Towards Flipped Learning in Upper Secondary Mathematics Education

Robert Weinhandl(1*), Zsolt Lavicza(2), Stefanie Schallert(3),

(1) Johannes Kepler University, Linz, Austria, School of Education
(2) Johannes Kepler University, Linz, Austria, School of Education
(3) Johannes Kepler University, Linz, Austria, School of Education
(*) Corresponding Author

Abstract


Challenges for students in the 21st century, such as acquiring technology, problem-solving, and cooperation skills, also necessitate changes in mathematics education to be able to respond to changing educational needs. One way to respond to these challenges is by utilizing recent educational innovations in schools, for instance, among others are flipped learning (FL) approaches. In this paper, we outline our explorative educational experiment that investigates vital elements of mathematics learning in FL approaches in upper secondary education. We describe the methodologies and findings of our qualitative study based on design-based research to discover key elements of FL approaches in upper secondary education. Analyzing the oral and written data collected over ten months using grounded theory approaches suggested categories (a) confidence when learning; (b) learning by working, and, and (c) flexibility when learning could be essential to understand FL approaches practices in mathematics classrooms. These categories indicate that when using FL approaches in mathematics learning, it could be essential for students to acquire knowledge in a confident and adaptable environment actively.

Keywords


flipped learning; mathematics education; student-centered learning

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References


Anderson, T., & Shattuck, J. (2012). Design-based research: A decade of progress in education research? Educational Researcher, 41, 16–25. https://doi.org/10.3102/0013189X11428813

Bell, C. V., & Pape, S. J. (2012). Scaffolding students’ opportunities to learn mathematics through social interactions. Mathematics Education Research Journal, 24, 423–445. https://doi.org/10.1007/s13394-012-0048-1

Bentley, M., Fleury, S. C., & Garrison, J. W. (2007). Critical constructivism for teaching and learning in a democratic society. Journal of Thought, 42, 9–22.

Bishop, J. L., & Verleger, M. A. (2013). The flipped classroom: A survey of the research. 30, Paper ID#6219. (http://www.studiesuccesho.nl/wp-content/uploads/2014/04/flipped-classroom-artikel.pdf) [accessed Jun 2019]

Breuer, F., Dieris, B., & Lettau, A. (2009). Reflexive Grounded Theory: Eine Einführungfür die Forschungspraxis. Wiesbaden: VS Verlag für Sozial wissen schaften.

Burton, L. (2004). “Confidence is Everything†– Perspectives of Teachers and Students on Learning Mathematics. Journal of Mathematics Teacher Education, 7, 357–381. https://doi.org/10.1007/s10857-004-3355-y

Chao, T., Chen, J., Star, J. R., & Dede, C. (2016). Using Digital Resources for Motivation and Engagement in Learning Mathematics: Reflections from Teachers and Students. Digital Experiences in Mathematics Education, 2, 253–277. https://doi.org/10.1007/s40751-016-0024-6

Charmaz, K. (2006). Constructing Grounded Theory: A Practical Guide through Qualitative Analysis. London; Thousand Oaks, Calif: SAGE Publications Ltd.

Cobb, P., Confrey, J., Disessa, A., Lehrer, R., & Schauble, L. (2003). Design Experiments in Educational Research. Educational Researcher, 32, 9–13. https://doi.org/10.3102/0013189X032001009

Coles, A., & Brown, L. (2016). Task design for ways of working: making distinctions in teaching and learning mathematics. Journal of Mathematics Teacher Education, 19, 149–168. https://doi.org/10.1007/s10857-015-9337-4

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, 113–121. https://doi.org/10.1093/teamat/hrx007

Denton, D. W. (2012). Enhancing instruction through constructivism, cooperative learning, and cloud computing. TechTrends, 56, 34–41.

Duit, R. (1995). Zur Rolle der konstruktivistischen sichtweise in der naturwissenschaftsdidaktischen Lehr-und Lernforschung. ZeitschriftFürPädagogik, 41, 905–923.

Elbers, E. (2003). Classroom interaction as reflection: Learning and teaching mathematics in a community of inquiry. Educational Studies in Mathematics, 54, 77. https://doi.org/10.1023/B:EDUC.0000005211.95182.90

Euler, D. (2001). Manche lernen es - aberwarum. ZeitschriftFürBerufs-Und Wirtschaftspädagogik, 97, 346–374.

Fadel, C. (2008). 21st Century Skills: How can you prepare students for the new Global Economy. (https://www.oecd.org/site/educeri21st/40756908.pdf) [accessed May 2019]

Flipped Learning Network (FLN). (2014). The Four Pillars of F-L-I-P. Retrieved from (https://flippedlearning.org/definition) [accessed Dec 2018]

Fogarty, G., Cretchley, P., Harman, C., Ellerton, N., & Konki, N. (2001). Validation of a questionnaire to measure mathematics confidence, computer confidence, and attitudes towards the use of technology for learning mathematics. Mathematics Education Research Journal, 13, 154–160. https://doi.org/10.1007/BF03217104

Gainsburg, J. (2008). Real-world connections in secondary mathematics teaching. Journal of Mathematics Teacher Education, 11, 199–219. https://doi.org/10.1007/s10857-007-9070-8

Galway, L. P., Corbett, K. K., Takaro, T. K., Tairyan, K., & Frank, E. (2014). A novel integration of online and flipped classroom instructional models in public health higher education. BMC Medical Education, 14, 181. https://doi.org/10.1186/1472-6920-14-181

García-Peñalvo, F. J., Fidalgo-Blanco, Ã., Sein-Echaluce, M. L., & Conde, M. Ã. (2016). Cooperative Micro Flip Teaching. In P. Zaphiris& A. Ioannou (Eds.), Learning and Collaboration Technologies: Third International Conference, LCT 2016, Held as Part of HCI International 2016, Toronto, ON, Canada, July 17-22, 2016, Proceedings, pp. 14–24. http://dx.doi.org/10.1007/978-3-319-39483-1_2

Glaser, B. G., & Strauss, A. L. (1999). Discovery of Grounded Theory: Strategies for Qualitative Research. New Brunswick: AldineTransaction.

Goerres, A., Kärger, C., & Lambach, D. (2015). AktivesLernen in der Massenveranstaltung: Flipped-Classroom-Lehreals Alternative zurklassischenVorlesung in der Politikwissenschaft. ZPolZeitschriftfürPolitikwissenschaft, 25, 135–152. https://doi.org/10.5771/1430-6387-2015-1-135

González-Gómez, D., Jeong, J. S., Airado Rodríguez, D., & Cañada-Cañada, F. (2016). Performance and Perception in the Flipped Learning Model: An Initial Approach to Evaluate the Effectiveness of a New Teaching Methodology in a General Science Classroom. Journal of Science Education and Technology, 25, 450–459. https://doi.org/10.1007/s10956-016-9605-9

Gräsel, C., Bruhn, J., Mandl, H., & Fischer, F. (1997). Lernenmit Computer netzenaus konstruktivistischer Perspektive. Unterrichtswissenschaft, 25, 4–18.

Harkness, S. S., & Stallworth, J. (2013). Photovoice: understanding high school females’ conceptions of mathematics and learning mathematics. Educational Studies in Mathematics, 84, 329–347. https://doi.org/10.1007/s10649-013-9485-3

Herreid, C. F., & Schiller, N. A. (2013). Case studies and the flipped classroom. Journal of College Science Teaching, 42, 62–66.

Hodges, T. E., & Hodge, L. L. (2017). Unpacking personal identities for teaching mathematics within the context of prospective teacher education. Journal of Mathematics Teacher Education, 20, 101–118. https://doi.org/10.1007/s10857-015-9339-2

Hung, C.-M., Huang, I., & Hwang, G.-J. (2014). Effects of digital game-based learning on students’ self-efficacy, motivation, anxiety, and achievements in learning mathematics. Journal of Computers in Education, 1, 151–166. https://doi.org/10.1007/s40692-014-0008-8

Hwang, G.-J., Lai, C.-L., & Wang, S.-Y. (2015). Seamless flipped learning: a mobile technology-enhanced flipped classroom with effective learning strategies. Journal of Computers in Education, 2, 449–473. https://doi.org/10.1007/s40692-015-0043-0

Kamin, A.-M. (2013). Die Methodologie der Grounded Theory alsübergeordnetesForschungsparadigma. In A.-M. Kamin (Ed.), BeruflichPflegendealsAkteure in digital unterstütztenLernwelten: EmpirischeRekonstruktion von berufsbiografischenLernmustern, pp. 20–28. https://doi.org/10.1007/978-3-658-02310-2_2

Kerres, M., & De Witt, C. (2004). PragmatismusalstheoretischeGrundlagefür die Konzeption von eLearning. In: D. Treichel& H.O. Meyer (Ed.): HandlungsorientiertesLernen und eLearning. Grundlagen und Beispiele. München: Oldenbourg Verlag.

Koohang, A., Riley, L., Smith, T., & Schreurs, J. (2009). E-learning and constructivism: From theory to application. Interdisciplinary Journal of E-Learning and Learning Objects, 5, 91–109.

Krathwohl, D. R. (2002). A revision of Bloom’s taxonomy: An overview. Theory into Practice, 41, 212–218.

Lee, J., Lim, C., & Kim, H. (2017). Development of an instructional design model for flipped learning in higher education. Educational Technology Research and Development, 65, 427–453. https://doi.org/10.1007/s11423-016-9502-1

Lee, C., & Johnston-Wilder, S. (2013). Learning mathematics—letting the pupils have their say. Educational Studies in Mathematics, 83, 163–180. https://doi.org/10.1007/s10649-012-9445-3

Long, T., Cummins, J., & Waugh, M. (2016). Use of the flipped classroom instructional model in higher education: instructors’ perspectives. Journal of Computing in Higher Education, 1–22. https://doi.org/10.1007/s12528-016-9119-8

Maciejewski, W. (2015). Flipping the calculus classroom: an evaluative study. Teaching Mathematics and Its Applications: An International Journal of the IMA, 35, 187–201. https://doi.org/10.1093/teamat/hrv019

Mey, G., & Mruck, K. (2011). Grounded Theory Reader (2nd ed.). Wiesbaden: VS Verlag fürSozialwissenschaften.

Mishra, P., & Koehler, M. J. (2006). Technological pedagogical content knowledge: A framework for teacher knowledge. Teachers College Record, 108, 1017–1054.

Reinmann, G. (2005). Innovation ohneForschung? Ein Plädoyerfür den Design-Based Research-Ansatz in der Lehr-Lernforschung. Unterrichtswissenschaft, 33, 52–69.

Rosenkranz, L. (2017). Qualitative Forschungsprinzipien der Grounded Theory. In L. Rosenkranz (Ed.), ExzessiveNutzung von OnlinespielenimJugendalter, pp. 83–94. https://doi.org/10.1007/978-3-658-15360-1_5

Samuelsson, J. (2006). ICT as a Change Agent of Mathematics Teaching in Swedish Secondary School. Education and Information Technologies, 11, 71–81. https://doi.org/10.1007/s10639-005-5713-5

Sharples, M. (2012). Innovating pedagogy 2012: exploring new forms of teaching, learning and assessment, to guide educators and policy makers. Milton Keynes: Open University.

Tait-Mccutcheon, S. L., & Loveridge, J. (2016). Examining equity of opportunities for learning mathematics through positioning theory. Mathematics Education Research Journal, 28, 327–348. https://doi.org/10.1007/s13394-016-0169-z

Tillmann, A., Niemeyer, J., & Krömker, D. (2014). ‘ImSchlafanzugbleibenkönnen’. E-Lectures zurDiversifizierung der LernangebotefürindividuelleLernräume. In Medien in Der Wissenschaft: Vol. 67. Rummler, Klaus (Eds.): Lernräumegestalten - Bildungskontextevielfältigdenken., pp. 317–331. (http://www.pedocs.de/volltexte/2015/10110/pdf/Lernraeume_gestalten_2014_Tillmann_ua_Im_Schlafanzug_bleiben_koennen.pdf) [accessed Jul 2018]

Von Glasersfeld, E. (1995). Aspekteeiner konstruktivistischen Didaktik. Regional Institute for School and Secondary Education (Eds.), Lehren Und Lernen Als Konstruktive Tätigkeit, Soest.

Vygotsky, L. S., & Cole, M. (1978). Mind in Society. Cambridge: Harvard University Press.

Wang, F. & Hannafin, M. J. (2005). Design-based research and technology-enhanced learning environments. Educational Technology Research and Development, 53(4), 5-23

Wasserman, N. H., Quint, C., Norris, S. A., & Carr, T. (2015). Exploring Flipped Classroom Instruction in Calculus III. International Journal of Science and Mathematics Education, 1–24. https://doi.org/10.1007/s10763-015-9704-8

Weidlich, J., & Spannagel, C. (2014). Die Vorbereitungsphaseim Flipped Classroom. Vorlesungsvideos versus Aufgaben - Sowiport. In Rummler, Klaus (Eds.), Lernräumegestalten - Bildungskontextevielfältigdenken. Münster u.a., pp. 237–248. (http://sowiport.gesis.org/search/id/fis-bildung-1056293) [accessed Jun 2017]

Weinhandl, R., & Lavicza, Z. (2018). Introducing teachers to a technology-supported flipped mathematics classroom teaching approach. Proceedings of the 5th ERME Topic Conference MEDA 2018. Presented at the ERME Topic Conference ‘Mathematics Education in the Digital Age’, Copenhagen., pp. 289–296.

Wong, L.-H. (2012). A learner-centric view of mobile seamless learning: Colloquium. British Journal of Educational Technology, 43, E19–E23. https://doi.org/10.1111/j.1467-8535.2011.01245.x

Wong, L.-H. (2015). A Brief History of Mobile Seamless Learning. In L.-H. Wong, M. Milrad, & M. Specht (Eds.), Seamless Learning in the Age of Mobile Connectivity, pp. 3–40. Singapore: Springer Singapore. https://doi.org/10.1007/978-981-287-113-8_1

Woods, P., Gapp, R., & King, M. A. (2016). Generating or developing grounded theory: methods to understand health and illness. International Journal of Clinical Pharmacy, 38, 663–670. https://doi.org/10.1007/s11096-016-0260-2

Zheng, L. (2015). A systematic literature review of design-based research from 2004 to 2013. Journal of Computers in Education, 2, 399–420. https://doi.org/10.1007/s40692-015-0036-z




DOI: https://doi.org/10.31327/jme.v5i1.1114

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