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Complex and Open-Ended Tasks to Enrich Mathematical Experiences of Kindergarten Students

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Mathematical Creativity and Mathematical Giftedness

Part of the book series: ICME-13 Monographs ((ICME13Mo))

Abstract

At a very young age, some children already manifest unusually strong mathematical abilities that need to be fully developed and nurtured in school. The chapter investigates in what way a kindergarten curriculum can offer all students a richer mathematical experience by means of open-ended and complex tasks. Hence, I developed and implemented challenging activities for kindergarten students. The data collected during the experiment helped us examine learning opportunities within challenging situations in terms of the mathematics structures the kindergarten students create during such activities and the strategies they use. The chapter analyses how kindergarten students approach three challenging situations, showing a great variety in students’ authentic strategies and mathematical approaches. While some students struggle with increasing complexity of tasks but still remain engaged and try to overcome obstacles, others seem to exhibit more structured (in terms of mathematical relationships), systematic (in terms of problem-solving strategies), and abstract (in terms of mathematical symbolism) approaches. In addition, all students, even at a very young age, can benefit from a classroom culture of questioning, investigating, communicating, and reflecting on more advanced and meaningful mathematics that can help develop their mathematical mind.

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References

  • Arsac, G., Germain, G., & Mante, M. (1988). Problème ouvert et situation-problème. Lyon: Université Claude Benau.

    Google Scholar 

  • Bachelard, G. (1967). La Formation de l’esprit scientifique (5e édition). Paris: Librairie Philosophique J. Vrin.

    Google Scholar 

  • Balfanz, R., Ginsburg, H. P., & Greenes, C. (2003). The big math for little kids early childhood mathematics program. Teaching Children Mathematics, 9(5), 264–268.

    Google Scholar 

  • Brousseau, G. (2002). Theory of didactical situations in mathematics. Dordrecht: Kluwer Academic Publishers.

    Google Scholar 

  • Burjan, V. (1991). Mathematical Giftedness—Some questions to be answered. In: F. Moenks, M. Katzko, & H. Van Roxtel (Eds.), Education of the gifted in Europe: Theoretical and research issues: Report of the educational research workshop held in Nijmegen (The Netherlands) (pp.165–170). Amsterdam / Lisse: Swetz & Zeitlingen Pub. Service. 23–26 July.

    Google Scholar 

  • Carpenter, T. P., Franke, M. L., & Levi, L. (2003). Thinking mathematically. Portsmouth, NH: Heinemann.

    Google Scholar 

  • Clements, D. H., & Sarama, J. (2009). Learning trajectories in early mathematics—Sequences of acquisition and teaching. Encyclopedia of language and literacy development (pp. 1–7). London, ON: Canadian Language and Literacy Research Network. Retrieved from http://literacyencyclopedia.ca/pdfs/topic.php?topId=270.

  • Department of Education and Early Child Development (DEECD). (2011). Kindergarten mathematics curriculum (in French). Canada: Government of New Brunswick.

    Google Scholar 

  • Department of Education and Early Child Development (DEECD). (2012). Putting children first: Positioning early childhood for the future. Canada: Government of New Brunswick.

    Google Scholar 

  • Diezmann, C. M., & English, L. D. (2001). Developing young children’s multi-digit number sense. Roeper Review, 24(1), 11–13.

    Article  Google Scholar 

  • Dunham, W. (1990). Journey through genius: The great theorems of mathematics (1st ed.). Wiley.

    Google Scholar 

  • Greenes, C. (1997). Honing the abilities of the mathematically promising. Math Teach, 582–586.

    Google Scholar 

  • Freiman, V. (2006). Problems to discover and to boost mathematical talent in early grades: A challenging situations approach. The Montana Mathematics Enthusiast, 3(1), 51–75.

    Google Scholar 

  • Freiman, V. (2009). Mathematical enrichment: Problem-of-the-week model. In R. Leikin, A. Berman, & B. Koichu (Eds.), Creativity in mathematics and the education of gifted students (pp. 367–382). Rotterdam: Sense Publishing.

    Google Scholar 

  • Freiman, V. (2010). Identification and fostering of mathematically gifted children. Saarbrueken, Germany: Lambert Academic Publishing.

    Google Scholar 

  • Freiman, V., & Lee, L. (2004). Tracking primary students’ understanding of the equal sign. Research Report. In M. Hoines & A. Fuglestad (Eds.), Proceedings of the 28th International Conference of the International Group for the Psychology of Mathematics Education (pp. 415–422). Bergen: University College.

    Google Scholar 

  • Garcia, F. J. G., & Ruiz-Higueras, L. (2013). Task design within the Anthropological Theory of the Didactics: Study and research courses for pre-school. In C. Margolinas (Ed.), Task design in mathematics education: Proceedings of ICMI Study 22 (pp. 421–430). Oxford: ICMI.

    Google Scholar 

  • Gelman, R., & Gallistel, C. (1978). The child’s understanding of number. Cambridge: Harward University Press.

    Google Scholar 

  • Greenes, C. (1981). Identifying the gifted student in mathematics. Arithmetic Teacher, 28(6), 14–17.

    Google Scholar 

  • Heinze, A. (2005). Differences in problem solving strategies of mathematically gifted and non-gifted elementary students. International Education Journal, 6(2), 175–183.

    Google Scholar 

  • Hershkovitz, S., Peled, I., & Littler, G. (2009). Mathematical creativity and giftedness in elementary school: Task and teacher promoting creativity for all. In R. Leikin, A. Berman, & B. Koichu (Eds.), Creativity in mathematics and the education of gifted students (pp. 255–270). Rotterdam, The Netherlands: Sense Publisher.

    Google Scholar 

  • Kennard, R. (1998). Providing for mathematically able children in ordinary classrooms. Gifted Education International, 13(1), 28–33.

    Article  Google Scholar 

  • Knuth, E. J., Stephens, A. C., McNeil, N. M., & Alibali, M. W. (2006). Does understanding the equal sign matter? Evidence from solving equations. Journal for Research in Mathematics Education, 36(4), 297–312.

    Google Scholar 

  • Kolmogorov, A. N. (1988). Mathematics as science and profession (in Russian). Moscow: Nauka. (Кoлмoгopoв A. H. Maтeмaтикa—нayкa и пpoфeccия. M.: Hayкa. Гл. peд. физ.-мaт. лит., 1988).

    Google Scholar 

  • Krutetskii, V. A. (1962). Problems of mathematical abilities in school children. In N. Levitov & V. Krutetskii (Eds.), Abilities and interests (in Russian). Moscow: Institute of the Academy of Pedagogical Sciences. (Кpyтeцкий B. Л. К вoпpocy o мaтeмaтичecкиx cпocoбнocтяx y шкoльникoв/Cпocoбнocти и интepecы/Peд. H. Д. Лeвитoв, B. A. Кpyтeцкий. - M.: Ин-т Aкaкдeмии Пeд. Hayк, 1962.

    Google Scholar 

  • Krutetskii, V. A. (1976). The psychology of mathematical abilities in school children. Chicago, IL: The University of Chicago Press.

    Google Scholar 

  • Kulm, G. (1990). Assessing higher order thinking in mathematics. Washington, DC: American Association for the Advancement of Science.

    Google Scholar 

  • Leeson, N. (1995). Investigation of kindergarten students’ spatial constructions. In B. Atweh & S. Flavel (Eds.), Proceedings of 18th Annual Conference of Mathematics Education Research Group of Australasia, (pp. 384–389). Darwin: Mathematics.

    Google Scholar 

  • Leikin, R. (2006). Learning by teaching: The case of Sieve of Eratosthenes and one elementary school teacher. In R. Zazkis & S. Campbell (Eds.), Number theory in mathematics education: Perspectives and prospects (pp. 115–140). Mahwah, NJ: Erlbaum.

    Google Scholar 

  • Leikin, R. (2009). Bridging research and theory in mathematics education with research and theory in creativity and giftedness. In R. Leikin, A. Berman, & B. Koichu (Eds.), Creativity in mathematics and the education of gifted students (pp. 385–411). Rotterdam, The Netherlands: Sense Publisher.

    Google Scholar 

  • Lesh, R., & Kelly, A. (2000). Multitiered teaching experiments. In A. Kelly & R. Lesh (Eds.), Research design in mathematics and science education (pp. 197–230). Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Lorenz, J. H. (1994). Mathematically retarded and gifted students. In R. Biehler, R. Scholz, R. Straesser, & B. Winkelman (Eds.), Didactics of mathematics as a scientific discipline (pp. 291–302). Dordrecht, Kluwer: Academics Publishers.

    Google Scholar 

  • Lyons, M., & Lyons, R. (1989). Défi mathématique. Manuel de l’élève. 3-4-5-6. Laval: Mondia Editeurs Inc.

    Google Scholar 

  • Lyons, M., & Lyons, R. (2001–2002). Défi mathématique. Cahier de l’élève. 1-2-3-4. Montréal: Chenelière McGraw-Hill.

    Google Scholar 

  • Massey, C. (1895). Conference report of the froebel society of Great Britain and Ireland. Kindergarten Mag, 8(3), 157–170.

    Google Scholar 

  • Mingus, T., & Grassl, R. (1999). What constitutes a nurturing environment for the growth of mathematically gifted students? School Science and Mathematics, 99(6), 286–293.

    Article  Google Scholar 

  • National Research Council. (2009). Mathematics learnin in early childhood: Paths toward excellence and equity. Committee on early childhood mathematics. In C. T. Cross, T. A. Woods, & H. Schweingruber (Eds.), Center for education, division of behavioral and social sciences and education. Washington, DC: The National Academies Press.

    Google Scholar 

  • Piaget, J. (1972). The psychology of the child. New York: Basic Books.

    Google Scholar 

  • Piaget, J. (1985). Equilibration of cognitive structures: The central problem of intellectual development. University of Chicago Press.

    Google Scholar 

  • Pletan, M. D., Robinson, N. M., Berninger, V. W., & Abbott, R. D. (1995). Parents’ observations of kindergartners who are advanced in mathematical reasoning. Journal for the Education of the Gifted, 19, 30–44.

    Article  Google Scholar 

  • Resnick, L. B. (1983). A developmental theory of number understanding. In H. P. Ginsburg (Ed.), The development of mathematical thinking (pp. 110–152). Academy Press Inc.

    Google Scholar 

  • Ridge, L., & Renzulli, J. (1981). Teaching mathematics to the talented and gifted. In V. Glennon (Ed.), The Mathematical education of exceptional children and youth, an interdisciplinary approach (pp. 191–266). NCTM.

    Google Scholar 

  • Rosskopf, M. F. (1975). Children’s mathematical concepts: Six Piagetian studies. New York: Teachers College, Columbia University.

    Google Scholar 

  • Rotigel, J. V., & Fello, S. (2004). Mathematically gifted students: How can we meet their needs? Gifted Child Today, 27(46–51), 65.

    Google Scholar 

  • Shchedrovitskii, G. (1993). Pedagogic and logic. Moscow, Russia: Kastal (in Russian) [Щeдpoвицкий Г. П. и дp. Пeдaгoгикa и лoгикa — Mocквa, Кacтaль 1993].

    Google Scholar 

  • Sheffield, L. J. (1999). Serving the needs of the mathematically promising. In L. Sheffield (Ed.), Developing mathematically promising students (pp. 43–56). London: NCTM.

    Google Scholar 

  • Sierpinska, A. (1994). Understanding in mathematics. The Falmer Press.

    Google Scholar 

  • Singer, F. M., Sheffield, L. J., Freiman, V., & Brandl, M. (2016). Research on and activities for mathematically gifted students. ICME-13 Topical Survey. Dordrecht: Springer.

    Google Scholar 

  • Skwarchuk, S.-L., Vandermaas-Peeler, M., & LeFevre, J. A. (2016). Optimizing the home numeracy environments of three- to six-year-old children in the United States and Canada. In: B. Blevins-Knabe & A.-B. Austin (Eds.), Early childhood mathematics skill development in the home environment (pp. 127–146). Switzerland: Springer International Publishing.

    Google Scholar 

  • Stipek, D. (2004). Teaching practices in kindergarten and first grade: Different strokes for different folks. Early Childhood Research Quarterly, 19, 548–568.

    Article  Google Scholar 

  • Taylor, C. H. (2008). Promoting mathematical understanding through open-ended tasks; Experiences of an eighth-grade gifted geometry class. Dissertation, Georgia State University. Retrieved from http://scholarworks.gsu.edu/msit_diss/36.

  • Tirosh, D., & Graeber, A. (2003). Challenging and changing mathematics classroom practices. In A. Bishop, J. Kilpatrick, C. Keitel, & K. Clements (Eds.), International handbook of mathematics education (2nd ed., pp. 643–687). Dordrecht, The Netherlands: Kluwer.

    Google Scholar 

  • Wadlington, E., & Burns, J. M. (1993). Math instructional practices within preschool/kindergarten gifted programs. Journal for the Education of the Gifted, 17(1), 41–52.

    Article  Google Scholar 

  • Young, P., & Tyre, C. (1992). Gifted or able? Realising children’s potential. Open University Press.

    Google Scholar 

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Authors and Affiliations

  1. Université de Moncton, Moncton, Canada

    Viktor Freiman

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  1. Viktor Freiman
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Correspondence to Viktor Freiman .

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  1. Faculty of Letters and Science, Oil & Gas University of Ploiești, Ploiești, Romania

    Florence Mihaela Singer

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Freiman, V. (2018). Complex and Open-Ended Tasks to Enrich Mathematical Experiences of Kindergarten Students. In: Singer, F. (eds) Mathematical Creativity and Mathematical Giftedness. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-73156-8_14

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  • DOI: https://doi.org/10.1007/978-3-319-73156-8_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-73155-1

  • Online ISBN: 978-3-319-73156-8

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