The role of and connection between systematization and representation when young children work on a combinatorial task

References

• Anderson, T., and J. Shattuck. 2012. “Design-Based Research: A Decade of Progress in Education Research?” Educational Researcher 41 (1): 16–25. doi: 10.3102/0013189X11428813
   Web of Science ®Google Scholar
• Björklund, C. 2014. “Less Is More – Mathematical Manipulatives in Early Childhood Education.” Early Child Development and Care 184 (3): 469–485. doi: 10.1080/03004430.2013.799154
   Google Scholar
• Carruthers, E., and M. Worthington. 2006. Children’s Mathematics. Making Marks, Making Meaning. 2nd ed.London: Sage.
   Google Scholar
• Cross, C. T., T. A. Woods, and H. Schweingruber. 2009. Mathematics Learning in Early Childhood. Paths Toward Excellence and Equity. Washington, DC: The National Academies Press.
   Google Scholar
• Devlin, K. 2000. The Math Gene: How Mathematical Thinking Evolved and Why Numbers Are Like Gossip. New York: Basic Books.
   Google Scholar
• Dowker, A. 2005. Individual Differences in Arithmetic. Implications for Psychology, Neuroscience and Education. New York: Psychology Press.
   Google Scholar
• English, L. D. 1991. “Young Children’s Combinatoric Strategies.” Educational Studies in Mathematics 22 (5): 451–474. doi: 10.1007/BF00367908
   Google Scholar
• English, L. D. 1996. “Children’s Construction of Knowledge in Solving Novel Isomorphic Problems in Concrete and Written Form.” Journal of Mathematical Behavior 15: 81–112. doi: 10.1016/S0732-3123(96)90042-5
   Google Scholar
• English, L. D. 2005. “Combinatorics and the Development of Children’s Combinatorial Reasoning.” In Exploring Probability in School: Challenges for Teaching and Learning, edited by G. A. Jones, 121–141. New York: Springer.
   Google Scholar
• Goldin, G., and N. Shteingold. 2001. “Systems of Representations and the Development of Mathematical Concepts.” In The Roles of Representation in School Mathematics: Yearbook, edited by A. A. Cuoco and F. R. Curcio, 1–23. Reston, VA: National Council of Teachers of Mathematics.
   Google Scholar
• Heddens, J. W. 1986. “Bridging the Gap Between the Concrete and the Abstract.” The Arithmetic Teacher 33 (6): 14–17.
   Google Scholar
• Hughes, M. 1986. Children and Number: Difficulties in Learning Mathematics. Oxford: Blackwell.
   Google Scholar
• Lesh, R., and J. Zawojewski. 2007. “Problem Solving and Modeling.” In Second Handbook of Research on Mathematics Teaching and Learning, edited by I. F. K. Lester (Red.), 763–799. Charlotte: National Council of Teachers of Mathematics & Information Age.
   Google Scholar
• Matthews, J. 2006. “Foreword.” In Children’s Mathematics: Making Marks, Making Meaning, 2nd ed., edited by E. Carruthers and M. Worthington. London: Sage.
   Google Scholar
• Mulligan, J., and M. Mitchelmore. 2009. “Awareness of Pattern and Structure in Early Mathematical Development.” Mathematics Education Research Journal 21 (2): 33–49. doi: 10.1007/BF03217544
   Google Scholar
• National Agency for Education. 2014a. Descriptive Data 2013 Pre-School, School and Adult Education. Report 399.
   Google Scholar
• National Agency for Education. 2014b. Preschool Class: Assignment, Content and Quality. Stockholm: Swedish National Agency for Education.
   Google Scholar
• Palmér, H., and C. Björklund. 2016. “Different Perspectives on Possible – Desirable – Plausible Mathematics Learning in Preschool.” Nordic Studies in Mathematics Education 21 (4): 177–191.
   Google Scholar
• Palmér, H., and A. Ebbelind. 2013. “What Is Possible to Learn? Using IPads in Teaching Mathematics in Preschool.” In Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education. Mathematics Learning Across the Life Span, edited by A. M. Lindmeier and A. Heinze, 425–432. Kiel: PME.
   Google Scholar
• Palmér, H., and van Bommel, J. (2017). Exploring the Role of Representations When Young Children Solve a Combinatorial Task. In ICT in Mathematics Education: The Future and the Realities: Proceedings of MADIF 10
The Tenth Research Seminar of the Swedish Society for Research in Mathematics Education, edited by J. Häggström, E. Norén, J. van Bommel, J. Sayers, O. Helenius, and Y. Liljekvist, January 26–27, 2016. Karlstad: Svensk förening för MatematikDidaktisk Forskning – SMDF.
   Google Scholar
• Perry, B., and S. Dockett. 2008. “Young Children’s Access to Powerful Mathematical Ideas.” In Handbook of International Research in Mathematics Education, edited by I. L. D. English, M. B. Bussi, G. A. Jones, R. A. Lesh, B. Sriraman, and D. Tirosh (Red.), 75–108. London: Routhledge.
   Google Scholar
• Piaget, J., and B. Inhelder. 1969. The Psychology of the Child. New York: Basic Books.
   Google Scholar
• Prediger, S., K. Gravemeijer, and J. Confrey. 2015. “Design Research with a Focus on Learning Processes: An Overview on Achievements and Challenges.” ZDM Mathematics Education 47: 877–891. doi: 10.1007/s11858-015-0722-3
   Web of Science ®Google Scholar
• Sinclair, A., F. Siegrist, and H. Sinclair. 1983. “Young Children’s Ideas About the Written Number System.” In The Acquisition of Symbolic Skills, edited by D. R. Rogers and J. A. Sloboda, 535–542. New York: Plenum Press.
   Google Scholar
• Swedish Research Council. 2011. God Forskningssed [Good Custom in Research].Stockholm: Vetenskapsrådet.
   Google Scholar
• van Bommel, J., and H. Palmér. 2017. “ Slow Down You Move Too Fast.” Poster presented at CERME10, Dublin, Ireland.
   Google Scholar