Higher Education Research
Volume 2, Issue 3, June 2017, Pages: 98-106
Received: Apr. 2, 2017;
Accepted: Apr. 13, 2017;
Published: May 26, 2017
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Robert Benjamin Armah, Center for Distance Education, Institute for Educational Development and Extension, University of Education, Winneba, Ghana
Primrose Otokonor Cofie, Department of Mathematics Education, University of Education, Winneba, Ghana
Christopher Adjei Okpoti, Department of Mathematics Education, University of Education, Winneba, Ghana
Teachers’ geometrical competencies are very critical to the effective teaching of the subject. This study focused on the van Hiele Levels of geometric thinking reached by Ghanaian pre-service teachers before leaving for their Student Internship Programme (Teaching Practice) at the basic schools. In all, 300 second year pre-service teachers from 4 Colleges of Education were involved in this study. These pre-service teachers were given the van Hiele Geometry Test adapted from the ‘Cognitive Development and Achievement in Secondary School Geometry Test’ items during their second year, first semester. The results showed that 16.33% of pre-service teachers attained van Hiele Level 0 (i.e. the Pre-recognition Level or Level for those who have not yet attained any van Hiele Level), 27% of pre-service teachers attained Level 1, 32% attained Level 2 while 17.67% of pre-service teachers attained Level 3. However, only 6% and 1% of Pre-service Teachers attained Levels 4 and 5 respectively. These results show that majority (75.33%) of pre-service teachers’ van Hiele Levels are lower than that expected of their future Junior High School 3 learners. This suggests that most of the pre-service teachers’ geometry knowledge is not sufficient to teach at basic schools.
Robert Benjamin Armah,
Primrose Otokonor Cofie,
Christopher Adjei Okpoti,
The Geometric Thinking Levels of Pre-service Teachers in Ghana, Higher Education Research.
Vol. 2, No. 3,
2017, pp. 98-106.
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.
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 Mathemtics and Science: Results from Ghana's participation in the 2007 Trends in International Mathemtics and Science Study. Accra: Ministry of Education Youth and Sports.
Asante, J. N. & Mereku, D. K. (2012). The Effect of Ghanaian Pre-service Teachers’ Content Knowledge on their Mathematical Knowledge for teaching Basic School Mathematics. African Journal of Educational Studies in Mathematics and Sciences, 10, 23-37.
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 Sciences, 8, 51-61.
Ball, D., Thames, M. & Phelps, G. (2007). Content Knowledge for Teaching: What Makes It Special? Journal of Teacher Education, 1-55.
Conference Board of the Mathematical Sciences (CBMS). (2001). The Mathematical Education of Teachers. Providence RI and Washington DC: American Mathematical Society and Mathematical Association of America.
Crowley, M. L. (1987). The van Hiele Model of development of geometric thought. In M. M. Lindquist, & A. P. Shulte (Eds.), Learning and teaching geometry, K-12, 1987 Yearbook (pp. 1-16). Reston, VA: National Council of Teachers of Mathematics.
De Villiers, M. (2004). Using dynamic geometry to expand Mathematics teachers’ understanding of proof. International Journal of Mathematical Education in Science and Technology, 35(5), 703–724.
Friedenberg, J. & Silverman, G. (2006). Cognitive Science. An introduction to the Study of Mind. London: Sage Publications.
Halat, E. & Şahin, O. (2008). Van Hiele Levels of Pre- and In- Service Turkish Elementary School Teachers and Gender Related Differences in Geometry. The Mathematics Educator, 11(1/2), 143-158.
Halat, E. (2008). In-Service Middle and High School Mathematics Teachers: Geometric Reasoning Stages and Gender. The Mathematics Educator, 18(1), 8–14.
Hill, H. C., Rowan, B. & Ball, D. L. (2005). Effects of Teachers’ Mathematical Knowledge for Teaching on Student Achievement. American Educational Research Journal, 42(2), 371- 406.
Howse, T. D. & Howse, M. E. (2015). Linking the Van Hiele Theory to Instruction. Teaching children mathematics, 21 (5), 305-313.
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.
National Council of Teachers of Mathematics (NCTM). (2009). Guiding Principles for Mathematics Curriculum and Assessment. Retrieved February, 2, 2014 from http://www.nctm.org/uploadedFiles/Math_Standards/NCTM%20Guiding%20Principles%206209.pdf.
Ndlovu, M. (2014). Preservice Teachers’ Understanding of Geometrical Definitions and Class inclusion: an Analysis using the van Hiele Model. Proceedings of INTED2014 Conference 10th-12th March 2014, Valencia, Spain.
Pandiscio, E. A. & Knight, K. C. (2010). An Investigation into the van Hiele Levels of Understanding Geometry of Pre-service Mathematics Teachers. Journal of Research in Education, 21(1), 45-53.
Piaget, J. & Inhelder, B. (1948). The Child’s conception of space. New York: W. W. Norton.
Shulman, L. S. (1986b). Those who understand: Knowledge growth in teaching. Educational Researcher, 15, 4-14.
University of Cape Coast (UCC), Institute of Education (2005). Three- Year Diploma in Basic Education Mathematics Syllabus. Cape Coast: University of Cape Coast- Institute of Education.
University of Cape Coast, Institute of Education (2011). Chief Examiner’s Report on the 2011 Three- Year Post-Secondary Teacher Training College Diploma in Basic Education Mathematics II (GEOMETRY & TRIGONOMETRY) Examination. Cape Coast: University of Cape Coast, Institute of Education.
University of Cape Coast, Institute of Education (2012). Chief Examiner’s Report on the 2012 Three-Year Post-Secondary Teacher Training College Diploma in Basic Education GEOMETRY Examination. Cape Coast: University of Cape Coast, Institute of Education.
University of Cape Coast, Institute of Education (2013). Chief Examiner’s Report on the 2013 Three-Year Post-Secondary Teacher Training College Diploma in Basic Education GEOMETRY Examination. Cape Coast: University of Cape Coast, Institute of Education.
University of Cape Coast, Institute of Education (2014). Chief Examiner’s Report on the 2014 Three-Year Post-Secondary Teacher Training College Diploma in Basic Education GEOMETRY Examination. Cape Coast: University of Cape Coast, Institute of Education.
Usiskin, Z. (1982). Van Hiele Levels and achievement in secondary school geometry: Cognitive development and achievement in secondary school geometry project. Chicago: University of Chicago Press.
Van Hiele, P. M. (1957). The Problem of Insight, in Connection With School-children’s Insight into the Subject Matter of Geometry. Doctorial dissertation, University of Utrecht.
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.
Vojkuvkova, I. (2012). The van Hiele Model of Geometric Thinking. WDS'12 Proceedings of Contributed Papers. 1: 72–75.
Yegambaram, P. & Naidoo, R. (2009). Better learning of geometry with computer. Retrieved January 16, 2014 from http://atcm.mathandtech.org/EP2009/papers_full/2812009_17080.pdf.