Fostering students’ definitions and images in parallelism and perpendicularity: A paper folding activity

Emine Catman-Aksoy 1 * , Mine Isiksal-Bostan 1
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1 Department of Mathematics and Science Education, Faculty of Education, Middle East Technical University, Ankara, TÜRKİYE
* Corresponding Author
EUR J SCI MATH ED, Volume 12, Issue 2, pp. 236-257. https://doi.org/10.30935/scimath/14360
Published Online: 14 March 2024, Published: 01 April 2024
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ABSTRACT

This study investigated the effect of a paper folding activity prepared to develop the sixth-grade students’ concept definitions and images of parallelism and perpendicularity concepts. The study also examined how the concept definition and images changed after the paper folding activity. A combination of quantitative and qualitative methods was used. A one-group pre-/post-test design revealed that the paper folding activity had a significant positive effect on students’ concept definitions and images. In addition, the interviews after pre- and post-tests indicated that the students’ personal concept definitions of parallelism and perpendicularity of two lines/line segments began to match the formal concept definitions of these concepts after the paper folding activity. Lastly, missing and mis-in concept image situations, encountered generally in the pre-test, were observed less after the paper folding activity.
Keywords: concept definition, concept image, paper folding, parallelism, perpendicularity

CITATION

Catman-Aksoy, E., & Isiksal-Bostan, M. (2024). Fostering students’ definitions and images in parallelism and perpendicularity: A paper folding activity. European Journal of Science and Mathematics Education, 12(2), 236-257. https://doi.org/10.30935/scimath/14360

REFERENCES

  • Boakes, N. (2009). Origami instruction in the middle school mathematics classroom: Its impact on spatial visualization and geometry knowledge of students. Research in Middle Level Education Online, 32(7), 1-12. https://doi.org/10.1080/19404476.2009.11462060
  • CCSSM. (2010). Common core state standards for mat­hematics. National Governors Association Center for Best Practices and the Council of Chief State School Officers. https://corestandards.org/wp-content/uploads/2023/09/Math_Standards1.pdf
  • Clements, D. H. (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). National Council of Teachers of Mathematics.
  • Clements, D. H., & Battista, M. T. (1992). Geometry and spatial reasoning. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 420-464). National Council of Teachers of Mathematics.
  • Cohen, J. (1977). Statistical power analysis for the behavioral sciences. Academic Press. https://doi.org/10.4324/9780203771587
  • Duatepe-Paksu, A., & Bayram, G. (2019). Altıncı sınıf öğrencilerinin paralel ve dik doğru/doğru parçalarını belirleme ve çizme durumları [Sixth grade students’ situations in identifying and drawing parallel and perpendicular lines/line segments]. Gazi Üniversitesi Gazi Eğitim Fakültesi Dergisi [Gazi University Gazi Faculty of Education Journal], 39(1), 115-145. https://doi.org/10.17152/gefad.346360
  • Edwards, B., & Ward, M. (2008). The role of mathematical definitions in mathematics and in undergraduate mathematics courses. In M. Carlson, & C. Rasmussen (Eds.), Making the connection: Research and teaching in undergraduate mathematics education (pp. 223-232). Mathematical Association of America. https://doi.org/10.5948/UPO9780883859759.018
  • Fraenkel, J. R., Wallen, N. E., & Hyun, H. H. (2012). How to design and evaluate research in education. McGraw-Hill.
  • Gal, H., & Linchevski. (2002). Analyzing geometry problematic learning situations by theory of perception. In A. Cockburn, & E. Nardi (Eds.), Proceedings of the 26th Conference of the International Group for the Psychology of Mathematics Education (pp. 400-407). PME.
  • Gal, H., & Linchevski, L. (2010). To see or not to see: Analyzing difficulties in geometry from the perspective of visual perception. Educational Studies in Mathematics, 74, 163-183. https://doi.org/10.1007/s10649-010-9232-y
  • Gal, H., & Vinner, S. (1997). Perpendicular lines–What is the problem? In E. Pehkonen (Ed.), Proceedings of the 21st Conference of the International Group for the Psychology of Mathematics Education (pp. 281-288). PME.
  • Georgeson, J. (2011). Fold in origami and unfold math. Mathematics Teaching in Middle School, 16(6), 354-361. https://doi.org/10.5951/MTMS.16.6.0354
  • Gravetter, F. J., & Wallnau, L. B. (2013). Statistics for the behavioral sciences. Cengage Learning.
  • 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
  • Haga K., Fonacier, J. C., & Isoda, M. (2008). Origamics: Mathematical explorations through paper folding. World Scientific. https://doi.org/10.1142/7023
  • Hershkowitz, R. (1989). Visualization in geometry–Two sides of the coin. Focus on Learning Problems in Mathematics, 11(1), 61-76.
  • Johnson, D. A. (1999). Paper folding for the mathematics class. National Council of Teachers of Mathematics.
  • Kandil, S., & Isiksal-Bostan, M. (2019). Effect of inquiry-based instruction enriched with origami activities on achievement, and self-efficacy in geometry. International Journal of Mathematical Education in Science and Technology, 50(4), 557-576. https://doi.prg/10.1080/0020739X.2018.1527407
  • Mansfield, H. M., & Happs, J. C. (1992). Using grade eight students’ existing knowledge to teach about parallel lines. School Science and Mathematics, 92(8), 450-454. https://doi.org/10.1111/j.1949-8594.1992.tb15628.x
  • MoNE. (2013). Ortaokul matematik dersi (5, 6, 7 ve 8. sınıflar) öğretim programı [Secondary school mathematics course (5th, 6th, 7th and 8th grades) curriculum]. Ministry of National Education.
  • MoNE. (2018). Matematik dersi (ilkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar) öğretim programı [Mathematics course (primary and secondary school 1st, 2nd, 3rd, 4th, 5th, 6th, 7th and 8th grades) curriculum]. Ministry of National Education.
  • NCTM. (2000). Principles and standards for school mathematics. National Council of Teachers of Mathematics.
  • Olson, A. T. (1975). Mathematics through paper folding. National Council of Teachers of Mathematics.
  • Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12, 151-169. https://doi.org/10.1007/BF00305619
  • Tirosh, D., & Tsamir, P. (2022). Missing and mis-in-concept images of parallelograms: The case of Tal. International Journal of Science and Mathematics Education, 20, 981-997. https://doi.org/10.1007/s10763-021-10175-0
  • Tsamir, P., Tirosh, D., & Levenson, E. (2008). Intuitive nonexamples: The case of triangles. Educational Studies in Mathematics, 69(2), 81-95. https://doi.org/10.1007/s10649-008-9133-5
  • Tsamir, P., Tirosh, D., Levenson, E., Barkai, R., & Tabach, M. (2015). Early-years teachers’ concept images and concept definitions: Triangles, circles, and cylinders. ZDM Mathematics Education, 47(3), 497-509. https://doi.org/10.1007/s11858-014-0641-8
  • Ulusoy, F. (2016). The role of learners’ example spaces in example generation and determination of two parallel and perpendicular line segments. In C. Cisikos, A. Rausch, & J. Szitanyi (Eds.), Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education (pp. 299-306). PME.
  • van Hiele, P. M. (1986). Structure and insight. Academic Press.
  • Vinner, S. (1983). Concept definition, concept image and the notion of function. International Journal of Mathematical Education in Science and Technology, 14(3), 293-305. https://doi.org/10.1080/0020739830140305
  • Vinner, S. (2011). The role of examples in the learning of mathematics and in everyday thought processes. ZDM Mathematics Education, 43(2), 247-256. https://doi.org/10.1007/s11858-010-0304-3
  • Vinner, S., & Hershkowitz, R. (1980). Concept images and common cognitive paths in the development of some simple geometrical concepts. In R. Karplus (Ed.), Proceedings of the 4th Conference of the International Group for the Psychology of Mathematics Education (pp. 177-185). PME.
  • Wares, A., & Elstak, I. (2017). Origami, geometry and art. International Journal of Mathematical Education in Science and Technology, 48(2), 317-324. https://doi.org/10.1080/0020739X.2016.1238521
  • Wilson, S. (1986). Feature frequency and the use of negative instances in a geometric task. Journal for Research in Mathematics Education, 17, 130-139. https://doi.org/10.2307/749258
  • Wilson, S. (1990). Inconsistent ideas related to definitions and examples. Focus on Learning Problems in Mathematics, 12, 31-47.
  • Winicki-Landman, G., & Leikin, R. (2000). On equivalent and non-equivalent definitions: Part 1. For the Learning of Mathematics, 20(1), 17-21. http://www.jstor.org/stable/40248314