Pre-Service Teachers’ Knowledge Regarding the Area of Triangle

Asli Bilik Durmaz 1 * , Mine Isiksal Bostan 2
More Detail
1 Namık Kemal Middle School, Şehitkamil, Gaziantep, TURKEY
2 Middle East Technical University, Ankara, TURKEY
* Corresponding Author
EUR J SCI MATH ED, Volume 10, Issue 2, pp. 208-224. https://doi.org/10.30935/scimath/11716
Published: 09 February 2022
OPEN ACCESS   1246 Views   819 Downloads
Download Full Text (PDF)

ABSTRACT

The aim of this study is to investigate the knowledge of pre-service middle school mathematics teachers on possible misconceptions and difficulties held by students regarding the area of triangle. In line with this aim, qualitative case study research design was used to obtain deep information. As the participants of the study, two pre-service middle school teachers were chosen purposively. Data were collected from lesson plans, semi-structured interviews and observations of pre-service teachers’ related lessons. The findings of the study showed that the pre-service teachers specified various misconceptions and difficulties regarding the area of triangle that might be observed among middle school students. When the determined misconceptions and difficulties were reviewed, it attracted attention that most of the misconceptions and difficulties were related to the concept of height. One of the findings of the study differed from other relevant studies in the respect that one of the pre-service teachers stated that students have the perception that a line segment cannot be extended. Difficulties and misconceptions and the reasons of them are discussed accordingly.

CITATION

Bilik Durmaz, A., & Isiksal Bostan, M. (2022). Pre-Service Teachers’ Knowledge Regarding the Area of Triangle. European Journal of Science and Mathematics Education, 10(2), 208-224. https://doi.org/10.30935/scimath/11716

REFERENCES

  • Aksu, Z., & Konyalıoğlu, A. (2015). Sınıf öğretmen adaylarının kesirler konusundaki pedagojik alan bilgileri [Pedagogical content knowledge of prospective classroom teachers on fractions]. Kastamonu Eğitim Dergisi, 23(2), 723-738. https://dergipark.org.tr/tr/pub/kefdergi/issue/22599/241424
  • Aslan Tutak, F., & Adams, T. L. (2017). A study of geometry content knowledge of elementary preservice teachers. International Electronic Journal of Elementary Education, 7(3), 301-318. https://www.iejee.com/index.php/IEJEE/article/view/82
  • Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389-407. https://doi.org/10.1177/0022487108324554
  • Baturo, A., & Nason, R. (1996). Student teachers’ subject matter knowledge within the domain of area measurement. Educational Studies in Mathematics, 31(3), 235-268. https://doi.org/10.1007/BF00376322
  • Borko, H., Eisenhart, M., Brown, C. A., Underhill, R. G., Jones, D., & Agard, P. C. (1992). Learning to teach hard mathematics: Do novice teachers and their instructors give up too easily?. Journal for Research in Mathematics Education, 23(3), 194-222. https://doi.org/10.5951/jresematheduc.23.3.0194
  • Bukova-Guzel, E. (2010). An investigation of pre-service mathematics teachers pedagogical content knowledge: Example of solid objects. Scientific Research and Essays, 5(14), 1872-1880. https://doi.org/10.5897/SRE.9000173
  • Burgess, T. A. (2006). A framework for examining teacher knowledge as used in action while teaching statistics. In Proceedings of the Seventh International Conference on Teaching Statistics. https://files.eric.ed.gov/fulltext/ED573184.pdf
  • Cavanagh, M. (2008). Reflections on measurement and geometry. Reflections, 33(1), 55.
  • Creswell, J. W. (1998). Qualitative inquiry and research design: Choosing among five traditions. Sage Publications.
  • Dede, Y., & Peker, M. (2007). Öğrencilerin cebire yönelik hata ve yanlış anlamaları: Matematik öğretmen adayları’nın bunları tahmin becerileri ve çözüm önerileri [Students' mistakes and misunderstandings about algebra: Pre-service mathematics teachers' estimation skills and solution suggestions]. İlköğretim Online, 6(1), 35-49. https://dergipark.org.tr/tr/pub/ilkonline/issue/8605/107187
  • Deniz-Yılmaz, D., & Küçük-Demir, B. (2021) Mathematics teachers’ pedagogical content knowledge involving the relationships between perimeter and area. Athens Journal of Education, 8, 1-24. https://doi.org/10.30958/aje.8-4-2
  • Fidan, Y., & Türnüklü, E. (2010). İlköğretim 5. sınıf öğrencilerinin geometric düşünme düzeylerinin bazı değişkenler açısından incelenmesi [Examination of geometric thinking levels of primary school 5th grade students in terms of some variables]. Pamukkale Üniversitesi Eğitim Fakültesi Dergisi, 27, 185-197. https://dergipark.org.tr/tr/pub/pauefd/issue/11116/132940
  • Fujita, T., & Jones, K. (2007). Learners’ understanding of the definitions and hierarchical classification of quadrilaterals: Towards a theoretical framing. Research in Mathematics Education, 9(1-2), 3-20. https://doi.org/10.1080/14794800008520167
  • Gökdal, N. (2004). İlköğretim 8. sınıf ve ortaöğretim 11. sınıf öğrencilerinin alan ve hakim konularındaki kavram yanılgıları [The misconceptions of primary school 8th grade and secondary school 11th grade students about domain and judge] (Unpublished master thesis). Gazi University.
  • Gökkurt, B., Şahin, Ö., Soylu, Y., & Doğan, Y. (2015). Öğretmen adaylarının geometrik cisimler konusuna ilişkin öğrenci hatalarına yönelik pedagojik alan bilgileri [Pedagogical content knowledge of prospective teachers about student mistakes on geometric objects.]. İlköğretim Online, 14(1). https://doi.org/10.17051/io.2015.55159
  • Grossman, P. L. (1990). The making of a teacher: Teacher knowledge and teacher education. Teachers College Press, Columbia University.
  • Gutiérrez, A., & Jaime, A. (1999). Preservice primary teachers' understanding of the concept of altitude of a triangle. Journal of Mathematics Teacher Education, 2(3), 253-275. https://doi.org/10.1023/A:1009900719800
  • Hershkowitz, R. (1989). Visualization in geometry-Two sides of the coin. Focus on Learning Problems in Mathematics, 11, 61-76. https://www.researchgate.net/publication/287200654_Visualization_in_geometry_two_sides_of_of_the_coin
  • Hill, H. C., Schilling, S. G., & Ball, D. L. (2004). Developing measures of teachers’ mathematics knowledge for teaching. The Elementary School Journal, 105(1), 11-30. https://doi.org/10.1086/428763
  • Huang, H. M. E., & Witz, K. G. (2013). Children’s conceptions of area measurement and their strategies for solving area measurement problems. Journal of Curriculum and Teaching, 2(1), 10-26. https://doi.org/10.5430/jct.v2n1p10
  • Isiksal, M., & Cakiroglu, E. (2011). The nature of prospective mathematics teachers’ pedagogical content knowledge: the case of multiplication of fractions. Journal of Mathematics Teacher Education, 14(3), 213-230. https://doi.org/10.1007/s10857-010-9160-x
  • Kamii, C., & Kysh, J. (2006). The difficulty of "length x width": Is a square the unit of measurement? Journal of Mathematical Behavior, 25, 105-115. https://doi.org/10.1016/j.jmathb.2006.02.001
  • Karaağaç, M. K., & Köse, L. (2015). Öğretmen ve öğretmen adaylarının öğrencilerin kesirler konusundaki kavram yanılgıları ile ilgili bilgilerinin incelenmesi [Examining the knowledge of teachers and prospective teachers about students' misconceptions about fractions]. Sakarya Üniversitesi Eğitim Fakültesi Dergisi, (30), 72-92. https://dergipark.org.tr/tr/pub/sakaefd/issue/11235/134244
  • Karahasan, B. (2010). Preservice secondary mathematics teachers’ pedagogical content knowledge of composite and inverse functions [Ph.D. thesis]. Middle East Technical University.
  • Kılıç, H. (2011). Preservice secondary mathematics teachers’ knowledge of students. Turkish Online Journal of Qualitative Inquiry, 2(2), 17-35. https://dergipark.org.tr/en/pub/tojqi/issue/21391/229349
  • Kubar, A. (2012). Pre-service elementary mathematics teachers’ knowledge about definitions of integers and their knowledge about elementary students’ possible misconceptions and errors in describing integers [M.S. thesis]. Middle East Technical University.
  • Kubar, A., & Cakiroglu, E. (2017). Prospective teachers‟ knowledge on middle school students‟ possible descriptions of integers. International Journal of Education in Mathematics, Science and Technology, 5(4), 279-294. https://doi.org/10.18404/ijemst.75211
  • Lee, E., & Luft, J. (2008). Experienced secondary science teachers' representation of pedagogical content knowledge. International Journal of Science Education, 30, 1343-1363. https://doi.org/10.1080/09500690802187058
  • Livy, S., Muir, T., & Maher, N. (2012). How do they measure up? Primary pre-service teachers’ mathematical knowledge of area and perimeter. Mathematics Teacher Education and Development, 12(2), 91-112. https://www.researchgate.net/publication/310874246_How_do_they_measure_up_Primary_pre-service_teachers'_mathematical_knowledge_of_area_and_perimeter
  • Machaba, F. M. (2016). The concepts of area and perimeter: Insights and misconceptions of Grade 10 learners. Pythagoras, 37(1), 304. https://doi.org/10.4102/pythagoras.v37i1.304
  • Magnusson, S., Krajcik, J., & Borko, H. (1999). Nature, sources and development of pedagogical content knowledge for science teaching, In J. Gess-Newsome & N. G. Lederman (Eds.). Examining pedagogical content knowledge: The construct and its implications for science education (pp. 95-132). Kluwer. https://doi.org/10.1007/0-306-47217-1_4
  • Marks, R. (1990). Pedagogical content knowledge. From a mathematical case to a modified concept. Journal of Teacher Education, 41(3), 3-11. https://doi.org/10.1177/002248719004100302
  • Moreira, C. Q. & Contente, M. do R. (1997). The role of writing to foster pupil’s learning about area. In Pehkonen, E. (Eds.), Proceedings of the Conference of the International Group for the Psychology of Mathematics Education (21st PME, Lahti, Finland), 3, 256-263.
  • National Council of Teachers of Mathematics [NCTM], (2000). Principles and standards for school mathematics.
  • National Council of Teachers of Mathematics [NCTM], (2014). Principles to actions: Ensuring mathematical success for all.
  • Nur, E., & Türnüklü, E. (2015). Middle school mathematics teachers’ pedagogical content knowledge regarding student knowledge about quadrilaterals. Elementary Education Online, 14(2), 744-756. https://doi.org/10.17051/io.2015.12002
  • Orhan, N. (2013). An Investigation of private middle school students’ common errors in the domain of area and perimeter and the relationship between their geometry self-efficacy beliefs and basic procedural and conceptual knowledge of area and perimeter [M.S. thesis]. Middle East Technical University.
  • Park, S., & Oliver, J. S. (2008). Revisiting the conceptualization of pedagogical content knowledge (PCK): PCK as a conceptual tool to understand teachers as professionals. Research in Science Education, 38(3), 261-284. https://doi.org/10.1007/s11165-007-9049-6
  • Rowland, T. (2013) The Knowledge Quartet: The genesis and application of a framework for analysing mathematics teaching and deepening teachers’ mathematics knowledge. SISYPHUS Journal of Education, 1(3), 15-43. https://doi.org/10.25749/sis.3705
  • Rowland, T., Huckstep, P., & Thwaites, A. (2003). The knowledge quartet. Proceedings of the British Society for Research into Learning Mathematics, 23(3), 97-102.
  • Rowland, T., Turner, F., Thwaites, A., & Huckstep, P. (2009). Developing primary mathematics teaching: Reflecting on practice with the Knowledge Quartet. Sage. https://doi.org/10.4135/9781446279571
  • Runnalls, C., & Hong, D. S. (2019). “Well, they understand the concept of area”: Preservice teachers’ responses to student area misconceptions. Mathematics Education Research Journal, 32(Jul), 629-651. https://doi.org/10.1007/s13394-019-00274-1
  • Sahin, O., Gokkurt, B., & Soylu, Y. (2016). Examining prospective mathematics teachers' pedagogical content knowledge on fractions in terms of students' mistakes. International Journal of Mathematical Education in Science and Technology, 47(4), 531-551. https://doi.org/10.1080/0020739X.2015.1092178
  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 4-14. https://doi.org/10.3102/0013189X015002004
  • Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1-23. https://doi.org/10.17763/haer.57.1.j463w79r56455411
  • Simsek, N. (2011). Investigation of pedagogical content knowledge of prospective mathematics teachers related to perimeter and area topics in the context of students’ difficulties (Unpublished master's thesis). Gazi University, Turkey.
  • Simsek, N., & Boz, N. (2015). Sınıf öğretmeni adaylarının uzunluk ölçme konusunda pedagojik alan bilgilerinin öğrenci kavrayışları bağlamında incelenmesi [Examination of primary school teacher candidates' pedagogical content knowledge about length measurement in the context of student comprehension]. Cumhuriyet Uluslararası Eğitim Dergisi, 4(3), 10-30. https://doi.org/10.30703/cije.321372
  • Tamir, P. (1988). Subject matter and related pedagogical knowledge in teacher education. Teaching and Teacher Education, 4(2), 99-110. https://doi.org/10.1016/0742-051X(88)90011-X
  • Tan- Sisman, G., & Aksu, M. (2009). Seventh grade students' success on the topic of area and perimeter. Elementary Online Education, 8(1), 243-253. https://dergipark.org.tr/tr/pub/ilkonline/issue/8599/107065
  • Tan- Sisman, G., & Aksu, M. (2012). Sixth grade students' performance on length, area, and volume measurement. Education & Science / Egitim ve Bilim, 37(166), 141-154. https://www.researchgate.net/publication/45361044_Sixth_Grade_Students'_Performance_on_Length_Area_and_Volume_Measurement
  • Tan- Sisman, G., & Aksu, M. (2012). The length measurement in the Turkish mathematics curriculum: Its potential to contribute to students’ learning. International Journal of Science and Mathematics Education, 10, 363-385. https://doi.org/10.1007/s10763-011-9304-1
  • Tanisli, D., Kose, N. Y., & Yavuzsoy, N. (2013). Pre-service mathematic teachers‟ knowledge of students about the algebraic concepts. Australian Journal of Teacher Education, 38(2), 1-18. https://doi.org/10.14221/ajte.2013v38n2.1
  • Tekin-Striva, R. (2014). An investigation into middle school mathematics teachers’ subject matter knowledge and pedagogical content knowledge regarding the volume of 3D solids (Unpublished doctoral dissertation). Middle East Technical University, Turkey.
  • Van Steenbrugge, H., Lesage, E., Valcke, M. & Desoete, A., (2014). Preservice elementary school teachers’ knowledge of fractions: a mirror of students’ knowledge?. Journal of Curriculum Studies, 46(1), 138-161. https://doi.org/10.1080/00220272.2013.839003
  • Weston, T. L., Kleve, B., & Rowland, T. (2012) Developing an online coding manual for the Knowledge Quartet: An international project. Proceedings of the British Society for Research into Learning Mathematics, 32(3), 179-184.
  • Yenilmez, K., & Yaşa, E. (2008). İlköğretim öğrencilerinin geometrideki kavram yanılgıları [Primary school students' misconceptions in geometry]. Eskişehir Osmangazi Üniversitesi Eğitim Fakültesi Dergisi, XXI(2), 461-483. https://dergipark.org.tr/tr/pub/uefad/issue/16688/173427
  • Yeo, J. K. K. (2008). Teaching area and perimeter: Mathematics-pedagogical-content knowledge-in-action [Paper presentation]. 31st Annual Conference of the Mathematis Education Reseach Group of Ustralasia Incorporated (MERGA, 2008). http://hdl.handle.net/10497/14397
  • Yurtyapan, M., & Karataş, İ. (2020). Ortaokul matematik öğretmenlerinin üçgenler ve dörtgenler konusuna ilişkin pedagojik alan bilgilerinin incelenmesi [Examination of secondary school mathematics teachers' pedagogical content knowledge on triangles and quadrilaterals]. Turkish Journal of Computer and Mathematics Education, 11(1), 53-90. https://doi.org/10.16949/turkbilmat.443825
  • Zacharos, K. (2006). Prevailing educational practices for area measurement and students’ failure in measuring areas. The Journal of Mathematical Behavior, 25, 224-239. https://doi.org/10.1016/j.jmathb.2006.09.003