Table of Contents Author Guidelines Submit a Manuscript
Education Research International
Volume 2016 (2016), Article ID 5240683, 9 pages
http://dx.doi.org/10.1155/2016/5240683
Review Article

What Is Known about Elementary Grades Mathematical Modelling

1University of Nevada, Las Vegas, NV 89154, USA
2Universitat Autònoma de Barcelona, Cerdanyola del Valles 08193, Spain

Received 11 April 2016; Revised 24 May 2016; Accepted 5 June 2016

Academic Editor: Shu-Sheng Liaw

Copyright © 2016 Micah S. Stohlmann and Lluís Albarracín. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. T. Ikeda and M. Stephens, “Three teaching principles for fostering students' thinking about modelling: an experimental teaching program for 9th grade students in Japan,” Journal of Mathematical Modelling and Application, vol. 1, no. 2, pp. 49–59, 2010. View at Google Scholar
  2. J. P. Brown and I. Edwards, “Modelling tasks: insight into mathematical understanding,” in Trends in Teaching and Learning of Mathematical Modelling, G. Kaiser, W. Blum, R. Ferri, and G. Stillman, Eds., pp. 187–197, Springer, New York, NY, USA, 2011. View at Google Scholar
  3. R. Lesh and G. Carmona, “Piagetian conceptual systems and models for mathematizing everyday experiences,” in Beyond Constructivism: Models and Modeling Perspectives on Mathematics Problem Solving, Teaching, and Learning, R. Lesh and H. Doerr, Eds., pp. 71–96, Routledge, New York, NY, USA, 2003. View at Google Scholar
  4. G. Kaiser and B. Schwarz, “Mathematical modelling as bridge between school and university,” ZDM, vol. 38, no. 2, pp. 196–208, 2006. View at Publisher · View at Google Scholar · View at Scopus
  5. K. MaaB, “Modeling in class and the development of beliefs about the usefulness of Mathematics,” in Modeling Students' Mathematical Modeling Competencies, R. Lesh, P. Galbraith, C. Haines, and A. Hurford, Eds., pp. 409–420, Springer, New York, NY, USA, 2010. View at Google Scholar
  6. L. D. English, “Mathematical modeling in the primary school: children's construction of a consumer guide,” Educational Studies in Mathematics, vol. 63, no. 3, pp. 303–323, 2006. View at Publisher · View at Google Scholar
  7. K. Karp, S. Bush, and B. Dougherty, “13 rules that expire,” Teaching Children Mathematics, vol. 21, no. 1, pp. 18–25, 2014. View at Publisher · View at Google Scholar
  8. L. Verschaffel, E. De Corte, and S. Lasure, “Realistic considerations in mathematical modeling of school arithmetic word problems,” Learning and Instruction, vol. 4, no. 4, pp. 273–294, 1994. View at Publisher · View at Google Scholar · View at Scopus
  9. A. Schoenfeld, “Mathematical modeling, sense making, and the common core state standards,” Journal of Mathematics Education at Teachers College, vol. 4, pp. 6–17, 2013. View at Google Scholar
  10. R. Lesh and H. M. Doerr, “Foundations of a models and modeling perspective on mathematics teaching, learning, and problem solving,” in Beyond Constructivism, R. Lesh and H. Doerr, Eds., pp. 3–38, Lawrence Erlbaum Associates, Mahwah, NJ, USA, 2003. View at Google Scholar
  11. R. Lesh, G. Carmona, and T. Moore, “Six sigma learning gains and long term retention of understandings and attitudes related to models & modeling,” Mediterranean Journal for Research in Mathematics education, vol. 9, no. 1, pp. 19–54, 2009. View at Google Scholar
  12. W. Blum and D. LeiB, “How do students and teachers deal with modelling problems,” in Mathematical modelling: Education, Engineering and Economics, C. Haines, P. Galbraith, W. Blum, and S. Khan, Eds., pp. 222–231, Horwood, Chichester, UK, 2007. View at Google Scholar
  13. R. Lesh and H. M. Doerr, “In what ways does a models and modeling perspective move beyond constructivism?” in Beyond Constructivism, R. Lesh and H. Doerr, Eds., pp. 519–556, Lawrence Erlbaum Associates, Mahwah, NJ, USA, 2003. View at Google Scholar
  14. R. Lesh, M. Hoover, B. Hole, A. Kelly, and T. Post, “Principles for developing thought-revealing activities for students and teachers,” in Research Design in Mathematics and Science Education, A. Kelly and R. Lesh, Eds., pp. 591–646, Lawrence Erlbaum and Associates, Mahwah, NJ, USA, 2000. View at Google Scholar
  15. A. Bryman, Social Research Methods, Oxford University Press, Oxford, UK, 2nd edition, 2004.
  16. N. V. Diaz and M. F. Cox, “An overview of the literature: research in p-12 engineering education,” Advances in Engineering Education, vol. 3, no. 2, pp. 1–37, 2012. View at Google Scholar · View at Scopus
  17. C. M. E. Chan, “Tracing primary 6 students model development within the mathematical modelling process,” Journal of Mathematical Modelling and Application, vol. 1, no. 3, pp. 40–57, 2010. View at Google Scholar
  18. L. Verschaffel and E. De Corte, “Teaching realistic mathematical modeling in the elementary school: a teaching experiment with fifth graders,” Journal for Research in Mathematics Education, vol. 28, no. 5, pp. 577–601, 1997. View at Publisher · View at Google Scholar · View at Scopus
  19. L. D. English and J. J. Watters, “Mathematical modelling in the early school years,” Mathematics Education Research Journal, vol. 16, no. 3, pp. 58–79, 2005. View at Publisher · View at Google Scholar · View at Scopus
  20. A. Peter-Koop, “Fermi problems in primary mathematics classrooms: pupils' interactive modelling processes,” in Mathematics Education for the Third Millenium: Towards 2010, pp. 454–461, 2004. View at Google Scholar
  21. M. C. C. T. Cyrino and H. M. Oliveira, “Pensamento algébrico ao longo do ensino básico em Portugal,” Bolema: Boletim de Educação Matemática, vol. 24, no. 38, pp. 97–126, 2011. View at Google Scholar
  22. L. D. English, “Modeling with complex data in the primary school,” in Modeling Students' Mathematical Modeling Competencies, R. Lesh, P. Galbraith, C. R. Haines, and A. Hurford, Eds., pp. 287–299, Springer, New York, NY, USA, 2010. View at Google Scholar
  23. L. M. W. de Almeida and E. Tortola, “Modelagem matemática no ensino fundamental: a linguagem de alunos como foco de análise,” Jornal Internacional de Estudos em Educação Matemática, vol. 7, no. 1, 2015. View at Google Scholar
  24. B. Greer, “The mathematical modeling perspective on wor(l)d problems,” The Journal of Mathematical Behavior, vol. 12, no. 3, pp. 239–250, 1993. View at Google Scholar
  25. K. Reusser and R. Stebler, “Every word problem has a solution—the social rationality of mathematical modeling in schools,” Learning and Instruction, vol. 7, no. 4, pp. 309–327, 1997. View at Publisher · View at Google Scholar · View at Scopus
  26. H. Yoshida, L. Verschaffel, and E. De Corte, “Realistic considerations in solving problematic word problems: do Japanese and Belgian children have the same difficulties?” Learning and Instruction, vol. 7, no. 4, pp. 329–338, 1997. View at Publisher · View at Google Scholar · View at Scopus
  27. R. Lesh, L. English, S. Sevis, and C. Riggs, “Modeling as a means for making powerful ideas accessible to children at an early age,” in The SimCalc Vision and Contributions, S. J. Hegedus and J. Roschelle, Eds., Advances in Mathematics Education, pp. 419–436, Springer, Amsterdam, The Netherlands, 2013. View at Publisher · View at Google Scholar
  28. A. V. de Almeida, E. G. Souza, and L. B. de Souza, “Mathematical texts in a mathematical modelling learning environment in primary school,” in Mathematical Modelling in Education Research and Practice, pp. 535–543, Springer, 2015. View at Google Scholar
  29. T. Kawakami, A. Saeki, and A. Matsuzaki, “How do students share and refine models through dual modelling teaching: the case of students who do not solve independently,” in Mathematical Modelling in Education Research and Practice, pp. 195–206, Springer, 2015. View at Google Scholar
  30. L. D. English, “Promoting interdisciplinarity through mathematical modelling,” ZDM—International Journal on Mathematics Education, vol. 41, no. 1-2, pp. 161–181, 2009. View at Publisher · View at Google Scholar · View at Scopus
  31. L. D. English, “Learning through modelling in the primary years,” in Mathematical Modelling: From Theory to Practice, N. H. Lee and D. K. E. Ng, Eds., pp. 99–124, National Institute of Education, Singapore, 2015. View at Google Scholar
  32. J. Mulligan, “Moving beyond basic numeracy: data modeling in the early years of schooling,” ZDM, vol. 47, no. 4, pp. 653–663, 2015. View at Publisher · View at Google Scholar · View at Scopus
  33. L. D. English, “Interdisciplinary modelling in the primary mathematics curriculum,” in Proceedings of the 30th Mathematics Education Research Group of Australasia Annual Conference, J. Watson and K. Beswick, Eds., pp. 275–284, MERGA, Hobart, Ohio, USA, 2007.
  34. L. D. English, “Data modelling with first-grade students,” Educational Studies in Mathematics, vol. 81, no. 1, pp. 15–30, 2012. View at Publisher · View at Google Scholar · View at Scopus
  35. J. Watters, L. English, and S. Mahoney, “Mathematical modeling in the elementary school,” in Proceedings of the American Educational Research Association Annual Meeting, AERA, San Diego, Calif, USA, April 2004.
  36. T. Kawakami, “Enhancing young children's reasoning about data distribution through model creating and sharing,” in Proceedings of the 7th ICMI-East Asia Regional Conference on Mathematics Education, Cebu City, Philippines, May 2015.
  37. R. Lehrer and L. Schauble, “Inventing data structures for representational purposes: elementary grade students' classification models,” Mathematical Thinking and Learning, vol. 2, no. 1-2, pp. 51–74, 2000. View at Publisher · View at Google Scholar
  38. A. Petrosino, R. Lehrer, and L. Schauble, “Structuring error and experimental variation as distribution in the fourth grade,” Mathematical Thinking and Learning, vol. 5, no. 2-3, pp. 131–156, 2003. View at Publisher · View at Google Scholar
  39. G. Carmona and S. Greenstein, “Investigating the relationship between the problem and the solver: who decides what math gets used?” in Modeling Students' Mathematical Modeling Competencies, R. Lesh, P. Galbraith, C. Haines, and A. Hurford, Eds., pp. 245–254, Springer, New York, NY, USA, 2010. View at Google Scholar
  40. R. Lehrer and T. Romberg, “Exploring children's data modeling,” Cognition and Instruction, vol. 14, no. 1, pp. 69–108, 1996. View at Publisher · View at Google Scholar · View at Scopus
  41. L. Verschaffel, E. De Corte, S. Lasure, G. Van Vaerenbergh, H. Bogaerts, and E. Ratinckx, “Learning to solve mathematical application problems: a design experiment with fifth graders,” Mathematical Thinking and Learning, vol. 1, no. 3, pp. 195–229, 2009. View at Publisher · View at Google Scholar
  42. L. D. English, “Young children's early modelling with data,” Mathematics Education Research Journal, vol. 22, no. 2, pp. 24–47, 2010. View at Publisher · View at Google Scholar · View at Scopus
  43. R. Lesh and A. E. Kelly, “Multi-tiered teaching experiments,” in Handbook of Research Design in Mathematics and Science Education, R. A. Lesh and A. Kelly, Eds., pp. 197–230, Lawrence Erlbaum Associates, Mahwah, NJ, USA, 2000. View at Google Scholar
  44. L. English, “Mathematical modelling with young learners,” in Mathematical Modelling: A Way of Life ICTMA11, S. J. Lamon, W. A. Parker, and S. K. Houston, Eds., pp. 3–17, Horwood, Chichester, UK, 2003. View at Google Scholar
  45. W. Blum and R. Borromeo Ferri, “Mathematical modelling: can it be taught and learnt?” Journal of Mathematical Modelling and Application, vol. 1, no. 1, pp. 45–58, 2009. View at Google Scholar
  46. Common Core State Standards Initiative, “Common core standards for mathematics,” 2010, http://www.corestandards.org/assets/CCSI_Math%20Standards.pdf.
  47. Australian Curriculum, Assessment and Reporting Authority, 2015, http://www.australiancurriculum.edu.au/mathematics/curriculum/f-10?layout=1.
  48. M. Stohlmann, C. Maiorca, and T. Olson, “Preservice secondary teachers' conceptions from a mathematical modeling activity and connections to the Common Core State Standards,” The Mathematics Educator Journal, vol. 24, no. 1, pp. 21–43, 2015. View at Google Scholar
  49. M. F. Pajares, “Teachers' beliefs and educational research: cleaning up a messy construct,” Review of Educational Research, vol. 62, no. 3, pp. 307–332, 1992. View at Publisher · View at Google Scholar
  50. P. Biccard and D. C. J. Wessels, “Documenting the development of modelling competencies of grade 7 mathematics students,” in Trends in Teaching and Learning of Mathematical Modelling, G. Kaiser, W. Blum, R. B. Ferri, and G. Stillman, Eds., vol. 1 of International Perspectives on the Teaching and Learning of Mathematical Modelling, pp. 375–383, Springer, New York, NY, USA, 2011. View at Publisher · View at Google Scholar
  51. S. Grünewald, “The development of modelling competencies by year 9 students: effects of a modelling project,” in Teaching Mathematical Modelling: Connecting to Research and Practice, G. A. Stillman, G. Kaiser, W. Blum, and J. P. Brown, Eds., International Perspectives on the Teaching and Learning of Mathematical Modelling, chapter 16, pp. 185–194, Springer, New York, NY, USA, 2013. View at Publisher · View at Google Scholar
  52. K. Maaß, “Modelling in class: what do we want the students to learn?” in Mathematical Modelling: Education, Engineering and Economics, C. Haines, P. Galbraith, W. Blum, and S. Khan, Eds., pp. 63–78, Horwood Publishing, Chichester, UK, 2007. View at Google Scholar
  53. K. Maaß, “What are modelling competencies?” ZDM, vol. 38, no. 2, pp. 113–142, 2006. View at Publisher · View at Google Scholar · View at Scopus
  54. H. Doerr and D. Lesh, “Models and Modelling perspectives on teaching and learning mathematics in the twenty-first century,” in Trends in Teaching and Learning of Mathematical Modelling, G. Kaiser, W. Blum, R. Ferri, and G. Stillman, Eds., pp. 247–268, Springer, New York, NY, USA, 2011. View at Google Scholar
  55. L. S. Shulman, “Those who understand: knowledge growth in teaching,” Educational Researcher, vol. 15, no. 2, pp. 4–14, 1986. View at Publisher · View at Google Scholar
  56. H. C. Hill, D. L. Ball, and S. G. Schilling, “Unpacking pedagogical content knowledge: conceptualizing and measuring teachers' topic-specific knowledge of students,” Journal for Research in Mathematics Education, vol. 39, no. 4, pp. 372–400, 2008. View at Google Scholar · View at Scopus
  57. K. E. D. Ng, “Initial perspectives of teacher professional development on mathematical modelling in Singapore: a framework for facilitation,” in Teaching Mathematical Modelling: Connecting to Research and Practice, G. Stillman, G. Kaiser, W. Blum, and J. Brown, Eds., International Perspectives on the Teaching and Learning of Mathematical Modelling, pp. 427–436, Springer, New York, NY, USA, 2013. View at Publisher · View at Google Scholar
  58. M. Winter and H. Venkat, “Pre-service teacher learning for mathematical modelling,” in Teaching Mathematical Modelling: Connecting to Research and Practice, G. A. Stillman, G. Kaiser, W. Blum, and J. P. Brown, Eds., International Perspectives on the Teaching and Learning of Mathematical Modelling, pp. 395–404, Springer, New York, NY, USA, 2013. View at Publisher · View at Google Scholar
  59. H. Burkhardt, “Modelling in mathematics classrooms: reflections on past developments and the future,” ZDM, vol. 38, no. 2, pp. 178–195, 2006. View at Publisher · View at Google Scholar · View at Scopus
  60. D. L. Ball, S. T. Lubienski, and D. Mewborn, “Research on teaching mathematics: the unsolved problem of teachers' mathematical knowledge,” in Handbook on Research in Teaching, V. Richardson, Ed., pp. 180–194, Macmillan, New York, NY, USA, 4th edition, 2001. View at Google Scholar
  61. OECD, “Mathematics framework,” in PISA 2012 Assessment and Analytical Framework: Mathematics, Reading, Science, Problem Solving and Financial Literacy, OECD Publishing, 2013. View at Publisher · View at Google Scholar
  62. A. Schoenfeld, Mathematical Problem Solving, Academic Press, New York, NY, USA, 1985.