A Design Based Study: Characteristics of Differentiated Tasks for Mathematically Gifted Students

Duygu Ozdemir 1 * , Mine Isiksal Bostan 2
More Detail
1 Department of Mathematics Education, Istanbul Aydin University, Istanbul, TURKEY
2 Department of Mathematics Education, Middle East Technical University, Ankara, TURKEY
* Corresponding Author
EUR J SCI MATH ED, Volume 9, Issue 3, pp. 125-144. https://doi.org/10.30935/scimath/10995
OPEN ACCESS   1516 Views   929 Downloads
Download Full Text (PDF)


Nowadays, the necessity of designing proper differentiated tasks for mathematically gifted students is a remarkable subject in international literature and practice. In this design-based study, it was aimed to analyze and construct characteristics for designing differentiated tasks of mathematically gifted students. Through this design process, preliminary and prototyping phases were used as a general framework to reveal these characteristics as design principles of the study. Literature reviews, experiences of practitioners and needs analysis studies about suggestions and key points reflecting the characteristics of differentiated tasks were conducted in preliminary research phase. After this phase, initial form of differentiated tasks with draft design principles were applied in classrooms in try-outs and field test with 12 mathematically gifted students and 4 mathematics teachers of these classrooms. The data obtained through qualitative methods lead to three categories; initial design principles as characteristics obtained through preliminary phase, modifications for tasks, and final design principles as characteristics obtained through prototyping phase.


Ozdemir, D., & Isiksal Bostan, M. (2021). A Design Based Study: Characteristics of Differentiated Tasks for Mathematically Gifted Students. European Journal of Science and Mathematics Education, 9(3), 125-144. https://doi.org/10.30935/scimath/10995


  • Anderson, L. W., Krathwohl, D. R., & Bloom, B. S. (2001). A taxonomy for learning, teaching, and assessing: A revision of Bloom’s taxonomy of educational objectives. Longman.
  • Arslan, Ç., & Altun, M. (2007). Learning to solve non-routine mathematical problems. İlköğretim Online, 6(1), 35-49.
  • Aydemir, D., & Çakıroğlu, E. (2013). Üstün yetenekli ilköğretim öğrencilerinin matematik derslerine ilişkin algıları [Gifted primary school students’ perceptions of mathematics lessons]. Proceedings of the 12th MATDER Semposium, (pp. 266-268), Ankara, Turkey.
  • Aydemir, D., & Teksöz, G. (2014, September). Çevre eğitiminin matematik derslerine entegre edilmesine ilişkin öğrenci görüşleri [Çevre eğitiminin matematik derslerine entegre edilmesine ilişkin öğrenci görüşleri] [Paper presentation]. XI. Ulusal Fen Bilimleri ve Matematik Eğitimi Kongresi 2014, Adana, Turkey.
  • Baykoç, N. (2014). Üstün yetenek gelişimleri ve eğitimleri [Development and training of gifted people]. Vize Yayıncılık.
  • Beane, J. (1997). Curriculum integration. Teachers College Press.
  • Berger, S. L. (1991). Differentiating curriculum for gifted students. ERIC Clearinghouse on Handicapped and Gifted Children.
  • Berry, J. (2002). Developing mathematical modelling skills: The role of CAS. Zentralblatt für Didaktik der Mathematik 34(5), 212-220. https://doi.org/10.1007/BF02655824
  • Bloom, B. S. (1956). Taxonomy of educational objectives: The classification of educational goals: Cognitive Domain. Mckay.
  • Blum, W. (2002). ICMI Study 14: Applications and modelling in mathematics education–Discussion document. Educational Studies in Mathematics, 51(1-2), 149-171. https://doi.org/10.1023/A:1022435827400
  • Bochkareva, T., Akhmetshin, E., Osadchy, E., Romanov, P., & Konovalova, E. (2018). Preparation of the future teacher for work with gifted children. Journal of Social Studies Education Research, 9(2), 251-265. https://doi.org/10.17499/jsser.76113
  • Brigandi, C. B., C. M. Gilson, & M. Miller. (2019). Professional development and differentiated instruction in an elementary school pullout program: A gifted education case study. Journal for the Education of the Gifted, 42(4), 362-395. https://doi.org/10.1177/0162353219874418
  • Chamberlin, M. T., & Chamberlin, S. A. (2010). Enhancing preservice teacher development: Field experiences with gifted students. Journal for the Education of the Gifted, 33(3), 381-416. https://doi.org/10.1177/016235321003300305
  • Collins, A. (1992). Toward a design science of education. In E. Scanlon and T. O’Shea (Eds.), New directions in educational technology (pp.15-22). Springer-Verlag. https://doi.org/10.1007/978-3-642-77750-9_2
  • Creswell, J. W. (2009). Qualitative inquiry and research design: Choosing among five traditions. Sage.
  • Denzin, N (1989). The Research Act: A Theoretical Introduction to Sociological Methods. Prentice Hall.
  • Deringöl, Y., & Davasligil, Ü. (2020). The Effect of Differentiated Mathematics Programs on the Mathematics Attitude of Gifted Children. Malaysian Online Journal of Educational Sciences, 8(1), 27-37.
  • Diezmann, C. M., & Watters, J. (2001). The collaboration of mathematically gifted students on challenging tasks. Journal for the Education of the Gifted, 25, 7-31. https://doi.org/10.1177/016235320102500102
  • Dimitriadis C. (2011). Provision for mathematically gifted children in primary schools: An Investigation of four different methods of organizational provision, Educational Review, 64(2), 241-260. https://doi.org/10.1080/00131911.2011.598920
  • English, L. D., and Watters, J. (2005). Mathematical modeling with 9-year-olds. In H. L. Chick, and J. L. Vincent (Eds.), Proceedings of 29th Conference of the Int. Group for the Psychology of Mathematics Education (pp. 297-304). Australia: University of Melbourne.
  • Fıçıcı, A., & Siegle, D. (2008). International teachers’ judgment of gifted mathematics student characteristics. Journal of Gifted Talented International, 23(1), 22-37. https://doi.org/10.1080/15332276.2008.11673510
  • Freiman, V. (2006). Problems to discover and to boost mathematical talent in early grades: A challenging situations approach. The Mathematics Enthusiast, 3(1), 51-75. https://scholarworks.umt.edu/tme/vol3/iss1/3
  • Gavin, M. K., Casa, T. M., Firmender, J. M., & Carroll, S. R. (2013). The impact of advanced geometry and measurement curriculum units on the mathematics achievement of first-grade students. Gifted Child Quarterly, 57(2), 71-84. https://doi.org/10.1177/0016986213479564
  • Glaser, B., and Strauss, A. (1967). The discovery of grounded theory. Strategies for Qualitative Research. The Sociology Press. https://doi.org/10.1097/00006199-196807000-00014
  • Gravemeijer, K. (2006). Developmental Research as a research method. In J. Van den Akker, K. Gravemeijer, S. McKenney & N. Nieveer (Eds). Educational Design Research (pp. 115-131). Routledge.
  • Greenes, C. (1997). Honing the abilities of the mathematically promising. The Mathematics Teacher, 90(7), 582. https://doi.org/10.5951/MT.90.7.0582
  • Herrington, J., McKenney, S., Reeves, T., & Oliver, R. (2007). Design-based research and doctoral students: Guidelines for preparing a dissertation proposal.
  • Heymann, H.W. (2003). Why teach mathematics? A focus on general education. Kluwer. https://doi.org/10.1007/978-94-017-3682-4
  • Jen, E., Moon, S., & Samarapungavan, A. (2015). Using design-based research in gifted education. Gifted Child Quarterly, 59(3), 190-200. https://doi.org/10.1177/0016986215583871
  • Jianguo, M. (2004). Teaching environmental awareness in mathematics. Chinese Education and Society, 37(4), 53-56. https://doi.org/10.1080/10611932.2004.11031651
  • Johnson, D. T. (2000). Teaching mathematics to gifted students in a mixed-ability classroom. Eric Clearinghouse.
  • Jolly, J. L. & Jarvis, J. M. (Eds.). (2018). Exploring Gifted Education: Australian and New Zealand Perspectives. Routledge. https://doi.org/10.4324/9781351227704
  • Kanevsky, L. (2011). Differential differentiated: What types of differentiation do students want? Gifted Child Quarterly, 55(4), 279-299. https://doi.org/10.1177/0016986211422098
  • Kaput, J. (1992). Technology and mathematics education. In D. Grouws (Ed.), A handbook of research on mathematics teaching and learning (pp. 515-556). Macmillan.
  • Karaduman, G. B. (2010). Üstün yetenekli öğrenciler için uygulanan farklılaştırılmış matematik eğitim programları [Differentiated mathematics education programs for gifted students]. Hasan Ali Yücel Eğitim Fakültesi Dergisi, 13(1), 1-12.
  • Karnes, M. B. & Johnson, L. J. (1991). The preschool/primary gifted child. Journal for the Education of the Gifted, 14(3), 267-283. https://doi.org/10.1177/016235329101400307
  • Kennedy-Clark, S. (2013). Research by design: Design-based research and the higher degree research student. Journal of Learning Design, 6(2), 26-32. https://doi.org/10.5204/jld.v6i2.128
  • Ktistis, S. (2014). Fostering critical thinking in gifted students in the heterogeneous classroom: General educators’ perceptions (Doctoral dissertation). North Central University, San Diego, CA.
  • Lesh, R., & Doerr, H. M. (2003). A modeling perspective on teacher development. In R. A. Lesh and H. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 3-33). Lawrence Erlbaum. https://doi.org/10.4324/9781410607713
  • Mafumiko, F. S. M. (2006). Micro-scale experimentation as a catalyst for improving the chemistry curriculum in Tanzania. Tijdschrift voor Didactiek der β-wetenschappen, 1(2), 69-74.
  • Manuel, D., & Freiman, V. (2017). Differentiating Instruction Using a Virtual Environment: A Study of Mathematical Problem Posing Among Gifted and Talented Learners. Global Education Review, 4(1).
  • Martin, R. M. (2002). Math Attitudes of Gifted Students: A Focus on Gifted Girls in the Elementary Grades (Doctoral dissertation, State University of New York). Available from ProQuest Dissertations and Theses database.
  • Masole, T. M. (2011). Enhancing the quality of performance assessment in agriculture in Botswana schools (Doctoral dissertation), University of Pretoria.
  • McKenney, S., Nieveen, N., & Van den Akker, J. (2006). Design research from a curriculum perspective. In J. V. D. Akker, K. Gravemeijer, S. McKenney and N. Nieveen (Eds.), Educational design research (pp. 67-90). Routledge. https://doi.org/10.4324/9780203088364
  • Merriam, S. B. (1998). Qualitative research and case study applications in education. Jossey-Bass Publishers.
  • Mhlolo, M. K., & Marumo, J. M. (2017). Preliminary findings from a study based on Gagne’s 10 commandments for the education of mathematically gifted learners. Association for Mathematics Education of South Africa, 41.
  • Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook. Beverly Hills: Sage Publications.
  • Mofield, E. L. (2020). Benefits and Barriers to Collaboration and Co-Teaching: Examining Perspectives of Gifted Education Teachers and General Education Teachers. Gifted Child Today, 43(1), 20-33. https://doi.org/10.1177/1076217519880588
  • Nieveen, N., & Folmer, E. (2013). Formative evaluation in educational design research. In Van den Akker, J., Gravemeijer, K. McKenney, S. & Nieveen, N. (Eds). Educational design research, (pp. 152-169). Routledge.
  • Özçakır, B. (2013). The effects of mathematics instruction supported by dynamic geometry activities on seventh grade students’ achievement in area of quadrilaterals (Unpublished master’s thesis). Middle East Technical University, Ankara.
  • Özdemir, D. (2016). Design and development of differentiated tasks for 5th and 6th grade mathematically gifted students (Unpublished doctoral dissertation). Middle East Technical University.
  • Özdemir, D. (2018). Matematikte Üstün Yetenekli İlköğretim Öğrencilerinin Okullarındaki Matematik Derslerine İlişkin Algıları [The Perceptions of Gifted Elementary School Students in Mathematics about Mathematics Lessons in Their Schools]. Kastamonu Eğitim Dergisi, 26(1), 153-160. https://doi.org/10.24106/kefdergi.375695
  • Özdemir, D. A., & Işiksal Bostan, M. (2021). Mathematically gifted students’ differentiated needs: what kind of support do they need?. International Journal of Mathematical Education in Science and Technology, 52(1), 65-83. https://doi.org/10.1080/0020739X.2019.1658817
  • Park, S. (2005). The comparison between scientifically gifted children and ordinary children in peer relationships and self-efficacy. Unpublished master thesis, Changwon National University, Gyeongnam.
  • Periathiruvadi, S., & Rinn, A. N. (2012). Technology in gifted education: A review of best practices and empirical research. Journal of Research on Technology in Education, 45(2), 153-169. https://doi.org/10.1080/15391523.2012.10782601
  • Pfeiffer, S. I., & Petscher, Y. (2008). Identifying young gifted children using the gifted rating scales—Preschool/kindergarten form. Gifted Child Quarterly, 52(1), 19-29. https://doi.org/10.1177/0016986207311055
  • Pierce R. L., Cassady J.C., Adams C. M., Neumeister K. L. S., Dixon F. A., & Cross T. L. (2011). The effects of clustering and curriculum on the development of gifted learners’ math achievement. Journal for the Education of the Gifted, 34(4), 569-594. https://doi.org/10.1177/016235321103400403
  • Plomp, T., & Nieveen, N. (Eds.) (2013). An introduction to educational design research. SLO.
  • Rakow, S. (2012). Helping gifted learners SOAR. Educatonal Leaderhip, 69(5), 34-40.
  • Renzulli, J. S. (1986) The three ring conception of giftedness: a developmental model of Creative productivity. In R. J. Sternberg
  • & J. E. Davidson (Eds) Conceptions of giftedness, (pp. 53-92). Cambridge University Press.
  • Rotigel, J. V., & Fello, S. (2004). Mathematically gifted students: How can we meet their needs? Gifted Child Today, 27(4), 46-
  • 51. https://doi.org/10.4219/gct-2004-150
  • Ryser, G.R., & Johnsen, S.K. (1998). Test of mathematical abilities for gifted students. Pro-ed.
  • Sankar‐DeLeeuw, N. (1999). Gifted preschoolers: Parent and teacher views on identification, early admission and programming.
  • Roeper Review, 21(3), 174-179. https://doi.org/10.1080/02783199909553957
  • Siegle, D. (2004). Identifying students with gifts and talents in technology. Gifted Child Today, 27(4), 30-33. https://doi.org/10.4219/gct-2004-146
  • Singer, F. M., Sheffield, L. J., Freiman, V., & Brandl, M. (2016). Research on and activities for mathematically gifted students. In Research on and activities for mathematically gifted students (pp. 1-41). Springer, Cham. https://doi.org/10.1007/978-3-319-39450-3_1
  • Sriraman, B. (2003). Mathematical giftedness, problem solving, and the ability to formulate generalizations: The problem-solving experiences of four gifted students. Prufrock Journal, 14(3), 151-165. https://doi.org/10.4219/jsge-2003-425
  • Sriraman, B., & Sondergaard, B. D. (2009). On bringing interdisciplinary ideas to gifted education. In L. V. Shavinina (Ed.) International handbook on giftedness (pp. 1235-1256). Springer. https://doi.org/10.1007/978-1-4020-6162-2_64
  • Sriraman, B., Haavold P., & Lee K. (2013). Mathematical creativity and giftedness: a commentary on and review of theory, new operational views, and ways forward. Mathematics Education, 45(1), 215-225. https://doi.org/10.1007/s11858-013-0494-6
  • Tieso, C. L. (2002). The effects of grouping and curricular practices on intermediate students’ math achievement. The National Research Center on the Gifted and Talented.
  • Van de Walle, J., Karp, K. S., & Bay-Williams, J. M. (2013). Elementary and middle school mathematics methods: Teaching developmentally. Allyn and Bacon.
  • Van den Akker, J., Gravemeijer, K, McKenney, S., & Nieveen, N. (Eds). (2006). Educational design research. Routledge. https://doi.org/10.4324/9780203088364
  • VanTassel-Baska, J., Hubbard, G. F., & Robbins, J. I. (2021). Differentiation of instruction for gifted learners: collated evaluative studies of teacher classroom practices. Handbook of Giftedness and Talent Development in the Asia-Pacific, 945-979. https://doi.org/10.1080/02783193.2020.1765919
  • Wilkins, M. M., Wilkins, J. L. M., & Oliver, T. (2006). Differentiating the curriculum for elementary gifted mathematics students. Teaching Children Mathematics, 13(1), 6-13. https://doi.org/10.5951/TCM.13.1.0006
  • Winebrenner, S. (2001). Teaching Gifted Kids in the Regular Classroom: Strategies and Techniques Every Teacher Can Use to Meet the Academic Needs of the Gifted and Talented. Free Spirit Publishing.
  • Yevdokimov, O. (2007). Using the history of mathematics for mentoring gifted students: Notes for teachers. Proceedings of the 21st Biennial Conference of the Australian Association of Mathematics Teachers (pp. 267-275). Hobart, Tasmania.
  • Zedan, R., & Bitar, J. (2017). Mathematically Gifted Students: Their Characteristics and Unique Needs. European Journal of Education Studies, 3(4), 236-259. https://doi.org/10.5281/zenodo.37595