Use of the van Hiele Theory in Investigating Teaching Strategies used by College of Education Geometry Tutors

Robert Benjamin Armah; Philip Siaw Kissi

doi:10.29333/ejmste/103562

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Robert Benjamin Armah ¹ ^* , Philip Siaw Kissi ²

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¹ Department of Mathematics Education, University of Education, Winneba, GHANA² Management Information Systems, School of Applied Sciences, Cyprus International University, Nicosia, Northern Cyprus, Mersin 10, TURKEY^* Corresponding Author

Abstract

The main purpose of this study is to explore the extent to which 11 selected mathematics tutors facilitate the teaching and learning of geometry at the van Hiele Levels 1, 2, 3 and 4 at the college of education level in Ghana. The van Hiele theory of geometric thinking was used to explore the type of teaching strategies employed by the mathematics tutors. The theory served as a guideline from which classroom observation protocol was developed. Results indicated that the tutors exhibit a good conceptual understanding in facilitating the teaching and learning of geometry that is consistent with van Hiele Levels 1 and 2. However, much of the geometry teaching and learning strategies of the mathematics tutors were not structured in a way that support the development of geometric thinking as described in van Hiele Levels 3 and 4. Implications for the involvement of college mathematics tutors in utilizing the van Hiele framework were discussed.

Keywords

teaching strategies
van Hiele Levels
pre-service teachers
college tutors

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, 2019, Volume 15, Issue 4, Article No: em1694

https://doi.org/10.29333/ejmste/103562

Publication date: 31 Jan 2019

Article Views: 4917

Article Downloads: 7232

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References

Abu, M. S. & Abidin, Z. Z. (2013). Improving the Levels of Geometric Thinking of Secondary School Students using Geometry Learning Video based on van Hiele Theory. International Journal of Evaluation and Research in Education (IJERE), 2(1), 16-22. https://doi.org/10.11591/ijere.v2i2.1935.
Al-ebous, T. (2016). Effect of the van Hiele Model in Geometric Concepts Acquisition: The Attitudes towards Geometry and Learning Transfer Effect of the First Three Grades Students in Jordan. International Education Studies, 9(4), 87-98. https://doi.org/10.5539/ies.v9n4p87.
Alex, J. K., & Mammen, K. J. (2012). A Survey of South African Grade 10 Learners’ Geometric Thinking Levels in Terms of the van Hiele Theory. Anthropologist, 14(2), 123-129. https://doi.org/10.1080/09720073.2012.11891229.
Alex, J. K., & Mammen, K. J. (2016). Lessons Learnt from Employing van Hiele Theory Based Instruction in Senior Secondary School Geometry Classrooms. Eurasia Journal of Mathematics, Science & Technology Education, 12(8), 2223-2236. https://doi.org/10.12973/eurasia.2016.1228a.
Ampiah, J. G. (2010). Quality Basic Education in Ghana: Prescription, Praxis and Problems. Paper Delivered at the Experience Sharing Seminar. Erata Hotel Accra: Ghana.
Anamuah-Mensah, J., & Mereku, D. K. (2005). Ghanaian Junior Secondary School two students abysmal Mathematics Achievement in TIMSS 2003: A consequence of the Basic school Mathematics. Mathematics Connection, 5(1), 1-11.
Anamuah-Mensah, J., Mereku, D. K., & Asabere-Ameyaw, A. (2008). Ghanaian Junior Secondary School Students’ Achievement in Mathematics and Science: Results from Ghana’s participation in the 2007 Trends in International Mathematics and Science Study. Accra: Ministry of Education Youth and Sports.
Armah, R. B., Cofie, P. O., & Okpoti, C. A. (2017). The Geometric Thinking Levels of Pre-service Teachers in Ghana. Higher Education Research, 2(3), 98-106.
Atebe, H. U. (2008). Students' van Hiele Levels of Geometric Thought and Conception in Plane Geometry: A Collective Case Study of Nigeria and South Africa. (Unpublished PhD. Thesis). Rhodes University, South Africa.
Baffoe, E., & Mereku, D. K. (2010). The Van Hiele Levels of understanding of students entering Senior High School in Ghana. African Journal of Educational Studies in Mathematics and Science, 8(1), 51-61.
Christou, C., Jones, K., Pitta, D., Pittalis, M., Mousoulides, N., & Boytchev, P. (2007). Developing Student Spatial Ability with 3-Dimensional Applications. Retrieved on July 30, 2014 from http://www.elica.net/download/papers/devstudspatabil3d.pdf.
De Villiers, M. (2012). Some Reflections on the van Hiele Theory. Retrieved on April 8, 2014 from http://frink.machighway.com/~dynamicm/vanhiele-reflection.pdf.
Ding, L., & Jones, K. (2007). Using the van Hiele theory to analyze the teaching of geometrical proof at grade 8 in Shanghai, China. European Society for Research in Mathematics Education, 612-621.
Erdogan, T., & Durmus, S. (2009). The effect of the instruction based on van Hiele model on the geometrical thinking Levels of preservice elementary school teachers. Procedia Social and Behavioral Sciences, 1, 154–159. https://doi.org/10.1016/j.sbspro.2009.01.029.
Furner, J. M., & Marinas, C. A. (2011). Geoboards to Geogebra: moving from the concrete to the abstract in geometry. Retrieved on October, 24, 2018 from http://archives.math.utk.edu/ICTCM/VOL23/S088/paper.pdf.
Gogoe, M. (2009). Ghanaian preservice teachers' Geometric knowledge for teaching. (Unpublished master's thesis). Department of Mathematics Education, University of Education, Winneba, Ghana.
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(11), 100-107.
Halat, E. (2008). In-Service Middle and High School Mathematics Teachers: Geometric Reasoning Stages and Gender. The Mathematics Educator, 18(1), 8–14.
Hittleman, D. R., & Simon, A. J. (2002). Interpreting educational research (3rd Ed.). Upper Saddle River, New Jersey: Merrill Prentice Hall.
Howse, T. D., & Howse, M. E. (2015). Linking the Van Hiele Theory to Instruction. Teaching children mathematics, 21(5), 305-313.
Institute of Education (2005). Three- year diploma in basic education Mathematics syllabus. Cape Coast: University A.
Jones, K. (2002). Issues in the Teaching and Learning of Geometry. In: Linda Haggarty (Ed), Aspects of Teaching Secondary Mathematics: perspectives on practice (pp.121-139). London: Routledge Falmer. https://doi.org/10.1002/tl.62.
Khalid, A., & Azeem, M. (2012). Constructivist Vs Traditional: Effective Instructional Approach in Teacher Education. International Journal of Humanities and Social Science, 2(5), 170-177.
Kilpatrick, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
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.
Ma, H. L., Lee, D. C., Lin, S. H., & Wu, D. B. (2015). A Study of Van Hiele of Geometric Thinking among 1st through 6th Graders. Eurasia Journal of Mathematics, Science & Technology Education, 11(5), 1181-1196.
Mason, M. (1998). The van Hiele Levels of geometric understanding. In L. McDougal (Ed.). The professional handbook for teachers: Geometry (pp. 4–8). Boston: McDougal-Littell/Houghton-Mifflin.
Mertler, C. A., & Charles, C.M. (5th Ed.) (2005). Introduction to educational research. New York: Pearson Education, Inc.
Ministry of Education, Science and Sports (MOESS) (2007). Mathematics Syllabus for Primary School. Accra: Ministry of Education, Science and Sports. GES: CRDD.
Mostafa, M., Javad, L. M., & Reza, O. H. (2017). The Effect of Van Hiele Theory-Based Teaching Educational Package on Achievement Goal Orientation of Student Teachers. Review of European Studies, 9(1), 93-105. https://doi.org/10.5539/res.v9n1p93.
Muyeghu, A. (2008). The use of the van Hiele theory in Investigating Teaching Strategies used by Grade 10 Geometry teachers in Namibia. (Unpublished Master’s Thesis). Rhodes University, Grahamstown, RSA.
Noh, F. N. B. M., & Abdullah, A. H. (2016). Primary School Students Level of Geometric Thinking. Retrieved on July 14, 2018 from https://www.researchgate.net/publication/308950262_PRIMARY_SCHOOL_.
STUDENTS_LEVEL_OF_GEOMETRIC_THINKING.
Pegg, J. (1995). Learning and teaching geometry. In L. Grimison & J. Pegg (Eds.), Teaching secondary school mathematics: Theory into practice (pp. 87–103). London: Harcourt Brace.
Rizki, H. T. N., Frentika, D., & Wijaya, A (2018). Exploring students’ adaptive reasoning skills and van Hiele levels of geometric thinking: a case study in geometry. https://doi.org/10.1088/1742-6596/983/1/012148.
Schwartz, J. E. (2008). Elementary Mathematics Pedagogical Content Knowledge: Powerful Ideas for Teachers. Retrieved on March 2, 2014 from http://www.education.com/reference/article/why-people-have-difficulty-geometry/.
Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1–22. https://doi.org/10.17763/haer.57.1.j463w79r56455411.
Stigler, J. W., & Hiebert, J. (1999). The teaching gap: Best ideas from the world’s teachers for improving education in the classroom. New York: The Free Press.
Suwito, A., Yuwono I, Parta, I. N., & Irawati, S. (2017). Geometry High School Students Thinking Ability based on level van Hiele. International Conference on Mathematics: Education, Theory and Application, Indonesia.
Thanh, N. C., & Thanh, T. T. L. (2015). The Interconnection Between Interpretivist Paradigm and Qualitative Methods in Education. American Journal of Educational Science, 1(2), 24-27.
Tieng, P. G., & Eu, L. K. (2014). Improving Students’ Van Hiele Level of Geometric Thinking using Geometer’s Sketchpad. The Malaysian Online Journal of Educational Technology, 2(3), 20-31.
Van Hiele, P. M. (1986). Structure and insight: A theory of Mathematics education. Orlando: Academic Press.
Van Hiele, P. M. (1999). Developing Geometric Thinking through Activities that Begin with Play. Teaching Children Mathematics, 6, 310–316.
van Putten S. (2008). Level of thought in geometry of pre-service mathematics educators according to the Van Hiele model. (Unpublished master's thesis). University of Pretoria, South Africa.
Vojkuvkova, I. (2012). The van Hiele Model of Geometric Thinking. WDS’12 Proceedings of Contributed Papers, 1, 72–75.
Willis, J. W. (2007). Foundations of qualitative research: interpretive and critical approaches. London: Sage. https://doi.org/10.4135/9781452230108.
Yanow, D., & Schwartz-Shea, P. (2011). Interpretive Approaches to Research Design: Concepts and Processes. Netherlands: Routledge.
Yazdani, M. A. (2007). Correlation between Students’ level of Understanding Geometry According to the van Hieles’ Model and Students’ Achievement in Plane Geometry. Journal of mathematical Sciences & Mathematics Education, 2(1), 40-45.
Yegambaram, P., & Naidoo, R. (2009). Better learning of geometry with computer. Retrieved on January 16, 2014 from http://atcm.mathandtech.org/EP2009/papers_full/2812009_17080.pdf.

How to cite this article

APA

Armah, R. B., & Kissi, P. S. (2019). Use of the van Hiele Theory in Investigating Teaching Strategies used by College of Education Geometry Tutors. Eurasia Journal of Mathematics, Science and Technology Education, 15(4), em1694. https://doi.org/10.29333/ejmste/103562

Vancouver

Armah RB, Kissi PS. Use of the van Hiele Theory in Investigating Teaching Strategies used by College of Education Geometry Tutors. EURASIA J Math Sci Tech Ed. 2019;15(4):em1694. https://doi.org/10.29333/ejmste/103562

AMA

Armah RB, Kissi PS. Use of the van Hiele Theory in Investigating Teaching Strategies used by College of Education Geometry Tutors. EURASIA J Math Sci Tech Ed. 2019;15(4), em1694. https://doi.org/10.29333/ejmste/103562

Chicago

Armah, Robert Benjamin, and Philip Siaw Kissi. "Use of the van Hiele Theory in Investigating Teaching Strategies used by College of Education Geometry Tutors". Eurasia Journal of Mathematics, Science and Technology Education 2019 15 no. 4 (2019): em1694. https://doi.org/10.29333/ejmste/103562

Harvard

Armah, R. B., and Kissi, P. S. (2019). Use of the van Hiele Theory in Investigating Teaching Strategies used by College of Education Geometry Tutors. Eurasia Journal of Mathematics, Science and Technology Education, 15(4), em1694. https://doi.org/10.29333/ejmste/103562

MLA

Armah, Robert Benjamin et al. "Use of the van Hiele Theory in Investigating Teaching Strategies used by College of Education Geometry Tutors". Eurasia Journal of Mathematics, Science and Technology Education, vol. 15, no. 4, 2019, em1694. https://doi.org/10.29333/ejmste/103562