Advertisement

ZDM

, Volume 48, Issue 7, pp 1079–1087 | Cite as

Revealing and capitalising on young children’s mathematical potential

  • Lyn D. English
Commentary Paper

Abstract

With ongoing concerns about environments that push teachers toward increasingly structured assessments, thus reducing opportunities to observe young learners’ mathematical capabilities, the publication of this special issue on formative assessment is especially significant and timely. The articles illustrate how we cannot rely solely on standardized achievement tests to determine learners’ actual mathematical competencies, or to determine their learning potential, or to fully identify possible areas in need of further development. In this commentary I first consider some of the important issues examined in the articles and then turn to Ginsburg’s general principles listed in his opening article. These principles are particularly helpful in not only guiding early assessment but also in providing quality mathematics education to young children. Building on ideas featured in this issue, I offer suggestions for how we might reveal and capitalise on young children’s mathematical talents. Examples from analogical and mathematical reasoning, spatial and numerical relations, numerical problem solving and posing, and combinatorial reasoning are presented.

Keywords

Professional Development Formative Assessment Young Learner Mathematical Reasoning Analogical Reasoning 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Alexander, P. A., & Buehl, M. M. (2004). Seeing the possibilities: Constructing and validating measures of mathematical and analogical reasoning for young children. In L. D. English (Ed.), Mathematical and analogical reasoning of young learners (pp. 23–46). Mahwah: Lawrence Erlbaum Associates.Google Scholar
  2. Alexander, P. A., White, C. S., & Daugherty, M. (1997). Children’s use of analogical reasoning in early mathematics learning. In L. D. English (Ed.), Mathematical reasoning: Analogies, metaphors, and images (pp. 117–147). Mahwah: Lawrence Erlbaum Associates.Google Scholar
  3. Alexander, P. A., Willson, V. L., White, C. S., & Fuqua, J. D. (1987). Analogical reasoning in young children. Journal of Educational Psychology, 79, 401–408.CrossRefGoogle Scholar
  4. Borovcnik, M., & Peard, R. (1996). Probability. In A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook in mathematics education (Part 1 (pp. 239–288). Dordrecht: Kluwer.Google Scholar
  5. Brown, S. I., & Walter, M. L. (2005). The art of problem posing. Mahwah: Lawrence Erlbaum Associates.Google Scholar
  6. Chui, S., & Tron, M. O. (2004). Classroom discourse and the development of mathematical and analogical reasoning. In L. D. English, (Ed.), Mathematical and analogical reasoning of young learners (pp. 75–96). Mahwah, New Jersey: Lawrence Erlbaum Associates.Google Scholar
  7. Claessens, A., & Engel, M. (2011). How important is where you start? Early mathematics knowledge and later school success. Teachers College Record, 115(6), 1–29.Google Scholar
  8. Clements, D. H., & Sarama, J. (2011). Early childhood mathematics intervention. Science, 333, 968–970.CrossRefGoogle Scholar
  9. Clements, D. H., & Sarama, J. (2013). Rethinking early mathematics: What is research-based curriculum for young children? In L. D. English & J. Mulligan (Eds.), Reconceptualizing early mathematics learning (pp. 121–148). Dordrecht: Springer.CrossRefGoogle Scholar
  10. Committee on Early Childhood Mathematics. (2009). Mathematics learning in early childhood: Paths toward excellence and equity. Washington: National Academies Press.Google Scholar
  11. English, L. D. (1991). Young children’s combinatoric strategies. Educational Studies in Mathematics, 22, 451–474.CrossRefGoogle Scholar
  12. English, L. D. (1993). Children’s strategies in solving two- and three-dimensional combinatorial problems. Journal for Research in Mathematics Education, 24(3), 255–273.CrossRefGoogle Scholar
  13. English, L. D. (2004). Mathematical and analogical reasoning in early childhood. In L. D. English (Ed.), Mathematical and analogical reasoning of young learners (pp. 1–22). Mahwah: Lawrence Erlbaum Associates.Google Scholar
  14. English, L. D. (2005). Combinatorics and the development of children’s combinatorial reasoning. In G. A. Jones (Ed.), Exploring probability in schools: Challenges for teaching and learning (pp. 121–141). Dordrecht: Kluwer.CrossRefGoogle Scholar
  15. English, L. D. (2012). Data modelling with first-grade students. Educational Studies in Mathematics Education, 81(1), 15–30.CrossRefGoogle Scholar
  16. English, L. D., & Mulligan, J. T. (Eds.). (2013). Reconceptualizing early mathematics learning. Dordrecht: Springer.Google Scholar
  17. Ertle, B., Rosenfeld, D., Presser, A. L., & Goldstein, M. (2016). Preparing preschool teachers to use and benefit from formative assessment: The Birthday Party Assessment professional development system. ZDM Mathematics Education, 48(7) (This issue). doi: 10.1007/s11858-016-0785-9.
  18. Gadanidis, G., Hughes, J. M., Minniti, L., & White, B. J. G. (2016). Computational thinking, grade 1 students and the binomial theorem. Digital Experiences in Mathematics Education, online, May, 2016. doi: 10.1007/s40751-016-0019-3.
  19. Gentner, D., Holyoak, K. J., & Kokinov, B. N. (2001). (Eds.). The analogical mind: Perspectives from cognitive science. Cambridge, MA: MIT Press.Google Scholar
  20. Ginsburg, H. P. (2009). The challenge of formative assessment in mathematics education: Children’s minds, teachers’ minds. Human Development, 52, 109–128.CrossRefGoogle Scholar
  21. Ginsburg, H. P. (2016). Helping early childhood educators to understand and assess young children’s mathematical minds. ZDM Mathematics Education, 48(7), (this issue).Google Scholar
  22. Ginsburg, H. P., Cannon, J., Eisenband, J. G., & Pappas, S. (2006). Mathematical thinking and learning. In K. McCartney & D. Phillips (Eds.), Handbook of early child development (pp. 208–230). Oxford: Blackwell.Google Scholar
  23. Ginsburg, H. P., Jamalian, A., & Creighan, S. (2013). Cognitive guidelines for the design and evaluation of early mathematics software: The example of MathemAntics. In L. D. English & J. Mulligan (Eds.), Reconceptualising early mathematics learning (pp. 83–120). Dordrecht: Springer.CrossRefGoogle Scholar
  24. Ginsburg, H. P., Lee., Y., & Pappas, S. (2016). Using the clinical interview and curriculum based measurement to examine risk levels. ZDM Mathematics Education, 48(7) (this issue). doi: 10.1007/s11858-016-0802-z.
  25. Ginsburg, H. P., & Pappas, S. (2016). Invitation to the Birthday Party: Rationale and description. ZDM Mathematics Education, 48(7) (this issue).Google Scholar
  26. Goswami, U. (2012). Analogical reasoning by young children. In N. M. Steele (Ed.), Encyclopedia of the sciences of learning (pp. 225–228). Dordrecht: Springer.Google Scholar
  27. Lee, Y. (2016). Psychometric analyses of the Birthday Party. ZDM Mathematics Education, 48(7) (this issue).Google Scholar
  28. Lee, Y., & Lembke, E. (2016). Developing and evaluating a kindergarten to third grade CBM mathematics and assessment. ZDM Mathematics Education, 48(7) (this issue). doi: 10.1007/s11858-016-0788-6.
  29. Lee, Y., Park, Y. S., & Ginsburg, H. P. (2016). Socio-economic status differences in mathematics accuracy, strategy use, and profiles in the early years of schooling. ZDM Mathematics Education, 48(7) (this issue). doi: 10.1007/s11858-016-0783-y.
  30. Lehrer, R., & English, L. D. (In press). Introducing children to modeling variability. In Ben-Zvi, D., Garfield, J., & Makar, K. (Eds.). International handbook of research in statistics education. Dordrecht: Springer.Google Scholar
  31. Lembke, E., Lee, Y. S., Park, Y. S., & Hampton, D. (2016). Longitudinal growth on curriculum-based measurement: Mathematics measures for early elementary students. ZDM Mathematics Education, 48(7) (this issue). doi: 10.1007/s11858-016-0804-x.
  32. Marshall, L. & Swan, P. (2008). Exploring the use of mathematics manipulative materials: Is it what we think it is? In Proceedings of the EDU-COM 2008 International Conference. Sustainability in Higher Education: Directions for Change. http://ro.ecu.edu.au/ceducom/33. Accessed 25 July 2016.
  33. Moss, J., Bruce, C. D., & Bobis, J. (2016). Young children’s access to powerful mathematics ideas: A review of current challenges and new developments in the early years. In L. D. English & Kirshner, D. (Eds.). Handbook of international research in mathematics education, Third Edition (pp. 153–190). New York: Routledge.Google Scholar
  34. Mulligan, J. T., & Mitchelmore, M. C. (2013). Early Awareness of Mathematical Pattern and Structure. In L. D. English, & J. T. Mulligan (Eds.). (2013). Reconceptualizing early mathematics learning (pp. 29–46). Dordrecht: Springer.Google Scholar
  35. Newton, K. J., & Alexander, P. A. (2013). Early mathematics learning in perspective:Eras and forces of change, In L. D. English (Ed.), Mathematical and analogical reasoning of young learners (pp. 5–28). Mahwah, New Jersey: Lawrence Erlbaum Associates.Google Scholar
  36. Perry, B., & Dockett, S. (2008). Young children’s access to powerful mathematical ideas. In L. D. English (Ed.), Handbook of international research in mathematics education (2nd ed., pp. 75–108). NY: Routledge.Google Scholar
  37. Piaget, J., & Inhelder, B. (1975). The origin of the idea of chance in children (L. Leake, Jr., P. Burrell, & H. D. Fishbein, Trans.). London: Routledge & Kegan Paul. (Original work published 1951).Google Scholar
  38. Polya, G. (1957). How to solve it. Princeton: Princeton University Press.Google Scholar
  39. Richland, L. E., Morrison, R. G., & Holyoak, K. J. (2006). Children’s development of analogical reasoning: Insights from scene analogy problems. Journal of Experimental Child Psychology, 94, 249–273.CrossRefGoogle Scholar
  40. Romberg, T. A. (1989). Curriculum and evaluation standards for school mathematics. Reston, National Council of Teachers of Mathematics. Google Scholar
  41. Serow, P., Callingham, R., & Tout, D. (2016). Assessment of mathematics learning: What are we doing? In K. Makar, S. Dole, M. Goos, J. Visnovska, A. Bennison, & K. Fry (Eds.), Research in Mathematics Education in Australasia 20122015 (pp. 235–254). Dordrecht: Springer. 235–254).Google Scholar
  42. Silver, E. A., Mesa, V. M., Morris, K. A., Star, J. R., & Benken, B. M. (2009). Teaching Mathematics for understanding: An analysis of lessons submitted by teachers seeking NBPTS certification. American Educational Research Journal, 46(2), 501–531.CrossRefGoogle Scholar
  43. Wager, A. M., Graue, M. E., & Harrigan, K. (2015). Swimming upstream in a torrent of assessment. In B. Perry, A. MacDonald, & Gervasoni, A. (Eds.), Mathematics and Transition to School: International Perspectives (pp. 17–34). Dordrecht: Springer.Google Scholar
  44. Wager, A. M., & Parks, A. N. (2016). Assessing early number learning in play. ZDM Mathematics Education, 48(7) (this issue).Google Scholar

Copyright information

© FIZ Karlsruhe 2016

Authors and Affiliations

  1. 1.Queensland University of TechnologyBrisbaneAustralia

Personalised recommendations