Skip to main content
SpringerLink
Log in

How Do Learners Approach Dialogic, On-Line Mathematics Videos?

  • Published:
Digital Experiences in Mathematics Education Aims and scope Submit manuscript

Abstract

On-line math videos for student learning are abundant; yet they are surprisingly uniform in their expository mode of presentation and their emphasis on procedural skill. In response, we created an alternative model of on-line math videos that are dialogue-intensive and focus on the development of mathematical meaning and problem solving. Each video shows a pair of students (called the talent) next to their mathematical inscriptions, which allows other students viewing the videos (called vicarious learners) to see both the talent and their work clearly. In this exploratory study, we investigated how eleven pairs of vicarious learners approached a research session in which they were asked to watch these videos and then solve a related mathematical task. We found qualitatively different ways that the vicarious learner pairs interpreted the goal of the research session, which, in turn, constrained their behavior when solving the task and getting information from the videos. Specifically, by drawing upon board-game theory, we inferred that the vicarious learners engaged in four different games: (a) the Definition game, (b) the Concept Image game, (c) the Procedure game and (d) the Video Expert game. The particular game that vicarious learners played had consequences for the productivity of their mathematical work. This article explores the significance and implications of these results.

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
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

Notes

  1. http://www.learner.org/resources/series196.html

  2. Available at: www.mathtalk.org

References

  • Arzarello, F., Paola, D., Robutti, O., & Sabena, C. (2009). Gestures as semiotic resources in the mathematics classroom. Educational Studies in Mathematics, 70(2), 97–109.

    Article  Google Scholar 

  • Berland, L., & Hammer, D. (2012). Framing for scientific argumentation. Journal of Research in Science Teaching, 49(1), 68–94.

    Article  Google Scholar 

  • Bhagat, K., Chang, C.-N., & Chang, C.-Y. (2016). The impact of the flipped classroom on mathematics concept learning in high school. Educational Technology and Society, 19(3), 134–142.

    Google Scholar 

  • Borba, M., Askar, P., Engelbrecht, J., Gadanidis, G., Llinares, S., & Aguilar, M. (2016). Blended learning, e-learning and mobile learning in mathematics education. ZDM, 48(5), 589–610.

    Article  Google Scholar 

  • Boston Globe, The (2011, August 12). Math instruction goes viral. (http://www.boston.com/bostonglobe/editorial_opinion/editorials/articles/2011/08/12/math_instruction_goes_viral/.)

  • Bowers, J., Passentino, G., & Connors, C. (2012). What is the complement to a procedural video? Journal of Computers in Mathematics and Science Teaching, 31(3), 213–248.

    Google Scholar 

  • Charmaz, K. (2008). Grounded theory as an emergent method. In S. Hesse-Biber & P. Leavy (Eds.), Handbook of emergent methods (pp. 155–170). New York, NY: Guilford Press.

    Google Scholar 

  • Chi, M., Roy, M., & Hausmann, R. (2008). Observing tutorial dialogues collaboratively: Insights about human tutoring effectiveness from vicarious learning. Cognitive Science, 32(2), 301–341.

    Article  Google Scholar 

  • Chieu, V., Herbst, P., & Weiss, M. (2011). Effect of an animated classroom story embedded in on-line discussion on helping mathematics teachers learn to notice. Journal of the Learning Sciences, 20(4), 589–624.

    Article  Google Scholar 

  • Clark, K. (2015). The effects of the flipped model of instruction on student engagement and performance in the secondary mathematics classroom. Journal of Educators On-line, 12(1), 91–115.

    Google Scholar 

  • Clark-Wilson, A., Sutherland, R., & Oldknow, A. (2011). Digital technologies and mathematics education 11–19. London, UK: Joint Mathematics Council.

    Google Scholar 

  • Collins, A., & Ferguson, W. (1993). Epistemic forms and epistemic games: Structures and strategies to guide inquiry. Educational Psychologist, 28(1), 25–42.

    Article  Google Scholar 

  • Craig, S., Sullins, J., Witherspoon, A., & Gholson, B. (2010). The deep-level-reasoning question effect: The role of dialogue and deep-level-reasoning questions during vicarious learning. Cognition and Instruction, 24(4), 565–591.

    Article  Google Scholar 

  • Danielson, C. & Goldenberg, M. (2012, July 27). How well does khan academy teach? The Washington Post. (http://www.washingtonpost.com/blogs/answer-sheet/post/how-well-does-khan-academy-teach/2012/07/27/gJQA9bWEAX_blog.html.)

  • Drijvers, P. (2015). Digital technology in mathematics education: Why it works (or doesn’t). In S. Cho (Ed.), Selected regular lectures from the 12 th international congress on mathematics education (pp. 135–151). Cham, Switzerland: Springer.

    Chapter  Google Scholar 

  • Drijvers, P., Doorman, M., Boon, P., Reed, H., & Gravemeijer, K. (2010). The teacher and the tool: Instrumental orchestrations in the technology-rich mathematics classroom. Educational Studies in Mathematics, 75(2), 213–234.

    Article  Google Scholar 

  • Esmonde, I. (2016). Power and sociocultural theories of learning. In I. Esmonde & A. Booker (Eds.), Power and privilege in the learning sciences: Critical and sociocultural theories of learning (pp. 6–27). New York, NY: Routledge.

    Chapter  Google Scholar 

  • Glaser, B. & Strauss, A. (1967). The discovery of grounded theory: Strategies for qualitative research. Hawthorne, NY: Aldine Publishing Company.

  • Goffman, E. (1974). Frame analysis: An essay on the organization of experience. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Hopper, K. (2001). Is the internet a classroom? TechTrends, 45(5), 35–44.

    Article  Google Scholar 

  • Hoyles, C., & Sutherland, R. (1987). Ways of learning in a computer-based environment: Some findings of the LOGO Maths project. Journal of Computer Assisted Learning, 3(2), 67–80.

    Article  Google Scholar 

  • Järvinen, A. (2008). Games without frontiers: Theories and methods for game studies and design. Unpublished doctoral dissertation. Tampere, Finland: University of Tampere. http://tampub.uta.fi/bitstream/handle/10024/67820/978-951-44-7252-7.pdf?sequence=1.

    Google Scholar 

  • Jaworski, B., & Potari, D. (2009). Bridging the macro–micro divide: Using an activity theory model to capture socio-cultural complexity in mathematics teaching and its development. Educational Studies in Mathematics, 72(2), 219–236.

    Article  Google Scholar 

  • Juul, J. (2010). The game, the player, the world: Looking for a heart of gameness. Plurais: Revista Multidisciplinar, 1(2), 248–270. http://www.revistas.uneb.br/index.php/plurais/article/view/880/624.

    Google Scholar 

  • Khan, S. (2012). The one world schoolhouse: Education reimagined. New York, NY: Hodder & Stoughton.

    Google Scholar 

  • Kolikant, Y., & Broza, O. (2011). The effect of using a video clip presenting a contextual story on low-achieving students’ mathematical discourse. Educational Studies in Mathematics, 76(1), 23–47.

    Article  Google Scholar 

  • Leung, A. (2011). An epistemic model of task design in dynamic geometry environment. ZDM, 43(3), 325–336.

    Article  Google Scholar 

  • Lin, G. & Michko, G. (2010). Beyond YouTube: Repurposing on-line video for Education In Z. Abas, I. Jung & J. Luca (Eds), Proceedings of Global Learn (No. 1, pp. 257–267). Waynesville, NC: Association for the Advancement of Computing in Education.

  • Lobato, J., Hohensee, C., & Rhodehamel, B. (2013). Students’ mathematical noticing. Journal for Research in Mathematics Education, 44(5), 809–850.

    Article  Google Scholar 

  • Lobato, J., Walters, C., & Walker, C. (2016, April). Beyond the demonstration of procedures in YouTube-style math videos. Paper presented at the NCTM research conference. San Francisco: CA. https://mathtalk.sdsu.edu/assets/lobato_walters_walker_nctm_2016.pdf.

  • Love, B., Hodge, A., Grandgenett, N., & Swift, A. (2014). Student learning and perceptions in a flipped linear algebra course. International Journal of Mathematical Education in Science and Technology, 45(3), 317–324.

    Article  Google Scholar 

  • Mayes, J., Dineen, F., McKendree, J., & Lee, J. (2002). Learning from watching others learn. In C. Steeples & C. Jones (Eds.), Networked learning: Perspectives and issues (pp. 213–227). London, UK: Springer-Verlag.

    Chapter  Google Scholar 

  • Miles, M. & Huberman, A. (1994, 2nd edn). Qualitative data analysis. Thousand Oaks, CA: Sage Publications.

  • Moore-Russo, D., Diletti, J., Strzelec, J., Reeb, C., Schillace, J., Martin, A., Arabeyyat, T., Prabucki, K., & Scanlon, S. (2015). A study of how angry birds has been used in mathematics education. Digital Experiences in Mathematics Education, 1(2–3), 107–132.

    Article  Google Scholar 

  • Muller, D. (2008). Designing effective multimedia for physics education. Unpublished doctoral dissertation. Sydney, Australia: University of Sydney. http://www.physics.usyd.edu.au/super/theses/PhD(Muller).pdf.

  • Muller, D., Bewes, J., Sharma, M., & Reimann, P. (2008). Saying the wrong thing: Improving learning with multimedia by including misconceptions. Journal of Computer-Assisted Learning, 24(2), 144–155.

    Article  Google Scholar 

  • NCTM. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Nemirovsky, R., Tierney, C., & Wright, T. (1998). Body motion and graphing. Cognition and Instruction, 16(2), 119–172.

    Article  Google Scholar 

  • Panero, M., & Aldon, G. (2016). How teachers evolve their formative assessment practices when digital tools are involved in the classroom. Digital Experiences in Mathematics Education, 2(1), 70–86.

    Article  Google Scholar 

  • Roorda, G., Vos, P., Drijvers, P., & Goedhart, M. (2016). Solving rate of change tasks with a graphing calculator: A case study on instrumental genesis. Digital Experiences in Mathematics Education, 2(3), 228–252.

    Article  Google Scholar 

  • Roschelle, J., Noss, R., Blikstein, P. & Jackiw, N. (2017). Technology for learning mathematics. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 853–878). Reston, VA: National Council of Teachers of Mathematics.

  • Roth, W.-M. (2012). Cultural–historical activity theory: Vygotsky’s forgotten and suppressed legacy and its implication for mathematics education. Mathematics Education Research Journal, 24(1), 87–104.

    Article  Google Scholar 

  • Schoenfeld, A. (1992). On paradigms and methods: What do you do when the ones you know don’t do what you want them to? Issues in the analysis of data in the form of videotapes. Journal of the Learning Sciences, 2(2), 179–214.

    Article  Google Scholar 

  • Solomon, C., & Papert, S. (1976). A case study of a young child doing turtle graphics in LOGO. In Proceedings of the June 7–10, 1976, National Computer Conference and exposition (pp. 1049–1056). New York, NY: Association for Computer Machinery. https://dspace.mit.edu/bitstream/handle/1721.1/6252/AIM-375.pdf?sequence=2&origin=publication_detail.

    Google Scholar 

  • Strauss, A. (1987). Qualitative analysis for social scientists. New York, NY: Cambridge University Press.

    Book  Google Scholar 

  • Strauss, A., & Corbin, J. (1990). Basics of qualitative research. Newbury Park, CA: Sage Publications.

    Google Scholar 

  • Subramaniam, S. & Muniandy, B. (2017, published on-line). The effect of flipped classroom on students’ engagement. Technology, Knowledge and Learning. (https://doi.org/10.1007/s10758-017-9343-y.)

  • Talbert, R. (2012, July 3). The trouble with khan academy. In The Chronicle of Higher Education http://www.chronicle.com/blognetwork/castingoutnines/2012/07/03/the-trouble-with-khan-academy/.

  • Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12(2), 151–169.

    Article  Google Scholar 

  • Tannen, D. (1993). Framing in discourse. New York, NY: Oxford University Press.

    Google Scholar 

  • Thompson, C. (2011, July 15). How Khan Academy is changing the rules of education. Wired Magazine. (https://www.wired.com/2011/07/ff_khan/.)

  • Trouche, L. (2004). Managing the complexity of human/machine interactions in computerized learning environments: Guiding students’ command process through instrumental orchestrations. International Journal of Computers for Mathematical Learning, 9(3), 281–307.

    Article  Google Scholar 

  • Tuminaro, J. & Redish, E. (2007). Elements of a cognitive model of physics problem solving: Epistemic games. Physical Review Special Topics: Physics Education Research, 3(2), 020101 (1–22).

  • Woods, S. (2012). Eurogames: The design, culture and play of modern European board games. Jefferson, NC: McFarland.

  • Zhang, D. (2005). Interactive multimedia-based e-learning: A study of effectiveness. The American Journal of Distance Education, 19(3), 149–162.

    Article  Google Scholar 

Download references

Acknowledgments

The development of this article was supported by the US National Science Foundation under grant DRL–1416789. The views expressed do not necessarily reflect official positions of the Foundation. An early draft of a subset of the results was presented at the 2017 NCTM Research Conference in San Antonio, TX. Development of the videos and data collection also involved technical specialist Michael McKean. We thank the project evaluator, Victor Cifarelli, for his valuable input and guidance.

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, San Diego State University, San Diego, CA, USA

    Joanne Lobato

  2. Center for Research in Mathematics and Science Education, San Diego State University, 6475 Alvarado Road, Suite 206, San Diego, CA, 92120, USA

    Joanne Lobato, Carren Walker & Matthew Voigt

  3. Department of Mathematics, Weber State University, Ogden, UT, USA

    C. David Walters

Authors
  1. Joanne Lobato
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. David Walters
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Carren Walker
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Matthew Voigt
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Joanne Lobato.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lobato, J., Walters, C.D., Walker, C. et al. How Do Learners Approach Dialogic, On-Line Mathematics Videos?. Digit Exp Math Educ 5, 1–35 (2019). https://doi.org/10.1007/s40751-018-0043-6

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40751-018-0043-6

Keywords

Search

Navigation