Abstract
Manipulatives—physical learning materials such as cubes or tiles—are prevalent in educational settings across cultures and have generated substantial research into how actions with physical objects may support children’s learning. The ability to integrate digital technology into physical objects—so-called ‘digital manipulatives’—has generated excitement over the potential to create new educational materials. However, without a clear understanding of how actions with physical materials lead to learning, it is difficult to evaluate or inform designs in this area. This paper is intended to contribute to the development of effective tangible technologies for children’s learning by summarising key debates about the representational advantages of manipulatives under two key headings: offloading cognition—where manipulatives may help children by freeing up valuable cognitive resources during problem solving, and conceptual metaphors—where perceptual information or actions with objects have a structural correspondence with more symbolic concepts. The review also indicates possible limitations of physical objects—most importantly that their symbolic significance is only granted by the context in which they are used. These arguments are then discussed in light of tangible designs drawing upon the authors’ current research into tangibles and young children’s understanding of number.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Notes
Blocks consisting of small unit cubes, rods made up of ten unit cubes and large cubes of 100 unit cubes in order to represent collections in base ten.
Clements makes the case that by using the root meaning of the term ‘concrete’ as ‘grow together’, virtual manipulatives actually present more potential to provide ‘concrete’ representations than physical materials. ‘Concrete’ in this paper will refer to ‘relating to real world objects or experiences’ and may therefore be used to describe either physical or virtual materials.
See Anderson [16] for a review of the field.
The authors actually use the term ‘pyfo’ to describe a physical object as part of a Tangible User interface to avoid possible interpretations suggested by the terms ‘object’ or ‘physical object’.
References
Blackwell A (2003) Cognitive dimensions of tangible programming languages. Paper presented at the Proceedings of the first joint conference of the empirical assessment in software engineering and psychology of programming interest groups
Salomon G (1990) Cognitive effects with and of computer technology. Commun Res 17(1):26–44
Cox R (1999) Representation construction, externalised cognition and individual differences. Learn Instr 9(4):343–363
Ainsworth S (2006) Deft: a conceptual framework for considering learning with multiple representations. Learn Instr 16(3):183–198
Marshall P (2007) Do tangible interfaces enhance learning? In: Proceedings of the 1st international conference on tangible and embedded interaction, Baton Rouge, Louisiana, 2007. ACM Press. doi:10.1145/1226969.1227004
O’Malley C, Stanton Fraser D (2004) Report 12: literature review in learning with tangible technologies. Futurelab series. Futurelab, Bristol
Montessori M (1912) The montessori method. Frederick Stokes Co, New York
Froebel F (1909) Pedagogics of the kindergarten. D.Appleton and Company, New York
McNeil NM, Jarvin L (2007) When theories don’t add up: disentangling the manipulatives debate. Theory Pract 46(4):309–316
Dienes Z (1964) Building up mathematics, 2nd edn. Hutchinson Educational, London
Clements DH (1999) ‘Concrete’ manipulatives, concrete ideas. Contemp Issues Early Child 1(1):45–60
Triona LM, Klahr D (2003) Point and click or grab and heft: comparing the influence of physical and virtual instructional materials on elementary school students’ ability to design experiments. Cogn Instr 21(2):149–173
Zhang JJ (1997) The nature of external representations in problem solving. Cogn Sci 21(2):179–217
Scaife M, Rogers Y (1996) External cognition: how do graphical representations work? Int J Hum-Comput Stud 45(2):185–213
Rogers Y (2004) New theoretical approaches for human-computer interaction. Annu Rev Inf Sci Technol 38:87–143
Anderson ML (2003) Embodied cognition: a field guide. Artif Intell 149(1):91–130
Mix KS (2009) Spatial tools for mathematical thought. In: Mix KS, Smith LB, Gasser M (eds) The spatial foundations of cognition and language. Oxford Scholarship Online Monographs, New York, pp 40–66
Hutchins E (2005) Material anchors for conceptual blends. J Pragmat 37(10):1555–1577
Hurtienne J (2009) Sad is heavy and happy is light. Population stereotypes of tangible object attributes. In: Third international conference on tangibles and embedded interaction, Cambridge, pp 61–68
Antle AN (2007) The cti framework: Informing the design of tangible systems for children. Paper presented at the proceedings of the 1st international conference on Tangible and embedded interaction, Baton Rouge, Louisiana
Antle AN, Droumeva M, Corness G (2008) Playing with the sound maker: do embodied metaphors help children learn? In: Proceedings of the 7th international conference on interaction design and children, ACM, pp 178–185
Larkin JH, Simon HA (1987) Why a diagram is (sometimes) worth 10000 words. Cogn Sci 11(1):65–99
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. Comput Educ 54(3):622–640
Mandler G, Shebo BJ (1982) Subitizing: an analysis of its component processes. J Exp Psychol-Gen 111(1):1–22
Riggs K, Ferrand L, Lancelin D, Fryziel L, Dumur G, Simpson A (2006) Subitizing in tactile perception. Psychol Sci 17(4):271–272
Patten J, Ishii H (2000) A comparison of spatial organization strategies in graphical and tangible user interfaces. Paper presented at the Proceedings of DARE 2000 on designing augmented reality environments, Elsinore, Denmark
Manches A, O’Malley C, Benford S (2009) Physical manipulation: evaluating the potential for tangible designs. In: Proceedings of the 3rd international conference on tangible and embedded interaction. ACM, Cambridge, UK, pp 77–84. doi:10.1145/1517664.1517688
Spelke ES (1990) Principles of object perception. Cogn Sci 14(1):29–56
Wilson M (2001) The case for sensorimotor coding in working memory. Psychon Bull Rev 8(1):44–57
Goldin-Meadow S, Nusbaum H, Kelly SD, Wagner S (2001) Explaining math: gesturing lightens the load. Psychol Sci 12(6):516–522
Roth W-M (2002) From action to discourse: the bridging function of gestures. Cogn Syst Res 3(3):535–554
Kirsh D, Maglio P (1994) On distinguishing epistemic from pragmatic action. Cogn Sci 18(4):513–549
Kaput J (1992) Technology and mathematics education. In: Grouws D (ed) Handbook of research on mathematics teaching and learning. Macmillan, New York
O’Hara KP, Payne S (1999) Planning and the user interface: The effects of lockout time and error recovery cost, vol 50. Academic Press, New York. First published. doi:10.1006/ijhc.1998.0234
Ellis S, Siegler RS (1997) Planning as strategy choice: why don’t children plan when they should? In: Friedman S, Scholnick EK (eds) The developmental psychology of planning. Lawrence Erlbaum Associates, London, pp 183–208
Martin T, Schwartz D (2005) Physically distributed learning: adapting and reinterpreting physical environments in the development of fraction concepts. Cogn Sci 29:587–625
Martin T (2007) Physically distributed learning with virtual manipulatives for elementary mathematics. In: Robinson D, Schraw G (eds) Recent innovations in educational technology that facilitate student learning. Information Age Publishing, Charlotte
Alibali MW, DiRusso AA (1999) The function of gesture in learning to count: more than keeping track. Cogn Dev 14(1):37–56
Gentner D (1983) Structure-mapping: a theoretical framework for analogy. Cogn Sci 7(2):155–170
Canobi KH, Reeve RA, Pattison PE (2002) Young children’s understanding of addition concepts. Educ Psychol 22(5):513–532
Lakoff G, Núñez R (2000) Where mathematics comes from: How the embodied mind brings mathematics into being. Basic Books, New York
Hatano G, Osawa K (1983) Digit memory of grand experts in abacus-derived mental calculation. Cognition 15(1–3):95–110
Moretto G, di Pellegrino G (2008) Grasping numbers. Exp Brain Res 188(4):505–515
Edwards L (2005) Metaphors and gestures in fraction talk. Paper presented at the 4th congress of the european society for research in mathematics education, Sant Feliu de Guixols, Spain
Goldin-Meadow S (2000) Beyond words: The importance of gesture to researchers and learners. Child Dev 71(1):231–239
Valenzeno L, Alibali MW, Klatzky R (2003) Teachers’ gestures facilitate students’ learning: a lesson in symmetry. Contemp Educ Psychol 28(2):187–204
Halford GS, Boulton-Lewis GM (1992) Value and limitations of analogs in teaching mathematics. In: Demetriou A, Efkliades A, Shayer M (eds) Modern theories of cognitive development go to school. Routledge and Kegan Paul, London
Uttal DH, Scudder KV, DeLoache JS (1997) Manipulatives as symbols: a new perspective on the use of concrete objects to teach mathematics. J Appl Dev Psychol 18(1):37–54
Meira L (1998) Making sense of instructional devices: the emergence of transparency in mathematical activity. J Res Math Educ 29(2):121–142
Fishkin KP (2004) A taxonomy for and analysis of tangible interfaces. Personal Ubiquitous Comput 8(5): 347–358. doi:10.1007/s00779-004-0297-4
Girouard A, Solovey ET, Hirshfield LM, Ecott S, Shaer O, Jacob RJK (2007) Smart blocks: a tangible mathematical manipulative. Paper presented at the Proceedings of the 1st international conference on tangible and embedded interaction, Baton Rouge, Louisiana
Wyeth P, Wyeth G (2001) Electronic blocks: tangible programming elements for preschoolers. In: Hirose M (ed) Proceedings of the Eighth IFIP TC13 conference on human-computer interaction. IOS Press, Amsterdam, pp 496–503
Lackner TM, Dobson K, Rodenstein R, Weisman L (1999) Sensory puzzles. Paper presented at the CHI ‘99 extended abstracts on Human factors in computing systems, Pittsburgh, Pennsylvania
Jones MG, Minogue J, Tretter TR, Negishi A, Taylor R (2006) Haptic augmentation of science instruction: does touch matter? Sci Educ 90(1):111–123
Resnick M (1998) Technologies for lifelong kindergarten. Educ Tech Res Dev 46(4):43–55
NLVM (2007) National library of virtual manipulatives. http://nlvm.usu.edu/
Raffle HS, Parkes AJ, Ishii H (2004) Topobo: A constructive assembly system with kinetic memory. Paper presented at the Proceedings of the SIGCHI conference on Human factors in computing systems, Vienna, Austria
Shaer O, Leland N, Calvillo-Gamez EH, Jacob RJK (2004) The tac paradigm: Specifying tangible user interfaces, vol 8. Springer-Verlag, Berlin. First published. doi:10.1007/s00779-004-0298-3
Price.S, Pontual T, Sheridan J, Roussos G (2009) The effect of representation location on interaction in a tangible learning environment. Paper presented at the Proceedings of the 3rd International Conference on Tangible and Embedded Interaction, Cambridge, United Kingdom
Wilkie K, Holland S, Mulholland P (2009) Evaluating musical software using conceptual metaphors. Br Comput Soc, pp 232–237
Khandelwal M, Mazalek A (2007) Teaching table: a tangible mentor for pre-k math education. In: Proceedings of the 1st international conference on tangible and embedded interaction (TEI ‘07). ACM Press, New York, pp 191–194. doi:10.1145/1226969.1227009
Scarlatos T, Scarlatos L (2009) Tangible maths application. http://xsrv.mm.cs.sunysb.edu/TS/research/Math.pdf. Accessed 12 Sept 2009
Acknowledgments
This research was supported by an Economic Social Research Council Case PhD studentship awarded to Professors Claire O’Malley and Steve Benford, and co-sponsored by Futurelab (Grant no. PTA-033-2006-00025). We would also like to thank the schools and children who have taken part and contributed greatly to our work.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Manches, A., O’Malley, C. Tangibles for learning: a representational analysis of physical manipulation. Pers Ubiquit Comput 16, 405–419 (2012). https://doi.org/10.1007/s00779-011-0406-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00779-011-0406-0