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Uses of Technology in Primary and Secondary Mathematics Education pp 101–118Cite as

Using Cluster Analysis to Enhance Student Learning When Using Geometry Mathematics Apps

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Part of the book series: ICME-13 Monographs ((ICME13Mo))

Abstract

Mathematical applications (apps) are becoming commonplace in educational settings. Despite their increasing use, limited quantitative research has been undertaken that might support teachers in making appropriate pedagogical decisions regarding their use, nor how teachers might go about selecting appropriate apps from the multitudes available at iTunes or Google Play. This chapter explores how cluster analysis can be used to identify homogeneity among elements within apps, thus assisting teachers to make decisions regarding which apps might be most appropriate. Based upon selection criteria and rankings generated via a number of scales, the cluster structure of 53 apps to support geometry learning in elementary mathematics classrooms is reported. The chapter concludes by exploring the homogeneity and heterogeneity of these clusters of apps and suggests how to use these apps to enhance student mathematical learning.

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References

  • Antonenko, P. D., Toy, S., & Niederhauser, D. S. (2012). Using cluster analysis for data mining in educational technology research. Educational Technology Research and Development, 60(3), 383–398.

    Article  Google Scholar 

  • Australian Curriculum and Reporting Authority (ACARA). (2009). Shape of the Australian Curriculum Mathematics. Retrieved from http://www.acara.edu.au/_resources/Australian_Curriculum_-_Maths.pdf.

  • Australian Curriculum Assessment and Reporting Agency (ACARA). (2015). Australian Curriculum: Mathematics. Retrieved from https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics/.

  • Battisa, M., & Clements, D. (2013). Investigations in number, data and space. Retrieved from http://investigations.terc.edu/library/bookpapers/geometryand_proof.cfm.

  • Bos, B. (2009). Technology with cognitive and mathematical fidelity: What it means for the Math classroom. Computers in the Schools, 26(2), 107–114.

    Article  Google Scholar 

  • Calder, N. (2015). Apps: Appropriate, applicable, and appealing? In T. Lowrie & R. Jorgensen (Zevenbergen) (Eds.), Digital games and mathematics learning. Potential, promises and pitfalls (Vol. 4, pp. 233–250). Springer Science+Business Media.

    Google Scholar 

  • Carbonneau, K. J., Marley, S. C., & Selig, J. (2013). A meta-analysis of the efficacy of teaching mathematics with concrete manipulatives. Journal of Educational Psychology, 105(2), 380–400.

    Article  Google Scholar 

  • Clements, D. H., & Battista, M. T. (1992). Geometry and spatial reasoning. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 420–464). New York: Macmillan.

    Google Scholar 

  • Clements, D. H., & Sarama, J. (2011). Early childhood teacher education: The case of geometry. Journal of Mathematics Teacher Education, 14, 133–148.

    Article  Google Scholar 

  • Crowley, M. (1987). The van Hiele model of the development of geometric thought. In M. M. Lindquist (Ed.), Learning and teaching geometry, K–12, 1987 Yearbook of the National Council of Teachers of Mathematics (pp. 1–16). Reston, Va: National Council of Teachers of Mathematics.

    Google Scholar 

  • Di Paola, B., Battaglia, O. R., & Fazio, C. (2016). Non-hierarchical clustering as a methods to analyse an open-ended questionnaire on algebraic thinking. South African Journal of Education, 36(1), 1–14. https://doi.org/10.15700/saje.v36n1a1142.

    Article  Google Scholar 

  • Dick, T. P. (2008). Fidelity in technological tools for Mathematics education. In G. W. Blume & M. K. Reid (Eds.), Research on technology and the teaching and learning of Mathematics (Vol. 2, pp. 333–339). Cases and perspectives Charlotte, N.C.: Information Age Publishing.

    Google Scholar 

  • Hair, J. F., Black, W. C., Babin, B. J., Anderson, R. E., & Tatham, R. L. (2006). Multivariate data analysis (6th ed.). Upper Saddle River, NJ: Pearson.

    Google Scholar 

  • Haugland, S. (1999). Computers and young children: The newest software that meets the developmental needs of young children. Early Childhood Education Journal, 26(4), 245–254.

    Article  Google Scholar 

  • Jones, K. (1998). Theoretical frameworks for the learning of geometrical reasoning. Proceedings of the British Society for Research into Learning Mathematics. Geometry Working Group, 18(1 and 2), 29–34.

    Google Scholar 

  • Jones, K., & Mooney, C. (2003). Making space for geometry in primary mathematics. In L. Thompson (Ed.), Enhancing primary mathematics teaching (pp. 3–15). London: Open University Press.

    Google Scholar 

  • 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 (Vol. 1, pp. 188–192). Kiel, Germany: PME.

    Google Scholar 

  • 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. Springer Press.

    Google Scholar 

  • Larkin, K. (2013). Mathematics education. Is there an App for that? In Proceedings of the 36th Annual Conference of the Mathematics Education Research Group of Australasia, Melbourne, July 7–11, 2013. Paper presented at the Mathematics Education: Yesterday, Today and Tomorrow.

    Google Scholar 

  • Larkin, K. (2015a). 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 (Vol. 4, pp. 251–276). Netherlands: Springer.

    Google Scholar 

  • Larkin, K. (2015b). The search for fidelity in geometry apps: An exercise in futility? In Proceedings of the 38th Annual Conference of the Mathematics Education Research Group of Australasia, Sunshine Coast, June 30–July 2, 2015. Paper presented at the Mathematics Education in the Margins.

    Google Scholar 

  • Larkin, K. (2016). Geometry and iPads in primary schools: Does their usefulness extend beyond tracing an Oblong? In P. S. Moyer-Packenham (Ed.), International perspectives on teaching and learning mathematics with virtual manipulatives, mathematics education in the digital era, 7. Netherlands: Springer.

    Google Scholar 

  • Manches, A., & O’Malley, C. (2012). Tangibles for learning: A representational analysis of physical manipulation. Personal and Ubiquitous Computing, 16(4), 405–419.

    Article  Google Scholar 

  • Moss, J., Hawes, Z., Naqvi, S., & Caswell, B. (2015). Adapting Japanese lesson study to enhance the teaching and learning of geometry and spatial reasoning in early years classrooms: A case study. ZDM Mathematics Education, 47, 377–390.

    Article  Google Scholar 

  • Moyer-Packenham, P., & Bolyard, J. (2016). Revisiting the definition of a virtual manipulative. In P. S. Moyer-Packenham (Ed.), International perspectives on teaching and learning mathematics with virtual manipulatives, mathematics education in the digital era.

    Google Scholar 

  • Moyer-Packenham, P. S., Shumway, J. F., Bullock, E., Tucker, S. I., Anderson-Pence, K. L., Westenskow, A., … 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 

  • National Governors Association (NGA) Center for Best Practices and Council of Chief State School Officers. (2016). Common core state standards. Retrieved from http://www.corestandards.org/Math/.

  • Pegg, J. (1985). How children learn geometry: The van Hiele theory. Australian Mathematics Teacher, 41(2), 5–8.

    Google Scholar 

  • Sarama, J., & Clements, D. H. (2009). Early childhood mathematics education research: Learning trajectories for young children. New York: Rutledge.

    Google Scholar 

  • Shavelson, R. J. (1979). Applications of cluster analysis in educational research: Looking for a needle in a haystack. British Educational Research Journal, 5(1), 45–53.

    Article  Google Scholar 

  • Sinclair, N., & Bruce, C. D. (2015). New opportunities in geometry education at the primary school. ZDM Mathematics Education, 47, 319–329.

    Article  Google Scholar 

  • Tavakol, M., & Dennick, R. (2011). Making sense of Cronbach’s alpha. International Journal of Medical Education, 2, 53–55.

    Article  Google Scholar 

  • Teppo, A. (1991). van Hiele levels of geometric thought revisited. The Mathematics Teacher, 84(3), 210–221.

    Google Scholar 

  • Zbiek, R. M., Heid, M. K., Blume, G. W., & Dick, T. P. (2007). Research on technology in mathematics education: A perspective of constructs. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 1169–1207). Charlotte, N.C.: National Council of Teachers of Mathematics.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Griffith University, Southport, Australia

    Kevin Larkin

  2. University of Victoria, Victoria, Canada

    Todd Milford

Authors
  1. Kevin Larkin
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  2. Todd Milford
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Correspondence to Kevin Larkin .

Editor information

Editors and Affiliations

  1. Melbourne Graduate School of Education, The University of Melbourne, Melbourne, Victoria, Australia

    Lynda Ball

  2. Freudenthal Institute, Utrecht University, Utrecht, The Netherlands

    Paul Drijvers

  3. University of Saarland, Saarbrücken, Germany

    Silke Ladel

  4. Institute of Mathematics, University of Würzburg, Würzburg, Germany

    Hans-Stefan Siller

  5. School of Education, Tel Aviv University, Tel Aviv, Israel

    Michal Tabach

  6. Faculty of Education, Monash University, Melbourne, Victoria, Australia

    Colleen Vale

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Larkin, K., Milford, T. (2018). Using Cluster Analysis to Enhance Student Learning When Using Geometry Mathematics Apps. In: Ball, L., Drijvers, P., Ladel, S., Siller, HS., Tabach, M., Vale, C. (eds) Uses of Technology in Primary and Secondary Mathematics Education. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-76575-4_6

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  • DOI: https://doi.org/10.1007/978-3-319-76575-4_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-76574-7

  • Online ISBN: 978-3-319-76575-4

  • eBook Packages: EducationEducation (R0)

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