Students’ Perceptions of Geometry: Geometry School Project


Zeybek N., Demiray E., Özyıldırım Gümüş F., Aydın Ş.

European Conference on Educational Research (ECER), Hamburg, Germany, 2 - 06 September 2019

  • Publication Type: Conference Paper / Summary Text
  • City: Hamburg
  • Country: Germany
  • Hacettepe University Affiliated: Yes

Abstract

Students’ perceptions have a significant effect on teaching and learning process (Biggs, 2001; Entwistle, Meyer, & Tait, 1991; Marton & Säljö, 1976). The positive perceptions of students about a course or a subject contribute to their motivation, engagement, and academic achievement (Hiebert & Grouws, 2007; Postareff, Mattsson, & Parpala, 2018; Walles & Munter, 2018). Researchers have conducted various studies to develop students’ perceptions positively (e.g., Schoenfeld, 1989; Walton & Brady, 2017). Hiebert and Grouws (2007) stated that students' perceptions are related to their experiences in the courses and emphasized that learners should be provided with various learning opportunities. In this manner, it can be stated that determining the perceptions of students and also helping them to develop positive perceptions should be considered as one of the important tasks by educators. This study aims to approach the concept of students’ perceptions in terms of geometry.

Considering geometry, Van Hiele (1986) emphasized that geometric experience is one of the most important factors in comprehension and achievement in geometry. The diversity of these experiences might affect students’ perceptions of geometry positively. Therefore, students should be provided various learning environments so that they can have opportunity to reach experiences needed to develop their perceptions of geometry (Devichi & Munier, 2013, Dogan, Ozkan, Cakir, Baysal, & Day, 2012; Luneta, 2015; Makhubele, Nkhoma, & Luneta, 2015). Moreover, in the literature review, it was seen that geometry is an area offering various experiences such as spatial ability, geometric construction, dynamic geometry programs, coding, origami, and educational game.

Spatial ability is an important element in the process of learning and teaching geometry (Battista, Wheatley, & Talsma, 1982). Studies showed that there is a positive relationship between spatial ability and geometry achievement (Ben-Haim, Lappan, & Houang, 1985; Cakmak, 2009; Clements & Battista, 1992; Gutierrez, 1996). The use of geometric construction in learning provides a better understanding of the concepts by emphasizing the basic foundations of the concepts (Kuzle, 2013). Also, dynamic geometry programs such as Geometer’s Sketchpad and GeoGebra enable students to be active in learning and increase their motivation and engagement (Dikovic, 2009; Hohenwarter & Jones, 2007; Pfeiffer, 2017).

The use of coding activities in teaching and learning geometry is one of the popular and remarkable teaching methods. With the use of coding, it was observed that the students' problem solving skills (Akcaoglu & Koehler, 2014; Kukul & Gökçe Arslan, 2014; Shin & Park, 2014) and operational thinking skills (Brennan & Resnick, 2012; Grover & Pea, 2013; Ruthmann, Heines, Greher, Laidler, & Saulters, 2010) developed and their academic achievement increased (Taylor, Harlow, & Forret, 2010; Wang, Huang, & Huang, 2014). In addition, it was determined that origami facilitated students' learning of geometry (Arslan & Işıksal-Bostan, 2016; Boakes, 2009) and also educational games increased students' motivation (Fisch, 2005; Gee, 2003; Samur, 2012), engagement (Huizenga, Admiraal, Akkerman, & ten Dam, 2009) and achievement (Ke & Grabowski, 2007; Tüzün, Yılmaz-Soylu, Karakuş, İnal, & Kizilkaya, 2009). It was emphasized that educational games have an impact on various learning outcomes and skills such as problem solving (Dempsey, Lucassen, Gilley, & Rasmussen, 1993), transfer and application of knowledge (Barab, Scott, Siyahhan, Goldstone, Ingram-Goble, Zuiker, & Warren, 2009).

This study is part of a broader project which was named as “Geometry School Project”. In this project, a geometry school was planned in a way that enriched geometry activities focusing on the mentioned concepts, which are spatial ability, geometric construction, dynamic geometry programs, coding, origami, and educational game, were prepared. The aim of this study is to examine and present the 7th grade students’ perceptions of geometry before and after geometry school.

Method

As the research method of this study, the case study which is one of the qualitative research methods was planned to use. According to Merriam (1998), the case study is used to examine a person, a program or a group in depth. It was also decided that the participants will be composed of 24 7th grade students in a medium-sized city center in Turkey. While selecting these 24 students, the opinions of mathematics teachers in the disadvantaged regions of the selected city will be asked. The study was planned to last five days and at least one enriched geometry activity will be held every day. To collect data before and after the application of enriched geometry activities, a structured interview form was prepared. That is, focus group interviews will be conducted to determine students’ perceptions of geometry both in the first day and in the last day of the study. Since each group was aimed to include four students, focus group interviews will be conducted with six groups. For the content validity of the questions, three experts from the field of mathematics education and one mathematics teacher were consulted and the questions were finalized according to their opinions. The questions in the form were listed as follows; What is geometry?, How do you describe it?, How much do you use geometry in your daily life?, and Where do you use it? The data obtained from the interview form will be examined by means of utilizing content analysis. The analysis of data will be carried out separately by researchers and then the findings will be discussed until reaching a consensus. Via this analysis, it was aimed to compare students’ perceptions of geometry before and after the utilization of the enriched geometry activities.

Expected Outcomes

Since the activities within the study will be implemented in July, the results cannot be presented at this point. As Hiebert and Grouws (2007) pointed out, students' perceptions are related to experiences. Therefore, it is expected that the enriched geometry activities would provide a positive contribution to students' perceptions of geometry. Also, due to the effects of these activities, it is expected that the participants will have a higher level of motivation and engagement related to geometry. In addition, it is thought that students who are not aware of it even if they use geometry in daily life will gain awareness with the help of the activities in this study.

References

Arslan, O., & Isiksal-Bostan, M. (2016). Turkish Prospective Middle School Mathematics Teachers' Beliefs and Perceived Self-Efficacy Beliefs Regarding the Use of Origami in Mathematics Education. Eurasia Journal of Mathematics, Science & Technology Education, 12(6), 1533-1548. Ben-Haim, D., Lappan, G., & Houang, R. T. (1985). Visualizing rectangular solids made of small cubes: Analyzing and effecting students' performance. Educational studies in Mathematics, 16(4), 389-409. Clements, D. H., & Battista, M. T. (1992). Geometry and spatial reasoning. Handbook of research on mathematics teaching and learning, 420-464. Devichi, C., & Munier, V. (2013). About the concept of angle in elementary school: Misconceptions and teaching sequences. The Journal of Mathematical Behavior, 32(1), 1-19. Entwistle, N. J., Meyer, J. H. F., & Tait, H. (1991). Student failure: Disintegrated patterns of study strategies and perceptions of the learning environment. Higher Education, 21(2), 249-261. Gee, J. P. (2003). What video games have to teach us about learning and literacy. Computers in Entertainment (CIE), 1(1), 20-20. Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students’ learning. Second handbook of research on mathematics teaching and learning, 1, 371-404. Ke, F., & Grabowski, B. (2007). Gameplaying for maths learning: cooperative or not? British Journal of Educational Technology, 38(2), 249-259. Kuzle, A. (2013). Patterns of metacognitive behavior during mathematics problem-solving in a dynamic geometry environment. International Electronic Journal of Mathematics Education, 8(1), 20-40. Marton, F., & Säljö, R. (1976). On qualitative differences in learning: I—Outcome and process. British journal of educational psychology, 46(1), 4-11. Merriam, S. B. (1998). Qualitative research and case study applications in education. Revised and expanded from "case study research in education."San Francisco: Jossey-Bass Publishers. Postareff, L., Mattsson, M., & Parpala, A. (2018). The effect of perceptions of the teaching-learning environment on the variation in approaches to learning–Between-student differences and within-student variation. Learning and Individual Differences, 68, 96-107. Taylor, M., Harlow, A., & Forret, M. (2010). Using a computer programming environment and an interactive whiteboard to investigate some mathematical thinking. Procedia-Social and Behavioral Sciences, 8, 561-570. Van Hiele, P. M. (1986). Is It Possible to Test Insight? Structure and insight A theory of mathematics education.