Construction strategies for parallelism and perpendicularity: a paper folding activity

Date

2019-04-14

Author

Çatman Aksoy, Emine
Işıksal Bostan, Mine

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One of the basic concepts in geometry is parallelism and perpendicularity of lines. Construction of these concepts have a significant role for understanding further geometric concepts such as interior and exterior angles or properties of quadrilaterals (Ulusoy, 2013). Available literature indicated that construction of parallel and perpendicular lines were difficult for students (Abravenel, 1977; Mitchelmore, 1992a). On the other hand, origami, the art of paper folding (Royo, 2002), can be useful for the construction of some geometric concepts (Boakes, 2009; Dagdelen, 2012). For instance, Dagdelen (2012) observed that student’ abilities of constructing some quadrilaterals developed after they were involved in an origami based instruction. Considering the findings of the above studies, the present study aimed to examine effect of a paper folding activity on strategies of sixth grade students in construction of parallel and perpendicular line segments. Qualitative survey is the appropriate design type to determine diversity of any topic in population (Jansen, 2010). In the present study, diversity of students’ construction strategies was aimed to be investigated through qualitative survey. Forty-five public middle school students who are in the sixth grade were selected conveniently as participants of this study. Paper folding activities were prepared by the researchers using the studies in the literature. The key characteristic of activities was that directions for constructions were not provided to students directly. Instead, they were directed to explore steps in the constructions through proper questions. Activities were implemented to students through ten lesson hours. Furthermore, students were requested to construct parallel and perpendicular line segments to given three line segments before and after the activities. All of the students’ constructions were examined through content analysis. Indepth analysis of students’ constructions and their explanations before the activities indicated three strategies for the construction of parallel and perpendicular line segments. Those strategies were constructions according to definitions, constructions by using the square paper and random constructions with and without rationale. On the other hand, it was realized that students enhanced their strategies after the paper folding activities. One more strategy for both constructions of parallel and perpendicular line segments emerged after the paper folding activities. Those strategies were constructions by using a perpendicular line segment for parallelism and constructions by taking 90° angle as a reference for perpendicularity. It can be deduced according to these findings that paper folding activities was effective for the construction of parallel and perpendicular line segments. However, the number of students using new strategies were low compared to the number of students using other strategies. Therefore, students are suggested to spend more time with such kind of activities.

Subject Keywords

Parallelism, Perpendicularity, Construction, Middle school mathematics

URI

https://hdl.handle.net/11511/74755
http://www.fmgtegitimikongresi.com/dosyalar/files/ozetler_v3.pdf

Conference Name

International Conference on Science, Mathematics, Entrepreneurship and Technology Education, (12 - 14 Nisan 2019)

Collections

Department of Mathematics and Science Education, Conference / Seminar

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Citation Formats

E. Çatman Aksoy and M. Işıksal Bostan, “Construction strategies for parallelism and perpendicularity: a paper folding activity,” İzmir, Türkiye, 2019, p. 494, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/74755.