Mathematics Education Research Journal

, Volume 28, Issue 1, pp 79–105 | Cite as

The role of affordances in children’s learning performance and efficiency when using virtual manipulative mathematics touch-screen apps

  • Patricia S. Moyer-Packenham
  • Emma K. Bullock
  • Jessica F. Shumway
  • Stephen I. Tucker
  • Christina M. Watts
  • Arla Westenskow
  • Katie L. Anderson-Pence
  • Cathy Maahs-Fladung
  • Jennifer Boyer-Thurgood
  • Hilal Gulkilik
  • Kerry Jordan
Original Article

Abstract

This paper focuses on understanding the role that affordances played in children’s learning performance and efficiency during clinical interviews of their interactions with mathematics apps on touch-screen devices. One hundred children, ages 3 to 8, each used six different virtual manipulative mathematics apps during 30–40-min interviews. The study used a convergent mixed methods design, in which quantitative and qualitative data were collected concurrently to answer the research questions (Creswell and Plano Clark 2011). Videos were used to capture each child’s interactions with the virtual manipulative mathematics apps, document learning performance and efficiency, and record children’s interactions with the affordances within the apps. Quantitized video data answered the research question on differences in children’s learning performance and efficiency between pre- and post-assessments. A Wilcoxon matched pairs signed-rank test was used to explore these data. Qualitative video data was used to identify affordance access by children when using each app, identifying 95 potential helping and hindering affordances among the 18 apps. The results showed that there were changes in children’s learning performance and efficiency when children accessed a helping or a hindering affordance. Helping affordances were more likely to be accessed by children who progressed between the pre- and post-assessments, and the same affordances had helping and hindering effects for different children. These results have important implications for the design of virtual manipulative mathematics learning apps.

Keywords

Affordances Virtual manipulative iPad Math apps Manipulatives 

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.

References

  1. Aronin, S., & Floyd, K. K. (2013). Using an iPad in inclusive preschool classrooms to introduce STEM concepts. Teaching Exceptional Children, 45(4), 34–39.Google Scholar
  2. 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, Belgium: Springer.Google Scholar
  3. Bertolo, D., Dinet, J., & Vivian, R. (2014). Reducing cognitive workload during 3D geometry problem solving with an app on iPad (Presented at the Science and Information Conference, pp. 896–900). London: IEEE. doi: 10.1109/SAI.2014.6918292.Google Scholar
  4. Bruner, J. S. (1964). The course of cognitive growth. American Psychologist, 19(1), 1–15.CrossRefGoogle Scholar
  5. Bullock, E. P., Moyer-Packenham, P. S., Shumway, J. F., Watts, C., & MacDonald, B. (2015). Effective teaching with technology: Managing affordances in iPad apps to promote young children’s learning. Unpublished manuscript.Google Scholar
  6. 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. Springer.Google Scholar
  7. Byers, P., & Hadley, J. (2013). Traditional and novel modes of activity in touch screen math apps. In J. P. Hourcade, N. Sawhney, & E. Reardon (Eds.), Proceedings of the 12th International Conference on Interaction Design and Children. New York: ACM.Google Scholar
  8. Cai, J., Lane, S., & Jakabcsin, M. S. (1996). The role of open-ended tasks and holistic scoring rubrics: Assessing students’ mathematical reasoning and communication. In P. C. Elliott (Ed.), Communication in mathematics, K-12 and beyond (pp. 137–145). Reston: The National Council of Teachers of Mathematics.Google Scholar
  9. Carr, J. M. (2012). Does math achievement h’app’en when iPads and game-based learning are incorporated into fifth-grade mathematics instruction? Journal of Information Technology Education, 11, 269–286.CrossRefGoogle Scholar
  10. Chemero, A. (2003). An outline of a theory of affordances. Ecological Psychology, 15(2), 181–195. doi: 10.1207/S15326969ECO1502_5.CrossRefGoogle Scholar
  11. Chen, L. L. (2011). Enhancing special needs student’s learning with iPad. In World Conference on E-Learning in Corporate, Government, Healthcare, and Higher Education (Vol. 2011, pp. 2324–2330). Retrieved from http://www.editlib.org/p/39076/.
  12. Chen, L. L. (2012). Integrating iPad in a special education class: A case study. In World Conference on E-Learning in Corporate, Government, Healthcare, and Highez Education (Vol. 2012, pp. 530–534). Retrieved from http://www.editlib.org/p/41645/.
  13. Cohen, B. H. (2014). Explaining psychological statistics (4th ed.). Hoboken: Wiley.Google Scholar
  14. Corbin, J., & Strauss, A. (2014). Basics of qualitative research: Techniques and procedures for developing grounded theory. Thousand Oaks: Sage publications. Retrieved from https://books.google.com/books?hl=en&lr=&id=MaKWBQAAQBAJ&oi=fnd&pg=PP1&dq=Basics+of+qualitative+research:+Techniques+and+procedures+for+developing+grounded+theory&ots=QrDevRc5O0&sig=4EBsGKn1LSLNVTMdws57MfHAOuo.Google Scholar
  15. Creswell, J. W., & Plano Clark, V. L. (2011). Designing and conducting mixed methods research (2nd ed.). Thousand Oaks: Sage Publications, Inc.Google Scholar
  16. DeCuir-Gunby, J. T., Marshall, P. L., & McCulloch, A. W. (2012). Using mixed methods to analyze video data: A mathematics teacher professional development example. Journal of Mixed Methods Research, 6(3), 199–216.CrossRefGoogle Scholar
  17. Gaver, W. W. (1991). Technology affordances. In Proceedings of the SIGCHI conference on human factors in computing systems (pp. 79–84). New York: ACM. doi: 10.1145/108844.108856.Google Scholar
  18. Gibson, J. J. (1986). The ecological approach to visual perception. Hillsdale: Lawrence Erlbaum Associates.Google Scholar
  19. Gravetter, F. J., & Wallnau, L. B. (2013). Statistics for the behavioral sciences (9th ed.). Belmont: Wadsworth.Google Scholar
  20. Greene, J. C., Caracelli, V. J., & Graham, W. F. (1989). Toward a conceptual framework for mixed-method evaluation design. Educational Evaluation and Policy Analysis, 11, 255–274.CrossRefGoogle Scholar
  21. Greeno, J. G. (1994). Gibson’s affordances. Psychological Review, 101(2), 336–342. doi: 10.1037/0033-295X.101.2.336.CrossRefGoogle Scholar
  22. Gröger, C., Silcher, S., Westkämper, E., & Mitschang, B. (2013). Leveraging apps in manufacturing. A framework for app technology in the enterprise. Procedia CIRP, 7, 664–669. doi: 10.1016/j.procir.2013.06.050.CrossRefGoogle Scholar
  23. Haydon, T., Hawkins, R., Denune, H., Kimener, L., McCoy, D., & Basham, J. (2012). A comparison of iPads and worksheets on math skills of high school students with emotional disturbance. Behavioral Disorders, 37(4), 232–243.Google Scholar
  24. Kilic, A. (2013). An investigation of the use of the iPad and textbooks on the achievement of students with special needs in algebra (Master’s thesis). New Jersey: Rowan University.Google Scholar
  25. Kortenkamp, U., & Ladel, S. (2013). Designing a technology based learning environment for place value using artifact-centric activity theory. In A. M. Lindmeier & A. Heinze (Eds.), Proceedings of the 37th conference of the International Group for the Psychology of Mathematics Education. Mathematics learning across the life span (Vol. 1, pp. 188–192).Google Scholar
  26. McGrenere, J., & Ho, W. (2000). Affordances: Clarifying and evolving a concept. In Graphics interface (Vol. 2000, pp. 179–186). Montreal: Lawrence Erlbaum Associates.Google Scholar
  27. Moyer, P. S., Bolyard, J. J., & Spikell, M. A. (2002). What are virtual manipulatives? Teaching Children Mathematics, 8(6), 372–377.Google Scholar
  28. 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
  29. Moyer-Packenham, P. S., Anderson, K. L., Shumway, J. F., Tucker, S., Westenskow, A., Boyer-Thurgood, J., Bullock, E., Mahamane, S., Baker, J., Gulkilik, H., Maahs-Fladung, C., Symanzik, J., Jordan, K., & The Virtual Manipulatives Research Group at Utah State University. (2014a). Developing research tools for young children’s interactions with mathematics apps on the iPad (pp. 1685–1694). Honolulu, Hawaii: Proceedings of the 12th Annual Hawaii International Conference on Education (HICE). ISSN# 1541–5880.Google Scholar
  30. Moyer-Packenham, P. S., Westenskow, A., Shumway, J. F., Bullock, E., Tucker, S. I., Anderson- Pence, K. L., Boyer-Thurgood, J., Maahs-Fladung, C., Symanzik, J., Mahamane, S., MacDonald, B., Jordan, K., & The Virtual Manipulatives Research Group at Utah State University. (2014b). The effects of different virtual manipulatives for second graders’ mathematics learning and efficiency in the touch-screen environment (Paper presentation). Herceg Novi, Montenegro: 12th International Conference of the Mathematics Education into the 21st Century Project.Google Scholar
  31. Moyer-Packenham, P. S., Shumway, J. F., Bullock, E., Tucker, S. I., Anderson-Pence, K. L., Westenskow, A., Boyer-Thurgood, J., Maahs-Fladung, C., Symanzik, J., Mahamane, S., MacDonald, B., & Jordan, K. (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
  32. 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
  33. Paek, S., Hoffman, D., Saravanos, A., Black, J., & Kinzer, C. (2011). The role of modality in virtual manipulative design. In D. Tan, B. Begole, & W. A. Kellogg (Eds.), CHI conference on human factors in computing systems (pp. 1747–1752). New York, NY: ACM. doi: 10.1145/1979742.1979839.
  34. Paek, S., Hoffman, D. L., & Black, J. B. (2013). Multi-modal interaction with virtual manipulatives: Supporting young children’s math learning. In N. Rummel, M. Kapur, M. Nathan, & S. Puntambekar (Eds.), Proceedings, 10th International Conference on Computer-Supported Collaborative Learning. (Vol. 2, pp. 117–120). Madison, WI.Google Scholar
  35. Patton, M. Q. (1990). Qualitative evaluation and research methods (2nd ed.). Newbury Park: Sage Publications, Inc.Google Scholar
  36. Piaget, J. (1970). The child’s conception of movement and speed. New York: Basic Books (Original work published 1946).Google Scholar
  37. Reid, D., & Ostashewski, N. (2011). iPads in the classroom–new technologies, old issues: Are they worth the effort? In World Conference on Educational Multimedia, Hypermedia and Telecommunications (Vol. 2011, pp. 1689–1694). Retrieved from http://www.editlib.org/p/38089/.
  38. Riconscente, M. M. (2012). Mobile learning game improves 5th graders’ fractions knowledge and attitudes (p. 46). Los Angeles: GameDesk Institute. Retrieved from http://www.gamedesk.org/reports/MM_FINAL_REPORT.pdf.Google Scholar
  39. Riconscente, M. M. (2013). Results from a controlled study of the iPad fractions game motion math. Games and Culture, 8(4), 186–214.CrossRefGoogle Scholar
  40. Roschelle, J. (2000). Choosing and using video equipment for data collection. In A. E. Kelly & R. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 709–729). Mahwah: Lawrence Erlbaum Associates, Inc.Google Scholar
  41. Schubert, C. (2009). Video analysis of practice and the practice of video analysis. In H. Knoblauch, B. Schnettler, J. Raab, & H. G. Soeffner (Eds.), Video analysis methodology and methods: Qualitative audiovisual data analysis and sociology (pp. 115–126). New York: Peter Lang.Google Scholar
  42. Shuler, C. (2009). Pockets of potential: Using mobile technologies to promote children’s learning. New York: The Joan Ganz Cooney Center at Sesame Workshop. Retrieved from http://hal.archives-ouvertes.fr/hal-00696254.Google Scholar
  43. Spencer, P. (2013). iPads: Improving numeracy learning in the early years. In V. Steinle, L. Ball, & C. Bardini (Eds.), Mathematics education: Yesterday, today, and tomorrow: Proceedings of the 36th annual conference of the Mathematics Education Research Group of Australasia (pp. 610–617). Melbourne: MERGA.Google Scholar
  44. Tashakkori, A., & Teddlie, C. (2008). Introduction to mixed method and mixed model studies in the social and behavioral sciences. The Mixed Methods Reader, 7–26.Google Scholar
  45. Teddlie, C., & Tasshakori, A. (2006). A general typology of research designs featuring mixed methods. Research in the Schools, 13(1), 12–28.Google Scholar
  46. 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). Vancouver: PME.Google Scholar
  47. Tucker, S. I., Moyer-Packenham, P. S., Shumway, J. F., & Jordan, K. (2014). Zooming in on students’ thinking: How a number line app revealed, concealed, and developed students’ number understanding. Unpublished manuscript.Google Scholar

Copyright information

© Mathematics Education Research Group of Australasia, Inc. 2015

Authors and Affiliations

  • Patricia S. Moyer-Packenham
    • 1
  • Emma K. Bullock
    • 1
  • Jessica F. Shumway
    • 1
  • Stephen I. Tucker
    • 2
  • Christina M. Watts
    • 1
  • Arla Westenskow
    • 1
  • Katie L. Anderson-Pence
    • 3
  • Cathy Maahs-Fladung
    • 1
  • Jennifer Boyer-Thurgood
    • 1
  • Hilal Gulkilik
    • 4
  • Kerry Jordan
    • 1
  1. 1.The Virtual Manipulatives Research GroupUtah State UniversityLoganUSA
  2. 2.Virginia Commonwealth UniversityRichmondUSA
  3. 3.University of Colorado Colorado SpringsColorado SpringsUSA
  4. 4.Gazi UniversityTeknikokullarTurkey

Personalised recommendations