A Study of Van Hiele of Geometric Thinking among 1st through 6th Graders

Hsiu-Lan Ma; De-Chih Lee; Szu-Hsing Lin; Der-Bang Wu

doi:10.12973/eurasia.2015.1412a

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Hsiu-Lan Ma ¹, De-Chih Lee ², Szu-Hsing Lin ² ^* , Der-Bang Wu ³

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¹ Professor, Department of Business Administration, Ling Tung University² Da Yeh University³ National Taichung University of Education^* Corresponding Author

Abstract

Background:
This study presents partial results from the project “A Study of perceptual apprehensive, operative apprehensive, sequential apprehensive, and discursive apprehensive for elementary school students (POSD)”, which was undertaken to explore gender differences and passing rate of van Hiele’s geometric thinking level.

Materials and methods:
The participants were 5,581 elementary school students randomly selected from 23 counties/cities in Taiwan.

Results:
This paper analysed the passing rate of van Heile geometric thinking of Taiwanese 1st to 6th graders, and studied the gender differences at different grades. The statement below shows the passed population and the passing rate.

Conclusions:
The conclusions drawn from this study were: (a) evidence supporting the hierarchy of the van Hiele levels, (b) students at different levels have different concepts of basic figures, and (c) for elementary school students, the passing rates of boys and girls have no significant differences in van Hiele’s geometric thinking level.

Keywords

van Hiele
Perceptual
operative
sequential
Discursive

License

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, 2015, Volume 11, Issue 5, 1181-1196

https://doi.org/10.12973/eurasia.2015.1412a

Publication date: 25 Aug 2015

Article Views: 3930

Article Downloads: 3582

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References

Burger, W. F., & Shaughnessy, J. M. (1986). Assessing children's intellectual growth in geometry (Final report of the Assessing Children's Intellectual Growth in Geometry project). Corvallis, OR: Oregon State University, Department of Mathematics.
Chen T. L., Wu, D. B., Ma, H. L., & Sheu, T. W. (2011). The passing rate of the van Hiele level of geometrical reasoning. In B. UBUZ (Ed.). Proc. of the 35th Conf. of the International Group for the Psychology of Mathematics Education. (Vol. 1, pp. 278). Ankara, Turkey: PME.
Eberle, R. S. (1989). The effects of instruction on the van Hiele levels of geometric reasoning in preservice elementary teachers. Unpublished master's thesis, The University of Texas at Austin.
Erdogan, T., Akkaya, R., &Lebi Akkaya, S. (2009). The Effect of the Van Hie le Model Based Instruction on the Creative Thinking Levels of 6th Grade Primary School Students. Educational Sciences: Theory & Practice, 181-194.
Fuys, D., Geddes, D., & Tischler, R. (1988). The van Hiele model of thinking in geometry among adolescents. Reston, VA: National Council of Teachers of Mathematics, Inc. DOI: 10.2307/749957:
Gutierrez, A., Jaime, D., & Fortuny, J. M. (1991). An alternative paradigm to evaluate the acquisition of the van Hiele levels. Journal for Research in Mathematics Education, 22(3), 237-251. DOI: 10.2307/749076
Haviger, J., and Vojkůvková, I. (2014). The van Hiele geometry thinking levels: gender and school type differences. Procedia - Social and Behavioral Sciences, 112, 977 – 981. DOI: 10.1016/j.sbspro.2014.01.1257
Hoffer, A. (1981). Geometry is more than proof. Mathematics Teacher, 74(1), 11-18.
Hoffer, A. (1983). Van Hiele based research. In R. Lesh & M. Landau (Eds.), Acquisition of mathematical concepts and processes (pp. 205-228). New York, NY: Academic Press.
Hyde, J. S., Fennema, E., & Lamon, S. J. (1990). Gender differences in mathematics performance: A meta-analysis. Psychological Bulletin, 107(2), 139-155. DOI: 10.1037/0033-2909.107.2.139
Ma, H. L. & Wu, D. B. (2000). An Introduction to the van Hiele Model of Geometric Thought. Journal of Ling-Tung College, 11, 289-310.
Ma, H. L., Wu, D. B., & Wu, S. J. (2012). Developing the test of the van Hiele levels of geometrical reasoning based on grey relational analysis. Advanced Materials Research, 374 - 377, pp. 1555-1558. DOI: 10.4028/www.scientific.net/AMR.374-377.1555
Ministry of Education of Taiwan (MET) (1993). Curriculum standards for national elementary school in Taiwan. Taipei, Taiwan: Author. [In Chinese]
Ministry of Education of Taiwan (MET) (2000). Grade 1-9 Curriculum Provisional Guidelines—Mathematics. Taipei, Taiwan: Author. [In Chinese]
Ministry of Education of Taiwan (MET) (2003). Grade 1-9 Curriculum Guidelines— Mathematics. Taipei, Taiwan: Author. [In Chinese]
Ministry of Education of Taiwan (MET) (2008). Grade 1-9 Curriculum Guidelines— Mathematics. Taipei, Taiwan: Author. [In Chinese]
Molina, D. D. (1990). The applicability of the van Hiele theory to transformational geometry. Unpublished doctoral dissertation, The University of Texas at Austin.
Senk, S. L. (1983). Proof writing achievement and van Hiele levels among secondary school geometry students (Doctoral Dissertation, The University of Chicago, 1983). Dissertation Abstracts International, 44, 417A.
National Academy for Educational Research (2001). Analysis of Elementary School Math Teaching Materials - Geometry, Taipei, http://wd.naer.edu.tw/216/book13/
National Council of Teachers of Mathematics (NCTM) (1989). Curriculum and evaluation standards for school mathematics. Reston, VA.: Author.
National Council of Teachers of Mathematics (NCTM) (1991). Professional standards for teaching mathematics. Reston, VA: Author.
National Council of Teachers of Mathematics (NCTM) (1995). Assessment standards for school mathematics. Reston, VA: Author.
National Council of Teachers of Mathematics (NCTM) (2000). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.
Patsiomitou, S., & Emvalotis, A. (2010). Students Movement Through Van Hiele Levels in a Dynamic Geometry Guided Reinvention Process. Journal of Mathematics and Technology, 1(1), 18-48.
Pegg, J. (1985). How children learn geometry: The van Hiele model. Australian Mathematics Teacher, 41(2), 2-4.
Pegg, J., & Davey, G. (1989). Clarifying level descriptors for children's understanding of some basic 2-D geometry shapes. Mathematics Education Research Journal, 1(1), 16-27. DOI: 10.1007/BF03217200
Pegg, J., & Davey, G. (1991). Levels of geometric understanding. Australian Mathematics Teacher, 47(2), 10-13.
Senk, S. L. (1983). Proof writing achievement and van Hiele levels among secondary school geometry students (Doctoral Dissertation, The University of Chicago, 1983). Dissertation Abstracts International, 44, 417A.
Senk, S. L. (1989). van Hiele levels and achievement in writing geometry proofs. Journal for Research in Mathematics Education, 20(3), 309-321. DOI: 10.2307/749519
Sharp, J. M. & Zachary, L. W. (2004). Using the van Hiele K-12 Geometry Learning Theory to Modify Engineering Mechanics Instruction. Journal of STEM Education, 5(1), 35-41.
Škrbec, M. & Čadež, T. H. (2015). Identifying and Fostering Higher Levels of Geometric Thinking. Eurasia Journal of Mathematics, Science & Technology Education, 11(3), 601- 617. DOI: 10.12973/eurasia.2015.1339a
Tutkun, O. F. & Ozturk, B. (2013). The Effect of Geogebra Mathematical Software to The Academic Success and The Level of Van Hiele Geomeyrical Thinking. International Journal of Academic Research, 5(4), 22-28. DOI: 10.7813/2075-4124.2013/5-4/B.3
Usiskin, Z. P. (1982). Van Hiele levels and achievement in secondary school geometry (Final Report of the Cognitive Development and Achievement in Secondary School Geometry Project). Chicago, IL: University of Chicago, Department of Education. (ERIC Reproduction Service No. ED 220 288).
Van Hiele, D. (1957). De didaktick van de Meetkunde in de eerste klass van het V.H.M.O. Summary of unpublished doctoral dissertation with English summary, University of Utrecht, Netherlands.
Van Hiele, P. M. (1984). English summary. [The problem of insight in connection with school children's insight into the subject matter of geometry.] In D. Fuys, D. Geddes, & R. Tischler (Eds. & Trans.), English translations of selected writings of Dina van Hiele-Geldorf and Pierre M. van Hiele (pp. 237-241). Columbus, OH: ERIC Information Analysis Center for Science, Mathematics, and Environmental Education. (ERIC Document Reproduction Service No. ED 287 697)
Van Hiele, P. M. (1986). Structure and insight: A theory of mathematics education. Orlando, FL: Academic Press.
Van Hiele, P. M. (1999). Developing Geometric Thinking through Activities that Begin with Play. Teaching Children Mathematics, 5, 310-316.
Wu, D. B. (1994). A study of the use of the van Hiele model in the teaching of non-Euclidean geometry to prospective elementary school teachers in Taiwan, the Republic of China. Unpublished Doctoral dissertation, University of Northern Colorado, Greeley.
Wu, D. B. (1995). A study of the use of the van Hiele model in the teaching of non-Euclidean geometry to prospective elementary school teachers in Taiwan, the Republic of China. Journal of National Taichung Teachers College, 9, 443-474. Wu, D. B. (2003). A study of perceptual apprehensive, operative apprehensive, sequential apprehensive and discursive apprehensive for elementary school students (Final Report of the A study perceptual apprehensive, operative apprehensive, sequential apprehensive and discursive apprehensive for elementary school students Project). Taichung, Taiwan: National Taichung Teachers College, Department of Mathematics Education. (National Science Council under Grant No. NSC91-2521-S-142-004. [In Chinese].
Wu, D. B., Ma, H. L. (2005a). A study of the geometric concepts of the elementary school students at the van Hiele level one. In Chick, H. L. & Vincent, J. L. (Eds.). Proceedings 29th Conference of the International Group for the Psychology of Mathematics Education, Vol. 4, pp. 329-336. Melbourne, Australia: PME.
Wu, D. B., Ma, H. L. (2005b). A study of the developing procedure of the van Hiele geometry test for elementary school students. Paper presented in The Third East Asia Regional Conference on Mathematics Education (ICMI Regional Conference). 7 Aug. – 12 Aug., 2005. Shanghai, Nanjing, and Hangzhou China.
Wu, D. B., Ma, H. L., & Lan, T. L. (2005). A Case Study of a Tactile Type Child on Triangle Concepts - Analysis from the Viewpoints of Van Hiele and Duval Theory. Paper presented in International Conference on Education, Redesigning Pedagogy: Research, Policy, Practice. 30 May – 1 June, 2005. National Institute of Education, Nanyang Technological University, Singapore.
Wu, D. B., Ma, H. L. (2006). The distributions of van hiele levels of geometric thinking among 1st through 6th graders. In Novotna J. (Eds.). Proceedings 30th Conference of the International Group for the Psychology of Mathematics Education, Vol. 5, pp. 409-416. Prague, Czech Republic.
Wu, D. B., Ma, H. L., & Chen, D. C. (2006). The developmental stages of representations of simple regular space figures of elementary school students. In Novotna J. (Eds.). Proceedings 30th Conference of the International Group for the Psychology of Mathematics Education, Vol. 1, p. 430. Prague, Czech Republic.
Wu, D. B., Ma, H. L., Lan, T. L., & Yao, R. F. (2006). A Case Study of a Visual Type of the Sixth Grader on Triangle Concepts. In Ana Breda, Rui Duarte, & Manuel Martins (Eds.). Proceedings of the International Conference in Mathematics, Sciences and Science Education (pp. 110-119). Paper presented in The International Conference on Mathematics, Science and Science Education (ICMSE 2006). 11 Jun. – 14 Jun., 2006. Aveiro, Portugal. (ISBN : 972-789-187-X)

How to cite this article

APA

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 and Technology Education, 11(5), 1181-1196. https://doi.org/10.12973/eurasia.2015.1412a

Vancouver

Ma HL, Lee DC, Lin SH, Wu DB. A Study of Van Hiele of Geometric Thinking among 1st through 6th Graders. EURASIA J Math Sci Tech Ed. 2015;11(5):1181-96. https://doi.org/10.12973/eurasia.2015.1412a

AMA

Ma HL, Lee DC, Lin SH, Wu DB. A Study of Van Hiele of Geometric Thinking among 1st through 6th Graders. EURASIA J Math Sci Tech Ed. 2015;11(5), 1181-1196. https://doi.org/10.12973/eurasia.2015.1412a

Chicago

Ma, Hsiu-Lan, De-Chih Lee, Szu-Hsing Lin, and Der-Bang Wu. "A Study of Van Hiele of Geometric Thinking among 1st through 6th Graders". Eurasia Journal of Mathematics, Science and Technology Education 2015 11 no. 5 (2015): 1181-1196. https://doi.org/10.12973/eurasia.2015.1412a

Harvard

Ma, H.-L., Lee, D.-C., Lin, S.-H., and Wu, D.-B. (2015). A Study of Van Hiele of Geometric Thinking among 1st through 6th Graders. Eurasia Journal of Mathematics, Science and Technology Education, 11(5), pp. 1181-1196. https://doi.org/10.12973/eurasia.2015.1412a

MLA

Ma, Hsiu-Lan et al. "A Study of Van Hiele of Geometric Thinking among 1st through 6th Graders". Eurasia Journal of Mathematics, Science and Technology Education, vol. 11, no. 5, 2015, pp. 1181-1196. https://doi.org/10.12973/eurasia.2015.1412a