology & Society, 19 (3), 134-142.
  • Bredow, C. A., Roehling, P. V., Knorp, A. J., & Sweet, A. M. (2021). To Flip or Not to Flip? A Meta-Analysis of the Efficacy of Flipped Learning in Higher Education. Review of Educational Research, 91(6), 878–918. https://doi.org/10.3102/00346543211019122
  • Bukova-Güzel, E. (2016). Matematik eğitiminde matematiksel modelleme [Mathematical modeling in mathematics education]. Ankara: Pegem Akademi.
  • Cohen, L., Manion, L., & Morrison, K. (2007). Research methods in education (6th ed.). New York, NY: Routledge.
  • Cronhjort, M., Filipsson, L., & Weurlander, M. (2017). Improved engagement and learning in flipped-classroom calculus. Teaching Mathematics and its Applications: An International Journal of the IMA, 37(3), 113-121. https://doi.org/10.1093/teamat/hrx007
  • Foldnes, N. (2016). The flipped classroom and cooperative learning: Evidence from a randomised experiment. Active Learning in Higher Education, 17(1), 39-49. https://doi.org/10.1177/1469787415616726
  • Geiger, V., & Kaiser, G. (2014, July). Initial thoughts on the instructional perspective. In Proceedings of the 2014 PME Conference (Vol. 1, pp. 159-162). Vancouver: Simon Fraser University.
  • Gravemeijer, K., & Doorman, M. (1999). Context problems in realistic mathematics education: A calculus course as an example. Educational Studies in Mathematics, 39(1-3), 111-129.
  • Guerrero, S., Beal, M., Lamb, C., Sonderegger, D., & Baumgartel, D. (2015). Flipping undergraduate finite mathematics: findings and implications, PRIMUS, 25(9-10), 814-832. https://doi.org/10.1080/10511970.2015.1046003
  • Heuett, W. J. (2017). Flipping the math classroom for non-math majors to enrich their learning experience, PRIMUS. https://doi.org/10.1080/10511970.2016.1256925
  • Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students’ learning. Second handbook of research on mathematics teaching and learning, 1, 371-404.
  • Jungić, V., Kaur, H., Mulholland, J., & Xin, C. (2015). On flipping the classroom in large first year calculus courses. International Journal of Mathematical Education in Science and Technology, 46(4), 508-520. https://doi.org/10.1080/0020739X.2014.990529
  • Kensington-Miller, B., Novak, J., & Evans, T. (2016). Just do it: flipped lecture, determinants and debate, International Journal of Mathematical Education in Science and Technology, 47(6), 853-862, https://doi.org/10.1080/0020739X.2015.1129075
  • Kirvan, R., Rakes, C. R., & Zamora, R. (2015). Flipping an algebra classroom: analyzing, modeling, and solving systems of linear equations, Computers in the Schools, 32(3-4), 201-223. https://doi.org/10.1080/07380569.2015.1093902
  • Lesh, R.A., & Doerr, H. M. (2003). Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching. Mahwah, NJ: Lawrence Erlbaum.
  • Lesh, R., Yoon, C., & Zawojewski, J. (2007). John Dewey revisited-making mathematics practical versus making practice mathematical. In R. Lesh, E. Hamilton & J. Kaput (Eds.), Foundations for the future in mathematics education (pp. 315-348). Mahwah, NJ: Lawrence Erlbaum.
  • Lesseig, K., & Krouss, P. (2017). Implementing a flipped instructional model in college algebra: profiles of student activity, International Journal of Mathematical Education in Science and Technology, 48(2), 202-214. https://doi.org/10.1080/0020739X.2016.1233586
  • Lewin, K. (1948). Resolving social conflicts; selected papers on group dynamics. New York, NY: Harper & Row.
  • McGivney-Burelle, J., & Xue, F. (2013). Flipping calculus. Primus, 23(5), 477-486.
  • Murphy, J., Chang, J-M., & Suaray, K. (2016). Student performance and attitudes in a collaborative and flipped linear algebra course, International Journal of Mathematical Education in Science and Technology, 47(5), 653-673. https://doi.org/10.1080/0020739X.2015.1102979
  • Naccarato, E., & Karakok, G. (2015). Expectations and implementations of the flipped classroom model in undergraduate mathematics courses. International Journal of Mathematical Education in Science and Technology, 46(7), 968-978.
  • Niss, M. (1999). Aspects of the nature and state of research in mathematics education. Educational Studies in Mathematics, 40(1), 1-24.
  • Novak, J., Kensington-Miller, B., & Evans, T. (2016). Flip or flop? Students’ perspectives of a flipped lecture in mathematics, International Journal of Mathematical Education in Science and Technology, https://doi.org/10.1080/0020739X.2016.1267810
  • OECD, (2010), PISA 2012 Field trial problem solving framework: draft subject to possible revision after the field trial, Available online at: 18.09.2018 http://www.oecd.org/pisa/pisaproducts/46962005.pdf Petrillo, J. (2016). On flipping first-semester calculus: A case study. International Journal of Mathematical Education in Science and Technology, 47(4), 573-582.
  • Schroeder, L.B., McGivney-Burelle, J., & Xue, F. (2015). To flip or not to flip? An exploratory study comparing student performance in calculus I, PRIMUS, 25(9-10), 876-885.
  • Sherrow, T., Lang, B., & Corbett, R. (2016). The flipped class: Experience in a university business communication course. Business and Professional Communication Quarterly, 79(2), 207-216. https://doi.org/10.1177/2329490615614840
  • Siller, H-S., Cevikbas, M., Geiger, V., & Greefrath, G. (2022, July). The role of digital resources in mathematical modelling research. In Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 152-155). Alicante: University of Alicante.
  • Sopamena, P., Sangadji, K., Riaddin, D., Kaliky, S., & Assgaf, G. (2023). Effectiveness of flipped classroom model on mathematics achievement at the university level: A meta-analysis study. International Journal of Instruction, 16(1), 767-780.
  • Stralan, P., Osborn, A., & Palmer, E. (2020). The flipped classroom: A meta-analysis of effects on student performance across disciplines and education levels. Educational Research Review,. 30, 100314. http://doi.org/10.1016/j.edurev.2020.100314
  • Strayer, J. (2007). The effects of the classroom flip on the learning environment: A comparison of learning activity in a traditional classroom and a flip classroom that used an intelligent tutoring system (Doctoral dissertation, The Ohio State University).
  • Şen, E-O. (2022). Thematic analysis of articles on flipped learning in Mathematics education. Turkish Online Journal of Distance Education-TOJDE, 23(2), 202-222.
  • Van Sickle, J. (2015). Adventures in flipping college algebra. PRIMUS, 25(8), 600-613. https://doi.org/10.1080/10511970.2015.1031299
  • Witt, C. M., Trivedi, C., & Aminalroayae, F. (2021). Using flipped instruction in a technology-enhanced learning environment: the case for scaffolding. Issues in Information Systems, 22(2), 52-62. https://doi.org/10.48009/2_iis_2021_52_62
  • Wright, S. E. (2015) Linear algebra and the experiences of a “Flipper”. PRIMUS, 25(8), 627-640. https://doi.org/10.1080/10511970.2015.1031304
  • Yıldırım, A. & Şimşek, H. (2005). Sosyal Bilimlerde Nitel Araştırma Yöntemleri [Qualitative Research Methods in Social Sciences]. Ankara: Seçkin Yayınları.
  • Yoon, C., Dreyfus, T., & Thomas, M. (2010). How high is the tramping track? Mathematising and applying in a calculus model-eliciting activity. Mathematics Education Research Journal, Australia, 22(1), 141-157.
  • Zainuddin, Z. (2017). First-year college students’ experiences in the EFL flipped classroom: A case study in Indonesia, International Journal of Instruction, 10(1), 133-150.
  • Zawojewski, J. S., Lesh, R., ve English, L. D. (2003). A models and modelling perspective on the role of small group learning. In R. A. Lesh & H. Doerr (Eds.), Beyond constructivism: models and modeling perspectives on mathematics problem solving, learning and teaching, (pp. 337- 358). Mahwah, NJ: Lawrence Erlbaum.
There are 42 citations in total.

Details

Primary Language English
Subjects Mathematics Education
Journal Section Research Article
Authors

Deniz Özen Ünal 0000-0002-9279-3452

Ersen Yazıcı 0000-0002-1310-2247

Taner Arabacıoglu 0000-0003-1116-1777

Early Pub Date October 7, 2023
Publication Date October 21, 2023
Submission Date April 24, 2023
Published in Issue Year 2023 Volume: 7 Issue: 15

Cite

APA Özen Ünal, D., Yazıcı, E., & Arabacıoglu, T. (2023). Implications from a Modelling based Flipped Mathematics Course. International E-Journal of Educational Studies, 7(15), 465-483. https://doi.org/10.31458/iejes.1286927

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