Skip to main content

Advertisement

SpringerLink
Log in

Mathematical modeling for theory-oriented research in educational technology

  • Development Article
  • Published:
Educational technology research and development Aims and scope Submit manuscript

Abstract

Mathematical modeling describes how events, concepts, and systems of interest behave in the world using mathematical concepts. This research approach can be applied to theory construction and testing by using empirical data to evaluate whether the specific theory can explain the empirical data or whether the theory fits the data available. Although extensively used in the physical sciences and engineering, as well as some social and behavioral sciences to examine theoretical claims and form predictions of future events and behaviors, theory-oriented mathematical modeling is less common in educational technology research. This article explores the potential of using theory-oriented mathematical modeling for theory construction and testing in the field of educational technology. It presents examples of how this approach was used in social, behavioral, and educational disciplines, and provides rationale for why educational technology research can benefit from a theory-oriented model-testing approach.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Adapted from Bessière et al. (2006)

Fig. 6

Adapted from Anderson (2011)

Fig. 7

Adapted from Picciano (2017)

Fig. 8

Adapted from Means et al. (2014)

Similar content being viewed by others

References

  • Anderson, T. (2008). The theory and practice of online learning (2nd ed.). AU Press.

    Google Scholar 

  • Anderson, T. (2011). The theory and practice of online learning. AU Press.

    Google Scholar 

  • Atkinson, R. C., & Schiffrin, R. M. (1971). The control of short-term memory. Scientific American, 225, 82–90.

    Google Scholar 

  • Atkinson, R. C., & Shiffrin, R. M. (1968a). Human memory: A proposed system and its control processes. In K. W. Spence & J. T. Spence (Eds.), The psychology of learning and motivation (Volume 2) (pp. 89–195). Academic Press.

    Google Scholar 

  • Atkinson, R. C., & Shiffrin, R. M. (1968b). Human memory: A proposed system and its control processes. In K. W. Spence & J. T. Spence (Eds.), The psychology of learning and motivation: Advances in research and theory (Vol 2) (pp. 89–195). Academic Press.

    Google Scholar 

  • Bessière, K., Newhagen, J. E., Robinson, J. P., & Shneiderman, B. (2006). A model for computer frustration: The role of instrumental and dispositional factors on incident, session, and post-session frustration and mood. Computers in Human Behavior, 22(6), 941–961. https://doi.org/10.1016/j.chb.2004.03.015

    Article  Google Scholar 

  • Blömeke, S., & Kaiser, G. (2011). Homogeneity or heterogeneity? Profiles of opportunities to learn in primary teacher education and their relationship to cultural context and outcomes. ZDM Mathematics Education, 44(3), 249–264. https://doi.org/10.1007/s11858-011-0378-6

    Article  Google Scholar 

  • Boland, L. A. (2014). Model building in economics: Its purposes and limitations. Cambridge University Press.

    Google Scholar 

  • Bulfin, S., Henderson, M., Johnson, N. F., & Selwyn, N. (2014). Methodological capacity within the field of “educational technology” research: An initial investigation. British Journal of Educational Technology, 45(3), 403–414.

    Google Scholar 

  • Cilesiz, S., & Spector, J. M. (2014). The philosophy of science and educational technology research. In J. M. Spector, M. D. Merrill, J. Elen, & M. J. Bishop (Eds.), Handbook of research on educational communications and technology (pp. 875–884). New York: Springer.

    Google Scholar 

  • Cronbach, L. J. (1975). Beyond the two disciplines of scientific psychology. American Psychologist, 20, 116–117.

    Google Scholar 

  • Dabbaghian, V., & Mago, V. K. (2014). Theories and simulations of complex social systems. Springer.

    Google Scholar 

  • Dym, C. (2004). Principles of mathematical modeling. Academic Press.

    Google Scholar 

  • Ertmer, P. A. (1999). Addressing first- and second-order barriers to change: Strategies for technology integration. Educational Technology Research and Development, 47(4), 47–61.

    Google Scholar 

  • Garrison, D. R., Anderson, T., & Archer, W. (2000). Critical inquiry in a text-based environment: Computer conferencing in higher education model. The Internet and Higher Education, 2(2–3), 87–105.

    Google Scholar 

  • Goe, L. (2007). The link between teacher quality and student outcomes: A research synthesis. Washington, DC: National Comprehensive Center for Teacher Quality. Retrieved from http://ncctq.learningpt.org/publications/LinkBetweenTQandStudentOutcomes.pdf

  • Gollwitzer, P. M. (1999). Implementation intentions. Strong effects of simple plans. American Psychologist, 54(7), 493–503.

    Google Scholar 

  • Harasim, L. (2012). Learning theory and online technologies. Routledge/Taylor & Francis.

    Google Scholar 

  • Hew, K. F., & Brush, T. (2007). Integrating technology into K-12 teaching and learning: Current knowledge gaps and recommendations for future research. Education Technology Research and Development, 55, 223–252. https://doi.org/10.1007/s11423-006-9022-5

    Article  Google Scholar 

  • Hew, K. F., Lan, M., Tang, Y., Jia, C., & Lo, C. K. (2019). Where is the “theory” within the field of educational technology research? British Journal of Educational Technology. https://doi.org/10.1111/bjet.12770

    Article  Google Scholar 

  • Hoffman, B. (2010). “I think I can, but I’m afraid to try”: The role of self-efficacy beliefs and mathematics anxiety in mathematics problem-solving efficiency. Learning and Individual Differences, 20(3), 276–283.

    Google Scholar 

  • Hoffman, R. (2003). Why buy that theory? In O. Sacks (Ed.), The best American science writing: 2003 (pp. 222–227). Harper-Collins.

    Google Scholar 

  • Hollander, E. P. (1967). Principles and methods of social psychology. Oxford University Press.

    Google Scholar 

  • Holmberg (1985). The feasibility of theory of teaching for distance education and a proposed theory (ZIFF Paiere 60). Hagen, West Germany: Fern Universitat, Zentrales Institute fur Fernstudienforscgung Arbeitsbereich. (ERIC Document Reproduction Service No. ED290013).

  • Huang, W.-H., Huang, W.-Y., & Tschopp, J. (2010). Sustaining iterative game playing processes in DGBL: The relationship between motivational processing and outcome processing. Computers & Education, 55(2), 789–797.

    Google Scholar 

  • Jaccard, J., & Jacoby, J. (2009). Theory construction and model building skills: A practical guide for social scientists. Guilford Press.

    Google Scholar 

  • Johns, G. (2006). The essential impact of context on organizational behavior. Academy of Management Review, 31(2), 386–408.

    Google Scholar 

  • Jones, C., & Czerniewicz, L. (2011). Theory in learning technology. Research in Learning Technology, 19(3), 173–177.

    Google Scholar 

  • Keller, J. M. (1999). Using the ARCS motivational process in computer-based instruction and distance education. New Directions for Teaching and Learning, 78, 39–48.

    Google Scholar 

  • Keller, J. M. (2008). An integrative theory of motivation, volition, and performance. Technology, Instruction, Cognition and Learning, 16, 79–104.

    Google Scholar 

  • Knowles, M. S., Holton, E. F., & Swanson, R. A. (1998). The adult learner (5th ed.). Butterworth-Heinemann Publishers.

    Google Scholar 

  • Kuhl, J. (1987). Action control: The maintenance of motivational states. In F. Halisch & J. Kuhl (Eds.), Motivation, intention and volition (pp. 279–291). Springer.

    Google Scholar 

  • Kuhn, T. S. (1996). The structure of scientific revolutions. University of Chicago Press.

    Google Scholar 

  • Malone, T. W. (1985). Designing organizational interfaces. In L. Borman & R. Smith (Eds.), Proceedings of the CHI’85 Conference on Human Factors in Computing Systems (pp. 66–71). New York, NY: ACM Press.

  • Markauskaite, L., & Reimann, P. (2014). Editorial: e-Research for education: Applied, methodological and critical perspectives. British Journal of Educational Technology, 45(3), 385–391.

    Google Scholar 

  • Mayer, R. E. (2001). Multimedia learning. Cambridge University Press.

    Google Scholar 

  • McDonnell, L. M. (1995). Opportunity to learn as a research concept and a policy instrument. Educational Evaluation and Policy Analysis, 17(3), 305–322.

    Google Scholar 

  • McKenney, S., & Reeves, T. C. (2014). Educational design research. In J. M. Spector, M. D. Merrill, J. Elen, & M. J. Bishop (Eds.), Handbook of research on educational communications and technology (pp. 131–140). Springer.

    Google Scholar 

  • Means, B., Bakia, M., & Murphy, R. (2014). Learning online: What research tells us about whether, when and how. Routledge.

    Google Scholar 

  • Means, B., Toyama, Y., Murphy, R., & Baki, M. (2013). The effectiveness of online and blended learning: A meta-analysis of the empirical literature. Teachers College Record, 115, 1–47.

    Google Scholar 

  • Mintzberg, H. (2005). Developing theory about the development of theory. In M. Hitt & K. Smith (Eds.), Minds in management: The process of theory development (pp. 355–372). Oxford University Press.

    Google Scholar 

  • Moore, M. G. (1997). Theory of transactional distance. In D. Keegan (Ed.), Theoretical principles of distance education (pp. 22–38). Routledge.

    Google Scholar 

  • Moore, M. G., & Diehl, W. C. (2018). Handbook of distance education. Routledge.

    Google Scholar 

  • Morgan, C., & Wildemuth, B. M. (2009). Questions related to theory. Applications of social research methods to questions in information and library science (pp. 40–50). Libraries Unlimited.

    Google Scholar 

  • Nelson, R., & Winter, S. (1974). Neoclassical vs. evolutionary theories of economic growth: Critique and prospectus. Economic Journal, 84(336), 886–905.

    Google Scholar 

  • Novak, E. (2014). Toward a mathematical model of motivation, volition, and performance. Computers & Education, 74, 73–80. https://doi.org/10.1016/j.compedu.2014.01.009

    Article  Google Scholar 

  • Novak, E., Daday, J., & McDaniel, K. (2018). Using a mathematical model of motivation, volition, and performance to examine students’ e-text learning experiences. Educational Technology Research & Development, 66(5), 1189–1209. https://doi.org/10.1007/s11423-018-9599-5

    Article  Google Scholar 

  • Novak, E., McDaniel, K., Daday, J., & Soyturk, I. (2021). Understanding student frustration with e-learning materials: Development and validation of an E-Text Frustration scale. Featured Research Paper presented at the Association for Educational Communications and Technology (AECT), Chicago, IL. November 2021.

  • Opp, K.-D. (1970). Theories of the middle range as a strategy for the construction of a general sociological theory. Quality and Quantity, 4(2), 243–253. https://doi.org/10.1007/BF00199565

    Article  Google Scholar 

  • Pearl, J. (2000). Causality: Models, reasoning, and inference. Cambridge University Press.

    Google Scholar 

  • Picciano, A. G. (2017). Theories and frameworks for online education: Seeking an integrated model. Online Learning, 21(3), 166–190. https://doi.org/10.24059/olj.v21i3.1225

    Article  Google Scholar 

  • Puntambekar, S., et al. (2018). Design-based research. In F. Fisher (Ed.), International handbook of the learning sciences (pp. 383–392). Routledge.

    Google Scholar 

  • Qian, H., & Youngs, P. (2016). The effect of teacher education programs on future elementary mathematics teachers’ knowledge: A five-country analysis using TEDS-M data. Journal of Mathematics Teacher Education, 19(4), 371–396. https://doi.org/10.1007/s10857-014-9297-0

    Article  Google Scholar 

  • Reeves, T. C. (2006). Design research from the technology perspective. In J. V. Akker, K. Gravemeijer, S. McKenney, & N. Nieveen (Eds.), Educational design research (pp. 86–109). Routledge.

    Google Scholar 

  • Rodgers, J. L. (2003). EMOSA sexuality models, memes, and the tipping point: Policy and program implications. In D. Romer (Ed.), Reducing adolescent risk: Toward an integrated approach (pp. 185–192). Sage.

    Google Scholar 

  • Rodgers, J. L. (2010). The epistemology of mathematical and statistical modeling: A quiet methodological revolution. American Psychologist, 65(1), 1–12.

    Google Scholar 

  • Rodgers, J. L., & Doughty, D. (2001). Does having boys or girls run in the family? Chance, 14, 8–13.

    Google Scholar 

  • Rodgers, J. L., & Rowe, D. C. (1993). Social contagion and adolescent sexual behavior: A developmental EMOSA model. Psychological Review, 100, 479–510. https://doi.org/10.1037/0033-295X.100.3.479

    Article  Google Scholar 

  • Rowe, D. C., & Rodgers, J. L. (1991). Adolescent smoking and drinking: Are they epidemics? Journal of Studies on Alcohol, 52, 110–117.

    Google Scholar 

  • Scheerens, J., & Blömeke, S. (2016). Integrating teacher education effectiveness research into educational effectiveness models. Educational Research Review, 18, 70–87. https://doi.org/10.1016/j.edurev.2016.03.002

    Article  Google Scholar 

  • Seel, N. M. (2009). Bonjour tristesse: Why don’t we research as we have been taught? Methodological considerations on instructional technology research. Technology, Instrustion, Cognition and Learning, 6, 151–176.

    Google Scholar 

  • Shadish, W., Cook, T. D., & Campbell, D. T. (2002). Experimental and quasi-experimental designs for generalized causal inference. Houghton Mifflin.

    Google Scholar 

  • Shepard, R. N. (1982). Geometrical approximations to the structure of musical pitch. Psychological Review, 89, 305–333.

    Google Scholar 

  • Siemens, G. (2004). Connectivism: A learning theory for the digital age. International Journal of Instructional Technology and Distance Learning, 2, 1–8.

    Google Scholar 

  • Simon, H. A., & Newell, A. (1956). Models: Their uses and limitations. In D. White (Ed.), The state of the social sciences (pp. 61–83). University of Chicago Press.

    Google Scholar 

  • Straub, D. W. (2009). Editor’s comments: Why top journals accept your paper. MIS Quarterly, 33(3), iii–x.

    Google Scholar 

  • Suppes, P. (1978). Impact of research on education: Some case studies. National Academy of Education.

    Google Scholar 

  • Tatto, M. T., Schwille, J., Senk, S., Ingvarson, L., Peck, R., & Rowley, G. (2008). Teacher education and development study in mathematics (TEDS-M): Policy, practice, and readiness to teach primary and secondary mathematics. Conceptual framework. Teacher Education and Development International, Study Center, College of Education, Michigan State University.

    Google Scholar 

  • Tipton, E., & Olsen, R. B. (2018). A review of statistical methods for generalizing from evaluations of educational interventions. Educational Researcher, 47(8), 516–524. https://doi.org/10.3102/0013189x18781522

    Article  Google Scholar 

  • Venkatesh, V., Morris, M. G., Davis, G. B., & Davis, F. D. (2003). User acceptance of information technology: Toward a unified view. MIS Quarterly, 27(3), 425–478.

    Google Scholar 

  • Venkatesh, V., Thong, J. Y. L., & Xu, X. (2016). Unified theory of acceptance and use of technology: A synthesis and the road ahead. Journal of the Association for Information Systems, 17(5), 328–376.

    Google Scholar 

  • Wedemeyer, C. A. (1981). Learning at the back door: Reflections on non-traditional learning in the lifespan. The University of Wisconsin Press.

    Google Scholar 

  • Wenger, E. (1998). Communities of practice: Learning, meaning, and identity. Cambridge University Press.

    Google Scholar 

  • Wenger, E., & Lave, J. (1991). Learning in doing: Social, cognitive and computational perspectives. Situated learning: Legitimate peripheral participation. Cambridge University Press.

    Google Scholar 

  • Willingham, D. (2008). What is developmentally appropriate? American Educator, 32(2), 34–39.

    Google Scholar 

  • Zawacki-Richter, O., Bäcker, E., & Vogt, S. (2009). Review of distance education research (2000 to 2008): Analysis of research areas, methods, and authorship patterns. International Review of Research in Open and Distributed Learning, 10(6), 21–50. https://doi.org/10.19173/irrodl.v10i6.741

    Article  Google Scholar 

  • Zimmerman, B. J. (2001). Theories of self-regulated learning and academic achievement: An overview and analysis. In B. J. Zimmerman & D. H. Schunk (Eds.), Self-regulated learning and academic achievement. Theoretical perspectives (pp. 1–38). Mahwah.

    Google Scholar 

Download references

Funding

N/A.

Author information

Authors and Affiliations

  1. School of Teaching, Learning and Curriculum Studies, Kent State University, 150 Terrace Drive, P.O. Box 5190, Kent, OH, 44242-0001, USA

    Elena Novak

Authors
  1. Elena Novak
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Elena Novak.

Ethics declarations

Conflict of interest

The author declares that she has no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Novak, E. Mathematical modeling for theory-oriented research in educational technology. Education Tech Research Dev 70, 149–167 (2022). https://doi.org/10.1007/s11423-021-10069-6

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11423-021-10069-6

Keywords

Search

Navigation