Improving undergraduate statistics education
Educational lessons from pedagogical experiments
DOI:
https://doi.org/10.32674/xcpag319Keywords:
statistics education, statistics achievement, college students, virtual manipulative, inverted classroomAbstract
This research explored instructional ways that engage students in college introductory statistics courses, with two pedagogical experiments. Focusing on statistics achievement, the first (N = 96) examined instructional effects of traditional versus online manipulatives; the second (N = 270) investigated instructional effects of traditional versus inverted classrooms. Study 1 indicated that after control for students’ gender, age, and high school ACT (American College Testing) mathematics scores, there were no significant differences in course average scores between students using traditional and online manipulatives (immediate pedagogical effects), and there were no significant differences in GPA (grade point average) between the two groups one year later (prolonged pedagogical effects). Study 2 indicated that after control for student individual background, high school background, and university program background, students in traditional classroom did better than students in inverted classroom in midterm grade, while the two groups did equally well in other outcomes (e.g., class final grade).
References
Al-Samarraie, H., Shamsuddin, A., & Alzahrani, A. I. (2020). A flipped classroom model in higher education: A review of the evidence across disciplines. Educational Technology Research and Development, 68(3), 1017-1051.
Alkan, M. F., Cladera-Munar, M., Sarikaya, E. E., Leavy, A., Maviş-Sevim, Ö., Paul, C. I., Primi, C., Schau, C., & Ustun, U. (2022). A systematic review and meta-analysis of the relationships among post-secondary students’ attitudes toward statistics and statistics achievement: A protocol. Social Science Protocols, 5(1), 1-9.
Batanero, C. (2020). Probability teaching and learning. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 682-686). Springer. https://doi.org/10.1007/978-3-030-15789-0_128
Ben-Zvi, D. (2016). Three paradigms in developing students’ statistical reasoning. In S. Estrella, M. Goizueta, C. Guerrero, A. Mena, J. Mena, E. Montoya, A. Morales, M. Parraguez, E. Ramos, P. Vásquez, & D. Zakaryan (Eds.), XX Actas de las jornadas nacionales de educación matemática (pp. 13-22). SOCHIEM. http://funes.uniandes.edu.co/14832/1/Ben-Zvi2016Three.pdf
Biehler, R., Frischemeier, D., Reading, C., & Shaughnessy, J. M. (2018). Reasoning about data. In D. Ben-Zvi, K. Makar, & J. Garfield (Eds.) International handbook of research in statistics education (pp. 139-192). Springer.
Bouck, E., Satsangi, R., Doughty, T., & Courtney, W. (2013). Virtual and concrete manipulatives: A comparison of approaches for solving mathematics problems for students with autism spectrum disorder. Journal of Autism and Developmental Disorders, 44(1), 180-193.
Brame, C. J. (2013). Flipping the classroom. Vanderbilt University Center for Teaching.
Budgett, S., Pfannkuch, M. (2019). Visualizing chance: Tackling conditional probability misconceptions. In G. Burrill & D. Ben-Zvi (Eds), Topics and trends in current statistics education research (pp. 3-25). Springer. https://doi.org/10.1007/978-3-030-03472-6_1
Burrill, G. F., de Oliveria Souza, L., & Reston, E. (Eds.). (2023). Research on reasoning with data and statistical thinking: International perspectives. Springer.
Carbonneau, K. J., & Marley, S. C. (2015). Instructional guidance and realism of manipulatives influence preschool children’s mathematics learning. The Journal of Experimental Education, 83(4), 495-513.
Chiesi, F., & Primi, C. (2015, February). Gender differences in attitudes toward statistics: Is there a case for a confidence gap? CERME 9 – Ninth congress of the European Society for Research in Mathematics Education, 622-628.
Cockett, A., & Kilgour, P. W. (2015). Mathematical manipulatives: Creating an environment for understanding, efficiency, engagement, and enjoyment. TEACH COLLECTION of Christian Education, 1(1), 47-54.
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum Associates.
Common Core State Standards Initiative (CCSSM). (2010). Common core state standards for mathematics. National Governors Association and Council of Chief State School Officers.
Delport, D. (2021). The impact of math manipulatives as a multi-sensory teaching technique in statistics. Journal of Mathematics Education, Science and Technology, 6(2), 186-206.
Dole, S., & Geiger, V. (2020). Numeracy across the curriculum: Research-based strategies for enhancing teaching and learning. Routledge.
Fabby, C. (2021). Identifying student difficulties in conditional probability within statistical reasoning (Unpublished doctoral dissertation). University of Cincinnati.
Franklin, C., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M., & Scheaffer, R. (2005). Guidelines for Assessment and Instruction in Statistics Education (GAISE) reports. American Statistical Association.
Fulton, K. P. (2012). 10 reasons to flip. Phi Delta Kappan, 94(2), 20-24.
Gal, I., & Ograjenšek, I. (2017). Official statistics and statistics education: Bridging the gap. Journal of Official Statistics, 33(1), 79-100.
Garfield, J., & Ben-Zvi, D. (2008). Developing students’ statistical reasoning: Connecting research and teaching practice. Springer.
Garfield, J., & Ben‐Zvi, D. (2009). Helping students develop statistical reasoning: Implementing a statistical reasoning learning environment. Teaching Statistics, 31(3), 72-77.
Garfield, J., delMas, R., & Zieffler, A. (2012). Developing statistical modelers and thinkers in an introductory, tertiary-level statistics course. ZDM Mathematics Education, 44, 883-898.
Geller, N. L. (2011). Statistics: An all-encompassing discipline. Journal of the American Statistical Association, 106(496), 1225-1229.
Goracke, M. A. (2009). The role of manipulatives in the eighth-grade mathematics classroom. Action Research Projects, 71. https://digitalcommons.unl.edu/mathmidactionresearch/71
Gould, R. (2017). Data literacy is statistical literacy. Statistics Education Research Journal, 16(1), 22-25.
Hamden, N., McKnight, P., McKnight, K., & Arfstrom, K. (2013). The flipped learning model: A white paper based on the literature review titled a review of flipped learning. Flipped Learning Network. https://flippedlearning.org/wp-content/uploads/2016/07/WhitePaper_FlippedLearning.pdf
Hartley, K. N. (2021). Comparing virtual and concrete manipulatives effect on the conceptual understanding of the FOIL method [Unpublished manuscript]. Georgia College and State University. https://www.gcsu.edu/sites/default/files/documents/2021-06/hartley.pdf
Huck, S. (2015). Statistical misconceptions: Classic edition. Routledge.
Huxley, T. H. (1870, September 14). President’s address to the British Association for the Advancement of Science. Liverpool, United Kingdom.
Immekus, J. C. (2019). Flipping statistics courses in graduate education: Integration of cognitive psychology and technology. Journal of Statistics Education, 27(2), 79-89.
Justo, E., Delgado, A., Llorente-Cejudo, C., Aguilar, R., & Cabero-Almenara, J. (2022). The effectiveness of physical and virtual manipulatives on learning and motivation in structural engineering. Journal of Engineering Education, 111(4), 813-851.
Kahneman, D., & Tversky, A. (2015). Causal schemas in judgments under uncertainty. In M. Fishbein (Ed.), Progress in social psychology (pp. 49-72). Psychology Press.
Kovacs, P., Kuruczleki, E., Kazar, K., Liptak, L., & Racz, T. (2021). Modern teaching methods in action in statistical classes. Statistical Journal of the IAOS, 3, 899-919.
Kurniawan, D., & Wahyuningsih, T. (2018). Analysis of student difficulties in statistics courses. International Journal of Trends in Mathematics Education Research, 1(2), 53-55.
Langdon, J., Sturges, D., & Schlote, R. (2018). Flipping the classroom: Effects on course experience, academic motivation, and performance in an undergraduate exercise science research methods course. Journal of the Scholarship of Teaching and Learning, 18(4), 13-27.
Larbi, E., & Mavis, O. (2016). The use of manipulatives in mathematics education. Journal of Education and Practice, 7(36), 53-61.
Maciejewski, W. (2016). Flipping the calculus classroom: An evaluative study. Teaching Mathematics and its Applications, 35(4), 187-201.
Mason, G. S., Shuman, T. R., & Cook, K. E. (2013). Comparing the effectiveness of an inverted classroom to a traditional classroom in an upper-division engineering course. IEEE Transactions on Education, 56(4), 430-435.
Moyer-Packenham, P. S., & Bolyard, J. J. (2016). Revisiting the definition of a virtual manipulative. In P. S. Moyer-Packenham (Ed.), International perspectives on teaching and learning mathematics with virtual manipulatives (pp. 3-23). Springer.
Nabbout-Cheiban, M. (2017). Intuitive thinking and misconceptions of independent events: A case study of US and French pre-service teachers. International Journal of Research in Undergraduate Mathematics Education, 3, 255-282.
Olakanmi, E. E. (2017). The effects of a flipped classroom model of instruction on students’ performance and attitudes towards chemistry. Journal of Science Education and Technology, 26, 127-137.
Palazuelos, K. (2017). The impact of virtual manipulatives on student achievement in mathematics [Unpublished master’s thesis]. California State University at Stanislaus.
Pappas, J. G. (2013). Differences between concrete and virtual manipulatives in preparing tenth grade math students for standardized tests [Master’s thesis, Montclair State University]. Theses, Dissertations and Culminating Projects, 943.
Pires, A. C., Perilli, F. G., Bakala, E., Fleisher, B., Sansone, G., & Marichal, S. (2019). Building blocks of mathematical learning: Virtual and tangible manipulatives lead to different strategies in number composition. Frontiers in Education, 4, Article B1.
Rahman, S. F. A., Yunus, M. M., & Hashim, H. (2020). The uniqueness of flipped learning approach. International Journal of Education and Practice, 8(3), 394-404.
Ramirez, C., Schau, C., & Emmioğlu, E. (2012). The importance of attitudes in statistics education. Statistics Education Research Journal, 11(2), 57-71.
Ramsey, J. B. (1999). Why do students find statistics so difficult. Proceedings of the 52nd Session of the International Statistics Institute, 10-18.
Reimer, K., & Moyer, P. S. (2005). Third graders learn about fractions using virtual manipulatives: A classroom study. Journal of Computers in Mathematics and Science Teaching, 24(1), 5-25.
Roehling, P. V. (2017). Flipping the college classroom: An evidence-based guide. Springer.
Rossman, A., & De Veaux, R. (2016). Interview with Richard De Veaux. Journal of Statistics Education, 24(3), 157-168.
Sarama, J., & Clements, D. H. (2016). Physical and virtual manipulatives: What is “concrete”? In P. S. Moyer-Packenham (Ed.), International perspectives on teaching and learning mathematics with virtual manipulatives (pp. 71-93). Springer.
Satsangi, R., Bouck, E. C., Taber-Doughty, T., Bofferding, L., & Roberts, C. A. (2016). Comparing the effectiveness of virtual and concrete manipulatives to teach algebra to secondary students with learning disabilities. Learning Disability Quarterly, 39(4), 240-253.
Sawka, K. (2020). The use and misuse of statistics. In C. W. Gruber (Ed.), The theory of statistics in psychology: Applications, use, and misunderstandings (pp. 95-110). Springer.
Schmit, M. (2022, July 13). Physical vs. virtual manipulatives: Is there a difference? Brainingcamp. https://www.brainingcamp.com/blog/posts/physical-vs-virtual-manipulatives-is-there-a-difference
Sowell, E. J. (1989). Effects of manipulative materials in mathematics instruction. Journal for Research in Mathematics Education, 20, 498-505.
Stains, M., Harshman, J., Barker, M. K., Chasteen, S. V., Cole, R., DeChenne-Peters, S. E., Eagan Jr., M. K., Esson, J. M., Knight, J. K., Laski, F. A., Levis-Fitzgerald, M., Lee, C. J., Lo, S. M., McDonnell, L. M., McKay, T. A., Michelotti, N., Musgrove, A., Palmer, M. S., Plank, K. M., … Young, A. M. (2018). Anatomy of STEM teaching in North American universities. Science, 359(6383), 1468-1470.
Stowell, J. R., & Addison, W. E. (2017). Activities for teaching statistics and research methods: A guide for psychology instructors. American Psychological Association.
Swan, P., & Marshall, L. (2010). Revisiting mathematics manipulative materials. Australian Primary Mathematics Classroom, 15(2), 13-19.
Talbert, R., & Bergmann, J. (2017). Flipped learning: A guide for higher education faculty. Routledge.
Tintle, N., Chance, B., Cobb, G., Roy, S., Swanson, T., & VanderStoep, J. (2015). Combating anti-statistical thinking using simulation-based methods throughout the undergraduate curriculum. The American Statistician, 69(4), 362-370.
Vessonen, T., Hakkarainen, A., Väisänen, E., Laine, A., Aunio, P., & Gagnon, J. C. (2021). Differential effects of virtual and concrete manipulatives in a fraction intervention on fourth and fifth grade students’ fraction skills. Investigations in Mathematics Learning, 13(4), 323-337.
Watson, J. M. (2013). Statistical literacy at school: Growth and goals. Routledge.
Weiland, T. (2017). Problematizing statistical literacy: An intersection of critical and statistical literacies. Educational Studies in Mathematics, 96(1), 33-47.
Wild, C. J., Utts, J. M., & Horton, N. J. (2018). What is statistics? In D. Ben-Zvi, K. Makar, & J. Garfield (Eds.), International handbook of research in statistics education (pp. 5-36). Springer.
Yildirim, F. S., & Kiray, S. A. (2016). Flipped classroom model in education. Research Highlights in Education and Science, 2(6), 1-8.
Zieffler, A., Garfield, J., & Fry, E. (2018). What is statistics education? In D. Ben-Zvi, K. Makar, & J. Garfield (Eds.), International handbook of research in statistics education (pp. 37-70). Springer.
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