Abstract
This study examines characteristics of mathematical giftedness in second graders. First, a possible system of characteristics was designed in theory. Then, this system was verified by giving a paper-and-pencil test with tasks developed for this purpose to 182 mathematically gifted children as well as 69 children of a reference group. In addition to the written tests, semi-structured interviews were conducted with all the participants regarding their results and strategies. The outcomes of the study show that all of the analyzed characteristics of mathematical giftedness can be confirmed. These include the ability to memorize mathematical issues by drawing on identified structures, the ability to construct and use mathematical structures, the ability to switch between modes of representation, the ability to reverse lines of thought, the ability to capture complex structures and work with them, the understanding of relational concepts and the ability to use relational concepts and connections.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
For this, the relevant parts of the interviews were transcribed.
- 2.
It should be mentioned that the described procedures after the test cannot be claimed to definitely correspond to the thinking processes during the study. This, however, applies to all attempts to reconstruct thinking processes and thus does not only concern this study.
References
Anderson, J. R. (2007). Kognitive Psychologie [Cognitive psychology] (6th ed.). Berlin, Heidelberg: Springer.
Assmus, D. (2016). Connections of working backwards and reversing lines of thought—Some theoretical considerations. In T. Fritzlar, D. Assmus, K. Bräuning, A. Kuzle, & B. Rott (Eds.), Problem solving in mathematics education. Proceedings of the 2015 Joint Conference of ProMath and the GDM Working Group on Problem Solving (pp. 33–39). Münster: WTM.
Assmus, D (2017). Mathematische Begabung im frühen Grundschulalter unter besonderer Berücksichtigung kognitiver Merkmale [Mathematical giftedness in the early primary grades with special consideration of cognitive characteristics]. Münster: WTM.
Assmus, D., & Förster, F. (2015). Analogical-reasoning abilities of mathematically gifted children—First results of the video study ViStAD. In F. M. Singer, F. Toader, & C. Voica (Eds.), Proceedings of the 9th International MCG Conference (pp. 154–159). Sinaia, Romania: MCG.
Assouline, S., & Lupkowski-Shoplik, A. (2005). Developing math talent. A guide for educating gifted and advanced learners in math. Waco: Prufrock Press.
Benbow, C. P., & Minor, L. L. (1990). Cognitive profiles of verbally and mathematically precocious students: Implications for identification of the gifted. Gifted Child Quarterly, 34(1), 21–26.
Benölken, R. (2015). “Mathe für kleine Asse”—An enrichment project at the University of Münster. In F. M. Singer, F. Toader, & C. Voica (Eds.), Proceedings of the 9th International MCG Conference (pp. 140–145). Sinaia, Romania: MCG.
Birx, E. (1988). Mathematik und Begabung. Evaluation eines Förderprogramms für mathematisch besonders befähigte Schüler [Mathematics and giftedness. Evaluation of a fostering program for pupils with high mathematical abilities]. Hamburg: Krämer.
Cohen, J. (1969). Statistical power analysis for the behavioral sciences. New York: Academic Press.
Fritz, A., & Ricken, G. (2008). Rechenschwäche [Dyscalculia]. München, Basel: E. Reinhardt.
Fritzlar, T. (2010). Gedankensplitter zum “Umkehren mentaler Prozesse” - gedacht zur Anregung weiterer Diskussionen [Aphorisms about “reversing of mental processes” - thought to stimulate further discussions]. In M. Nolte (Ed.), Was macht Mathematik aus? Nachhaltige paradigmatische Ansätze für die Förderung mathematisch begabter Schülerinnen und Schüler. Festschrift aus Anlass des 80. Geburtstages von Prof. Dr. Karl Kießwetter (pp. 27–39). Münster: WTM.
Fritzlar, T. (2013). Mathematische Begabungen (im jungen Schulalter) [Mathematical giftedness (in early grades)]. Beiträge zum Mathematikunterricht, 45–52.
Fuchs, M. (2006). Vorgehensweisen mathematisch potentiell begabter Dritt- und Viertklässler beim Problemlösen. empirische Untersuchungen zur Typisierung spezifischer Problembearbeitungsstile [Potentially mathematically gifted third- and fourth-graders in problem solving. Empirical studies to characterize specific problem-processing styles]. Berlin: LIT.
Fuchs, M., & Käpnick, F. (2004). Mathe für kleine Asse. Empfehlungen zur Förderung mathematisch interessierter und begabter Kinder im 1. und 2. Schuljahr [Maths for young talents. Recommendations for the fostering of mathematically interested and gifted children in the first and second school year]. Berlin: Cornelsen.
Gagné, F. (2003). Transforming gifts into talent: The DMGT as a developmental theory. In N. Colangelo, & G. A. Davis (Eds.), Handbook of gifted education (3rd ed., pp. 60–74). Boston: Allyn and Bacon.
Gawlick, T., & Lange, D. (2010). Allgemeine vs. mathematische Begabung bei Fünftklässlern [General vs. mathematical giftedness]. Beiträge zum Mathematikunterricht, 329–332.
Greenes, C. (1981). Identifying the gifted student in mathematics. Arithmetic Teacher, 28(6), 14–18.
Gullasch, R. (1973). Denkpsychologische Analysen mathematischer Fähigkeiten [Psychological analysis of mathematical abilities]. Berlin: Volk und Wissen.
Heilmann, K. (1999). Begabung - Leistung - Karriere. Die Preisträger im Bundeswettbewerb Mathematik 1971–1995 [Giftedness - Performance - Career. The prize winners of the “Bundeswettbewerb Mathematik” 1971–1995]. Göttingen, Bern, Toronto, Seattle: Hogrefe.
Heller, K. (2004). Identification of gifted and talented students. Psychology Science, 46(3), 302–323.
House, P. A. (1987). Providing opportunities for the mathematically gifted, K-12. Reston, VA: National Council of Teachers of Mathematics.
House, P. A. (1999). Promises, promises, promises. In L. J. Sheffield (Ed.), Developing mathematically promising students (pp. 1–7). Reston, VA: National Council of Teachers of Mathematics.
Käpnick, F. (1998). Mathematisch begabte Kinder [Mathematically gifted children]. Frankfurt am Main: Lang.
Kießwetter, K. (1985). Die Förderung von mathematisch besonders begabten und interessierten Schülern - ein bislang vernachlässigtes sonderpädagogisches Problem [The fostering of mathematically talented and interested pupils - a so far neglected special educational problem]. MNU, 38(5), 300–306.
Kontoyianni, K., Kattou, M., Pitta-Pantazi, D., & Christou, C. (2013). Integrating mathematical abilities and creativity in the assessment of mathematical giftedness. Psychological Test and Assessment Modeling, 55(3), 289–315.
Krajewski, K. (2008). Prävention der Rechenschwäche [Prevention of dyscalculia]. In W. Schneider, & M. Hasselhorn (Eds.), Handbuch der Pädagogischen Psychologie (pp. 360–370). Göttingen: Hogrefe.
Krutetskii, V. A. (1976). The psychology of mathematical abilities in schoolchildren. Chicago: University of Chicago Press.
Lubinski, D., & Humphreys, L. G. (1990). A broadly based analysis of mathematical giftedness. Intelligence, 14, 327–355.
Mayring, P. (2015). Qualitative Inhaltsanalyse. Grundlagen und Techniken [Qualitative content analysis. Basics and techniques] (12th ed.). Weinheim: Beltz.
Miller, R. C. (1990). Discovering mathematical talent. Eric Digest #E482. Available at http://www.eric.ed.gov/ERICWebPortal/contentdelivery/servlet/ERICServlet?accno=ED321487. Accessed 22 May 2017.
Mulligan, J. T., & Mitchelmore, M. (2009). Awareness of pattern and structure in early mathematical development. Mathematics Education Research Journal, 21(2), 33–49.
Mulligan, J. T., Mitchelmore, M., & Prescott, A. (2005). Case studies of children’s development of structure in early mathematics: A two-year longitudinal study. In H. L. Chick, & J. L. Vincent (Eds.), Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 1–8). Melbourne: PME.
Nolte, M. (2004). Der Mathe-Treff für Mathe-Fans. Fragen zur Talentsuche im Rahmen eines Forschungs- und Förderprojekts zu besonderen mathematischen Begabungen im Grundschulalter [The math-circle for math fans. Questions about scouting in the context of a research and development project for mathematical talent in primary grades]. Hildesheim: Franzbecker.
Nolte, M. (2013). “Du Papa, die interessieren sich für das, was ich denke!”. Zur Arbeit mit mathematisch besonders begabten Grundschulkindern [“Dad, they are interested in what I think!”. To work with mathematically talented primary school children]. In T. Trautmann, & W. Manke (Eds.), Begabung - Individuum - Gesellschaft. Begabtenförderung als pädagogische und gesellschaftliche Herausforderung (pp. 128–143). Weinheim, Basel: Beltz Juventa.
Nolte, M., & Kießwetter, K. (1996). Können und sollen mathematisch besonders befähigte Schüler schon in der Grundschule identifiziert und gefördert werden? Ein Bericht über einschlägige Überlegungen und erste Erfahrungen [Can and should mathematically particularly qualified students be identified and fostered in primary school? A report on relevant considerations and initial experiences]. ZDM Mathematics Education, 5, 143–157.
Primi, R., Ferrão, M. E., & Almeida, L. S. (2010). Fluid intelligence as a predictor of learning: A longitudinal multilevel approach applied to math. Learning and Individual Differences, 20, 446–451.
Sheffield, L. J. (2003). Extending the challenge in mathematics. Developing mathematical promise in K-8. Thousands Oaks, CA: Corvin Press.
Singer, F. M., Sheffield, L., Freiman, V., & Brandl, M. (2016). Research on and activities for mathematically gifted students. London: SpringerOpen.
Stacey, K. (1989). Finding and using patterns in linear generalising problems. Educational Studies in Mathematics, 20, 147–164.
Stern, E. (1998). Die Entwicklung des mathematischen Verständnisses im Kindesalter [The development of mathematical understanding in childhood]. Lengerich: Pabst Science Publishers.
Taub, G. E., Floyd, R. G., Keith, T. Z., & McGrew, K. S. (2008). Effects of general and broad cognitive abilities on mathematics achievement. School Psychology Quaterly, 23(2), 187–198.
van der Meer, E. (1985). Mathematisch-naturwissenschaftliche Hochbegabung [Giftedness in mathematics and in natural sciences]. Zeitschrift für Psychologie, 193(3), 229–258.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this chapter
Cite this chapter
Assmus, D. (2018). Characteristics of Mathematical Giftedness in Early Primary School Age. In: Singer, F. (eds) Mathematical Creativity and Mathematical Giftedness. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-73156-8_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-73156-8_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-73155-1
Online ISBN: 978-3-319-73156-8
eBook Packages: EducationEducation (R0)