Abstract
One approach to identifying mathematical talent in students is to work with complex word problems, the solution of which can be influenced by the nature of the problems and different talent profiles. The study focuses on how these factors influence the identification of mathematically gifted students in the 5th grade of primary school. The aim was (1) to determine the degree of correlation between three methods of identifying talent–teacher assessment, standardized test results and research didactic test results – and (2) to identify tasks that best distinguish gifted students from others. The research test included five subtests, four algebraic and one combinatorial, focused on manifestations typical of gifted students, such as flexibility of thinking, ability to generalize and creativity in problem solving. The study emphasizes the analysis of the subtest with tasks of the “I think of a number” type, which allow to reveal hidden manifestations of talent and contribute to its more accurate diagnosis. The research involved 45 students from a school focused on supporting the gifted. The pilot nature of the study is intended to serve as a basis for the creation of a standardized test for students in grades 5–7. The results show a moderate to strong correlation between the methods used, but also the existence of phenomena that may lead to the overlooking of mathematically gifted students.
References
Adetula, L. O. (1990). Language factor: Does it affect children’s performance on word problems? Educational Studies in Mathematics, 21, 351–365.
Alexander, J. M., Carr, M., & Schwanenflugel, P. J. (1995). Development of metacognition in gifted children: Directions for future research. Developmental Review, 15(1), 1–37. https://doi.org/10.1006/drev.1995.1001
Betts, G. T., & Neihart, M. (1988). Profiles of the gifted and talented. Gifted Child Quarterly, 32(2), 248–253. https://doi.org/10.1177/001698628803200202
Bloom, B. S. (1956). Taxonomy of educational objectives: The classification of educational goals. Handbook 1: Cognitive domain. McKay.
Boonen, A. J., de Koning, B. B., Jolles, J., & Van der Schoot, M. (2016). Word problem solving in contemporary math education: A plea for reading comprehension skills training. Frontiers in Psychology, 7, Article 191. https://doi.org/10.3389/fpsyg.2016.00191
Bransford, J. D., Brown, A. L., & Cocking, R. R. (Eds.) (2004). How people learn. National Academy Press.
Brown, A. (1987). Metacognition, executive control, self-regulation, and other more mysterious mechanisms. In F. E. Weinert & R. H. Kluwe (Eds.), Metacognition, motivation and understanding (pp. 65–116). Erlbaum.
Budínová, I. (2018). Přístupy nadaných žáků 1. a 2. stupně základní školy k řešení některých typů úloh v matematice. Muni Press. https://doi.org/10.5817/CZ.MUNI.M210-9216-2018
Budínová, I. (2025). Word problems with Diophantine equations solved by gifted 5th grade elementary school pupils. In J. Novotná & H. Moraová (Eds.), International symposium elementary mathematics teaching. Elementary mathematics: Building strong foundations (pp. 86–94). Charles University, Faculty of Education.
Cígler, H., Jabůrek, M., Straka, H., & Portešová, Š. (2017). Test pro identifikaci nadaných žáků v matematice TIM 3–5. Masarykova univerzita. https://www.nadanedeti.cz/testy-matematicky-test-tim
Cummins, D. D., Kintsch, W., Reusser, K., & Weimer, R. (1988). The role of understanding in solving word problems. Cognitive Psychology, 20(4), 405–438. https://doi.org/10.1016/0010-0285(88)90011-4
Fořtík, V. & Fořtíková, J. (2007). Nadané dítě a rozvoj jeho schopností. Portál.
ČŠI (2022). Podpora vzdělávání nadaných a mimořádně nadaných žáků v základních a středních školách. https://www.csicr.cz/cz/Aktuality/Tematicka-zprava-%E2%80%93-Podpora-vzdelavani-nadanych-a-m
Gagné, F. (2005). From gifts to talents. The DMGT as a developmental model. In R. J. Sternberg & J. E. Davidson (Eds.), Conceptions of giftedness (pp. 98–119). Cambridge University Press. https://doi.org/10.1017/CBO9780511610455.008
Gardner, H. (2006). Multiple intelligences: New horizons in theory and practice. Perseus Books.
Gutiérrez, A., Benedicto, C., Jaime, A., & Arbona, E. (2018). The cognitive demand of a gifted student’s answers to geometric pattern problems: Analysis of key moments in a pre-algebra teaching sequence. In F. M. Singer (Ed.), Mathematical creativity and mathematical giftedness (ICME-13 Monographs) (pp. 169–198). Springer. https://doi.org/10.1007/978-3-319-73156-8 7
Hadamard, J. (1945). An essay on the psychology of invention in the mathematical field. Dover Publication.
Havigerová, J. M. (2011). Pět pohledů na nadání. Grada.
Hendl, J. (2012). Přehled statistických metod: analýza a metaanalýza dat. Portál.
Hříbková, L. (2009). Nadání a nadaní. Grada.
Jabůrek, M., Cígler, H., Valešová, T., & Portešová, Š. (2022). What is the basis of teacher judgment of student cognitive abilities and academic achievement and what affects its accuracy? Contemporary Educational Psychology, 69, 1–16. https://doi.org/10.1016/j.cedpsych.2022.102068
Krathwohl, D. R. (2002). A revision of Bloom’s taxonomy: An overview. Theory into practice, 41(4), 212–218. https://doi.org/10.1207/s15430421tip4104 2
Krutetskii, V. A. (1976). The psychology of mathematical abilities in schoolchildren. University of Chicago Press.
Liljedahl, P., Santos-Trigo, M., Malaspina, U., & Bruder, R. (2016). Problem solving in mathematics education. ICME-13 Topical Surveys. Springer. https://doi.org/10.1007/978-3-319-40730-2 1
Lithner, J. (2017). Principles for designing mathematical tasks that enhance imitative and creative reasoning. ZDM, 49(6), 937–949. https://doi.org/10.1007/s11858-017-0867-3
Machů, E., Kočvarová, I., Císlerová, T., & Vápeník, P. (2013). Kvalita školy z hlediska péče o nadané žáky. Univerzita Tomáše Bati ve Zlíně.
McBee, M. T., & Makel, M. C. (2019). The quantitative implications of definitions of giftedness. AERA Open, 5(1). https://doi.org/10.1177/2332858419831007
Ministerstvo školství, mládeže a tělovýchovy. (2024). Statistická ročenka školství – výkonové ukazatele 2023/24. https://statis.msmt.cz/rocenka/rocenka.asp
Nathan, M. J., Kintsch, W., & Young, E. (1992). A theory of algebra-word- problem comprehension and its implications for the design of learning environments. Cognition and Instruction, 9, 329–389. https://doi.org/10.1207/s1532690xci0904 2
Portešová, Š. (2011). Rozumově nadané děti s dyslexií. Portál.
Portešová, Š., Poledňová, I., Macek, D., Růžička, M., Straka, O., & Urmanová, J. (2014). Rozumově nadaní studenti s poruchou učení. Masarykova univerzita.
Renzulli, J. S. (1978). What makes giftedness? Reexamining a definition. Phi Delta Kappan, 60(3), 180–184.
Renzulli, J. S. (2005). Equity, excellence, and economy in a system for identifying students in gifted education: A guidebook (RM 05208). University of Connecticut, National Research Center on the Gifted and Talented.
Sternberg, R. J., & Williams, W. M. (2002). Educational psychology. Allyn & Bacon.
Straka, O. (2021). Jak měřit metakognici (nejen) u nadaných dětí. Masarykova univerzita. https://doi.org/10.5817/CZ.MUNI.M210-9905-2021
Straker, A. (1980). Identification of mathematically gifted pupils. Mathematics in School, 9(4), 4–8.
Szabo, A., Tillnert, A. S., & Mattsson, J. (2024). Displaying gifted students’ mathematical reasoning during problem solving: Challenges and possibilities. The Mathematics Enthusiast, 21(1), 179–202. https://doi.org/10.54870/1551-3440.1623
Tannenbaum, A. J., & Baldwin, L. J. (1983). Giftedness and learning disability: A paradoxical combination. In L. H. Fox, L. Brody & D. Tobin (Eds.), Learning disabled/gifted children: Identification and programming (pp. 11–36). University Park Press.
Vondrová, N. (2020). Didaktika matematiky jako nástroj zvládání kritických míst. Pedagogická fakulta, Univerzita Karlova.
Vondrová, N., Havlíčková, R., Hirschová, M., Chvál, M., Novotná, J., Páchová, A., Smetáčková, I., Šmejkalová, M., & Tůmová, V. (2019). Matematická slovní úloha. Mezi matematikou, jazykem a psychologií. Karolinum.
Warne, R. T. (2012). History and development of above-level testing of the gifted. Roeper Review, 34(3), 183–193. https://doi.org/10.1080/02783193.2012.686425
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