Investigation of the Development of van Hiele Levels of Geometric Thinking in a Computer Supported Collaborative Learning (CSCL) Environment

Yıl 2019, Cilt: 15 Sayı: 2, 473 - 490, 26.08.2019

Emre Özkan Diler Öner

https://doi.org/10.17860/mersinefd.522491

Cited By: 2

Öz

This
study investigated the use of a well-designed computer-supported collaborative learning
environment, namely Virtual Math Teams (VMT), to develop middle school students’
geometric thinking. It also looked into students’ VMT discourse to better
understand factors leading to higher van Hiele levels of geometric thinking.
The participants of the study were selected from middle school students who
were at the visual geometric thinking level. For treatment, students were
presented with a set of activities on quadrilaterals, which were developed
based on van Hiele’s phases of learning geometry, within the VMT environment.
The data were collected by using the van Hiele Geometry Test. The VMT chat logs
were qualitatively analyzed using the three-core collaborative problem-solving
competencies used in the Programme for International Student Assessment (PISA)
2015. The results showed that the participants significantly developed their van
Hiele Geometry Test scores after the intervention. Qualitative results pointed
out that collaborative competencies could be essential in developing students’
geometric thinking levels within the VMT environment. Considering that Turkish
students score lower than the international average in geometry and the lowest
in collaborative problem solving area in international assessments, it becomes even
more important to integrate CSCL environments into Turkish curricula.

Anahtar Kelimeler

Computer-supported collaborative learning, virtual math teams, van Hiele levels of geometric thinking, geometry learning, collaborative competencies

Bilgisayar Destekli İş Birliğiyle Öğrenme Ortamında van Hiele Geometrik Düşünme Seviyelerinin Gelişiminin İncelenmesi

Öz

This study investigated the use of a well-designed computer-supported collaborative learning (CSCL) environment, namely Virtual Math Teams (VMT), to develop middle school students’ geometric thinking. It also looked into students’ VMT discourse to better understand factors leading to higher van Hiele levels of geometric thinking. The participants of the study were selected from middle school students who were at the visual geometric thinking level. For treatment, students were presented with a set of activities on quadrilaterals, which were developed based on van Hiele’s phases of learning geometry, within the VMT environment. The data were collected using the van Hiele Geometry Test. The VMT chat logs were qualitatively analyzed using the three-core collaborative problem-solving competencies used in the Programme for International Student Assessment (PISA) 2015. The results showed that the participants significantly developed their van Hiele Geometry Test scores after the intervention. Qualitative results pointed out that collaborative competencies could be essential in developing students’ geometric thinking levels within the VMT environment. Considering that in international assessments Turkish students score lower than the international average in geometry and the lowest in the collaborative problem-solving area, it becomes even more important to integrate CSCL environments into Turkish curricula.

Anahtar Kelimeler

Bilgisayar destekli iş birliğiyle öğrenme, sanal matematik takımları, van Hiele geometrik düşünme seviyesi, geometri öğrenimi, iş birliği yeterlikleri

Kaynakça

• Abdullah, A., & Zakaria, E. (2013). The effects of van Hiele’s phase-based instruction using the geometer’s sketchpad (GSP) on students’ levels of geometric thinking. Research Journal of Applied Sciences, Engineering, and Technology, 5(5), 1652-1660.
• Abdullah, A., Surif, J., Tahir, Tahir, L., Ibrahim, N., & Zakaria, E. (2015). Enhancing students’ geometrical thinking levels through van Hiele’s phase-based Geometer’s Sketchpad-aided learning. Engineering Education (ICEED), IEEE 7th International Conference, (pp. 106-111).
• Burger, W., & Shaughnessy, J. (1986). Characterizing the van Hiele levels of development in geometry. Journal for Research in Mathematics Education, 31-48.
• Creswell, J. (2014). Research design: Qualitative, quantitative, and mixed methods approaches (4th ed.). Thousand Oaks: Sage.
• Crowley, M. L. (1987). The van Hiele model of the development of geometric thought. Teaching and Learning, K-12 – 1987 Yearbook. Virginia, USA, NCTM.
• Duatepe, A. (2000). An investigation of the relationship between van Hiele geometric level of thinking and demographic variables for preservice elementary school teachers. (Unpublished Master’s thesis). Middle East Technical University, Ankara, Turkey.
• Duatepe-Paksu, A., & Ubuz, B. (2009). Effects of drama-based geometry instruction on student achievement, attitudes, and thinking levels. The Journal of Educational Research, 102(4), 272-286.
• Duatepe-Paksu, A. (2016). van Hiele geometrik düşünme düzeyleri. E. Bingölbali, S. Arslan, & İ. Ö. Zembat (Eds.). In Matematik Eğitiminde Teoriler (pp. 266-275). Ankara: Pegem Akademi.
• Güven, B., & Kosa, T. (2008). The effect of dynamic geometry software on student mathematics teachers’ spatial visualization skills. The Turkish Online Journal of Educational Technology, 7(4).
• Halat, E. (2006). Sex-related differences in the acquisition of the van Hiele levels and motivation in learning geometry. Asia Pacific Education Review, 7(2), 173-183. Hsieh, H., & Shannon, S. (2005). Three approaches to qualitative content analysis. Qualitative Health Research, 15(9), 1277-1288.
• Karakuş, F., & Peker, M. (2015). The effects of dynamic geometry software and physical manipulatives on pre-service primary teachers’ van Hiele levels and spatial abilities. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 6(3), 338-365.
• Koschmann, T. (1996). Paradigm shifts and instructional technology: An introduction. T. Koschmann (Ed.). CSCL: Theory and Practice of an Emerging Paradigm, (pp. 1–23). Mahwah, NJ: Lawrence Erlbaum Associates.
• Köseleci-Blanchy, N., & Şaşmaz, A. (2011). PISA 2009: Where does Turkey stand. Turkish Policy Quarterly, 10(2), 126-134.
• Kutluca, T. (2013). The effect of geometry instruction with dynamic geometry software; GeoGebra on van Hiele geometry understanding levels of students. Educational Research and Reviews, 8(17), 1509-1518.
• OECD. (2017a). PISA 2015 collaborative problem‑solving framework, in PISA 2015 Assessment and Analytical Framework: Science, Reading, Mathematics, Financial Literacy, and Collaborative Problem Solving. Paris, OECD Publishing. https://doi.org/10.1787/9789264281820-8-en.
• OECD. (2017b). PISA 2015 results (Volume V): Collaborative problem solving, PISA. Paris, OECD Publishing. https://doi.org/10.1787/9789264285521-en.
• Olkun, S., Sinoplu, N., & Deryakulu, D. (2009). Geometric explorations with dynamic geometry applications based on van Hiele levels. International Journal for Mathematics Teaching and Learning, 6, 1-12.
• Öner, D. (2016a). Bilgisayar destekli iş birliğiyle öğrenme: Sanal matematik takımları örneği. A. İşman, H. F. Odabaşı, & B. Akkoyunlu (Eds.). In Eğitim Teknolojileri Okumaları 2016 (pp. 107-120). TOJET.
• Öner, D. (2016b). Tracing the change in discourse in a collaborative dynamic geometry environment: From visual to more mathematical. International Journal of Computer-Supported Collaborative Learning, 11(1), 59-88.
• Oral, I., & McGivney, E. (2013). Türkiye’de matematik ve fen bilimleri alanlarında öğrenci performansı ve başarının belirleyicileri, TIMSS 2011 Analizi. ERG Analiz Raporu. Retrieved from http://erg.sabanciuniv.edu/sites/erg.sabanciuniv.edu/files/ERG%20-TIMSS%202011%20Analiz%20Raporu-03.09.2013.pdf.
• Senk, S. (1989). van Hiele levels and achievement in writing geometry proofs. Journal for Research in Mathematics Education, 309-321.
• Siew, N., Chong, C., & Abdullah, M. (2013). Facilitating students’ geometric thinking through van Hiele’s phased-based learning using tangram. Journal of Social Sciences, 9(3), 101-111.
• Stahl, G. (2013). Translating Euclid: Creating a human-centered mathematics. San Rafael, CA: Morgan & Claypool Publishers.
• Stahl, G., Koschmann, T., & Suthers, D. (2006). Computer-supported collaborative learning: An historical perspective. In Cambridge Handbook of the Learning Sciences (pp. 409-426).
• Şener-Akbay, P. (2012). A cross-sectional study on grades, geometry achievement and van Hiele levels of geometric thinking. (Unpublished Master’s thesis). Boğaziçi University, Istanbul, Turkey.
• Usiskin, Z. (1982). van Hiele levels and achievement in secondary school geometry. Columbus, USA: ED220288.
• van Hiele, P. (1999). Developing geometric thinking through activities. Teaching Children Mathematics, 5(6), 310-316.
• van Hiele, P. M., (1986). Structure and insight. A theory of mathematics education. London: Academic Press Inc.