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Using the ACAT Framework to Evaluate the Design of Two Geometry Apps: an Exploratory Study

  • Kevin Larkin
  • Ulrich Kortenkamp
  • Silke Ladel
  • Heiko Etzold
Article

Abstract

It is an increasingly common phenomenon that elementary school students are using mobile applications (apps) in their mathematics classrooms. Classroom teachers, who are using apps, require a tool, or a set of tools, to help them determine whether or not apps are appropriate and how enhanced educational outcomes can be achieved via their use. In this article we investigate whether Artifact Centric Activity Theory (ACAT) can be used to create a useful tool for evaluating apps, present a review guide based on the theory and test it using a randomly selected geometry app [Pattern Shapes] built upon different (if any at all) design principles. In doing so we broaden the scope of ACAT by investigating a geometry app that has additional requirements in terms of accuracy of external representations, and depictions of mathematical properties (e.g. reflections and rotations), than is the case for place value concepts in [Place Value Chart] which was created using ACAT principles and has been the primary app evaluated using ACAT. We further expand the use of ACAT via an independent assessment of a second app [Click the Cube] by a novice, using the ACAT review guide. Based on our latest research, we argue that ACAT is highly useful for evaluating any mathematics app and this is a critical contribution if the evaluation of apps is to move beyond academic circles and start to impact student learning and teacher pedagogy in mathematics.

Keywords

Mathematics education Mathematics apps Activity theory Artifact-centric activity theory Geometry App design App reviews 

References

  1. ACARA (2012). Australian curriculum: Mathematics structure. Sydney, Australia: Australian Curriculum, Assessment and Reporting Agency. (https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics/structure/). Accessed 27 Sept 2018.
  2. Alqahtani, M., & Powell, A. (2017). Teachers’ instrumental genesis and their geometrical understanding in a dynamic geometry environment. Digital Experiences in Mathematics Education, 3(1), 9–38.CrossRefGoogle Scholar
  3. Baccaglini-Frank, A., & Maracci, M. (2015). Multi-touch technology and pre-schoolers’ development of number sense. Digital Experiences in Mathematics Education, 1(1), 7–27.CrossRefGoogle Scholar
  4. Carbonneau, K., Marley, S., & Selig, J. (2013). A meta-analysis of the efficacy of teaching mathematics with concrete manipulatives. Journal of Educational Psychology, 105(2), 380–400.CrossRefGoogle Scholar
  5. Clements, D. (2000). Concrete’ manipulatives, concrete ideas. Contemporary Issues in Early Childhood, 1(1), 45–60.CrossRefGoogle Scholar
  6. Clements, D., & Battista, M. (1992). Geometry and spatial reasoning. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 420–464). New York: Macmillan.Google Scholar
  7. Dick, T. (2008). Fidelity in technological tools for mathematics education. In G. Blume & K. Heid (Eds.), Research on technology and the teaching and learning of mathematics: Volume 2. Syntheses, cases and perspectives (pp. 333–339). Charlotte: Information Age Publishing.Google Scholar
  8. Engeström, Y. (1987/2014). Learning by expanding: An activity-theoretical approach to developmental research (2nd ed.). New York: Cambridge University Press.Google Scholar
  9. Engeström, Y. (1999). Activity theory and individual and social transformation. In Y. Engeström, R. Miettinen, & R.-L. Punamäki (Eds.), Perspectives on activity theory (pp. 19–38). Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  10. Engeström, Y., Miettinen, R., & Punamäki, R.-L. (Eds.). (1999). Perspectives on activity theory. Cambridge: Cambridge University Press.Google Scholar
  11. Etzold, H., Kortenkamp, U., & Ladel, S. (2018). ACAT-Review-Guide: Ein tätigkeitstheoretischer Blick auf die Beurteilung von Mathematik-Apps. In S. Ladel, U. Kortenkamp, & H. Etzold (Eds.), Mathematik mit digitalen Medien – konkret: Ein Handbuch für Lehrpersonen der Primarstufe (pp. 91–98). Münster: WTM-Verlag.Google Scholar
  12. Giest, H., & Lompscher, J. (2004). Tätigkeitstheoretische Überlegungen zu einer neuen Lernkultur. Sitzungsberichte der Leibniz-Sozietät, 72, 101–125.Google Scholar
  13. Highfield, K., & Goodwin, K. (2013). Apps for mathematics learning: A review of ‘educational’ apps from the iTunes app store. In V. Steinle, L. Ball, & C. Bardini (Eds.), Proceedings of the 36 th annual conference of the Mathematics Education Research Group of Australasia (pp. 378–385). Adelaide: MERGA.Google Scholar
  14. Holgersson, I., Barendregt, W., Emanuelsson, J., Ottosson, T., Rietz, E., & Lindström, B. (2016). Fingu – A game to support children’s development of arithmetic competence: Theory, design and empirical research. In P. Moyer-Packenham (Ed.), International perspectives on teaching and learning mathematics with virtual manipulatives (pp. 123–145). Cham: Springer.Google Scholar
  15. Jorgensen, R., & Larkin, K. (2017). Analysing the relationships between students and mathematics: A tale of two paradigms. Mathematics Education Research Journal, 29(1), 113–130.CrossRefGoogle Scholar
  16. Kaptelinin, V. (1996). Activity theory: Implications for human–computer interaction. In B. Nardi (Ed.), Context and consciousness: Activity theory and human–computer interaction (3rd ed., pp. 103–116). Cambridge: MIT Press.Google Scholar
  17. Kaptelinin, V., & Nardi, B. (2006). Acting with technology: Activity theory and interaction design. Cambridge: MIT Press.Google Scholar
  18. KMK (2013). The Education System in the Federal Republic of Germany. Berlin: Kultusministerkonferenz. (http://kmk.org/fileadmin/doc/Dokumentation/Bildungswesen_en_pdfs/primary.pdf). Accessed 27 Sept 2018.
  19. Ladel, S. (2009). Multiple externe Repräsentationen (MERs) und deren Verknüpfung durch Computereinsatz: Zur Bedeutung für das Mathematiklernen im Anfangsunterricht. Hamburg: Verlag Dr. Kovač.Google Scholar
  20. Ladel, S. (2018). Kombinierter Einsatz virtueller und physischer Materialien: Zur handlungsorientierten Unterstützung des Erwerbs mathematischer Kompetenzen. In B. Brandt & H. Dausend (Eds.), Digitales Lernen in der Grundschule: Fachliche Lernprozesse anregen (pp. 53–72). Münster: Waxmann.Google Scholar
  21. Ladel, S. & Kortenkamp, U. (2011). An activity-theoretic approach to multi-touch tools in early Maths learning. Paper presented at the Activity-Theoretic Approaches to Technology-Enhanced Mathematics Learning Orchestration Symposium (ATATEMLO), Paris, France.Google Scholar
  22. Ladel, S., & Kortenkamp, U. (2013a). An activity-theoretic approach to multi-touch tools in early mathematics learning. International Journal for Technology in Mathematics Education, 20(1), 3–8.Google Scholar
  23. Ladel, S., & Kortenkamp, U. (2013b). Designing a technology-based learning environment for place value using artifact-centric activity theory. In A. Lindmeier & A. Heinze (Eds.), Proceedings of the 37th conference of the International Group for the Psychology of mathematics education. Mathematics (Vol. 1, pp. 188–192). Kiel: PME.Google Scholar
  24. Ladel, S., & Kortenkamp, U. (2014). Number concepts: Processes of internalization and externalization by the use of multi-touch technology. In U. Kortenkamp, B. Brandt, C. Benz, G. Krummheuer, S. Ladel, & R. Vogel (Eds.), Early mathematics learning: Selected papers of the POEM 2012 conference (pp. 237–253). New York: Springer-Verlag.CrossRefGoogle Scholar
  25. Ladel, S., & Kortenkamp, U. (2016). Artifact-centric activity theory: A framework for the analysis of the design and use of virtual manipulatives. In P. Moyer-Packenham (Ed.), International perspectives on teaching and learning mathematics with virtual manipulatives (pp. 25–40). Cham: Springer.Google Scholar
  26. Larkin, K. (2013). Mathematics education: Is there an app for that? In V. Steinle, L. Ball, & C. Bardini (Eds.), Proceedings of the 36th annual conference of the Mathematics Education Research Group of Australasia (pp. 426–433). Adelaide: MERGA.Google Scholar
  27. Larkin, K. (2015). “An app! An app! My kingdom for an app”: An 18-month quest to determine whether apps support mathematical knowledge building. In T. Lowrie & R. Jorgensen (Eds.), Digital games and mathematics learning: Potential, promises and pitfalls (pp. 251–276). Dordrecht: Springer.CrossRefGoogle Scholar
  28. Larkin, K. (2016). Geometry and iPads in primary schools: Does their usefulness extend beyond tracing an oblong? In P. Moyer-Packenham (Ed.), International perspectives on teaching and learning mathematics with virtual manipulatives (pp. 247–274). Cham: Springer.Google Scholar
  29. Larkin, K., & Finger, G. (2011). Netbook computers as an appropriate solution for one-to-one computer use in primary schools. Australian Educational Computing, 26(1), 27–34.Google Scholar
  30. Larkin, K., & Milford, T. (2018a). Using cluster analysis to enhance student learning when using geometry mathematics apps. In L. Ball, P. Drijvers, S. Ladel, H.-S. Siller, M. Tabach, & C. Vale (Eds.), Uses of technology in primary and secondary mathematics education: Tools, topics and trends (pp. 101–118). Cham: Springer.CrossRefGoogle Scholar
  31. Larkin, K., & Milford, T. (2018b). Mathematics apps – Stormy with the weather clearing: Using cluster analysis to enhance app use in mathematics classrooms. In N. Calder, K. Larkin, & N. Sinclair (Eds.), Using mobile technologies in the teaching and learning of mathematics (pp. 11–30). Cham: Springer.CrossRefGoogle Scholar
  32. Leontiev, A. (1972/1981). The problem of activity in psychology. In J. Wertsch (Ed.), The concept of activity in soviet psychology (pp. 37–71). New York: M.E. Sharpe.Google Scholar
  33. Lommatsch, C., Tucker, S., Moyer-Packenham, P., & Symanzik, J. (2018). Heatmap and hierarchical clustering analysis to highlight changes in young children’s developmental progressions using virtual manipulative mathematics apps. In N. Calder, K. Larkin, & N. Sinclair (Eds.), Using mobile technologies in the teaching and learning of mathematics (pp. 167–187). Cham: Springer.CrossRefGoogle Scholar
  34. Lowrie, T., Logan, T., & Ramful, A. (2017). Visuospatial training improves elementary students’ mathematics performance. British Journal of Educational Psychology, 87(2), 170–186.CrossRefGoogle Scholar
  35. Moyer, P., Bolyard, J., & Spikell, J. (2002). What are virtual manipulatives? Teaching Children Mathematics, 8(6), 372–377.Google Scholar
  36. Moyer-Packenham, P., & Bolyard, J. (2016). Revisiting the definition of a virtual manipulative. In P. Moyer-Packenham (Ed.), International perspectives on teaching and learning mathematics with virtual manipulatives (pp. 3–23). Cham: Springer.Google Scholar
  37. Moyer-Packenham, P., Bullock, E., Shumway, J., Tucker, S., Watts, C., Westenskow, A., Anderson-Pence, K., Maahs-Fladung, C., Boyer-Thurgood, J., Gulkilik, H., & Jordan, K. (2016). The role of affordances in children’s learning performance and efficiency when using virtual manipulative mathematics touch-screen apps. Mathematics Education Research Journal, 28(1), 79–105.CrossRefGoogle Scholar
  38. Moyer-Packenham, P., Salkind, G., & Bolyard, J. (2008). Virtual manipulatives used by K–8 teachers for mathematics instruction: Considering mathematical, cognitive, and pedagogical fidelity. Contemporary Issues in Technology and Teacher Education, 8(3), 202–218.Google Scholar
  39. Namukasa, I., Gadanidis, G., Sarina, V., Scucuglia, S., & Aryee, K. (2016). Selection of apps for teaching difficult mathematics topics: An instrument to evaluate touch-screen tablet and smartphone mathematics apps. In P. Moyer-Packenham (Ed.), International perspectives on teaching and learning mathematics with virtual manipulatives (pp. 275–300). Cham: Springer.Google Scholar
  40. Nardi, B. (1996). Activity theory and human–computer interaction. In B. Nardi (Ed.), Context and consciousness: Activity theory and human–computer interaction (3rd ed., pp. 7–16). Cambridge: MIT Press.Google Scholar
  41. NCTM (2018). Principles and standards/geometry. (http://www.nctm.org/Standards-and-Positions/Principles-and-Standards/Geometry/). Accessed 27 Sept 2018.
  42. Özel, S. (2012). Learning rational numbers: An experimental multi-model representation approach via technology. Mediterranean Journal for Research in Mathematics Education, 11(1–2), 59–79.Google Scholar
  43. Papadakis, S., Kalogiannakis, M., & Zaranis, N. (2018). Educational apps from the android Google play for Greek preschoolers: A systematic review. Computers & Education, 116, 139–160.CrossRefGoogle Scholar
  44. Papic, M., Mulligan, J., & Mitchelmore, M. (2011). Assessing the development of preschoolers’ mathematical patterning. Journal for Research in Mathematics Education, 42(3), 237–269.CrossRefGoogle Scholar
  45. Pimm, D. (1995). Symbols and meanings in school mathematics. London: Routledge.Google Scholar
  46. PG (2018). App store metrics. (http://www.pocketgamer.biz/metrics/app-store/). Accessed 27 Sept 2018.
  47. Powell, S. (2014). Choosing iPad apps with a purpose: Aligning skills and standards. Teaching Exceptional Children, 47(1), 20–26.CrossRefGoogle Scholar
  48. Scanlon, E., & Issroff, K. (2005). Activity theory and higher education: Evaluating learning technologies. Journal of Computer Assisted Learning, 21(6), 430–439.CrossRefGoogle Scholar
  49. Sinclair, N., & Bruce, C. (2015). New opportunities in geometry education at the primary school. ZDM: The International Journal on Mathematics Education, 47(3), 319–329.CrossRefGoogle Scholar
  50. Sinclair, N., & Pimm, D. (2015). Mathematics using multiple senses: Developing finger gnosis with three- and four-year-olds in an era of multi-touch technologies. Asia-Pacific Journal of Research in Early Childhood Education, 9(3), 99–109.CrossRefGoogle Scholar
  51. Sinclair, N., Chorney, S., & Rodney, S. (2016). Rhythm in number: Exploring the affective, social and mathematical dimensions of using TouchCounts. Mathematics Education Research Journal, 28(1), 31–51.CrossRefGoogle Scholar
  52. Soury-Lavergne, S. (2016). Duos of artefacts, connecting technology and manipulatives to enhance mathematical learning. (https://hal.archives-ouvertes.fr/hal-01492990/document). Accessed 27 Sept 2018.
  53. Tucker, S. (2016). The modification of attributes, affordances, abilities, and distance for learning framework and its applications to interactions with mathematics virtual manipulatives. In P. Moyer-Packenham (Ed.), International perspectives on teaching and learning mathematics with virtual manipulatives (pp. 41–69). Cham: Springer.Google Scholar
  54. Tucker, S., & Johnson, T. (2017). I thought this was a study on math games: Attribute modification in children’s interactions with mathematics apps. Education Sciences, 7(2), 50 (20 pp).CrossRefGoogle Scholar
  55. Uttal, D. (2003). On the relation between play and symbolic thought: The case of mathematics manipulatives. In O. Saracho & B. Spodek (Eds.), Contemporary perspectives on play in early childhood education (pp. 97–114). Charlotte: Information Age Publishing.Google Scholar
  56. Uttal, D., & Cohen, C. (2012). Spatial thinking and STEM education: When, why, and how? In B. Ross (Ed.), The psychology of learning and motivation (pp. 148–181). San Diego: Elsevier.Google Scholar
  57. van Hiele, P. (1999). Developing geometric thinking through activities that begin with play. Teaching Children Mathematics, 5(6), 310–316.Google Scholar
  58. Vygotsky, L. (1980). Mind in society: The development of higher psychological processes. Cambridge: Harvard University Press.Google Scholar
  59. Zbiek, R., Heid, K., Blume, G., & Dick, T. (2007). Research on technology in mathematics education: A perspective of constructs. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 1169–1207). Reston: National Council of Teachers of Mathematics.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.School of Education and Professional StudiesGriffith UniversityGold CoastAustralia
  2. 2.Institute of MathematicsPotsdam UniversityPotsdamGermany
  3. 3.University of Education Schwäbisch GmündSchwäbisch GmündGermany

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