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Technology, Knowledge and Learning

, Volume 21, Issue 3, pp 341–360 | Cite as

The Complexity of the Affordance–Ability Relationship When Second-Grade Children Interact with Mathematics Virtual Manipulative Apps

  • Stephen I. Tucker
  • Patricia S. Moyer-Packenham
  • Arla Westenskow
  • Kerry E. Jordan
Original research
First Online:

Abstract

The purpose of this study was to explore relationships between app affordances and user abilities in second graders’ interactions with mathematics virtual manipulative touchscreen tablet apps. The research questions focused on varying manifestations of affordance–ability relationships during children’s interactions with mathematics virtual manipulative touchscreen tablet apps. Researchers qualitatively analyzed video recordings and ethograms from clinical interviews of 33 second-grade children. Each 45-min clinical interview involved one child interacting with two sequences of mathematics virtual manipulative touchscreen tablet apps: one sequence focusing on place value concepts and the other sequence focusing on skip counting concepts. Results provided evidence of Moyer-Packenham and Westenskow’s (Int J Virtual Pers Learn Environ 4(3):35–50, 2013) five affordance categories of virtual manipulatives. Approach to and degree of affordance access varied depending on a child’s corresponding ability, and some children modified their affordance access as their ability changed. Results also indicated that outcomes of accessing an affordance also related to a child’s ability. Context also influenced affordance access. These results imply that affordance–ability relationships are multifaceted. Overall, these results imply that is important to consider affordance–ability relationships in relation to mathematics education technology.

Keywords

Virtual manipulatives Affordances Mathematics Mobile devices 
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Notes

Acknowledgments

Financial support for the work reported in this paper was provided for a project titled: Captivated! Young Children’s Learning Interactions with iPad Mathematics Apps, funded by the Vice President for Research Office category of Research Catalyst Funding at Utah State University, 2605 Old Main Hill, Logan, UT 84322, USA.

Compliance with Ethical Standards

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. Alibali, M. W., & Nathan, M. J. (2012). Embodiment in mathematics teaching and learning: Evidence from learners’ and teachers’ gestures. Journal of the Learning Sciences, 21(2), 247–286. doi: 10.1080/10508406.2011.611446.CrossRefGoogle Scholar
  2. Baccaglini-Frank, A., & Maracci, M. (2015). Multi-touch technology and preschoolers’ development of number-sense. Digital Experiences in Mathematics Education, 1(1), 7–27. doi: 10.1007/s40751-015-0002-4.CrossRefGoogle Scholar
  3. Barendregt, W., Lindström, B., Rietz-Leppänen, E., Holgersson, I., & Ottosson, T. (2012). Development and evaluation of Fingu: A mathematics iPad game using multi-touch interaction. In H. Schelhowe (Ed.), Proceedings of the 11th international conference on interaction design and children (pp. 204–207). New York, NY: ACM. doi: 10.1145/2307096.2307126.CrossRefGoogle Scholar
  4. Bartoschek, T., Schwering, A., Li, R., & Münzer, S. (2013). Ori-Gami: An App fostering spatial competency development and spatial learning of children. In D. Vandenbroucke, B. Bucher, & J. Crompvoets (Eds.), Proceedings of the 15th AGILE international conference on geographic information science. Leuven: Springer.Google Scholar
  5. Burlamaqui, L., & Dong, A. (2014). The use and misuse of the concept of affordance. In J. S. Gero (Ed.), Design computing and cognition DCC’14 (pp. 1–20). London: Springer.Google Scholar
  6. Burlamaqui, L., & Dong, A. (2015). The identification of perceived intended affordances. In V. Popovic, A. L. Blackler, D.-B. Luh, N. Nimkulrat, B. Kraal, & Y. Nagai (Eds.), IASDR2015 Interplay (pp. 266–280). Australia: Brisbane.Google Scholar
  7. Chemero, A. (2003). An outline of a theory of affordances. Ecological Psychology, 15(2), 181–195. doi: 10.1207/S15326969ECO1502_5.CrossRefGoogle Scholar
  8. Gaver, W. W. (1991). Technology affordances. In Proceedings of the SIGCHI Conference on Human Factors in Computing Systems (pp. 79–84). New York, NY, USA: ACM. doi: 10.1145/108844.108856
  9. Gibson, J. J. (1986). The ecological approach to visual perception. Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
  10. Ginsburg, H. P., & Pappas, S. (2004). SES, ethnic, and gender differences in young children’s informal addition and subtraction: A clinical interview investigation. Journal of Applied Developmental Psychology, 25(2), 171–192. doi: 10.1016/j.appdev.2004.02.003.CrossRefGoogle Scholar
  11. Greene, J. C. (2007). Mixed methods in social inquiry. New York: Wiley.Google Scholar
  12. Greeno, J. G. (1994). Gibson’s affordances. Psychological Review, 101(2), 336–342. doi: 10.1037/0033-295X.101.2.336.CrossRefGoogle Scholar
  13. Ladel, S., & Kortenkamp, U. (2012). Early maths with multi-touch—an activity-theoretic approach. In Proceedings of POEM 2012. http://cermat.org/poem2012/main/proceedings_files/Ladel-Kortenkamp-POEM2012.pdf
  14. MacNulty, D. R., Mech, L. D., & Smith, D. W. (2007). A proposed ethogram of large-carnivore predatory behavior, exemplified by the wolf. Journal of Mammalogy, 88(3), 595–605. doi: 10.1644/06-MAMM-A-119R1.1.CrossRefGoogle Scholar
  15. McLeod, J., Vasinda, S., & Dondlinger, M. J. (2012). Conceptual visibility and virtual dynamics in technology-scaffolded learning environments for conceptual knowledge of mathematics. Journal of Computers in Mathematics and Science Teaching, 31(3), 283–310.Google Scholar
  16. Miles, M. B., Huberman, A. M., & Saldaña, J. (2013). Qualitative data analysis: A methods sourcebook (3rd ed.). Thousand Oaks, CA: Sage.Google Scholar
  17. Moyer, P. S., Bolyard, J. J., & Spikell, M. A. (2002). What are virtual manipulatives? Teaching Children Mathematics, 8(6), 372–377.Google Scholar
  18. Moyer-Packenham, P. S., Anderson, K. L., Shumway, J. F., Tucker, S. I., Westenskow, A., Boyer-Thurgood, J. M., et al. (2014). Developing research tools for young children’s interactions with mathematics apps on the iPad. In Proceedings of the 12th annual hawaii international conference on education (HICE) (pp. 1685–1694). Honolulu, Hawaii.Google Scholar
  19. Moyer-Packenham, P. S., Baker, J., Westenskow, A., Anderson, K. L., Shumway, J. F., & Jordan, K. E. (2014b). Predictors of achievement when virtual manipulatives are used for mathematics instruction. REDIMAT - Journal of Research in Mathematics Education, 3(2), 121–150. doi: 10.4471/redimat.Google Scholar
  20. Moyer-Packenham, P. S., Bullock, E. P., Shumway, J. F., Tucker, S. I., Watts, C., Westenskow, A., et al. (2016). The role of affordances in children’s learning performance and efficiency when using virtual manipulatives mathematics iPad apps. Mathematics Education Research Journal,. doi: 10.1007/s13394-015-0161-z.Google Scholar
  21. Moyer-Packenham, P. S., Shumway, J. F., Bullock, E., Tucker, S. I., Anderson-Pence, K. L., Westenskow, A., et al. (2015). Young children’s learning performance and efficiency when using virtual manipulative mathematics iPad apps. Journal of Computers in Mathematics and Science Teaching, 34(1), 41–69.Google Scholar
  22. Moyer-Packenham, P. S., & Suh, J. M. (2012). Learning mathematics with technology: The influence of virtual manipulatives on different achievement groups. Journal of Computers in Mathematics & Science Teaching, 31(1), 39–59.Google Scholar
  23. Moyer-Packenham, P. S., & Westenskow, A. (2013). Effects of virtual manipulatives on student achievement and mathematics learning. International Journal of Virtual and Personal Learning Environments, 4(3), 35–50.CrossRefGoogle Scholar
  24. Moyer-Packenham, P. S., & Westenskow, A. (2016). Revisiting the effects and affordances of virtual manipulatives for mathematics learning. In K. Terry & A. Cheney (Eds.), Utilizing virtual and personal learning environments for optimal learning (pp. 186–215). Hershey, PA: Information Science Reference. doi: 10.4018/978-1-4666-8847-6.ch009.CrossRefGoogle Scholar
  25. Murray, T., & Arroyo, I. (2002). Toward measuring and maintaining the Zone of Proximal Development in adaptive instructional systems. In S. A. Cerri, G. Gouardères, & F. Paraguaçu (Eds.), Intelligent tutoring systems (pp. 749–758). Berlin: Springer. doi: 10.1007/3-540-47987-2_75.CrossRefGoogle Scholar
  26. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics. http://www.nctm.org/standards/content.aspx?id=26792
  27. Nemirovsky, R., Kelton, M. L., & Rhodehamel, B. (2013). Playing mathematical instruments: Emerging perceptuomotor integration with an interactive mathematics exhibit. Journal for Research in Mathematics Education, 44(2), 372–415. doi: 10.5951/jresematheduc.44.2.0372.CrossRefGoogle Scholar
  28. Norman, D. A. (1988). The psychology of everyday things. New York: Basic Books.Google Scholar
  29. Norman, D. A. (1999). Affordance, conventions, and design. Interactions, 6(3), 38–43. doi: 10.1145/301153.301168.CrossRefGoogle Scholar
  30. Paek, S. (2012). The impact of multimodal virtual manipulatives on young children’s mathematics learning (Doctoral dissertation). Retrieved from ProQuest Dissertations & Theses Full Text. (UMI No. 3554708)Google Scholar
  31. Quintana, C., Reiser, B. J., Davis, E. A., Krajcik, J., Fretz, E., Duncan, R. G., et al. (2004). A scaffolding design framework for software to support science inquiry. The Journal of the Learning Sciences, 13(3), 337–386.CrossRefGoogle Scholar
  32. Saldaña, J. (2013). The coding manual for qualitative researchers (2nd ed.). Thousand Oaks, CA: Sage.Google Scholar
  33. Sarama, J., & Clements, D. H. (2009). Early childhood mathematics education research: Learning trajectories for young children. New York: Routledge.Google Scholar
  34. Tucker, S. I. (2015). An exploratory study of attributes, affordances, abilities, and distance in children’s use of mathematics virtual manipulative iPad apps (Doctoral dissertation). http://gradworks.umi.com/37/23/3723089.html
  35. Tucker, S. I. (in press). The modification of attributes, affordances, abilities, and distance for learning framework and its applications to interactions with mathematics virtual manipulatives. In International perspectives on teaching and learning mathematics with virtual manipulatives. Berlin: Springer.Google Scholar
  36. Tucker, S. I., & Moyer-Packenham, P. S. (2014). Virtual manipulatives’ affordances influence student learning. In S. Oesterle, C. Nicol, P. Liljedahl, & D. Allan (Eds.), Proceedings of the Joint Meeting of PME 38 and PME-NA 36 (Vol. 6, p. 251). PME: Vancouver.Google Scholar
  37. Tucker, S. I., Moyer-Packenham, P. S., Shumway, J. F., & Jordan, K. (in press). Zooming in on students’ thinking: How a number line app revealed, concealed, and developed students’ number understanding. Australian Primary Mathematics Classroom.Google Scholar
  38. Wood, D., Bruner, J. S., & Ross, G. (1976). The role of tutoring in problem solving. Journal of Child Psychology and Psychiatry, 17(2), 89–100. doi: 10.1111/j.1469-7610.1976.tb00381.x.CrossRefGoogle Scholar
  39. Zanchi, C., Presser, A. L., & Vahey, P. (2013). Next generation preschool math demo: Tablet games for preschool classrooms. In Proceedings of the 12th international conference on interaction design and children (pp. 527–530). New York, NY: ACM. doi: 10.1145/2485760.2485857

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Stephen I. Tucker
    • 1
    • 2
  • Patricia S. Moyer-Packenham
    • 2
  • Arla Westenskow
    • 2
  • Kerry E. Jordan
    • 2
  1. 1.VCU School of EducationVirginia Commonwealth UniversityRichmondUSA
  2. 2.The Virtual Manipulatives Research GroupUtah State UniversityLoganUSA

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