Abstract
Flipping a mathematical classroom is a pedagogical approach designed to increase student engagement within the classroom. By moving lectures to the outside of classroom meetings, students can actively engage in the application of mathematical content while in the presence of the teacher. The in-class focus shifts to creating connections to content while allowing the teacher to assist with technique, application, and conceptual concerns. Benefits of this model include increased faculty/student interaction, collaboration with peers to view alternate strategies for solutions, and differentiated instruction for varying student levels. This model can assist with self-efficacy and motivation for struggling learners. While many advantages exist with the model, the chapter also addresses implementation resistance from students, parents, and teachers as the pedagogy changes from a lecture-based model to one of active learning.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Adler, J. (1999). The dilemma of transparency: Seeing and seeing through talk in the mathematics classroom. Journal for Research in Mathematics Education,30, 47–64. https://doi.org/10.2307/749629.
Allsopp, D. H., Kyger, M. M., & Lovin, L. H. (2007). Teaching mathematics meaningfully: Solutions for reaching struggling learners. Baltimore, MD: Brooks.
Anderson, L., & Brennan, J. P. (2015). An experiment in “Flipped” teaching in freshman calculus. PRIMAS,25(9–10), 861–875.
Ashcraft, M. H. (2002). Math anxiety: Personal, educational, and cognitive consequences. Current Directions in Psychological Science,11(5), 181–185. https://doi.org/10.1111/1467-8721.00196.
Ashcraft, M. H., & Krause, J. A. (2007). Working memory, math performance, and math anxiety. Psychonomic Bulletin & Review,14(2), 243–248.
Bachman, H. J., Votruba-Drzal, E., El Nokali, N. E., & Heatly, M. C. (2015). Opportunities for learning math in elementary school: Implications for SES disparities in procedural and conceptual math skills. American Educational Research Journal,52(5), 894–923. https://doi.org/10.3102/0002831215594877.
Bargh, J. A., & Schul, Y. (1980). On the cognitive benefits of teaching. Journal of Educational Psychology,72, 593–604. https://doi.org/10.1037/0022-0663.72.5.593.
Bandura, A. (1977). Self-efficacy: Toward a unifying theory of behavioral change. Psychological Review,84, 191–215.
Bergmann, J., & Sams, A. (2012). Flip your classroom: Reach every student in every class every day. Eugene, OR: International Society for Technology. in Education.
Bergmann, J., & Sams, A. (2013). The flipped classroom. CSE,17(3), 24–27.
Berlinski, S., & Busso, M. (2017). Challenges in educational reform: An experiment on active learning in mathematics. Economics Letters,156, 172–175. https://doi.org/10.1016/j.econlet.2017.05.007.
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.
Boaler, J. (2013). Ability and mathematics: The mindset revolution that is reshaping education. Forum,55(1), 143–152.
Boylan, H. R. (2011). Improving success in developmental mathematics: An interview with Paul Nolting. Journal of Developmental Education,34(3), 20–27.
Byron High School Mathematics Department. (n.d.). Flipped Classroom. Retrieved from https://sites.google.com/a/byron.k12.mn.us/byron-high-school-mathematics-department/flipped-classroom.
Carbaugh, E. M., & Doubet, K. J. (2016). The differentiated flipped classroom guide: A Practice guide to digital learning. London, England: Sage Publications.
Chen, S. C., Yang, S. J., & Hsiao, C. C. (2016). Exploring student perceptions, learning outcome and gender differences in a flipped mathematics course. British Journal of Educational Technology,47(6), 1096–1112. https://doi.org/10.1111/bjet.12278.
Chickering, A. W., & Gamson, Z. F. (1987). Seven principles for good practice in undergraduate education. AAHE Bulletin,3, 3–7.
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.
Dale, E. (1946). Audio-visual methods in teaching. New York: Dryden Press.
Esperanza, P., Fabian, K., & Toto, C. (2016). Flipped classroom model: Effects on performance, attitudes and perceptions in high school algebra. In K. Verbert, M. Sharples & T. Klobucar (Eds.), Adaptive and adaptable learning: Lecture notes in computer science (Vol. 9891, pp. 85–97). Berlin, Germany: Springer-Verlag. https://doi.org/10.1007/978-3-319-45153-4_7.
Flipped Learning Model Increases Student Engagement. (2013). Retrieved from: http://assets.pearsonschool.com/asset_mgr/current/201320/Byron_standalone_casestudy.pdf.
Flipped Learning Model Dramatically Improves Course Pass Rate for At-Risk Students. (2013). Retrieved from http://assets.pearsonschool.com/asset_mgr/current/201317/Clintondale_casestudy.pdf.
Frayer Model, (n.d.). National Behavior Support Service. Retrieved from https://www.nbss.ie/sites/default/files/publications/frayer_model_-_vocbulary_strategy_handout__copy_3.pdf.
Freeman, S., Eddy, S. L., McDonough, M., Smith, M. K., Okoroafor, N., Jordt, H., et al. (2014). Active learning increases student performance in science, engineering, and mathematics. Proceedings of the National Academy Science of the USA,111(23), 8410–8415. https://doi.org/10.1073/pnas.1319030111.
Gettinger, M., & Seibert, J. K. (2002). Contributions of study skills to academic competence. School Psychology Review, 31(3), 350–365.
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.
Guerrero, S., Beal, M., Lamb, C., Sonderegger, D., & Baumgartel. (2015). Flipping undergraduate finite mathematics: Findings and implications. PRIMAS, 25(9–10), 814–832. https://doi.org/10.1080/10511970.2015.1046003
Hannula, M. S. (2002). Attitude towards mathematics: Emotions, expectations and values. Educational Studies in Mathematics,49(1), 25–46. https://doi.org/10.1023/A:1016048823497.
Hao, Y., & Lee, K. S. (2016). Teaching in flipped classrooms: Exploring pre-service teachers’ concerns. Computers in Human Behavior,57, 250–260. https://doi.org/10.1016/j.chb.2015.12.022.
Hart, L. C. (1993). Some factors that impede or enhance performance in mathematical problem solving. Journal for Research in Mathematics Education,24(2), 167–171. https://doi.org/10.2307/749219.
Helpman, E., & Rangel, A. (1999). Adjusting to a new technology: Experience and training. Journal of Economic Growth, 359–383. https://doi.org/10.1023/A:1009888907797.
Helwig, R., Rozek-tedesco, M. A., Tindal, G., Heath, B., & Almond, P. J. (1999). Reading as an access to mathematics problem solving on multiple-choice tests in sixth-grade students. Journal of Educational Research,93(2), 113–125. https://doi.org/10.1080/00220679909597635.
Hendy, H. M., Schorschinsky, N., & Wade, B. (2014). Measurement of math beliefs and their associations with math behaviors in college students. Psychological Assessment,26(4), 1225–1234. https://doi.org/10.1037/a0037688.
Hodges, T. S., & Weber, N. D. (2015). Making heads or tails of classroom flipping. Kappa Delta Pi Record,51(2), 57–63. https://doi.org/10.1080/00228958.2015.1023135.
Hollebrands, K., & Okumus, S. (2018). Secondary mathematics teachers’ instrumental integration in technology-rich geometry classrooms. The Journal of Mathematical Behavior,49, 82–94. https://doi.org/10.1016/j.jmathb.2017.10.003.
Houghton, W. (2004). Engineering subject centre guide: Learning and teaching theory for engineering academics. Loughborough: HEA Engineering Subject Centre.
Inspiring Ways to Kahoot! (2019). Retrieved from https://kahoot.com/how-to-play-kahoot/
Jonassen, D. H. (1997). Instructional design models for well-structured and ill-structured problem solving learning outcomes. ETR&D,45(1), 66–94.
Kelton, S. (n.d.). An introduction to teaching mathematics at the college level. Retrieved from https://www.ams.org/profession/career-info/grad-school/Kelton-TEACH.pdf.
Kloosterman, P. (1988). Self-confidence and motivation in mathematics. Journal of Educational Psychology,80(3), 345–351. https://doi.org/10.1037/0022-0663.80.3.345.
Kosko, K. W., & Wilkins, J. L. M. (2012). Students’ quality of mathematical discussion and their self-determination in mathematics. Investigations in Mathematics Learning,4(3), 15–31. https://doi.org/10.1080/24727466.2012.11790314.
Liew, J., Lench, H. C., Kao, G., Yeh, Y., & Kwok, O. (2014). Avoidance temperament and social-evaluative threat in college students’ math performance: A mediation model of math and test anxiety. Anxiety, Stress, & Coping Journal,27(6), 650–661. https://doi.org/10.1080/10615806.2014.910303.
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(4), 1–22. https://doi.org/10.1186/s41039-016-0044-2.
Maciejewski, W. (2016). Flipping the calculus classroom: An evaluative study. Teaching Mathematics and its Applications: An International Journal of the IMA,35(4), 187–201. https://doi.org/10.1093/teamat/hrv019.
McCallum, S., Schultz, J., Sellke, K., & Spartz, J. (2015). An examination of the flipped classroom approach on college student academic achievement. International Journal of Teaching and Learning in Higher Education,27(1), 42–55.
McDiarmid, G. W. (1990). The liberal arts: Will more result in better subject matter understanding? Theory into Practice,29(1), 21–29. https://doi.org/10.1080/00405849009543426.
Molenda, M., & Pershing, J. A. (2008). Improving performance. In A. Januszewski & M. Molenda (Eds.), Educational technology: A definition with commentary (pp. 49–80). New York, NY: Routledge.
Nunez-Pena, M. I., Suarez-Pellicioni, M., & Bono, R. (2013). Effects of math anxiety on student success in higher education. International Journal of Educational Research,58, 36–43. https://doi.org/10.1016/j.ijer.2012.12.004.
Ogden, L., Pyzdrowski, L. J., & Shambaugh, N. (2015). A teaching model for college algebra flipped classroom. Curriculum design and classroom management: Concepts, methodologies, tools, and applications (pp. 513–536). IGI Global: Hershey, PA.
Ogden, L., & Shambaugh, N. (2016). The continuous and systematic study of the college algebra flipped classroom. Handbook of research on active learning and the flipped classroom model in the digital age (pp. 41–71). IGI Global: Hershey, PA.
Pajares, F., & Miller, M. D. (1994). Role of self-efficacy and self-concept beliefs in mathematical problem solving: A path analysis. Journal of Educational Psychology,86(2), 193–203.
Pugalee, D. K. (2004). A comparison of verbal and written descriptions of students’ problem-solving processes. Educational Studies in Mathematics,55, 27–47. https://doi.org/10.1023/B:EDUC.0000017666.11367.c7.
Resnick, L. B. (1987). Education and learning to think. Washington, DC: National Academies Press.
Reyes, L. H., & Stanic, G. M. (1988). Race, sex, and socioeconomic status, and mathematics. Journal for Research in Mathematics Education,19(1), 26–43. https://doi.org/10.2307/749109.
Rylands, L. J., & Coady, C. (2009). Performance of students with weak mathematics in first-year mathematics and science. International Journal of Mathematical Education in Science and Technology,40(6), 741–753. https://doi.org/10.1080/00207390902914130.
Schaffhauser, D. (2014, August 13). 2 great techniques for the flipped classroom. Retrieved from https://campustechnology.com/Articles/2014/08/13/2-Great-Techniques-for-the-Flipped-Classroom.aspx?p=1.
Siegle, D. (2013). Differentiating instruction by flipping the classroom. Gifted Child Today,37(1), 51–55. https://doi.org/10.1177/1076217513497579.
New York University. (n.d.). Steps to flipping your class. Retrieved from https://www.nyu.edu/faculty/teaching-and-learning-resources/strategies-for-teaching-with-tech/flipped-classes/steps-to-flipping-your-class.html.
Strayer, J. F. (2012). How learning in an inverted classroom influences cooperation, innovation and talk orientation. Learning Environments Research,15(2), 171–193. https://doi.org/10.1007/s10984-012-9108-4.
Urquhart, V. (2009). Using writing in mathematics to deepen student learning. Denver, CO: Mid-continent Research for Education and Learning.
Webb, N. M. (1991). Task-related verbal interaction and mathematics learning in small groups. Journal for Research in Mathematics Education,22(5), 366–389.
Weigel, V. B. (2002). Deep learning for a digital age. San Francisco, CA: Jossey-Bass.
Weng, P. (2015). Developmental math, flipped and self-paced. PRIMAS,25(9–10), 768–781. https://doi.org/10.1080/10511970.2015.1031297.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Stapleton, L.L. (2020). Flipping the Mathematics Classroom. In: Walker, Z., Tan, D., Koh, N.K. (eds) Flipped Classrooms with Diverse Learners. Springer Texts in Education. Springer, Singapore. https://doi.org/10.1007/978-981-15-4171-1_3
Download citation
DOI: https://doi.org/10.1007/978-981-15-4171-1_3
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-4170-4
Online ISBN: 978-981-15-4171-1
eBook Packages: EducationEducation (R0)