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The Sixth-Grade Students’ Conceptualization of Angle

Cilt: 42 Sayı: 3 31 Aralık 2025
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The Sixth-Grade Students’ Conceptualization of Angle

Öz

This study investigated sixth-grade students' conceptualization of angles. A structured interview was implemented with eight students to examine how they verbally described angles, represented them in figures, and interpreted them in real-life contexts such as slope, turn, and openness. The findings revealed that students primarily understood angles through static components such as corners and intersection, consistent with the standard definition of angles. Only one student demonstrated a more comprehensive understanding by relating angles to slope and space contexts through reflective abstraction of the formal angle definition. Educational implications are discussed, highlighting that most students struggled to connect angles across different contexts, such as slope and turn, despite the inclusion of real-life examples and physical experiences in the primary school curriculum. Practical implications emphasize the importance of facilitating reflective abstraction through multiple representations and contexts of angles in classroom instruction.

Anahtar Kelimeler

mathematics education, middle school, sixth grade, angle concept, conceptualization

Kaynakça

  1. Battista, M. T. (2007). The development of geometric and spatial thinking. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 843–908). Information Age.
  2. Browning, C. A., Garza-Kling, G., & Sundling, E. H. (2008). What’s your angle on angles? Teaching Children Mathematics, 14(5), 283–287. https://doi.org/10.5951/TCM.14.5.0283
  3. Bütüner, S. Ö., & Filiz, M. (2017) Exploring high-achieving sixth grade students’ erroneous answers and misconceptions on the angle concept. International Journal of Mathematical Education in Science and Technology, 48(4), 533–554. https://doi.org/10.1080/0020739X.2016.1256444
  4. Casas-Garcia, L.M., & Luengo-González, R. (2013). The study of the pupil’s cognitive structure: The concept of angle. European Journal of Psychology of Education, 28, 373–398. https://doi.org/10.1007/s10212-012-0119-4
  5. Charmaz, K. (2005). Grounded theory in the 21st century: Applications for advancing social justice studies. In N. K. Denzin & Y. E. Lincoln (Eds.), Handbook of qualitative research (3rd ed., pp. 507–535). Sage.
  6. Clements, D. (2003). Teaching and learning geometry. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 151–178). The National Council of Teachers of Mathematics.
  7. Clements, D. H., & Battista, M. T. (1992). Geometry and spatial reasoning. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (pp. 420–464). Macmillan Publishing Co, Inc.
  8. Clements, D. H., & Burns, B. A. (2000). Students’ development of strategies for turn and angle measure. Educational Studies in Mathematics, 41(1), 31–45. http://www.jstor.org/stable/3483059
  9. Clements, D. H., Wilson, D. C., & Sarama, J. (2004). Young children's composition of geometric figures: A learning trajectory. Mathematical Thinking and Learning, 6(2), 163–184. https://doi.org/10.1207/s15327833mtl0602_5
  10. Common Core State Standards Initiative: Preparing America’s Students for College and Career (2010). Common Core State Standards for Mathematics. https://learning.ccsso.org/wpcontent/uploads/2022/11/Math_Standards1.pdf

Kaynak Göster

APA
Acar, F., Toker Kekik, H., Duran, N. B., & Işıksal, M. (2025). The Sixth-Grade Students’ Conceptualization of Angle. Bogazici University Journal of Education, 42(3), 19-34. https://doi.org/10.52597/buje.1537486
AMA
1.Acar F, Toker Kekik H, Duran NB, Işıksal M. The Sixth-Grade Students’ Conceptualization of Angle. BUJE. 2025;42(3):19-34. doi:10.52597/buje.1537486
Chicago
Acar, Fatma, Habibe Toker Kekik, Nur Banu Duran, ve Mine Işıksal. 2025. “The Sixth-Grade Students’ Conceptualization of Angle”. Bogazici University Journal of Education 42 (3): 19-34. https://doi.org/10.52597/buje.1537486.
EndNote
Acar F, Toker Kekik H, Duran NB, Işıksal M (01 Aralık 2025) The Sixth-Grade Students’ Conceptualization of Angle. Bogazici University Journal of Education 42 3 19–34.
IEEE
[1]F. Acar, H. Toker Kekik, N. B. Duran, ve M. Işıksal, “The Sixth-Grade Students’ Conceptualization of Angle”, BUJE, c. 42, sy 3, ss. 19–34, Ara. 2025, doi: 10.52597/buje.1537486.
ISNAD
Acar, Fatma - Toker Kekik, Habibe - Duran, Nur Banu - Işıksal, Mine. “The Sixth-Grade Students’ Conceptualization of Angle”. Bogazici University Journal of Education 42/3 (01 Aralık 2025): 19-34. https://doi.org/10.52597/buje.1537486.
JAMA
1.Acar F, Toker Kekik H, Duran NB, Işıksal M. The Sixth-Grade Students’ Conceptualization of Angle. BUJE. 2025;42:19–34.
MLA
Acar, Fatma, vd. “The Sixth-Grade Students’ Conceptualization of Angle”. Bogazici University Journal of Education, c. 42, sy 3, Aralık 2025, ss. 19-34, doi:10.52597/buje.1537486.
Vancouver
1.Fatma Acar, Habibe Toker Kekik, Nur Banu Duran, Mine Işıksal. The Sixth-Grade Students’ Conceptualization of Angle. BUJE. 01 Aralık 2025;42(3):19-34. doi:10.52597/buje.1537486