Abstract
Thousands of educational applications are available for the latest touch screen devices. Unfortunately, quantity does not guarantee quality: most applications are limited in focus and do not promote conceptual knowledge. This chapter explores how cognitive psychology can inform the design and evaluation of software for early mathematics education so as to promote conceptual understanding, problem solving, and the excitement of learning. We propose six cognitive design principles that can exploit the new technological affordances available on the latest devices, particularly touch screen tablets. For each design principle, we outline important issues that software developers need to consider, and then we discuss examples of how cognitive principles can inform design. We also discuss two added benefits of mathematics software running on the new technology: the software can provide innovative approaches to the evaluation of learning and to basic cognitive research. We argue that when cognitive psychology shapes the development of software the results can be improved achievement, teaching, and testing. And a non-trivial added benefit can be that children will enjoy learning meaningful mathematics.
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References
Alibali, M. W. (1999). How children change their minds: strategy change can be gradual or abrupt. Developmental Psychology, 35, 127–145.
Barlow, A., & Harmon, Sh. E. (2012). Problem contexts for thinking about equality: an additional resource. Childhood Education, 88(2), 96–101.
Baroody, A. J. (2004). The developmental bases for early childhood number and operations standards. In D. H. Clements, J. Sarama, & A.-M. DiBiase (Eds.), Engaging young children in mathematics: standards for early childhood mathematics education (pp. 173–219). Mahwah: Erlbaum.
Booth, J. L., & Siegler, R. S. (2006). Developmental and individual differences in pure numerical estimation. Developmental Psychology, 41(6), 189–201.
Brown, J. S., & Burton, R. R. (1978). Diagnostic models for procedural bugs in basic mathematical skills. Cognitive Science, 2, 155–192.
Brown, J. S., & VanLehn, K. (1982). Towards a generative theory of “bugs”. In T. P. Carpenter, J. M. Moser, & T. A. Romberg (Eds.), Addition and subtraction: a cognitive perspective (pp. 117–135). Hillsdale: Erlbaum.
Brian, M. (2012). Apple: 1.5 million iPads are used in educational programs, with over 20,000 education apps [Web log post]. Retrieved January 19, 2012, from http://thenextweb.com/apple/2012/01/19/apple-1-5-million-ipads-in-use-in-educational-programs-offering-over-20000-education-apps/.
Bull, R., & Scerif, G. (2001). Executive functioning as a predictor of children’s mathematics ability: inhibition, switching, and working memory. Developmental Neuropsychology, 19(3), 273–293.
Butterworth, B. (1999). The mathematical brain. London: Macmillan.
Butterworth, B., & Laurillard, D. (2010). Low numeracy and dyscalculia: identification and intervention. ZDM Mathematics Education, 42, 527–539.
Carpenter, T. P., & Moser, J. M. (1984). The acquisition of addition and subtraction concepts in grades one through three. Journal for Research in Mathematics Education, 15, 179–202.
Chard, D. J., Baker, S. K., Clarke, B., Jung, J. K., Davis, K., & Smolkowski, K. (2008). Preventing early mathematics difficulties: the feasibility of a rigorous kindergarten mathematics curriculum. Learning Disability Quarterly, 31, 11–20.
Chen, Z., & Klahr, D. (1999). All other things being equal: children’s acquisition of the control of variables strategy. Child Development, 70, 1098–1120.
Clearleft Limited (2010). Silverback (version 2.0) [computer application software]. Available from. http://silverbackapp.com/.
Clements, D. H., & Sarama, J. (2007). Early childhood mathematics learning. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 461–555). New York: Information Age.
Clements, D. H., & Sarama, J. (2008). Experimental evaluation of the effects of a research based preschool mathematics curriculum. American Educational Research Journal, 45, 443–494.
Common Core State Standards Initiative (2010). Common Core State Standards for mathematics. Retrieved from http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf.
Cook, S. W., Yip, T., & Goldin-Meadow, S. (2012). Gestures, but not meaningless movements, lighten working memory load when explaining math. Language and Cognitive Processes, 27(4), 594–610.
Cordes, S., & Gelman, R. (2005). The young numerical mind: when does it count? In J. Campbell (Ed.), Handbook of mathematical cognition (pp. 127–142). London: Psychology Press.
Cross, C. T., Woods, T. A., & Schweingruber, H. (Eds.) (2009). Mathematics learning in early childhood: paths toward excellence and equity. Washington: National Academy Press.
Cunha, F., Heckman, J., Lochner, L., & Masterov, D. (2006). Interpreting the evidence on life cycle skill formation. In E. Hanushek & F. Welch (Eds.), Handbook of the economics of education (pp. 307–451). North Holland: Elsevier.
Dewey, J. (1976). The child and the curriculum. In J. A. Boydston (Ed.), John Dewey: the middle works, 1899–1924. Vol. 2: 1902–1903 (pp. 273–291). Carbondale: Southern Illinois University Press.
Diamond, A. (2008). Cognitive control (executive functions) in young children: relevance of what we know to what can be done to help children. In Emotion regulation, children’s brains and learning, plenary session presented at head start’s ninth national research conference, Washington.
Dick, A., Goldin-Meadow, S., Solodkin, A., & Small, S. (2012). Gesture in the developing brain. Developmental Science, 15(2), 165–180.
Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P., Pagani, L. S., Feinstein, L., Engel, M., Brooks-Gunn, J., Sexton, H., Duckworth, K., & Japel, C. (2007). School readiness and later achievement. Developmental Psychology, 43(6), 1428–1446.
Feigenson, L., Dehaene, S., & Spelke, E. S. (2004). Core systems of number. Trends in Cognitive Sciences, 8(10), 307–314.
Fisher, C. E. (2012). Guidelines for successful mobile interactive apps for children. Paper presented at the annual meeting of game developer conference, San Francisco, CA.
Fuson, K. C. (1992a). Research on learning and teaching addition and subtraction of whole numbers. In G. Leinhardt, R. T. Putnam, & R. A. Hattrup (Eds.), The analysis of arithmetic for mathematics teaching (pp. 53–187). Hillsdale: Erlbaum.
Fuson, K. C. (1992b). Research on whole number addition and subtraction. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 243–275). New York: Macmillan.
Fuson, K. C., Richards, J., & Briars, D. J. (1982). The acquisition and elaboration of the number word sequences. In C. Brainerd (Ed.), Progress in cognitive development: Vol. 1. Children’s logical and mathematical cognition (pp. 33–92). New York: Springer.
Gelman, R. (1993). A rational-constructivist account of early learning about numbers and objects. In D. Medin (Ed.), Learning and motivation (Vol. 30, pp. 61–96). New York: Academic Press.
Gelman, R., & Gallistel, C. R. (1978). The child’s understanding of number. Cambridge: Harvard University Press.
Gelman, R., & Gallistel, C. R. (1986). The child’s understanding of number. Cambridge: Harvard University Press.
Gelman, R., Massey, C., & McManus, M. (1991). Characterizing supporting environments for cognitive development: lessons from children in a museum. In J. M. Levine, L. B. Resnick, & S. D. Teasley (Eds.), Perspectives on socially shared cognition (pp. 226–256). Washington: American Psychological Association.
Ginsburg, H. P. (1989). Children’s arithmetic (2nd ed.). Austin: Pro-Ed.
Ginsburg, H. P. (1997). Entering the child’s mind: the clinical interview in psychological research and practice. New York: Cambridge University Press.
Goldin-Meadow, S., & Alibali, M. W. (2002). Looking at the hands through time: a microgenetic perspective on learning and instruction. In N. Granott & J. Parziale (Eds.), Microdevelopment: transition processes in development and learning (pp. 80–105). Cambridge: Cambridge University Press.
Goldin-Meadow, S., Cook, S. W., & Mitchell, Z. A. (2009). Gesturing gives children new ideas about math. Psychological Science, 20(3), 267–272.
Goldin-Meadow, S., & Alibali, M. W. (2013). Gesture’s role in learning and development. Annual Review of Psychology, 64, 257–283. doi:10.1146/annurev-psych-113011-143802.
Granott, N. (2002). How microdevelopment creates macrodevelopment: reiterated sequences, backward transitions, and the zone of current development. In N. Granott & J. Parziale (Eds.), Microdevelopment: transition processes in development and learning (pp. 213–242). Cambridge: Cambridge University Press.
Hourcade, J. P., Bederson, B. B., Druin, A., & Guimbretiere, F. (2004). Differences in pointing task performance between preschool children and adults using mice. ACM Transactions on Computer-Human Interaction, 11(4), 357–386.
Hoyles, C., & Noss, R. (2009). The technological mediation of mathematics and its learning. Human Development, 52, 129–147.
Hoyles, C., Noss, R., & Adamson, R. (2002). Rethinking the microworld idea. Journal of Educational Computing Research, 27(1), 29–53.
iTot Apps, LLC (2011). Toddler counting (version 1.5) [mobile application software]. Retrieved from http://itunes.apple.com/.
Jamalian, A., & Tversky, B. (2012). Gestures alter thinking about time. In N. Miyake, D. Peebles, & R. P. Cooper (Eds.), Proceedings of the 34th annual conference of the Cognitive Science Society (pp. 551–557). Austin: Cognitive Science Society. IES Prize for Excellence in Research on Cognition and Student Learning (pp. 503–508).
Jordan, N. C., Kaplan, D., Oláh, L. N., & Locuniak, M. N. (2006). Number sense growth in kindergarten: a longitudinal investigation of children at risk for mathematics difficulties. Child Development, 77(1), 153–175.
Kessell, A. M., & Tversky, B. (2006). Using gestures and diagrams to think and talk about insight problems. In R. Sun & N. Miyake (Eds.), Proceedings of the 28th annual conference of the Cognitive Science Society (p. 2528).
Kuhn, D., Garcia-Mila, M., Zohar, A., & Anderson, C. (1995). Strategies of knowledge acquisition. Monographs of the Society for Research in Child Development (Serial No. 245).
Laski, E. V., & Siegler, R. S. (2007). Is 27 a big number? Correlational and causal connections among numerical categorization, number line estimation, and numerical magnitude comparison. Child Development, 78(6), 1723–1743.
Lepper, M. R., & Malone, Th. W. (1987). Intrinsic motivation and instructional effectiveness in computer-based education. In R. E. Snow & M. J. Farr (Eds.), Aptitude, learning, and instruction: Vol. 3. Conative and affective process analyses (pp. 255–286). Hillsdale: Erlbaum.
Malone, T. W., & Lepper, M. R. (1987). Making learning fun: a taxonomy of intrinsic motivations for learning. In R. E. Snow & M. J. Farr (Eds.), Aptitude, learning, and instruction: Vol. 3. Cognitive and affective process analysis (pp. 223–253). Hillsdale: Erlbaum.
Mclean, R. (2012). Space Math (version 1.4.2) [mobile application software]. Retrieved from http://itunes.apple.com/.
Mix, K. S. (1999). Similarity and numerical equivalence: appearances count. Cognitive Development, 14, 269–297.
Mix, K. S. (2010). Spatial tools for mathematical thought. In K. S. Mix, L. B. Smith, & M. Gasser (Eds.), The spatial foundations for language and cognition (pp. 41–66). Oxford: Oxford University Press.
Moeller, K., Pixner, S., Kaufmann, L., & Nuerk, H.-C. (2008). Children’s early mental number line: logarithmic or decomposed linear? Journal of Experimental Child Psychology, 103(4), 503–515.
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, in press). Effects of virtual manipulatives on student achievement and mathematics learning. International Journal of Virtual and Personal Learning Environments.
Mullis, I. V. S., Martin, M. O., Beaton, A. E., Gonzalez, E. J., Kelly, D. L., & Smith, T. A. (1997). Mathematics achievement in the primary school years. In IEA’s third international mathematics and science study (TIMSS). Chestnut Hill: Center for the Study of Testing, Evaluation, and Educational Policy, Boston College.
Papert, S. (1980). Mindstorms: children, computers, and powerful ideas. New York: Basic Books.
Petitto, A. L. (1990). Development of numberline and measurement concepts. Cognition and Instruction, 7(1), 55–78.
Piaget, J. (1952a) The child’s conception of number. London: Routledge & Kegan Paul Ltd. C. Gattegno & F. M. Hodgson, trans.
Piaget, J. (1952b). The origins of intelligence in children. New York: International Universities Press. M. Cook, trans.
Piaget, J. (1976) The child’s conception of the world. Totowa: Littlefield, Adams & Co. J. Tomlinson & A. Tomlinson, trans.
Ping, R., & Goldin-Meadow, S. (2008). Hands in the air: using ungrounded iconic gestures to teach children conservation of quantity. Developmental Psychology, 44(5), 1277–1287.
Ramani, G. B., & Siegler, R. S. (2008). Promoting broad and stable improvements in low-income children’s numerical knowledge through playing number board games. Child Development, 79(2), 375–394.
Rodrigo, M. M. T., & Baker, R. S. J. d. (2011). Comparing the incidence and persistence of learners’ affect during interactions with different educational software packages. In R. A. Calvo & S. K. D’Mello (Eds.), New perspectives on affect and learning technologies (pp. 183–200).
Russell-Pinson, D. (2012). Rocket Math (version 1.8) [mobile application software]. Retrieved from http://itunes.apple.com/.
Sarama, J., & Clements, D. H. (2002). Linking research and software development. In Research on technology in the teaching and learning of mathematics: cases and perspectives (pp. 113–130).
Sarama, J., & Clements, D. H. (2009a). “Concrete” computer manipulatives in mathematics education. Child Development Perspectives, 3(3), 145–150.
Sarama, J., & Clements, D. H. (2009b). Early childhood mathematics education research: learning trajectories for young children. New York: Routledge.
Sawyer, R. K. (2006). The Cambridge handbook of the learning sciences. The new science of learning (pp. 1–16). New York: Cambridge University Press.
Saxe, G. B., Earnest, D., Sitabkhan, Y., Halder, L. C., Lewis, K. E., & Zheng, Y. (2010). Supporting generative thinking about the integer number line in elementary mathematics. Cognition and Instruction, 28(4), 433–474.
Schneider, M., & Siegler, R. S. (2010). Representations of the magnitudes of fractions. Journal of Experimental Psychology. Human Perception and Performance, 36(5), 1227–1238.
Segal, A. (2011). Do gestural interfaces promote thinking? Embodied interaction: congruent gestures and direct touch promote performance in math. Unpublished Dissertation, Columbia University.
Shuler, C. (2009). Pockets of potential: using mobile technologies to promote children’s learning. New York: The Joan Ganz Cooney Center at Sesame Workshop.
Siegler, R. S., & Booth, J. L. (2004). The development of numerical estimation in young children. Child Development, 75(2), 428–444.
Siegler, R. S., & Jenkins, E. A. (1989). How children discover new strategies. Hillsdale: Erlbaum.
Siegler, R. S., & Svetina, M. (2006). What leads children to adopt new strategies? A microgenetic/cross sectional study of class inclusion. Child Development, 77, 997–1015.
Starkey, P., & Klein, A. (2008). Sociocultural influences on young children’s mathematical knowledge. In O. N. Seracho & B. Spodek (Eds.), Contemporary perspectives on mathematics in early childhood education. Charlotte: Information Age.
Vygotsky, L. S. (1978). Mind in society: the development of higher psychological processes. Cambridge: Harvard University Press.
Vygotsky, L. S. (1986). Thought and language. Cambridge: MIT Press. A. Kozulin, trans.
Weir, S., Russell, S. J., & Valente, J. A. (1982). Logo: an approach to educating disabled children. BYTE, 7, 342–360.
Wilson, M. (2002). Six views of embodied cognition. Psychonomic Bulletin & Review, 9(4), 625–636.
Wilson, A. J., Dehaene, S., Pinel, P., Revkin, S. K., Cohen, L., & Cohen, D. (2006a). Principles underlying the design of “The Number Race”, an adaptive computer game for remediation of dyscalculia. Behavioral and Brain Functions, 2(1), 19.
Wilson, A. J., Revkin, S. K., Cohen, D., Cohen, L., & Dehaene, S. (2006b). An open trial assessment of “The Number Race”, an adaptive computer game for remediation of dyscalculia. Behavioral and Brain Functions, 2(20). doi:10.1186/1744-9081-2-20.
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Ginsburg, H.P., Jamalian, A., Creighan, S. (2013). Cognitive Guidelines for the Design and Evaluation of Early Mathematics Software: The Example of MathemAntics . In: English, L., Mulligan, J. (eds) Reconceptualizing Early Mathematics Learning. Advances in Mathematics Education. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6440-8_6
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