<<PART III: Virtual Manipulatives: their potential in developing mathematical conceptual understanding
Three key recommendations are as follows:
1. The formation of a school-based research group to build a bank of resources.
Led by a curriculum coordinator, this group should explore the range of virtual manipulatives currently available and build a levelled library of tools they consider most useful for their cohort. Bookmarking these sites or preloading apps onto devices will encourage use. Physical manipulatives should remain an integral part of this library as they remain useful, both in themselves and as a point of comparison
2. The provision of timely and well-structured staff professional development
Teachers are the gatekeepers and providers of educational materials for their students. Helping teachers become aware of what and how manipulatives are best implemented is often a slow process; one that often involves the re-examination of long-held beliefs which can be challenging for all involved. It is however, one that can ultimately result in greater conceptual understanding and learning outcomes for students. Training student leaders can also be helpful and benefit teachers and students alike.
3. A commitment to mathematical dialogue in the classroom
Talking about mathematics is key to understanding it. Digital technologies can sometimes be side-lined or used as a babysitter and when using virtual manipulatives students may not be involved in the discussions they need to build connections and expose misconceptions. Shared learning experiences where ideas are shared, challenged and reflected on, are vital.
After analysing the available literature, it appears that virtual manipulatives may well have potential to develop mathematical conceptual understandings but it is relatively early days for these tools, and further research is needed before any firm affordances can be established.
However, in light of the ever-increasing role digital technologies are playing in education and the associated curricular expectations, schools need to make informed decisions now. It therefore make sense to revisit the use of physical manipulatives and envision how virtual manipulatives may aid the development of conceptual development.
Australian Curriculum, Assessment and Reporting Authority. (2013). General capabilities in the Australian curriculum. Retrieved from http://www.australiancurriculum.edu.au/GeneralCapabilities/Overview/General-capabilities-in-the-Australian-Curriculum
Bodemer, D., Ploetzner, R., Feuerlein, I., & Spada, H. (2004). The active integration of information during learning with dynamic and interactive visualisations. Learning and Instruction, 14(3), 325-341.
Brown, M. C., McNeil, N. M. and Glenberg, A. M. (2009). Using Concreteness in
Education: Real Problems, Potential Solutions. Child Development Perspectives, 3, 160–164.
Clements, D. (1999) ‘Concrete’ Manipulatives, Concrete Ideas. Contemporary Issues in Early Childhood, 1, 45-60.
Dienes, Z. P. (1971). Building up mathematics. London: Hutchinson Educational.
Hiebert, J. (Ed.). (2013). Conceptual and procedural knowledge: The case of mathematics. Routledge.
Hunt, A. W., Nipper, K. L., & Nash, L. E. (2011). Virtual vs. concrete manipulatives in mathematics teacher education: Is one type more effective than the other. Current Issues in Middle Level Education, 16(2), 1-6.
Jarvin, L. & McNeil,N. (2007). When Theories Don’t Add Up: Disentangling the Manipulatives Debate. Theory Into Practice,46,4.
Manches, A., O’Malley, C., & Benford, S. (2010). The Role of Physical Representations in Solving Number Problems: A Comparison of Young Children’s Use of Physical and Virtual Materials. Computers & Education, 54(3), 622-640.
Mildenhall, P., Swan, P., Northcote, M. & Marshall, L. (2008). Virtual Manipulatives on the Interactive Whiteboard: A Preliminary Investigation. Australian Primary Mathematics Classroom, 13(1), 9-14.
Moyer, P. S., Bolyard, J. J., & Spikell, M. A. (2002). What are virtual manipulatives?. Teaching children mathematics, 8(6), 372-377
Moyer-Packenham, P.S., Salkind, G., & Bolyard, J.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.
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 (IJVPLE), 4(3), 35-50.
Mix, K. S. (2009). Spatial tools for mathematical thought. The spatial foundations of cognition and language. Oxford Scholarship Online Monographs, New York, 40-66.
McNeil, N. M., & Uttal, D. H. (2009). Rethinking the use of concrete materials in learning: Perspectives from development and education. Child development perspectives, 3(3), 137-139.
Petit, M. (2013) Comparing Concrete to Virtual Manipulatives in Mathematics Education. Retrieved from http://sciencelib.fr/IMG/pdf/Manipulatives_MPetit_ScienceLib_17juillet13
Resnick, M., & Rosenbaum, E. (2013). Designing for Tinkerability. In Honey, M., & Kanter, D. (eds.), Design, Make, Play: Growing the Next Generation of STEM Innovators, pp. 163-181. Routledge.
Sarama, J. and Clements, D. H. (2009), “Concrete” Computer Manipulatives in Mathematics Education. Child Development Perspectives, 3145–150.
Uttal, D. H., O’Doherty, K., Newland, R., Hand, L. L. and DeLoache, J. (2009), Dual Representation and the Linking of Concrete and Symbolic Representations. Child Development Perspectives, 3: 156–159.