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An Investigation of the Measurement Estimation Strategies Used by Gifted Students

Year 2020, Volume: 8 Issue: 15, 201 - 223, 25.03.2020
https://doi.org/10.18009/jcer.680284

Abstract

This study aimed to investigate the measurement estimation strategies used by gifted students. Case study was used. 17 seventh grade students who were studying in the Science and Art Center located in a province in Eastern Anatolia Region of Turkey and who were identified as gifted participated in this study. The data was obtained through “The Measurement Estimation Skill Form” which includes nine open-ended tasks. In addition, clinical interviews were conducted with five students. The data were analyzed using descriptive analysis. The findings of this study indicates that students use eight different strategies, which rough guess ,breaking down, using prior knowledge, reference point, unit iteration, comparison with referents, subdivision clues and squeezing, in cases requiring measurement estimation. It was also found that while gifted students mostly used strategy “rough guess”, strategies “subdivision clues” and “squeezing” are used very little. Furthermore, the findings of this study show that gifted students did not use different strategies at the expected level in the measurement estimation situations.

References

  • Akar, Ş. Ş. (2017). Üstün yetenekli öğrencilerin matematiksel yaratıcılıklarının matematiksel modelleme etkinlikleri sürecinde incelenmesi [Examining mathematically gifted students’ mathematical creativity through the process of model eliciting activities] (Unpublished doctoral dissertation). Hacettepe University, Ankara.
  • Assmus, D., & Fritzlar, T. (2018). Mathematical giftedness and creativity in primary grades. In F. M. Singer (Ed.), Mathematical creativity and mathematical giftedness: Enhancing creative capacities in mathematically promising students (pp. 373–404). New York: Springer.
  • Aytekin, C., & Toluk-Uçar, Z. (2014). Investigation of middle school students’ estimation ability with fractions. Elementary Education Online, 13(2), 546-563.
  • Baroody, A. J., & Gatzke, M. R. (1991). The estimation of set size by potentially gifted kindergarten-age children. Journal for Research in Mathematics Education, 22(1), 59–68.
  • Boz-Yaman, B., & Bulut, S. (2017). Middle school mathematics teachers’ opinions on estimation. Necatibey Faculty of Education Electronic Journal of Science and Mathematics Education, 11(1), 48-80.
  • Clement, J. (2000). Analysis of clinical interviews: Foundations and model viability. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 547-589). London: Lawrence Erlbaum Associates, Publishers.
  • Dai, D. Y., Moon S. M., & Feldhusen, J. F. (1998). Achievement motivation and gifted students: A social cognitive perspective. Educational Psychologist, 33(2-3), 45-63.
  • Davis, G. A., & Rimm, S. B. (2004). Education of the gifted and talented. Boston, MA: Pearson Education Press.
  • Desli, D., & Giakoumi, M. (2017). Children’s length estimation performance and strategies in standard and non-standard units of measurement. International Journal for Research in Mathematics Education, 7(3), 61-84.
  • Freiman, V. (2018). Complex and open-ended tasks to enrich mathematical experiences of kindergarten students. In F. M. Singer (Ed.), Mathematical creativity and mathematical giftedness: Enhancing creative capacities in mathematically promising students (pp. 373–404). New York: Springer.
  • Gagné, F. (2009). Building gifts into talents: Detailed overview of the DMGT 2.0. In B. MacFarlane & T. Stambaugh (Eds.), Leading change in gifted education: The Festschrift of Dr. Joyce Vantassel-Baska (pp. 61–80). Waco, TX: Prufrock Press.
  • Gooya, Z., Khosroshahi, L. G., & Teppo, A. R. (2011). Iranian students’ measurement estimation performance involving linear and area attributes of real-world objects. ZDM Mathematics Education, 43(5), 709-722.
  • Gutierrez, 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). New York: Springer.
  • Hartono, R. (2015). Promoting the development of students’ ındividual frame of reference to support length approximation/estimation skills. (Unpublished master dissertation). Sriwijaya University, Palembang.
  • Hodgson, T., Simonsen, L., Lubek, J., & Anderson, L. (2003). Measuring Montana: An episode in estimation. In D. H. Clements & G. Bright (Eds.), Learning and teaching measurement (pp. 221–230). Reston, VA: National Council of Teachers of Mathematics.
  • Hogan, T. P., & Brezinski, K. L. (2003). Quantitative estimation: One, two, or three abilities?, Mathematical Thinking and Learning, 5(4), 259-280.
  • Hu, H. (2019). Implementing resilience recommendations for policies and practices in gifted curriculum. Roeper Review, 41(1), 42-50.
  • Jones, G., Taylor, A., & Broadwell, B. (2009). Estimating linear size and scale: Body rulers. International Journal of Science Education, 31(11), 1495-1509.
  • Jones, M. G., Gardner, G. E., Taylor, A. R., Forrester, J. H., & Andre, T. (2012). Students' accuracy of measurement estimation: Context, units, and logical thinking. School Science and Mathematics, 112(3), 171-178.
  • Joram, E., Gabriele, A. J., Bertheau, M., Gelman, R., & Subrahmanyam, K. (2005). Children's use of the reference point strategy for measurement estimation. Journal for Research in Mathematics Education, 36(1), 4-23.
  • Karp, A. (2017). Some thoughts on gifted education and creativity. ZDM Mathematics Education, 49, 159–168.
  • Kılıç, Ç., & Olkun, S. (2013). Primary school students’ measurement estimation performance and strategies they used in real life situations. Elementary Education Online, 12(1), 295-307.
  • Leikin, R. (2011). The education of mathematically gifted students: Some complexities and questions. The Mathematics Enthusiast, 8(1-2), 167–188
  • 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, 65–80.
  • Lemonidis, C., & Likidis, N. (2019). An integrated hierarchical model of 5th grade students’ computational estimation strategies. International Journal of Mathematical Education in Science and Technology, 1-23.
  • Liu, F. (2009). Multiplication estimation by third and fifth-grade Chinese students. School Science and Mathematics, 107(9), 325-337.
  • Liu, P. H., & Niess, M. L. (2006). An exploratory study of college students' views of mathematical thinking in a historical approach calculus course. Mathematical Thinking and Learning, 8(4), 373-406.
  • Mcmillan, H. J., & Schumacher, S. (2010). Research in education. Boston, USA: Pearson Education.
  • Meissner, H. (2000, July–August). Creativity in mathematics education. Paper presented at the meeting of the International Congress on Mathematical Education, Tokyo, Japan.
  • Miles, M. B., Huberman, A. M., & Saldana, J. (2014). Qualitative Data Analysis. CA:SAGE.
  • Ministry of National Education [MoNE]. (2018). Matematik dersi öğretim programı (İlkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar) [Mathematics curriculum (Primary and secondary 1, 2, 3, 4, 5, 6, 7, and 8 grades)]. Ankara: MEB Publ.
  • Montague, M., & van Garderen, D. (2003). A cross-sectional study of mathematics achievement, estimation skills, and academic self-perception in students of varying ability. Journal of Learning Disabilities, 36, 437– 448.
  • Möhring, W., Frick, A., & Newcombe, N. S. (2018). Spatial scaling, proportional thinking, and numerical understanding in 5- to 7-year-old children. Cognitive Development, 45, 57–67.
  • National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
  • Nolte, M. (2018). Twice-exceptional students: Students with special needs and a high mathematical potential. In F. M. Singer (Ed.), Mathematical creativity and mathematical giftedness (pp. 199-225). New York: Springer.
  • Özçelik, T. (2017). Üstün yetenekli öğrencilere yönelik geliştirilen farklılaştırılmış matematik dersi öğretim programının etkililiği [Efficiency of differentiated mathematics curriculum designed for gifted and talented students] (Unpublished doctoral dissertation). Hacettepe University, Ankara.
  • Patkin, D., & Gazit, A. (2013). On roots and squares-estimation, intuition and creativity. International Journal of Mathematical Education in Science and Technology, 44(8), 1191-1200.
  • Patton, M. Q. (2002). Qualitative research and evaluation methods (3rd ed.). California: Sage.
  • Pitta-Pantazi, D., Kattou, M., & Christou, C. (2018). Mathematical creativity: Product, person, process and press. In F. M. Singer (Ed.), Mathematical creativity and mathematical giftedness (pp. 27-53). New York: Springer.
  • Renzulli, J. S. (1986). The three ring conception of giftedness: A developmental model of creative productivity. In Sternberg, R. J. & Davidson, J. E. (Eds.), Conceptions of Giftedness (pp. 53-92). New York, Cambridge University Press.
  • Renzulli, J. S. (2012). Reexamining the role of gifted education and talent development for the 21st century: A four-part theoretical approach. Gifted Child Quarterly, 56(3), 150–159.
  • Segovia, I., & Castro, E. (2009). Computational and measurement estimation; curriculum foundations and research carried out at the University of Granada. Electronic Journal of Research in Educational Psychology, 7(1), 499-536.
  • Sheffield, L. J. (2018). Commentary paper: a reflection on mathematical creativity and giftedness. In F. M. Singer (Ed.), Mathematical creativity and mathematical giftedness (pp. 405-428). New York: Springer.
  • Singer, F. M., Sheffield, L., Freiman, V., & Brandl, M. (2016). Research on and activities for mathematically gifted students. New York: Springer Nature.
  • Singh, P., Rahmanb, N. A., Ramlyc, M. A., & Hoon, T. S. (2019). From nonsense to number sense: Enumeration of numbers in math classroom learning. The European Journal of Social and Behavioural Sciences, 25, 2933- 2947.
  • Smedsrud, J. (2018) Mathematically gifted accelerated students participating in an ability group: A qualitative interview study. Front. Psychol., 9, 1-12.
  • Sowder, J. T. (1992). Estimation and number sense. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 371 – 389). New York: Macmillan.
  • Sriraman, B., & Knott, L. (2009). The mathematics of estimation: Possibilities for interdisciplinary pedagogy and social consciousness. Interchange, 40(2), 205–223.
  • Starko, A. (2005). Creativity in the classroom: Schools of curious delight (3rd ed.). Mahwah, NJ: Lawrence Erlbaum Associates.
  • Subotnik, R. F., Olszewski-Kubilius, P., & Worrell, F. C. (2011). Rethinking giftedness and gifted education: A proposed direction forward based on psychological science. Psychological Science In The Public Interest, 12(1), 3-54.
  • Torrance, E. P. (1974). Torrance tests of creative thinking: Norms-technical manual. Lexington, MA: Ginn.
  • Usiskin, Z. (2000). The development into the mathematically talented. The Journal of Secondary Gifted Education, 11, 152–162.
  • Usta, N. (2018). The prospective teachers’ skills of identifying students’ mistakes about the topic “measures” and their suggestions for eliminating the mistakes. Journal of Computer and Education Research, 6(12), 247-284.
  • van de Walle, J. A., Karp, K. S., & Williams, J. M. B. (2016). Elementary and middle school mathematics. Teaching developmentally. Boston: Pearson.
  • Wang, J. J., Halberda, J., & Feigenson, L. (2017). Approximate number sense correlates with math performance in gifted adolescents. Acta Psychologica, 176, 78–84.
  • Yin, R. K. (2017). Case study research and applications: Design and methods. Sage publications.
  • Yun-hing, L. (2007). The relationship between numerical estimation and number sense in students’ learning of mathematics. (Unpublished Master of Dissertation). The University of Honkong, Hongkong.

An Investigation of the Measurement Estimation Strategies Used by Gifted Students

Year 2020, Volume: 8 Issue: 15, 201 - 223, 25.03.2020
https://doi.org/10.18009/jcer.680284

Abstract

This study aimed to investigate the measurement estimation strategies used by gifted students. Case study was used. 17 seventh grade students who were studying in the Science and Art Center located in a province in Eastern Anatolia Region of Turkey and who were identified as gifted participated in this study. The data was obtained through “The Measurement Estimation Skill Form” which includes nine open-ended tasks. In addition, clinical interviews were conducted with five students. The data were analyzed using descriptive analysis. The findings of this study indicates that students use eight different strategies, which rough guess ,breaking down, using prior knowledge, reference point, unit iteration, comparison with referents, subdivision clues and squeezing, in cases requiring measurement estimation. It was also found that while gifted students mostly used strategy “rough guess”, strategies “subdivision clues” and “squeezing” are used very little. Furthermore, the findings of this study show that gifted students did not use different strategies at the expected level in the measurement estimation situations.

References

  • Akar, Ş. Ş. (2017). Üstün yetenekli öğrencilerin matematiksel yaratıcılıklarının matematiksel modelleme etkinlikleri sürecinde incelenmesi [Examining mathematically gifted students’ mathematical creativity through the process of model eliciting activities] (Unpublished doctoral dissertation). Hacettepe University, Ankara.
  • Assmus, D., & Fritzlar, T. (2018). Mathematical giftedness and creativity in primary grades. In F. M. Singer (Ed.), Mathematical creativity and mathematical giftedness: Enhancing creative capacities in mathematically promising students (pp. 373–404). New York: Springer.
  • Aytekin, C., & Toluk-Uçar, Z. (2014). Investigation of middle school students’ estimation ability with fractions. Elementary Education Online, 13(2), 546-563.
  • Baroody, A. J., & Gatzke, M. R. (1991). The estimation of set size by potentially gifted kindergarten-age children. Journal for Research in Mathematics Education, 22(1), 59–68.
  • Boz-Yaman, B., & Bulut, S. (2017). Middle school mathematics teachers’ opinions on estimation. Necatibey Faculty of Education Electronic Journal of Science and Mathematics Education, 11(1), 48-80.
  • Clement, J. (2000). Analysis of clinical interviews: Foundations and model viability. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 547-589). London: Lawrence Erlbaum Associates, Publishers.
  • Dai, D. Y., Moon S. M., & Feldhusen, J. F. (1998). Achievement motivation and gifted students: A social cognitive perspective. Educational Psychologist, 33(2-3), 45-63.
  • Davis, G. A., & Rimm, S. B. (2004). Education of the gifted and talented. Boston, MA: Pearson Education Press.
  • Desli, D., & Giakoumi, M. (2017). Children’s length estimation performance and strategies in standard and non-standard units of measurement. International Journal for Research in Mathematics Education, 7(3), 61-84.
  • Freiman, V. (2018). Complex and open-ended tasks to enrich mathematical experiences of kindergarten students. In F. M. Singer (Ed.), Mathematical creativity and mathematical giftedness: Enhancing creative capacities in mathematically promising students (pp. 373–404). New York: Springer.
  • Gagné, F. (2009). Building gifts into talents: Detailed overview of the DMGT 2.0. In B. MacFarlane & T. Stambaugh (Eds.), Leading change in gifted education: The Festschrift of Dr. Joyce Vantassel-Baska (pp. 61–80). Waco, TX: Prufrock Press.
  • Gooya, Z., Khosroshahi, L. G., & Teppo, A. R. (2011). Iranian students’ measurement estimation performance involving linear and area attributes of real-world objects. ZDM Mathematics Education, 43(5), 709-722.
  • Gutierrez, 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). New York: Springer.
  • Hartono, R. (2015). Promoting the development of students’ ındividual frame of reference to support length approximation/estimation skills. (Unpublished master dissertation). Sriwijaya University, Palembang.
  • Hodgson, T., Simonsen, L., Lubek, J., & Anderson, L. (2003). Measuring Montana: An episode in estimation. In D. H. Clements & G. Bright (Eds.), Learning and teaching measurement (pp. 221–230). Reston, VA: National Council of Teachers of Mathematics.
  • Hogan, T. P., & Brezinski, K. L. (2003). Quantitative estimation: One, two, or three abilities?, Mathematical Thinking and Learning, 5(4), 259-280.
  • Hu, H. (2019). Implementing resilience recommendations for policies and practices in gifted curriculum. Roeper Review, 41(1), 42-50.
  • Jones, G., Taylor, A., & Broadwell, B. (2009). Estimating linear size and scale: Body rulers. International Journal of Science Education, 31(11), 1495-1509.
  • Jones, M. G., Gardner, G. E., Taylor, A. R., Forrester, J. H., & Andre, T. (2012). Students' accuracy of measurement estimation: Context, units, and logical thinking. School Science and Mathematics, 112(3), 171-178.
  • Joram, E., Gabriele, A. J., Bertheau, M., Gelman, R., & Subrahmanyam, K. (2005). Children's use of the reference point strategy for measurement estimation. Journal for Research in Mathematics Education, 36(1), 4-23.
  • Karp, A. (2017). Some thoughts on gifted education and creativity. ZDM Mathematics Education, 49, 159–168.
  • Kılıç, Ç., & Olkun, S. (2013). Primary school students’ measurement estimation performance and strategies they used in real life situations. Elementary Education Online, 12(1), 295-307.
  • Leikin, R. (2011). The education of mathematically gifted students: Some complexities and questions. The Mathematics Enthusiast, 8(1-2), 167–188
  • 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, 65–80.
  • Lemonidis, C., & Likidis, N. (2019). An integrated hierarchical model of 5th grade students’ computational estimation strategies. International Journal of Mathematical Education in Science and Technology, 1-23.
  • Liu, F. (2009). Multiplication estimation by third and fifth-grade Chinese students. School Science and Mathematics, 107(9), 325-337.
  • Liu, P. H., & Niess, M. L. (2006). An exploratory study of college students' views of mathematical thinking in a historical approach calculus course. Mathematical Thinking and Learning, 8(4), 373-406.
  • Mcmillan, H. J., & Schumacher, S. (2010). Research in education. Boston, USA: Pearson Education.
  • Meissner, H. (2000, July–August). Creativity in mathematics education. Paper presented at the meeting of the International Congress on Mathematical Education, Tokyo, Japan.
  • Miles, M. B., Huberman, A. M., & Saldana, J. (2014). Qualitative Data Analysis. CA:SAGE.
  • Ministry of National Education [MoNE]. (2018). Matematik dersi öğretim programı (İlkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar) [Mathematics curriculum (Primary and secondary 1, 2, 3, 4, 5, 6, 7, and 8 grades)]. Ankara: MEB Publ.
  • Montague, M., & van Garderen, D. (2003). A cross-sectional study of mathematics achievement, estimation skills, and academic self-perception in students of varying ability. Journal of Learning Disabilities, 36, 437– 448.
  • Möhring, W., Frick, A., & Newcombe, N. S. (2018). Spatial scaling, proportional thinking, and numerical understanding in 5- to 7-year-old children. Cognitive Development, 45, 57–67.
  • National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
  • Nolte, M. (2018). Twice-exceptional students: Students with special needs and a high mathematical potential. In F. M. Singer (Ed.), Mathematical creativity and mathematical giftedness (pp. 199-225). New York: Springer.
  • Özçelik, T. (2017). Üstün yetenekli öğrencilere yönelik geliştirilen farklılaştırılmış matematik dersi öğretim programının etkililiği [Efficiency of differentiated mathematics curriculum designed for gifted and talented students] (Unpublished doctoral dissertation). Hacettepe University, Ankara.
  • Patkin, D., & Gazit, A. (2013). On roots and squares-estimation, intuition and creativity. International Journal of Mathematical Education in Science and Technology, 44(8), 1191-1200.
  • Patton, M. Q. (2002). Qualitative research and evaluation methods (3rd ed.). California: Sage.
  • Pitta-Pantazi, D., Kattou, M., & Christou, C. (2018). Mathematical creativity: Product, person, process and press. In F. M. Singer (Ed.), Mathematical creativity and mathematical giftedness (pp. 27-53). New York: Springer.
  • Renzulli, J. S. (1986). The three ring conception of giftedness: A developmental model of creative productivity. In Sternberg, R. J. & Davidson, J. E. (Eds.), Conceptions of Giftedness (pp. 53-92). New York, Cambridge University Press.
  • Renzulli, J. S. (2012). Reexamining the role of gifted education and talent development for the 21st century: A four-part theoretical approach. Gifted Child Quarterly, 56(3), 150–159.
  • Segovia, I., & Castro, E. (2009). Computational and measurement estimation; curriculum foundations and research carried out at the University of Granada. Electronic Journal of Research in Educational Psychology, 7(1), 499-536.
  • Sheffield, L. J. (2018). Commentary paper: a reflection on mathematical creativity and giftedness. In F. M. Singer (Ed.), Mathematical creativity and mathematical giftedness (pp. 405-428). New York: Springer.
  • Singer, F. M., Sheffield, L., Freiman, V., & Brandl, M. (2016). Research on and activities for mathematically gifted students. New York: Springer Nature.
  • Singh, P., Rahmanb, N. A., Ramlyc, M. A., & Hoon, T. S. (2019). From nonsense to number sense: Enumeration of numbers in math classroom learning. The European Journal of Social and Behavioural Sciences, 25, 2933- 2947.
  • Smedsrud, J. (2018) Mathematically gifted accelerated students participating in an ability group: A qualitative interview study. Front. Psychol., 9, 1-12.
  • Sowder, J. T. (1992). Estimation and number sense. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 371 – 389). New York: Macmillan.
  • Sriraman, B., & Knott, L. (2009). The mathematics of estimation: Possibilities for interdisciplinary pedagogy and social consciousness. Interchange, 40(2), 205–223.
  • Starko, A. (2005). Creativity in the classroom: Schools of curious delight (3rd ed.). Mahwah, NJ: Lawrence Erlbaum Associates.
  • Subotnik, R. F., Olszewski-Kubilius, P., & Worrell, F. C. (2011). Rethinking giftedness and gifted education: A proposed direction forward based on psychological science. Psychological Science In The Public Interest, 12(1), 3-54.
  • Torrance, E. P. (1974). Torrance tests of creative thinking: Norms-technical manual. Lexington, MA: Ginn.
  • Usiskin, Z. (2000). The development into the mathematically talented. The Journal of Secondary Gifted Education, 11, 152–162.
  • Usta, N. (2018). The prospective teachers’ skills of identifying students’ mistakes about the topic “measures” and their suggestions for eliminating the mistakes. Journal of Computer and Education Research, 6(12), 247-284.
  • van de Walle, J. A., Karp, K. S., & Williams, J. M. B. (2016). Elementary and middle school mathematics. Teaching developmentally. Boston: Pearson.
  • Wang, J. J., Halberda, J., & Feigenson, L. (2017). Approximate number sense correlates with math performance in gifted adolescents. Acta Psychologica, 176, 78–84.
  • Yin, R. K. (2017). Case study research and applications: Design and methods. Sage publications.
  • Yun-hing, L. (2007). The relationship between numerical estimation and number sense in students’ learning of mathematics. (Unpublished Master of Dissertation). The University of Honkong, Hongkong.
There are 57 citations in total.

Details

Primary Language English
Subjects Other Fields of Education
Journal Section Research Article
Authors

Fatma Erdoğan 0000-0002-4498-8634

Tuba Erben 0000-0003-4532-8328

Publication Date March 25, 2020
Submission Date January 26, 2020
Acceptance Date February 29, 2020
Published in Issue Year 2020 Volume: 8 Issue: 15

Cite

APA Erdoğan, F., & Erben, T. (2020). An Investigation of the Measurement Estimation Strategies Used by Gifted Students. Journal of Computer and Education Research, 8(15), 201-223. https://doi.org/10.18009/jcer.680284

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