Research Article
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Reflections from the generalization strategies used by gifted students in the growing geometric pattern task

Year 2022, Volume 9, Issue 4, 369 - 385, 30.12.2022

Abstract

One of the cognitive characters emphasized by different researchers in mathematically gifted students is generalization of mathematical structures and patterns. In particular, experience with growing geometric patterns is important for initiating and developing algebraic thinking. In this context, this study aimed to explore the generalization strategies used by gifted students in the growing geometric pattern task. The study was designed in a case study. The participants of the study are five eighth grade students who were diagnosed as gifted through diagnostic tests. The data of the study were collected with the "Geometric Pattern Task Form" consisting of open-ended problems. The geometric pattern task consists of linear and quadratic patterns. Data were collected by task-based interview method and analyzed with thematic analysis. The results of the study show that gifted students exhibit figural and numerical approaches while solving pattern problems. In particular, for quadratic (non-linear) pattern, gifted students used functional strategy in all problems of finding near, far terms, and general rule of pattern. However, in the problems of finding the number of white balls (linear pattern), different strategies (e.g., recursive, chunking, contextual) than the functional strategy were also used. Based on the results of the study, it is suggested that geometric pattern tasks involving linear and non-linear relationships may be centralized in the development of functional thinking and generalization skills of gifted students in classroom practices.

References

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  • Amit, M., & Neria, D. (2008). Rising to the challenge: Using generalization in pattern problems to unearth the algebraic skills of talented prealgebra students. ZDM-Mathematics Education, 40(1), 111–129. https://doi.org/10.1007/S11858-007-0069-5
  • Arbona, E., Beltrán-Meneu, M. J., & Gutiérrez, Á. (2019). Strategies exhibited by good and average solvers of geometric pattern problems as source of traits of mathematical giftedness in grades 4-6. Eleventh Congress of the European Society for Research in Mathematics Education, Utrecht, The Netherlands.
  • Assmus, D., & Fritzlar, T. (2022). Mathematical creativity and mathematical giftedness in primary school age-An interview study on creating figural patterns. ZDM-Mathematics Education, 54, 113–131. https://doi.org/10.1007/s11858-022-01328-8
  • Benedicto, C., Jaime, A., & Gutiérrez, A. (2015). Análisis de la demanda cognitiva de problemas de patrones geométricos. In C. Fernández, M. Molina, & N. Planas (Eds.), Investigación en educación matemática XIX (pp. 153–162). SEIEM.
  • Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3(2), 77–101. https://doi.org/10.1191/1478088706qp063oa
  • Cai, J. (2003). Singaporean students' mathematical thinking in problem solving and problem posing: An exploratory study. International Journal of Mathematical Education in Science and Technology, 34(5), 719-737.
  • Chua, B. L., & Hoyles, C. (2014a). Generalisation of linear figural patterns in secondary school mathematics. The Mathematics Educator, 15(2), 1–30.
  • Chua, B. L., & Hoyles, C. (2014b). Modalities of rules and generalising strategies of Year 8 students for a quadratic pattern. In C. Nicol, P. Liljedahl, S. Oesterle & D. Allan (Eds.), Proceedings of the joint meeting of PME 38 and PME-NA 36 (Vol. 2, pp. 305–312). Vancouver, Canada: PME.
  • Dayan, S. (2017). The examination of gifted and normal students' mathematical pattern achievements (Unpublished master's thesis). Abant Izzet Baysal University.
  • El Mouhayar, R., & Jurdak, M. (2015). Variation in strategy use across grade level by pattern generalization types. International Journal of Mathematical Education in Science and Technology, 46(4), 553–569. https://doi.org/10.1080/0020739X.2014.985272
  • Eraky, A., Leikin, R., & Hadad, B. S. (2022). Relationships between general giftedness, expertise in mathematics, and mathematical creativity that associated with pattern generalization tasks in different representations. Asian Journal for Mathematics Education, 1(1), 36-51.
  • Friel, S. N., & Markworth, K. A. (2009). A framework for analyzing geometric pattern tasks. Mathematics Teaching in the Middle School, 15(1), 24–33.
  • Girit-Yildiz, D., & Durmaz, B. (2021). A gifted high school student’s generalization strategies of linear and nonlinear patterns via Gauss’s approach. Journal for the Education of the Gifted, 44(1), 56-80. https://doi.org/10.1177/0162353220978295
  • Goldin, G. A. (2000). A scientific perspective on structured, task-based interviews in mathematics education research. In A. E. Kelly & R. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 517–546). Lawrence Erlbaum.
  • Greenes, C. (1981). Identifying the gifted student in mathematics. Arithmetic Teacher, 28, 14–18.
  • Gutiérrez, A., Benedicto, C., Jaime, A., & Arbona, E. (2018). The cognitive demand of a gifted student’s answers to geometric pattern problems. In F. M. Singer (Ed.), Mathematical creativity and mathematical giftedness (pp. 196-198). Springer International Publishing.
  • Kidd, J., Lyu, H., Peterson, M., Hassan, M., Gallington, D., Strauss, L., Patterson, A., & Pasnak, R. (2019). Patterns, mathematics, early literacy, and executive functions. Creative Education, 10(13), 3444–3468. https://doi.org/10.4236/ce.2019.1013266
  • Kieran, C. (2022). The multi-dimensionality of early algebraic thinking: background, overarching dimensions, and new directions. ZDM–Mathematics Education, 54, 1131–1150. https://doi.org/10.1007/s11858-022-01435-6
  • Krutetskii, V. A. (1976). The psychology of mathematical abilities in schoolchildren. University of Chicago Press.
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  • Leikin R. (2018). Giftedness and high ability in mathematics. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 247-251). Springer, Cham. https://doi.org/10.1007/978-3-319-77487-9_ 65-4
  • Leikin, R. (2021). When practice needs more research: the nature and nurture of mathematical giftedness. ZDM-Mathematics Education, 53, 1579–1589. https://doi.org/10.1007/s11858-021-01276-9
  • Leikin, R., Koichu, B., Berman, A., & Dinur, S. (2017). How are questions that students ask in high level mathematics classes linked to general giftedness? ZDM-Mathematics Education, 49(1), 65-80. https://doi.org/10.1007/s11858-016-0815-7
  • Leikin, R., & Sriraman, B. (2022). Empirical research on creativity in mathematics (education): From the wastelands of psychology to the current state of the art. ZDM-Mathematics Education, 54(1), 1–17. https://doi.org/10.1007/s11858-022-01340-y
  • Lobato, J., Hohensee, C., & Rhodehamel, B. (2013). Students’ mathematical noticing. Journal for Research in Mathematics Education, 44(5), 809–850.
  • Lobato, J., Hohensee, C., Rhodehamel, B., & Diamond, J. (2012). Using student reasoning to inform the development of conceptual learning goals: The case of quadratic functions. Mathematical Thinking and Learning, 14(2), 85–119. https:// doi. org/ 10. 1080/ 10986 065. 2012. 656362
  • Lüken, M. M., Peter-Koop, A., & Kollhoff, S. (2014). Influence of early repeating patterning ability on school mathematics learning. In P. Liljedahl, S. Oesterle, C. Nicol, & D. Allan (Eds.), Proceedings of the Joint Meeting of PME 38 and PME-NA 36 (Vol. 4, pp. 137–144). PME.
  • MacKay, K., & De Smedt, B. (2019). Patterning counts: Individual differences in children’s calculation are uniquely predicted by sequence patterning. Journal of Experimental Child Psychology, 177, 152–165. https://doi.org/10.1016/j. jecp.2018.07.016
  • Maher, C. A., & Sigley, R. (2014). Task-based interviews in mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 579–582). Springer.
  • Markworth, K. A. (2010). Growing and growing: Promoting functional thinking with geometric growing patterns. (Unpublished doctoral dissertation), University of North Carolina at Chapel Hill. Available from ERIC (ED519354).
  • Mason, J. (1996). Expressing generality and roots of algebra. In N. Bednarz, C. Kieran & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 65 - 86). Kluwer Academic Publishers.
  • Mason, J., Graham, A., & Johnston-Wilder, S. (2005). Developing thinking in algebra. The Open University y Paul Chapman Publishing.
  • Merriam, S. B., & Tisdell, E. J. (2015). Qualitative research: A guide to design and implementation. John Wiley & Sons.
  • Montenegro, P., Costa, C., & Lopes, B. (2018). Transformations in the visual representation of a figural pattern. Mathematical Thinking and Learning, 20(2), 91–107. https://doi.org/10.1080/10986065.2018.1441599
  • Mulligan, J., & Mitchelmore, M. (2009). Awareness of pattern and structure in early mathematical development. Mathematics Education Research Journal, 21(2), 33–49. https://doi.org/10. 1007/BF03217544
  • Nolte, M., & Pamperien, K. (2017). Challenging problems in a regular classroom setting and in a special foster programme. ZDM-Mathematics Education, 49(1), 121–136.
  • Ozturk, M., Akkan, Y., & Kaplan, A. (2018). The metacognitive skills performed by 6th-8th grade gifted students during the problem-solving process: Gumushane sample. Ege Journal of Education, 19(2), 446-469. https://doi.org/10.12984/egeefd.316662
  • Patton, M. Q. (1990). Qualitative evaluation and research methods (2nd ed.). Sage.
  • Paz-Baruch, N., Leikin, M., & Leikin, R. (2022). Not any gifted is an expert in mathematics and not any expert in mathematics is gifted. Gifted and Talented International, 37(1), 25-41. https://doi.org/10.1080/15332276.2021.2010244
  • Pitta-Pantazi, D. (2017). What have we learned about giftedness and creativity? An overview of a five years journey. In Leikin, R., Sriraman, B. (Eds.), Creativity and giftedness. Advances in mathematics education. Springer, Cham. https://doi.org/10.1007/978-3-319-38840-3_13
  • Radford, L. (2010). Algebraic thinking from a cultural semiotic perspective. Research in Mathematics Education, 12(1), 1–19. https://doi.org/10.1080/14794800903569741
  • Radford, L. (2018). The emergence of symbolic algebraic thinking in primary school. In C. Kieran (Ed.), Teaching and learning algebraic thinking with 5- to 12-year-olds (pp. 3–25). Springer.
  • Radford, L., Bardini, C., & Sabena, C. (2007). Perceiving the general: the multisemiotic dimension of students’ algebraic activity. Journal for Research in Mathematics Education, 38(5), 507–530.
  • Ramírez, R., Cañadas, M. C., & Damián, A. (2022). Structures and representations used by 6th graders when working with quadratic functions. ZDM-Mathematics Education, 54(6). https://doi.org/10.1007/s11858-022-01423-w
  • Renzulli, J. S. (1978). What makes giftedness? Reexamining a definition. Phi Delta Kappan, 60(3), 180–184
  • Rivera, F. (2010). Visual templates in pattern generalization activity. Educational Studies in Mathematics, 73(3), 297–328.
  • Rivera, F. D., & Becker, J. R. (2005). Figural and numerical modes of generalizing in algebra. Mathematics Teaching in the Middle School, 11(4), 198–203.
  • Rivera, F. D., & Becker, J. R. (2008). Middle school children’s cognitive perceptions of constructive and deconstructive generalizations involving linear figural patterns. ZDM-Mathematics Education, 40(1), 65–82.
  • Rivera, F. D., & Becker, J. R. (2011). Formation of pattern generalization involving linear figural patterns among middle school students: results of a three-year study. In J. Cai & E. Knuth (Eds.), Early algebraization: a global dialogue from multiple perspectives (pp. 277–301). Springer.
  • Singer, F. M., Sheffield, L. J., Freiman, V., & Brandl, M. (2016). Research on and activities for mathematically gifted students. Springer Nature.
  • Singer, F. M., & Voica, C. (2022). Playing on patterns: is it a case of analogical transfer? ZDM-Mathematics Education, 54(1), 211–229. https://doi.org/10.1007/s11858-022-01334-w
  • Smith, E. (2008). Representational thinking as a framework for introducing functions in the elementary curriculum. In J. L. Kaput, D. W. Carraher, & M. L. Blanton (Eds.), Algebra in the early grades (pp. 133-160). Taylor & Francis Group.
  • Sriraman, B. (2003). Mathematical giftedness, problem solving, and the ability to formulate generalizations: The problem-solving experiences of four gifted students. Journal of Secondary Gifted Education, 14(3), 151-165.
  • Stacey, K. (1989). Finding and using patterns in linear generalising problems. Educational Studies in Mathematics, 20(2), 147-164.
  • Steele, D. (2008). Seventh-grade students’ representations for pictorial growth and change problems. ZDM- Mathematics Education, 40(1), 97–110.
  • Steen, L. A. (1988). The Science of patterns. Science, 240(4852), 611-616. https://doi.org/10.1126/science.240.4852.611
  • Sternberg, R. J., Chowkase, A., Desmet, O., Karami, S., Landy, J., & Lu, J. (2021). Beyond transformational giftedness. Education Sciences, 11(5), 192. https://doi.org/10.3390/educsci11050192
  • Sternberg, R. J., & Davidson, J. E. (Eds.). (1986). Conceptions of giftedness. Cambridge University Press.
  • Sternberg, R. J., & Grigorenko, E. L. (2004). Successful intelligence in the classroom. Theory Into Practice, 43(4), 274–280.
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Year 2022, Volume 9, Issue 4, 369 - 385, 30.12.2022

Abstract

References

  • Akkan, Y., & Cakıroglu, U. (2012). Generalization strategies of linear and quadratic pattern: a comparison of 6th-8th grade students. Education and Science, 37(165), 104-120.
  • Amit, M., & Neria, D. (2008). Rising to the challenge: Using generalization in pattern problems to unearth the algebraic skills of talented prealgebra students. ZDM-Mathematics Education, 40(1), 111–129. https://doi.org/10.1007/S11858-007-0069-5
  • Arbona, E., Beltrán-Meneu, M. J., & Gutiérrez, Á. (2019). Strategies exhibited by good and average solvers of geometric pattern problems as source of traits of mathematical giftedness in grades 4-6. Eleventh Congress of the European Society for Research in Mathematics Education, Utrecht, The Netherlands.
  • Assmus, D., & Fritzlar, T. (2022). Mathematical creativity and mathematical giftedness in primary school age-An interview study on creating figural patterns. ZDM-Mathematics Education, 54, 113–131. https://doi.org/10.1007/s11858-022-01328-8
  • Benedicto, C., Jaime, A., & Gutiérrez, A. (2015). Análisis de la demanda cognitiva de problemas de patrones geométricos. In C. Fernández, M. Molina, & N. Planas (Eds.), Investigación en educación matemática XIX (pp. 153–162). SEIEM.
  • Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3(2), 77–101. https://doi.org/10.1191/1478088706qp063oa
  • Cai, J. (2003). Singaporean students' mathematical thinking in problem solving and problem posing: An exploratory study. International Journal of Mathematical Education in Science and Technology, 34(5), 719-737.
  • Chua, B. L., & Hoyles, C. (2014a). Generalisation of linear figural patterns in secondary school mathematics. The Mathematics Educator, 15(2), 1–30.
  • Chua, B. L., & Hoyles, C. (2014b). Modalities of rules and generalising strategies of Year 8 students for a quadratic pattern. In C. Nicol, P. Liljedahl, S. Oesterle & D. Allan (Eds.), Proceedings of the joint meeting of PME 38 and PME-NA 36 (Vol. 2, pp. 305–312). Vancouver, Canada: PME.
  • Dayan, S. (2017). The examination of gifted and normal students' mathematical pattern achievements (Unpublished master's thesis). Abant Izzet Baysal University.
  • El Mouhayar, R., & Jurdak, M. (2015). Variation in strategy use across grade level by pattern generalization types. International Journal of Mathematical Education in Science and Technology, 46(4), 553–569. https://doi.org/10.1080/0020739X.2014.985272
  • Eraky, A., Leikin, R., & Hadad, B. S. (2022). Relationships between general giftedness, expertise in mathematics, and mathematical creativity that associated with pattern generalization tasks in different representations. Asian Journal for Mathematics Education, 1(1), 36-51.
  • Friel, S. N., & Markworth, K. A. (2009). A framework for analyzing geometric pattern tasks. Mathematics Teaching in the Middle School, 15(1), 24–33.
  • Girit-Yildiz, D., & Durmaz, B. (2021). A gifted high school student’s generalization strategies of linear and nonlinear patterns via Gauss’s approach. Journal for the Education of the Gifted, 44(1), 56-80. https://doi.org/10.1177/0162353220978295
  • Goldin, G. A. (2000). A scientific perspective on structured, task-based interviews in mathematics education research. In A. E. Kelly & R. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 517–546). Lawrence Erlbaum.
  • Greenes, C. (1981). Identifying the gifted student in mathematics. Arithmetic Teacher, 28, 14–18.
  • Gutiérrez, A., Benedicto, C., Jaime, A., & Arbona, E. (2018). The cognitive demand of a gifted student’s answers to geometric pattern problems. In F. M. Singer (Ed.), Mathematical creativity and mathematical giftedness (pp. 196-198). Springer International Publishing.
  • Kidd, J., Lyu, H., Peterson, M., Hassan, M., Gallington, D., Strauss, L., Patterson, A., & Pasnak, R. (2019). Patterns, mathematics, early literacy, and executive functions. Creative Education, 10(13), 3444–3468. https://doi.org/10.4236/ce.2019.1013266
  • Kieran, C. (2022). The multi-dimensionality of early algebraic thinking: background, overarching dimensions, and new directions. ZDM–Mathematics Education, 54, 1131–1150. https://doi.org/10.1007/s11858-022-01435-6
  • Krutetskii, V. A. (1976). The psychology of mathematical abilities in schoolchildren. University of Chicago Press.
  • Lannin, J, Barker, D., &Townsend B. (2006). Algebraic generalization strategies: factors influencing student strategy selection. Mathematics Education Research Journal, 18(3), 3-28.
  • Leikin R. (2018). Giftedness and high ability in mathematics. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 247-251). Springer, Cham. https://doi.org/10.1007/978-3-319-77487-9_ 65-4
  • Leikin, R. (2021). When practice needs more research: the nature and nurture of mathematical giftedness. ZDM-Mathematics Education, 53, 1579–1589. https://doi.org/10.1007/s11858-021-01276-9
  • Leikin, R., Koichu, B., Berman, A., & Dinur, S. (2017). How are questions that students ask in high level mathematics classes linked to general giftedness? ZDM-Mathematics Education, 49(1), 65-80. https://doi.org/10.1007/s11858-016-0815-7
  • Leikin, R., & Sriraman, B. (2022). Empirical research on creativity in mathematics (education): From the wastelands of psychology to the current state of the art. ZDM-Mathematics Education, 54(1), 1–17. https://doi.org/10.1007/s11858-022-01340-y
  • Lobato, J., Hohensee, C., & Rhodehamel, B. (2013). Students’ mathematical noticing. Journal for Research in Mathematics Education, 44(5), 809–850.
  • Lobato, J., Hohensee, C., Rhodehamel, B., & Diamond, J. (2012). Using student reasoning to inform the development of conceptual learning goals: The case of quadratic functions. Mathematical Thinking and Learning, 14(2), 85–119. https:// doi. org/ 10. 1080/ 10986 065. 2012. 656362
  • Lüken, M. M., Peter-Koop, A., & Kollhoff, S. (2014). Influence of early repeating patterning ability on school mathematics learning. In P. Liljedahl, S. Oesterle, C. Nicol, & D. Allan (Eds.), Proceedings of the Joint Meeting of PME 38 and PME-NA 36 (Vol. 4, pp. 137–144). PME.
  • MacKay, K., & De Smedt, B. (2019). Patterning counts: Individual differences in children’s calculation are uniquely predicted by sequence patterning. Journal of Experimental Child Psychology, 177, 152–165. https://doi.org/10.1016/j. jecp.2018.07.016
  • Maher, C. A., & Sigley, R. (2014). Task-based interviews in mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 579–582). Springer.
  • Markworth, K. A. (2010). Growing and growing: Promoting functional thinking with geometric growing patterns. (Unpublished doctoral dissertation), University of North Carolina at Chapel Hill. Available from ERIC (ED519354).
  • Mason, J. (1996). Expressing generality and roots of algebra. In N. Bednarz, C. Kieran & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 65 - 86). Kluwer Academic Publishers.
  • Mason, J., Graham, A., & Johnston-Wilder, S. (2005). Developing thinking in algebra. The Open University y Paul Chapman Publishing.
  • Merriam, S. B., & Tisdell, E. J. (2015). Qualitative research: A guide to design and implementation. John Wiley & Sons.
  • Montenegro, P., Costa, C., & Lopes, B. (2018). Transformations in the visual representation of a figural pattern. Mathematical Thinking and Learning, 20(2), 91–107. https://doi.org/10.1080/10986065.2018.1441599
  • Mulligan, J., & Mitchelmore, M. (2009). Awareness of pattern and structure in early mathematical development. Mathematics Education Research Journal, 21(2), 33–49. https://doi.org/10. 1007/BF03217544
  • Nolte, M., & Pamperien, K. (2017). Challenging problems in a regular classroom setting and in a special foster programme. ZDM-Mathematics Education, 49(1), 121–136.
  • Ozturk, M., Akkan, Y., & Kaplan, A. (2018). The metacognitive skills performed by 6th-8th grade gifted students during the problem-solving process: Gumushane sample. Ege Journal of Education, 19(2), 446-469. https://doi.org/10.12984/egeefd.316662
  • Patton, M. Q. (1990). Qualitative evaluation and research methods (2nd ed.). Sage.
  • Paz-Baruch, N., Leikin, M., & Leikin, R. (2022). Not any gifted is an expert in mathematics and not any expert in mathematics is gifted. Gifted and Talented International, 37(1), 25-41. https://doi.org/10.1080/15332276.2021.2010244
  • Pitta-Pantazi, D. (2017). What have we learned about giftedness and creativity? An overview of a five years journey. In Leikin, R., Sriraman, B. (Eds.), Creativity and giftedness. Advances in mathematics education. Springer, Cham. https://doi.org/10.1007/978-3-319-38840-3_13
  • Radford, L. (2010). Algebraic thinking from a cultural semiotic perspective. Research in Mathematics Education, 12(1), 1–19. https://doi.org/10.1080/14794800903569741
  • Radford, L. (2018). The emergence of symbolic algebraic thinking in primary school. In C. Kieran (Ed.), Teaching and learning algebraic thinking with 5- to 12-year-olds (pp. 3–25). Springer.
  • Radford, L., Bardini, C., & Sabena, C. (2007). Perceiving the general: the multisemiotic dimension of students’ algebraic activity. Journal for Research in Mathematics Education, 38(5), 507–530.
  • Ramírez, R., Cañadas, M. C., & Damián, A. (2022). Structures and representations used by 6th graders when working with quadratic functions. ZDM-Mathematics Education, 54(6). https://doi.org/10.1007/s11858-022-01423-w
  • Renzulli, J. S. (1978). What makes giftedness? Reexamining a definition. Phi Delta Kappan, 60(3), 180–184
  • Rivera, F. (2010). Visual templates in pattern generalization activity. Educational Studies in Mathematics, 73(3), 297–328.
  • Rivera, F. D., & Becker, J. R. (2005). Figural and numerical modes of generalizing in algebra. Mathematics Teaching in the Middle School, 11(4), 198–203.
  • Rivera, F. D., & Becker, J. R. (2008). Middle school children’s cognitive perceptions of constructive and deconstructive generalizations involving linear figural patterns. ZDM-Mathematics Education, 40(1), 65–82.
  • Rivera, F. D., & Becker, J. R. (2011). Formation of pattern generalization involving linear figural patterns among middle school students: results of a three-year study. In J. Cai & E. Knuth (Eds.), Early algebraization: a global dialogue from multiple perspectives (pp. 277–301). Springer.
  • Singer, F. M., Sheffield, L. J., Freiman, V., & Brandl, M. (2016). Research on and activities for mathematically gifted students. Springer Nature.
  • Singer, F. M., & Voica, C. (2022). Playing on patterns: is it a case of analogical transfer? ZDM-Mathematics Education, 54(1), 211–229. https://doi.org/10.1007/s11858-022-01334-w
  • Smith, E. (2008). Representational thinking as a framework for introducing functions in the elementary curriculum. In J. L. Kaput, D. W. Carraher, & M. L. Blanton (Eds.), Algebra in the early grades (pp. 133-160). Taylor & Francis Group.
  • Sriraman, B. (2003). Mathematical giftedness, problem solving, and the ability to formulate generalizations: The problem-solving experiences of four gifted students. Journal of Secondary Gifted Education, 14(3), 151-165.
  • Stacey, K. (1989). Finding and using patterns in linear generalising problems. Educational Studies in Mathematics, 20(2), 147-164.
  • Steele, D. (2008). Seventh-grade students’ representations for pictorial growth and change problems. ZDM- Mathematics Education, 40(1), 97–110.
  • Steen, L. A. (1988). The Science of patterns. Science, 240(4852), 611-616. https://doi.org/10.1126/science.240.4852.611
  • Sternberg, R. J., Chowkase, A., Desmet, O., Karami, S., Landy, J., & Lu, J. (2021). Beyond transformational giftedness. Education Sciences, 11(5), 192. https://doi.org/10.3390/educsci11050192
  • Sternberg, R. J., & Davidson, J. E. (Eds.). (1986). Conceptions of giftedness. Cambridge University Press.
  • Sternberg, R. J., & Grigorenko, E. L. (2004). Successful intelligence in the classroom. Theory Into Practice, 43(4), 274–280.
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Details

Primary Language English
Subjects Education and Educational Research
Published Date December 2022
Journal Section Thinking Skills at Gifted Education
Authors

Fatma ERDOĞAN> (Primary Author)
FIRAT UNIVERSITY, FACULTY OF EDUCATION
0000-0002-4498-8634
Türkiye


Neslihan GÜL>
Elazığ Bilim ve Sanat Merkezi
0000-0003-2137-0206
Türkiye

Publication Date December 30, 2022
Published in Issue Year 2022, Volume 9, Issue 4

Cite

APA Erdoğan, F. & Gül, N. (2022). Reflections from the generalization strategies used by gifted students in the growing geometric pattern task . Journal of Gifted Education and Creativity , 9 (4) , 369-385 . Retrieved from https://dergipark.org.tr/en/pub/jgedc/issue/74010/1223156

Sponsorship: Journal of Gifted Education and Creativity supported by Association for Young Scientists and Talent Education and International Congress on Gifted Youth and Sustainability of the Education

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Journal of Gifted Education and Creativity indexed in DOAJ since March 15, 2020. 3rd  International Congress on Gifted Youth and Sustainability of the Education (ICGYSE) 15-16 December 2022 (Please click for attendance).

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