632
Views
1
CrossRef citations to date
0
Altmetric
Articles

Comparing the concept images and hierarchical classification skills of students at different educational levels regarding parallelograms: a cross-sectional study

ORCID Icon & ORCID Icon
Pages 850-882 | Received 01 Dec 2020, Published online: 01 Apr 2022

References

  • Akkaş, E. N., & Türnüklü, E. (2015). Middle school mathematics teachers’ pedagogical content knowledge regarding student knowledge about quadrilaterals. İlköğretim Online, 14(2), 744–756. https://doi.org/10.17051/io.2015.12002
  • Aktaş, D. Y., & Cansız-Aktaş, M. (2012). Eighth grade students’ understanding and hierarchical classification of quadrilaterals. Elementary Education Online, 11(3), 714–728. https://dergipark.org.tr/tr/download/article-file/90562.
  • Ay, Y., & Başbay, A. (2017). Çokgenlerle İlgili kavram yanılgıları ve olası nedenler. Ege Eğitim Dergisi, 18(1), 83–104. https://doi.org/10.12984/egeefd.328377
  • Baki, A. (2008). Mathematics education theory to practice [kuramdan uygulamaya matematik eğitimi]. Harf Publication.
  • Baktemur, G., Ayan Civak, R., & Isiksal Bostan, M. (2021). Pre-service middle school mathematics teachers’ (mis)conceptions of definitions, classifications, and inclusion relations of quadrilaterals. European Journal of Science and Mathematics Education, 9(4), 183–198. https://doi.org/10.30935/scimath/11206
  • Bal, A. P. (2012). Teacher candidates’ geometric thinking levels and attitudes to geometry. Journal of Educational Sciences Research, 2(1), 17–34. https://dergipark.org.tr/tr/pub/ebader/issue/44650/554613.
  • Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching. Journal of Teacher Education, 59(5), 389–407. https://doi.org/10.1177/0022487108324554
  • Birgin, O., Akçakın, V., & Bozkurt, E. (2018, March 23–25). An investigation of secondary school students’ Van Hiele geometric thinking levels. Paper presented at the First International Congress on Science and Education, Afyonkarahisar.
  • Birgin, O., & Özkan, K. (2012, June 27–30). Investigation of the knowledge levels and misconceptions of primary school teacher candidates regarding the concept of the trapezoid. Proceedings of 10th National Science and Mathematics Education Congress (p. 458–459). Pegem Academic Publishing.
  • Birgin, O., & Özkan, K. (2014, September 11–14). Examining the concept images of the students at different education levels regarding the regular polygon. Paper presented at the 11th National Science and Mathematics Education Congress, Cukurova University, Adana.
  • Birgin, O., & Topuz, F. (2021). Effect of the GeoGebra software-supported collaborative learning environment on seventh grade students’ geometry achievement, retention and attitudes. The Journal of Educational Research, 114(5), 474–494. https://doi.org/10.1080/00220671.2021.1983505
  • Bozkurt, A., & Koç, Y. (2012). Investigating first year elementary mathematics teacher education students’ knowledge of prism. Educational Sciences: Theory & Practice, 12(4), 2941–2952. https://files.eric.ed.gov/fulltext/EJ1002894.pdf.
  • Bütüner, SÖ, & Filiz, M. (2017). Exploring Turkish mathematics teachers’ content knowledge of quadrilaterals. International Journal of Research in Education and Science, 3(2), 395–395. https://doi.org/10.21890/ijres.327898
  • Cansız Aktaş, M. (2016). Turkish high school students’ definitions for parallelograms: Appropriate or inappropriate? International Journal of Mathematical Education in Science and Technology, 47(4), 583–596. https://doi.org/10.1080/0020739X.2015.1124931
  • Cansız Aktaş, M., & Aktaş, D. Y. (2012). Students’ understanding of quadrilaterals: The sample of parallelogram. Journal of Research in Education and Teaching, 1(2), 319–329. http://www.jret.org/FileUpload/ks281142/File/36.aktas.pdf.
  • Creswell, J. W. (2012). Educational research: Planning, conducting, and evaluating quantitative and qualitative research (4th ed.). Pearson.
  • Çontay, E. G., & Duatepe-Paksu, A. (2019). 8 th grade students’ understanding of the definition of rectangle. Acta Didactica Napocensia, 12(1), 225–238. https://doi.org/10.24193/adn.12.1.17
  • de Villiers, M. (1994). The role and function of a hierarchical classification of quadrilaterals. For the Learning of Mathematics, 14(1), 11–18. http://www.jstor.org/stable/40248098.
  • Disbudak, O., & Akyuz, D. (2019). The comparative effects of concrete manipulates and dynamic software on the geometry achievement of fifth-grade students. International Journal for Technology in Mathematics Education, 26(1), 3–20. https://doi.org/10.1564/tme_v26.1.01
  • Duatepe-Paksu, A. (2017). Constructing a rhombus through paper folding. International Journal of Mathematical Education in Science and Technology, 48(5), 763–767. https://doi.org/10.1080/0020739X.2017.1282048
  • Duatepe-Paksu, A., İymen, E., & Pakmak, G. S. (2012). How well elementary teachers identify parallelogram? Educational Studies, 38(4), 415–418. https://doi.org/10.1080/03055698.2011.643106
  • Duatepe-Paksu, A., İymen, E., & Pakmak, G. S. (2013). Pre-service elementary teachers’ concept images on diagonal of quadrilaterals. Education and Science, 38(167), 162–178. http://egitimvebilim.ted.org.tr/index.php/EB/article/view/1633.
  • Erdogan, E. O., & Dur, Z. (2014). Preservice mathematics teachers’ personal figural concepts and classifications about quadrilaterals. Australian Journal of Teacher Education, 39(6), 107–133. https://doi.org/10.14221/ajte.2014v39n6.1
  • Ergün, S. (2010). 7th grade students’ perception, definition and classification of the polygons [Unpublished master's thesis]. Dokuz Eylül University.
  • Erşen, Z., & Karakuş, F. (2013). Evaluation of preservice elementary teachers’ concept images for quadrilaterals. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 4(2), 124–146. https://doi.org/10.16949/turcomat.21946
  • Fidan, Y., & Türnüklü, E. (2010). Examination of 5th grade students’ levels of geometric thinking in terms of some variables. Pamukkale University Journal of Education, 27(27), 185–197. https://dergipark.org.tr/tr/pub/pauefd/issue/11116/132940.
  • Fischbein, E. (1993). The theory of figural concepts. Educational Studies in Mathematics, 24(2), 139–162. https://doi.org/10.1007/BF01273689
  • Fujita, T. (2012). Learners’ level of understanding of the inclusion relations of quadrilaterals and prototype phenomenon. The Journal of Mathematical Behavior, 31(1), 60–72. https://doi.org/10.1016/j.jmathb.2011.08.003
  • Fujita, T., & Jones, K. (2006). Primary trainee teacherś knowledge of parallelograms. In D. Hewitt (Ed.), Proceedings of the British society for Research into learning mathematics, 26(2) (pp. 25–30). University of Bristol.
  • 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
  • Gökbulut, Y., Sidekli, S., & Yangın, B. (2010). Researching prospective primary teacher's van Hiele geometric thinking levels according to some variables (graduation type of high school, high school sphere, high school average, ÖSS (öğrenci seçme sınavı) points, university academic average and sex). The Journal of Turkish Educational Sciences, 8(2), 375–396. https://dergipark.org.tr/en/pub/tebd/issue/26104/275039.
  • Guncaga, J., Tkacik, S., & Zilkova, K. (2017). Understanding of selected geometric concepts by pupils of pre-primary and primary level education. European Journal of Contemporary Education, 6(3), 497–515. https://doi.org/10.13187/ejced.2017.3.497
  • Günhan, B. C. (2014). An investıgatıon of Pre-servıce elementary school teachers’ knowledge concernıng quadrilaterals. Cukurova University Faculty of Education Journal, 43(2), 137–154. https://doi.org/10.14812/cufej.2014.017
  • Gürel, ZÇ, & Okur, M. (2018). Defining and classifying skills of pre-service secondary school mathematics teachers in quadrilaterals: The example of trapezoid. International Journal of Educational Studies in Mathematics, 5(4), 140–161. https://dergipark.org.tr/tr/pub/ijesim/issue/40295/472208.
  • Halas, Z., Robova, J., Moravcova, V., & Hromodova, J. (2019). Students’ concepts of the trapezoid at the end of lower secondary level education. Open Education Studies, 1(1), 184–197. https://doi.org/10.1515/edu-2019-0013
  • Hershkowitz, R. (1990). Psychological aspects of learning geometry. In P. Nesher, & J. Kilpatrick (Eds.), Mathematics and cognition (pp. 70–95). Cambridge University Press.
  • Hershkowitz, R., & Vinner, S. (1983). The role of critical and non-critical attributes in the concept image of geometrical concepts. In R. Hershkowitz (Ed.), Proceeding of the 7th International Conference for the Psychology of Mathematics education (pp. 223–228). Weizmann Institute of Science.
  • Horzum, T. (2018). The investigation of preservice mathematics teachers’ knowledge about quadrilaterals through concept maps. Turkish Journal of Computer and Mathematics Education, 9(1), 1–30. https://doi.org/10.17762/turcomat.v9i1.169
  • Kartal, B., & Çınar, C. (2017). Examining pre-service mathematics teachers’ geometry knowledge of polygons. Journal of Kırşehir Education Faculty, 18(2), 451–482. https://dergipark.org.tr/tr/pub/kefad/issue/59416/853255.
  • Küçük, A., & Demir, B. (2009). A study on some misperceived concepts in the teaching of mathematics in 6th-8th grades. Dicle University Journal of Ziya Gökalp Faculty of Education, 13(1), 97–112. https://dergipark.org.tr/tr/pub/zgefd/issue/47954/606734.
  • Leung, F., & Park, K. (2009). The influence of language on the conception of geometric figures. In M. Tzekaki, M. Kaldrimidou, & H. Sakonidis (Eds.), Proceedings of 33rd Conference of the International Group for the Psychology of Mathematics education (pp. 81–88). PME.
  • Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook (2nd ed.). Sage Publications.
  • Minister of National Education (MoNE). (2013). Ortaokul matematik dersi 5-8.sınıflar öğretim programı [Middle school mathematics curriculum for grades 5-8]. Republic of Turkish Ministry of National Education.
  • Minister of National Education (MoNE). (2018). Matematik dersi öğretim programı (İlkokul ve ortaokul 1-8. sınıflar) [Primary and middle school mathematics curriculum (grades 1-8)]. Republic of Turkish Ministry of National Education.
  • Monaghan, F. (2000). What difference does it make? Children’s views of the differences between some quadrilaterals. Educational Studies in Mathematics, 42(2), 179–196. https://doi.org/10.1023/A:1004175020394
  • Moss, J., & Case, R. (1999). Developing children's understanding of the rational numbers: A New model and an experimental curriculum. Journal for Research in Mathematics Education, 30(2), 122–147. https://doi.org/10.2307/749607
  • Mullis, I. V., Martin, M. O., Foy, P., & Arora, A. (2012). TIMSS 2011 international results in mathematics. TIMSS & PIRLS International Study Center.
  • National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. NCTM.
  • Okazaki, M., & Fujita, T. (2007). Prototype phenomena and common cognitive paths in the understanding of the inclusion relations between quadrilaterals in Japan and Scotland. In J. H. Woo, J. H. Lew, K. S. Park, & D. Y. Seo (Eds.), Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics education 4 (pp. 41–48). PME.
  • Ozkan, M., & Bal, A. P. (2017). Analysis of the misconceptions of 7th grade students on polygons and specific quadrilaterals. Eurasian Journal of Educational Research, 17(67), 161–182. https://doi.org/10.14689/ejer.2017.67.10
  • Özgen, K. (2016). Investigation of Van Hiele geometry thinking levels of high school students’ in terms of some variables. In M. Riedler, E. Yolcu, S. Z. Genç, & M. Y. Eryaman (Eds.), Proceeding of 8th International Congress of Educational research (pp. 1506–1523). Turkish Educational Research Association Press.
  • Pickreign, J. (2007). Rectangle and rhombi: How well do pre-service teachers know them? Issues in the Undergraduate Mathematics Preparation of School Teachers, 1(1), 1–7. http://www.k-12prep.math.ttu.edu/journal/1.contentknowledge/pickreign01/article.pdf.
  • Popovic, G. (2012). On My mind: Who Is this trapezoid, anyway?. Mathematics Teaching in the Middle School, 18(4), 196–199. https://doi.org/10.5951/mathteacmiddscho.18.4.0196
  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14. https://doi.org/10.3102/0013189X015002004
  • Tall, D. O., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12(2), 151–169. https://doi.org/10.1007/BF00305619
  • Tsamir, P., Tirosh, D., Levenson, E., Barkai, R., & Tabach, M. (2015). Early-years teachers’ concept images and concept definitions: Triangles, circles, and cylinders. ZDM, 47(3), 497–509. https://doi.org/10.1007/s11858-014-0641-8
  • Türnüklü, E. (2014a). Construction of inclusion relations of quadrilaterals: Analysis of preservice elementary mathematics teachers’ lesson plans. Education and Science, 39(173), 198–208. http://egitimvebilim.ted.org.tr/index.php/EB/article/view/2705.
  • Türnüklü, E. (2014b). Concept images of trapezoid: Some cases from Turkey. Education Journal, 3(3), 179–185. https://doi.org/10.11648/j.edu.20140303.19
  • Türnüklü, E., Alaylı, F. G., & Akkaş, E. N. (2013). Investigation of prospective primary mathematics teachers’ perceptions and images for quadrilaterals. Educational Sciences: Theory & Practice, 13(2), 1225–1232. https://files.eric.ed.gov/fulltext/EJ1017328.pdf.
  • Ubuz, B. (2017). Relations among quadrilaterals: 7th grade students’ concept images. Yaşadıkça Eğitim Dergisi (Journal of Education for Life), 31(1), 55–68. http://journals.iku.edu.tr/yed/index.php/yed/article/view/58.
  • Ubuz, B., & Üstün, I. (2004). Figural and conceptual aspects in defining and identifying polygons. Eurasian Journal of Educational Research, 16(1), 15–26.
  • Ulusoy, F., & Çakıroğlu, E. (2017). Ortaokul Öğrencilerinin paralelkenari ayirt etme biçimleri: Aşiri Özelleme Ve aşiri genelleme. Abant İzzet Baysal Üniversitesi Eğitim Fakültesi Dergisi, 17(1), 457–475. https://doi.org/10.17240/aibuefd.2017.17.28551-304648
  • Usiskin, Z., Griffin, J., Witonsky, D., & Willmore, E. (2008). The classification of quadrilaterals: A study in definition. Information Age Publishing.
  • Van Hiele, P. M. (1986). Structure and insight: A theory of mathematics education. Academic Pres.
  • Vinner, S. (1991). The role of definitions in the teaching and learning of mathematics. In D. Tall (Ed.), Advanced mathematical thinking (pp. 65–81). Kluwer.
  • Vinner, S., & Hershkowitz, R. (1980). Concept images and some common cognitive paths in the development of some simple geometric concepts. In R. Karplus (Ed.), Proceedings of the 4th International Conference for the Psychology of Mathematics education (pp. 177–184). University of California.
  • Walcott, C., Mohr, D., & Kastberg, S. E. (2009). Making sense of shape: An analysis of children's written responses. The Journal of Mathematical Behavior, 28(1), 30–40. https://doi.org/10.1016/j.jmathb.2009.04.001
  • Yavuzsoy Kose, N., Yilmaz, T. Y., Yesil, D., & Yildirim, D. (2019). Middle school students’ interpretation of definitions of the parallelogram family: Which definition for which parallelogram? International Journal of Research in Education and Science (IJRES), 5(1), 157–175. https://www.ijres.net/index.php/ijres/article/view/466.
  • Zaskis, R., & Leikin, R. (2008). Exemplifying definitions: A case of a square. Educational Studies in Mathematics, 69(2), 131–148. https://doi.org/10.1007/s10649-008-9131-7
  • Zeybek Şimşek, Z. (2019). Investigating pre-service teachers’ ability to recognize and classify geometric concepts hierarchically. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 10(3), 680–710. https://doi.org/10.16949/turkbilmat.491564

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.