Effectiveness of the Flipped Classroom in the Teaching of Mathematics in an Online Environment: Identification of Factors Affecting the Learning Process
DOI:
https://doi.org/10.24059/olj.v27i2.3239Keywords:
students, Flipped Classroom, research methods, online education, academic achievementAbstract
The purpose of this study was to analyse the effectiveness of the Flipped Classroom methodology for teaching mathematics, geometry in particular, in an online environment. Specifically, we measured: 1) the academic achievement of students who were taught in this way; and 2) perceptions of satisfaction with this methodology and the virtual sessions attended through digital resources. For this purpose, a pre-experimental and ex-post-facto design was used with a sample of 113 Secondary Education students. With regard to academic performance, positive and significant differences were found between the pre-test and the post-test, with previous underachievement in mathematics, efforts made towards learning and the educational level of the parents being predictors. In respect of the students' perceptions, the results showed a favourable satisfaction with the use of the Flipped Classroom, where the environmental context in which the educational process takes place interferes with their perceptions. However, slightly negative perceptions were found on the use of virtual sessions with digital resources, where the frequency of use of some resources and electronic devices has a significant influence. These results add value on how to further integrate this methodology in the subject of mathematics, where the use of digital resources to learn geometry helps to improve the different competences and skills of the students.
References
Abín, A., Núñez, J.C., Rodríguez, C., Cueli, M., García, T., & Rosario, P. (2020) Predicting Mathematics Achievement in Secondary Education: The Role of Cognitive, Motivational, and Emotional Variables. Frontiers in Psychology, 11, e876. https://doi.org/10.3389/fpsyg.2020.00876
Adams, C., & Dove, A. (2016). Flipping calculus: The potential influence, and the lessons learned. Electronic Journal of Mathematics & Technology, 10(3),154-164.
Adarkwah, M. A. (2021). “I’m not against online teaching, but what about us?”: ICT in Ghana post Covid-19. Education and Information Technologies, 26(2), 1665-1685. https://doi.org/10.1007/s10639-020-10331-z
Alexander, V., & Maeda, Y. (2015). Understanding student achievement in mathematics and science: The case of Trinidad and Tobago. Prospects, 45(4), 577-591. http://www.doi.org/10.1007/s11125-015-9373-y
Aljaraideh, Y. (2019). Students' perception of flipped classroom: A case study for private universities in Jordan. JOTSE: Journal of Technology and Science Education, 9(3), 368-377. http://dx.doi.org/10.3926/jotse.648
Arvanitaki, M., & Zaranis, N. (2020). The use of ICT in teaching geometry in primary school. Education and Information Technologies, 25(6), 5003-5016. https://doi.org/10.1007/s10639-020-10210-7
Azevedo, G. T. D., & Maltempi, M. V. (2020). The Process of Learning Math in light of Active Methodologies and Computational Thinking. Ciência & Educação (Bauru), 26, 1-18. https://doi.org/10.1590/1516-731320200061
Balan, P., Clark, M., & Restall, G. (2015). Preparing students for Flipped or Team-Based Learning methods. Education + Training, 57(6), 639-657. https://doi.org/10.1108/ET-07-2014-0088
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.
Bulut, C., & Kocoglu, Z. (2020). The Flipped Classroom’s Effect on EFL Learners’ Grammar Knowledge: International Journal of Mobile and Blended Learning, 12(4), 69-84. https://doi.org/10.4018/IJMBL.2020100105
Byrne, B. M. (2010). Structural equation modeling with AMOS: basic concepts, applications, and programming (multivariate applications series). New York: Taylor & Francis Group, 396, 7384.
Camacho, A.C.L.F., Fuly, P.S.C., Santos, M.L.S.C., & Menezes, H.F. (2020). Students in social vulnerability in distance education disciplines in times of COVID-19. (2020). Research, Society and Development, 9(7),1-12. http://dx.doi.org/10.33448/rsd-v9i7.3979
Campillo-Ferrer, J. M., & Miralles-Martínez, P. (2021). Effectiveness of the flipped classroom model on students’ self-reported motivation and learning during the COVID-19 pandemic. Humanities and Social Sciences Communications, 8(1), 1-9. https://doi.org/10.1057/s41599-021-00860-4
Chiquito, M., Castedo, R., Santos, A. P., López, L. M., & Alarcón, C. (2020). Flipped classroom in engineering: The influence of gender. Computer Applications in Engineering Education, 28(1), 80-89.
Cho, H. J., Zhao, K., Lee, C. R., Runshe, D., & Krousgrill, C. (2021). Active learning through flipped classroom in mechanical engineering: improving students’ perception of learning and performance. International Journal of STEM Education, 8(1), 1-13. https://doi.org/10.1186/s40594-021-00302-2
Clark, K.R. (2015). The effects of the flipped model of instruction on student engagement and performance in the secondary mathematics classroom. Journal of Educators Online, 12(1), 91-115.
Colomo-Magaña, E., Soto-Varela, R., Ruiz-Palmero, J., & Gómez-García, M. (2020). University students’ perception of the usefulness of the flipped classroom methodology. Education Sciences, 10(10), 275. https://doi.org/10.3390/educsci10100275
Cronhjort, M., Filipsson, L., & Weurlander, M. (2018). 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
Dockendorff, M., & Solar, H. (2018). ICT integration in mathematics initial teacher training and its impact on visualization: the case of GeoGebra. International Journal of Mathematical Education in Science and Technology, 49(1), 66-84. https://doi.org/10.1080/0020739X.2017.1341060
Flores, M. A., & Swennen, A. (2020). The COVID-19 pandemic and its effects on teacher education. European Journal of Teacher Education, 43(4), 453-456. https://doi.org/10.1080/02619768.2020.1824253
Fung, C.H. (2020). How Does Flipping Classroom Foster the STEM Education: A Case Study of the FPD Model. Technology, Knowledge and Learning, 30(14), 1945-1969. https://doi.org/10.1007/s10758-020-09443-9
Galindo-Domínguez, H. (2021). Flipped Classroom in the Educational System. Educational Technology & Society, 24(3), 44-60.
Gilar-Corbi, R., Miñano, P., Veas, A., & Castejón, J. L. (2019). Testing for invariance in a structural model of academic achievement across underachieving and non-underachieving students. Contemporary Educational Psychology, 59, e101780. https://doi.org/10.1016/j.cedpsych.2019.101780
Gjicali, K., & Lipnevich, A.A. (2021). Got math attitude? (In)direct effects of student mathematics attitudes on intentions, behavioral engagement, and mathematics performance in the U.S. PISA. Contemporary Educational Psychology, 67, e102019. https://doi.org/10.1016/j.cedpsych.2021.102019
Gomes, C.M.A., Fleith, D.S., Marinho-Araujo, C.M., & Rabelo, M.L. (2020). Predictors of Students’ Mathematics Achievement in Secondary Education. Psicologia: Teoria e Pesquisa, 36. https://doi.org/10.1590/0102.3772e3638
Gómez, I., Castro, N., & Toledo, P. (2015). The flipped classroom through the smartphone: Effects of ITS experimentation in high school physical education. Prisma social: revista de investigación social, (15), 296-351.
Gómez, M., Hossein, H., Trujillo, J.M., Hossein, H., & Aznar, I. (2020). Technological Factors That Influence the Mathematics Performance of Secondary School Students. Mathematics, 8(11), e1935. https://doi.org/10.3390/math8111935
González, D., Jeong, J. S., Airado, D., & 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(3), 450-459. https://doi.org/10.1007/s10956-016-9605-9
Gross, D., Pietri, E. S., Anderson, G., Moyano-Camihort, K., & Graham, M. J. (2015). Increased preclass preparation underlies student outcome improvement in the flipped classroom. CBE—Life Sciences Education, 14(4), 1-8. https://doi.org/10.1187/cbe.15-02-0040
Guillén-Gámez, F. D., Colomo, E., Sánchez, E., & Pérez, R. (2020). Efectos sobre la metodología Flipped Classroom a través de Blackboard sobre las actitudes hacia la estadística de estudiantes del Grado de Educación Primaria: Un estudio con ANOVA mixto. Texto Livre: Linguagem e Tecnologia, 13(3), 121-139. https://doi.org/10.35699/1983-3652.2020.25107
Guillén-Gámez, F. D., Mayorga-Fernández, M.J., & De La Fuente-Conde, M. C. (2019). Univariate Analysis of the Impact of the Flipped Classroom through Moodle as a Process to Improve Learning and Academic Performance. The International Journal of Technologies in Learning 26 (1), 35-48. http://www.doi.org/10.18848/2327-0144/CGP/v26i01/35-48.
Hair, J., Hult, G., Ringle, C. y Sarstedt, M. (2017). A Primer on Partial Least Square Structural Equation Modeling (PLS-SEM). Estados Unidos, California: Sage.
Hammoudi, M. H. (2019). Predictive factors of students’ motivation to succeed in introductory mathematics courses: evidence from higher education in the UAE. International Journal of Mathematical Education in Science and Technology, 50, 647–664. https://doi.org/10.1080/0020739X.2018.1529339
Henson, R. K., & Roberts, J. K. (2006). Use of exploratory factor analysis in published research: Common errors and some comment on improved practice. Educational and Psychological measurement, 66(3), 393-416. https://doi.org/10.1177/0013164405282485
Hernández-Martín, A., Martín-del-Pozo, M., & Iglesias-Rodríguez, A. (2021). Pre-adolescents’ digital competences in the area of safety. Does frequency of social media use mean safer and more knowledgeable digital usage?. Education and Information Technologies, 26(1), 1043-1067. https://doi.org/10.1007/s10639-020-10302-4
Hossein, H, Gómez, M, Trujillo, J-M, Hossein, H, & Boumadan, M. (2021). Uses and Resources of Technologies by Mathematics Students Prior to COVID-19. Sustainability, 13(4), e1630. https://doi.org/10.3390/su13041630
Hu, L. y Bentler, P. (1999). Cutoff criteria for fitindexes in covariance structure analysis: conventional criteria versus new alternative. Structural Equation Modeling, 6(1), 1-55.
Hu, X., Gong, Y., Lai, C., & Leung, F. K. (2018). The relationship between ICT and student literacy in mathematics, reading, and science across 44 countries: A multilevel analysis. Computers & Education, 125, 1-13. https://doi.org/10.1016/j.compedu.2018.05.021
Husein, N.A., Rahman, N.F.A., Phang, F.A., Abu Bakar, A.H., Ahmad, R.R., Kasim, N., & Duralim, M. (2018). The Relationship between Mentoring in Students’ Perception towards STEM Education. Advance Science Letters, 24(1), 72–73. https://doi.org/10.1166/asl.2018.11923
Jeong, J. S., González-Gómez, D., & Cañada-Cañada, F. (2021). How does a flipped classroom course affect the affective domain toward science course? Interactive Learning Environments, 29(5), 707-719. https://doi.org/10.1080/10494820.2019.1636079
Kadry, S., & El Hami, A. (2014). Flipped classroom model in calculus II. Education, 4(4), 103-107. http://www.doi.org/10.5923/j.edu.20140404.04
Kazu, İ. Y., & Kurtoglu, C. (2020). Research of Flipped Classroom Based on Students' Perceptions. Asian Journal of Education and Training, 6(3), 505-513. http://www.doi.org/10.20448/journal.522.2020.63.505.513
Kim, M. K., Kim, S. M., Khera, O., & Getman, J. (2014). The experience of three flipped classrooms in an urban university: An exploration of design principles. The Internet and Higher Education, 22, 37-50. https://doi.org/10.1016/j.iheduc.2014.04.003
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
Kline, R. B. (2011). Principles and practice of structural equation modeling (3ª ed.). 9 New York: The Guilford Press
Kristianti, Y., Prabawanto, S., & Suhendra, S. (2017). Critical Thinking Skills of Students through Mathematics Learning with ASSURE Model Assisted by Software Autograph. Journal of Physics, 895, 012063. http://doi.org/10.1088/1742-6596/895/1/012063
Lape, N. K., Levy, R., Yong, D. H., Haushalter, K. A., Eddy, R., & Hankel, N. (2014). Probing the inverted classroom: A controlled study of teaching and learning outcomes in undergraduate engineering and Mathematics, 121st ASEE Annual Conference Expo, 9475.
Liberatore, M. J., & Wagner, W. P. (2021). User performance on laptops vs. tablets: an experiment in the field. Behaviour & Information Technology, 1-9. https://doi.org/10.1080/0144929X.2021.1956589
Limniou, M., Schermbrucker, I., & Lyons, M. (2018). Traditional and flipped classroom approaches delivered by two different teachers: The student perspective. Education and Information Technologies, 23(2), 797-817. https://doi.org/10.1007/s10639-017-9636-8
Lipnevich, A. A., Preckel, F., & Krumm, S. (2016). Mathematics attitudes and their unique contribution to achievement: Going over and above cognitive ability and personality. Learning and Individual Differences, 47, 70–79. https://doi.org/0.1016/j.lindif.2015.12.027
Lo, C. K., & Hew, K. F. (2017). A critical review of flipped classroom challenges in K-12 education: Possible solutions and recommendations for future research. Research and practice in technology enhanced learning, 12(1), 1-22. https://doi.org/10.1186/s41039-016-0044-2
Lo, C.K., Lie, C.W., & Hew, K.F. (2018). Applying “First Principles of Instruction” as a design theory of the flipped classroom: Findings from a collective study of four secondary school subjects. Computers and Education, 118, 150-165. https://doi.org/10.1016/j.compedu.2017.12.003
López-Belmonte J., Fuentes-Cabrera A., López-Núñez J.A., Pozo-Sánchez S. (2019). Formative transcendence of flipped learning in mathematics students of secondary education. Mathematics, 7(12), e1226. https://doi.org/10.3390/math7121226
López-Noguero, F., Gallardo-López, J. A., & García-Lázaro, I. (2021). The Educational Community in the Face of COVID-19. Discursive Analysis on Vulnerability and Education. International Journal of Environmental Research and Public Health, 18(13), 6716. https://doi.org/10.3390/ijerph18136716
Maass, K., Geiger, V., Ariza, M. R., & Goos, M. (2019). The role of mathematics in interdisciplinary STEM education. ZDM. Mathematics Education, 51, 869-884. https://doi.org/10.1007/s11858-019-01100-5
McCulloch, A. W., Lovett, J. N., Dick, L. K., & Cayton, C. (2021). Positioning Students to Explore Math with Technology. Mathematics Teacher: Learning and Teaching PK-12, 114(10), 738-749. https://doi.org/10.5951/MTLT.2021.0059
Mengual-Andres, S., Lopez Belmonte, J., Fuentes Cabrera, A., & Pozo Sanchez, S. (2020). Structural model of influential extrinsic factors in flipped learning. EDUCACION XX1, 23(1), 75-101. http://www.doi.org/10.5944/educXX1.23840
Meza-Cascante, L., Suárez-Valdés-Ayala, Z., Agüero-Calvo, E., Calderón-Ferrey, M., Jiménez-Céspedes, R., Sancho-Martínez, L., Pérez-Tyteca, P., & Monje-Parrilla, J. (2021). Attitude towards mathematics from parents of secondary students. Uniciencia, 35(1), 384-395. https://doi.org/10.15359/ru.35-1.24
Onojah, A. O., Olumorin, C. O., Adegbija, M., & Babalola, T. O. (2019). Perception of Undergraduate Students on the Utilisation of Flipped Classroom for Learning in South-West Nigeria. Malaysian Journal of Distance Education, 21(1), 31-47.
Peytcheva-Forsyth, R., Yovkova, B., & Aleksieva, L. (2018, December). Factors affecting students’ attitudes towards online learning-The case of Sofia University. In AIP conference proceedings (Vol. 2048, No. 1, p. 020025). AIP Publishing LLC.
Romero Martínez, S. J., Ordóñez Camacho, X. G., Guillén-Gamez, F. D., & Bravo Agapito, J. (2020). Attitudes toward Technology among Distance Education Students: Validation of an Explanatory Model. Online Learning, 24(2), 59-75. https://doi.org/10.24059/olj.v24i2.2028
Schallert, S., & Weinhandl. R. (2019, February). Exploring critical aspects of students’ mathematics learning in technology-enhanced and student-led flipped learning environments [Conferencie presentation]. Eleventh Congress of the European Society for Research in Mathematics Education, Utrecht University, Utrecht, Netherlands. ⟨hal-02428813⟩
Sharp, L.A., & Hamil, M. (2018). Impact of a web-based adaptive supplemental digital resource on student mathematics performance. Online Learning, 22(1), 81-92. https://doi.org/10.24059/olj.v22i1.1133
Stratton, E., Chitiyo, G., Mathende, A. M., & Davis, K. M. (2020). Evaluating flipped versus face-to-face classrooms in middle school on science achievement and student perceptions. Contemporary Educational Technology, 11(1), 131-142.
Strelan, 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. https://doi.org/10.1016/j.edurev.2020.100314
UNESCO (2020). UN Secretary-General warns of education catastrophe, pointing to UNESCO estimate of 24 million learners at risk of dropping out. https://en.unesco.org/news/secretary-general-warns-education-catastrophe-pointing-unesco-estimate-24-million-learners-0
Wagner, M., Gegenfurtner, A., & Urhahne, D. (2020). Effectiveness of the flipped classroom on student achievement in secondary education: A meta-analysis. Zeitschrift für Pädagogische Psychologie, 35(1), 11-31. https://doi.org/10.1024/1010-0652/a000274
Weinhandl, R., & Lavicza, Z. (2021). Real-World Modelling to Increase Mathematical Creativity. Journal of Humanistic Mathematics, 11(1), 265-299. http://doi.org/10.5642/jhummath.202101.13
Weinhandl, R., Lavicza, Z., & Schallert, S. (2020). Towards Flipped Learning in Upper Secondary Mathematics Education. JME (Journal of Mathematics Education), 5(1), 1–15. https://doi.org/10.31327/jme.v5i1.1114
Xiao, N., Thor, D., & Zheng, M. (2021). Student Preferences Impact Outcome of Flipped Classroom in Dental Education: Students Favoring Flipped Classroom Benefited More. Education Sciences, 11(4), 150. https://doi.org/10.3390/educsci11040150
Yang, C. C. R. (2017). An investigation of the use of the ‘flipped classroom’ pedagogy in secondary English language classrooms. Journal of Information Technology Education: Innovations in Practice, 16, 1-20. http://www.informingscience.org/Publications/3635
Young, A. (2015). Flipping the calculus classroom: A cost-effective approach. Problems, Resources, and Issues in Mathematics Undergraduate Studies (PRIMUS), 25(8), 713–723. https://doi.org/10.1080/10511970.2015.1031298
Zainuddin, Z., & Perera, C. J. (2019). Exploring students’ competence, autonomy and relatedness in the flipped classroom pedagogical model. Journal of Further and Higher Education, 43(1), 115-126. https://doi.org/10.1080/0309877X.2017.1356916
Zaranis, N., & Synodi, E. (2017). A comparative study on the effectiveness of the computer assisted method and the interactionist approach to teaching geometry shapes to young children. Education and Information Technologies, 22(4), 1377-1393. https://doi.org/10.1007/s10639-016-9500-2
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