한국수학교육학회지시리즈D:수학교육연구 (Research in Mathematical Education)

  • 제25권2호
  • /
  • Pages.99-115
  • /
  • 2022
  • /
  • 1226-6191(pISSN)
  • /
  • 2287-9943(eISSN)
한국수학교육학회 (Korean Society of Mathematical Education)
권호 표지
DOI QR코드

DOI QR Code

Effects of a Flipped Classroom using Khan Academy and Mathematical Modeling on Overcoming Difficulties in Learning Mathematics

  • 투고 : 2022.05.13
  • 심사 : 2022.06.22
  • 발행 : 2022.06.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

This study examined difficulties middle school students have in learning mathematics and proposed a flipped classroom consisting of Khan Academy activities, small-group problem solving, and mathematical modeling to help improve their learning. A mixed-method approach was used to identify difficulties students have in learning mathematics, explore how the flipped classroom helped them reduce the learning difficulties identified, and examine if there were differences in students' mathematics achievement and their affective characteristics after participating in the flipped classroom. Qualitative analyses showed that students had difficulties in understanding mathematical concepts and finding effective ways to learn as well as negative views towards learning mathematics. This study also found that each activity of the flipped classroom had a different impact on student learning. Before class, the Khan Academy activities were most likely to help students understand mathematical concepts. In class, small-group problem solving activities were most helpful for students who had trouble finding effective learning methods and environments. Mathematical modeling activities were most likely effective in changing students' negative views towards mathematics. A quantitative analysis showed that the flipped classroom not only significantly improved the students' mathematics achievement, but also positively affected their confidence and motivation and how much they valued learning mathematics.

키워드

과제정보

This research was supported by Research Program through the NAVER Connect Foundation.

참고문헌

  1. Abramovich, S., Schunn, C., & Higashi, R. M. (2013). Are badges useful in education?: It depends upon the type of badge and expertise of learner. Educational Technology Research and Development, 61(2), 217-232. https://doi.org/10.1007/s11423-013-9289-2
  2. Akcayir, G., & Akcayir, M. (2018). The flipped classroom: A review of its advantages and challenges. Computers & Education, 126, 334-345. https://doi.org/10.1016/j.compedu.2018.07.021
  3. 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.
  4. Bliss, K. & Libertini, J. (2016). What is mathematical modeling? In Garfunkel, S., & Montgomery, M. (Eds). Guidelines for assessment & instruction in mathematical modeling education (GAIMME) (pp. 7-21). Consortium for Mathematics and Its Applications (COMAP) & Society for Industrial and Applied Mathematics (SIAM).
  5. Blum, W., & Ferri, R. B. (2009). Mathematical modeling: Can it be taught and learnt? Journal of Mathematical Modeling and Application, 1(1), 45-58.
  6. Cai, J., & Wang, T. (2010). Conceptions of effective mathematics teaching within a cultural context: Perspectives of teachers from China and the United States. Journal of Mathematics Teacher Education, 13(3), 265-287. https://doi.org/10.1007/s10857-009-9132-1
  7. Cargile, L. A., & Harkness, S. S. (2015). Flip or flop: Are math teachers using Khan Academy as envisioned by Sal Khan? TechTrends, 59(6), 21-28. https://doi.org/10.1007/s11528-015-0900-8
  8. Carmichael, C., Callingham, R., & Watt, H. M. (2017). Classroom motivational environment influences on emotional and cognitive dimensions of student interest in mathematics. ZDM, 49(3), 449-460. https://doi.org/10.1007/s11858-016-0831-7
  9. C ekmez, E. (2020). Using dynamic mathematics software to model a real-world phenomenon in the classroom. Interactive Learning Environments, 28(4), 526-538. https://doi.org/10.1080/10494820.2019.1674882
  10. Chen, Y., Wang, Y., Kinshuk, & Chen, N. S. (2014). Is FLIP enough? or should we use the FLIPPED model instead? Computers & Education, 79, 16-27. https://doi.org/10.1016/j.compedu.2014.07.004
  11. Chiang, F. K., & Chen, C. (2017). Modified flipped classroom instructional model in "learning sciences" course for graduate students. The Asia-Pacific Education Researcher, 26(1-2), 1-10. https://doi.org/10.1007/s40299-016-0321-2
  12. Chiu, T. K., & Mok, I. A. (2017). Learner expertise and mathematics different order thinking skills in multimedia learning. Computers & Education, 107, 147-164. https://doi.org/10.1016/j.compedu.2017.01.008
  13. Common Core State Standards Initiative. (2010). Common Core State Standards for mathematics. Retrieved from http://corestandards.org/asserts/CCSSI_Math%20Standards.pdf
  14. de Almeida, L. M. W. (2018). Considerations on the use of mathematics in modeling activities. ZDM, 50(1-2), 19-30. https://doi.org/10.1007/s11858-017-0902-4
  15. Delice, A., & Kertil, M. (2015). Investigating the representational fluency of pre-service mathematics teachers in a modeling process. International Journal of Science and Mathematics Education, 13(3), 631-656. https://doi.org/10.1007/s10763-013-9466-0
  16. Elo, S., & Kyngas, H. (2008). The qualitative content analysis process. Journal of Advanced Nursing, 62(1), 107-115. https://doi.org/10.1111/j.1365-2648.2007.04569.x
  17. Ferrucci, B. J., & Carter, J. A. (2003). Technology-active mathematical modeling. International Journal of Mathematical Education in Science and Technology, 34(5), 663-670. https://doi.org/10.1080/0020739031000148921
  18. Gilboy, M. B., Heinerichs, S., & Pazzaglia, G. (2015). Enhancing student engagement using the flipped classroom. Journal of Nutrition Education and Behavior, 47(1), 109-114. https://doi.org/10.1016/j.jneb.2014.08.008
  19. Hsiao, C. C., Huang, J. C., Huang, A. Y., Lu, O. H., Yin, C. J., & Yang, S. J. (2019). Exploring the effects of online learning behaviors on short-term and long-term learning outcomes in flipped classrooms. Interactive Learning Environments, 27(8), 1160-1177. https://doi.org/10.1080/10494820.2018.1522651
  20. Hung, C. Y., Sun, J. C. Y., & Liu, J. Y. (2019). Effects of flipped classrooms integrated with MOOCs and game-based learning on the learning motivation and outcomes of students from different backgrounds. Interactive Learning Environments, 27(8), 1028-1046. https://doi.org/10.1080/10494820.2018.1481103
  21. Hwang, G. J., & Lai, C. L. (2017). Facilitating and bridging out-of-class and in-class learning: An interactive e-book-based flipped learning approach for math courses. Journal of Educational Technology & Society, 20(1), 184-197.
  22. Kaiser, G., & Schwarz, B. (2006). Mathematical modeling as bridge between school and university. ZDM, 38(2), 196-208. https://doi.org/10.1007/BF02655889
  23. Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modeling in mathematics education. ZDM, 38(3), 302-310. https://doi.org/10.1007/BF02652813
  24. Kong, S. C. (2014). Developing information literacy and critical thinking skills through domain knowledge learning in digital classrooms: An experience of practicing flipped classroom strategy. Computers & Education, 78, 160-173. https://doi.org/10.1016/j.compedu.2014.05.009
  25. Krathwohl, D. R. (2002). A revision of Bloom's taxonomy: An overview. Theory into Practice, 41(4), 212-218. https://doi.org/10.1207/s15430421tip4104_2
  26. Lai, C. L., & Hwang, G. J. (2016). A self-regulated flipped classroom approach to improving students' learning performance in a mathematics course. Computers & Education, 100, 126-140. https://doi.org/10.1016/j.compedu.2016.05.006
  27. Lee, K., Rim, H., Park, I., Seo, M., & Kim, B. (2016). A study on development of the survey items for affective domain in mathematics of NAEA. The Journal of Curriculum and Evaluation, 19(4), 45-70. https://doi.org/10.29221/jce.2016.19.4.45
  28. Lithner, J. (2000). Mathematical reasoning and familiar procedures. International Journal of Mathematical Education in Science and Technology, 31(1), 83-95. https://doi.org/10.1080/002073900287417
  29. Lo, C. K., & Hew, K. F. (2017). Using "First Principles of Instruction" to design secondary school mathematics flipped classroom: The findings of two exploratory studies. Educational Technology & Society, 20(1), 222-236.
  30. Lo, C. K., Hew, K. F., & Chen, G. (2017). Toward a set of design principles for mathematics flipped classrooms: A synthesis of research in mathematics education. Educational Research Review, 22, 50-73. https://doi.org/10.1016/j.edurev.2017.08.002
  31. Murphy, R., Gallagher, L., Krumm, A., Mislevy, J., & Hafter, A. (2014). Research on the use of Khan Academy in schools. SRI Education.
  32. Musu-Gillette, L. E., Wigfield, A., Harring, J. R., & Eccles, J. S. (2015). Trajectories of change in students' self-concepts of ability and values in math and college major choice. Educational Research and Evaluation, 21(4), 343-370. https://doi.org/10.1080/13803611.2015.1057161
  33. Overmyer, J. (2015). Research on flipping college algebra: Lessons learned and practical advice for flipping multiple sections. PRIMUS, 25(9-10), 792-802. https://doi.org/10.1080/10511970.2015.1045572
  34. Phillips, D., & Cohen, J. (2015). Learning gets personal: How Idaho students and teachers are embracing personalized learning through Khan Academy. Retrieved from https://s3.amazonaws.com/KA-share/impact/learning-gets-personal.pdf
  35. Ruiperez-Valiente, J. A., Munoz-Merino, P. J., Leony, D., & Kloos, C. D. (2015). ALASKA: A learning analytics extension for better understanding the learning process in the Khan Academy platform. Computers in Human Behavior, 47, 139-148. https://doi.org/10.1016/j.chb.2014.07.002
  36. Sergis, S., Sampson, D. G., & Pelliccione, L. (2018). Investigating the impact of flipped classroom on students' learning experiences: A self-determination theory approach. Computers in Human Behavior, 78, 368-378. https://doi.org/10.1016/j.chb.2017.08.011
  37. Shalev, R. S., Manor, O., Kerem, B., Ayali, M., Badichi, N., Friedlander, Y., & Gross-Tsur, V. (2001). Developmental dyscalculia is a familial learning disability. Journal of Learning Disabilities, 34(1), 59-65. https://doi.org/10.1177/002221940103400105
  38. Song, Y., Jong, M. S., Chang, M., & Chen, W. (2017). Guest editorial: "HOW" to design, implement and evaluate the flipped classroom? A synthesis. Journal of Educational Technology & Society, 20(1), 180-183.
  39. Tawfik, A. A., & Lilly, C. (2015). Using a flipped classroom approach to support problem-based learning. Technology, Knowledge and Learning, 20(3), 299-315. https://doi.org/10.1007/s10758-015-9262-8
  40. UNESCO Institute for Statistics. (2017). More than one-half of children and adolescents are not learning worldwide. Fact Sheet No. 46, September 2017. UNESCO Institute for Statistics. Retrieved from: http://uis.unesco.org/sites/default/les/documents/fs46-more-than-half-children-not-learning-en-2017.pdf
  41. Yang, Q. F., Lin, C. J., & Hwang, G. J. (2021). Research focuses and findings of flipping mathematics classes: a review of journal publications based on the technology-enhanced learning model. Interactive Learning Environments, 29(6), 905-938. https://doi.org/10.1080/10494820.2019.1637351
  42. 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
  43. Zengin, Y. (2017). Investigating the use of the Khan Academy and mathematics software with a flipped classroom approach in mathematics teaching. Educational Technology & Society, 20(2), 89-100.
  44. Zhu, Y., & Leung, F. K. (2011). Motivation and achievement: Is there an East Asian model? International Journal of Science and Mathematics Education, 9(5), 1189-1212. https://doi.org/10.1007/s10763-010-9255-y