Geometric Thinking of Prospective Mathematics Teachers: Assessing the Foundation Built by University Undergraduate Education in Ghana

Robert Benjamin Armah

doi:doi:10.11648/j.tecs.20240902.12

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Geometric Thinking of Prospective Mathematics Teachers: Assessing the Foundation Built by University Undergraduate Education in Ghana

Robert Benjamin Armah^*

Published in Teacher Education and Curriculum Studies (Volume 9, Issue 2)

Received: 25 June 2024 Accepted: 11 July 2024 Published: 23 July 2024

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Abstract

This study investigates the geometric thinking levels of final year prospective mathematics teachers in Ghana, utilizing the van Hiele model to evaluate their proficiency. The main purpose was to assess whether university undergraduate mathematics education provides a sufficiently strong foundation for teaching senior high school geometry. A descriptive survey design was employed, involving 1,255 prospective mathematics teachers from three universities: University of Education Winneba (UEW), University of Cape Coast (UCC), and Akenten Appiah-Menka University of Skills Training and Entrepreneurial Development (AAMUSTED). The van Hiele Geometry Test (VHGT) was administered to measure participants’ levels of geometric thinking. The results revealed that 8.8% of participants attained van Hiele Level 1 (visualization), 30.0% reached Level 2 (analysis), and 32.4% achieved Level 3 (abstraction). However, only 15.9% and 12.9% of prospective teachers reached Levels 4 (deduction) and 5 (rigor), respectively. These findings indicate a significant gap between the current geometric thinking skills of prospective teachers and the expectations of the Ghanaian mathematics curriculum, which anticipates higher-order thinking skills. The study concludes that the current undergraduate mathematics education programs in Ghanaian universities may not be adequately preparing future teachers to teach senior high school geometry effectively. It is recommended that these programs be revised to include more focus on developing higher-order geometric thinking skills, with an emphasis on deductive reasoning, formal proof-based learning and rigor in geometry thinking. Enhancing the curriculum and teaching methods could narrow this gap and improve the overall quality of geometry education in Ghana.

Published in	Teacher Education and Curriculum Studies (Volume 9, Issue 2)
DOI	10.11648/j.tecs.20240902.12
Page(s)	40-51
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Geometric Thinking, van Hiele Levels, Prospective Mathematics Teachers, Undergraduate Education, Ghana

References

[1]	Akayuure, P., Asiedu-Addo, S. K., & Alebna, V. (2016). Investigating the effect of origami instruction on pre-service teachers’ spatial ability and geometric knowledge for teaching. International Journal of Education in Mathematics, Science and Technology, 4(3), 198-209. https://doi.org/10.18404/ijemst.78424
[2]	Akayuure, P., Oppong, R. A., Addo, D. A., & Yeboah, D. O. (2022). Geometric Thinking Behaviours of Undergraduates on-Entry and at-Exit of Online Geometry Course. Science Journal of Education, 10(5), 155-163. http://doi.org/10.11648/j.sjedu.20221005.12
[3]	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.
[4]	Alex, J. K., & Mammen, K. J. (2018). Students’ understanding of geometry terminology through the lens of Van Hiele theory. Pythagoras, 39(1), 376-384. https://doi.org/10.4102/pythagoras.v39i1.376
[5]	Armah, R. B., Cofie, P. O., & Okpoti, C. A. (2018). Investigating the effect of van Hiele Phase- based instruction on pre-service teachers’ geometric thinking. International Journal of Research in Education and Science, 4(1), 314-330. https://doi.org/10.21890/ijres.383201
[6]	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
[7]	Asemani, E., Asiedu-Addo, S. K., & Oppong, R. A. (2017). The Geometric Thinking Levels of Senior High School students in Ghana. International Journal of Mathematics and Statistics Studies, 5(3), 1-8.
[8]	Battista, M. T. (2007). The development of geometric and spatial thinking. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 843-908). National Council of Teachers of Mathematics.
[9]	Breyfogle, M. L. & Lynch, C. M. (2010). Van Hiele Revisited. Mathematics Teaching in the Middle School, 16(4), 232-238.
[10]	Burger, W., & Shaughnessy, J. M. (1986). Characterizing the van Hiele levels of development in geometry. Journal for Research in Mathematics Education, 17(1), 31–48.
[11]	Erdogan, F. (2020). Prospective Middle School Mathematics Teachers’ Problem Posing Abilities in Context of Van Hiele Levels of Geometric Thinking. International Online Journal of Educational Sciences, 12(2), 132-152. https://doi.org/10.15345/iojes.2020.02.009
[12]	Gunhan, B. C. (2014). A Case Study on the investigation of reasoning skills in Geometry. South African Journal of Education, 34(2), 1-19.
[13]	Halat, E. (2008). In-Service Middle and High School Mathematics Teachers: Geometric Reasoning Stages and Gender. The Mathematics Educator, 18(1), 8–14.
[14]	Howse, T. D. & Howse, M. E. (2015). Linking the Van Hiele Theory to Instruction. Teaching children mathematics, 21(5), 305-313.
[15]	Jones, K. (2002). Issues in the Teaching and Learning of Geometry. In: Linda Haggarty (Ed), Aspects of Teaching Secondary Mathematics: perspectives on practice. Routledge Falmer.
[16]	Knight, K. C. (2006). An investigation into the van Hiele level of understanding geometry of pre-service elementary and secondary mathematics teachers. [master’s thesis, University of Maine]. https://digitalcommons.library.umaine.edu/etd/1361/
[17]	Luneta, K. (2015). Understanding students’ misconceptions: An analysis of final Grade 12 examination questions in geometry. Pythagoras, 36(1), 1-11.
[18]	Ministry of Education (MOE) (2010). Teaching Syllabus for Core Mathematics (Senior High School 1-3). Ministry of Education.
[19]	Ministry of Education (MOE) (2012). Teaching Syllabus for Core Mathematics (Senior High School 1-3). Ministry of Education.
[20]	Moru, E., Malebanye, M., Morobe, N., & George, M. (2021). A Van Hiele Theory analysis for teaching volume of three-dimensional geometric shapes. Journal of Research and Advances in Mathematics Education, 6(1), 17-31. https://doi.org/10.23917/jramathedu.v6i1.11744
[21]	Mukuka, A. & Alex, J. K. (2024). Student teachers’ knowledge of school-level geometry: Implications for teaching and learning. European Journal of Educational Research, 13(3), 1375-1389. https://doi.org/10.12973/eu-jer.13.3.1375
[22]	National Council for Curriculum and Assessment (NaCCA) (2019). Mathematics Curriculum for Primary Schools (Basic 4 - 6). Ministry of Education.
[23]	Schwartz, J. E. (2008). Elementary Mathematics Pedagogical Content Knowledge: Powerful Ideas for Teachers. http://www.education.com/reference/article/why-people-have-difficulty-geometry/
[24]	Senk, S. L. (1989). Van Hiele levels and achievement in writing geometry proofs. Journal for Research in Mathematics Education, 20(3), 309–321.
[25]	Trimurtini, D. Waluya, S. B., Sukestiyarno, Y. L., & Kharisudin, Q. (2023). Effect of Two-Dimensional Geometry Learning on Geometric Thinking of Undergraduate Students During the COVID-19 Pandemic. Journal of Higher Education Theory and Practice, 23(3), 177-187. https://doi.org/10.17051/ilkonline.2021.01.91
[26]	Usiskin, Z. (1982). Van Hiele Levels and achievement in secondary school geometry: Cognitive development and achievement in secondary school geometry project. University of Chicago Press.
[27]	van Hiele, P. M. (1986). Structure and insight: A theory of mathematics education. Orlando: Academic Press.
[28]	van Hiele, P. M. (1999). Developing Geometric Thinking through Activities that Begin with Play. Teaching Children Mathematics, 6, 310–316.
[29]	Yegambaram, P. & Naidoo, R. (2009). Better learning of geometry with computer. http://atcm.mathandtech.org/EP2009/papers_full/2812009_17 080.pdf
[30]	Yi, M., Flores, R. & Wang, J. (2020). Examining the influence of van Hiele theory-based instructional activities on elementary preservice teachers’ geometry knowledge for teaching 2-D shapes. Teaching and Teacher Education, 91, 1-12. https://doi.org/10.1016/j.tate.2020.103038

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APA Style

Armah, R. B. (2024). Geometric Thinking of Prospective Mathematics Teachers: Assessing the Foundation Built by University Undergraduate Education in Ghana. Teacher Education and Curriculum Studies, 9(2), 40-51. https://doi.org/10.11648/j.tecs.20240902.12

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Armah, R. B. Geometric Thinking of Prospective Mathematics Teachers: Assessing the Foundation Built by University Undergraduate Education in Ghana. Teach. Educ. Curric. Stud. 2024, 9(2), 40-51. doi: 10.11648/j.tecs.20240902.12

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AMA Style

Armah RB. Geometric Thinking of Prospective Mathematics Teachers: Assessing the Foundation Built by University Undergraduate Education in Ghana. Teach Educ Curric Stud. 2024;9(2):40-51. doi: 10.11648/j.tecs.20240902.12

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@article{10.11648/j.tecs.20240902.12,
  author = {Robert Benjamin Armah},
  title = {Geometric Thinking of Prospective Mathematics Teachers: Assessing the Foundation Built by University Undergraduate Education in Ghana
},
  journal = {Teacher Education and Curriculum Studies},
  volume = {9},
  number = {2},
  pages = {40-51},
  doi = {10.11648/j.tecs.20240902.12},
  url = {https://doi.org/10.11648/j.tecs.20240902.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.tecs.20240902.12},
  abstract = {This study investigates the geometric thinking levels of final year prospective mathematics teachers in Ghana, utilizing the van Hiele model to evaluate their proficiency. The main purpose was to assess whether university undergraduate mathematics education provides a sufficiently strong foundation for teaching senior high school geometry. A descriptive survey design was employed, involving 1,255 prospective mathematics teachers from three universities: University of Education Winneba (UEW), University of Cape Coast (UCC), and Akenten Appiah-Menka University of Skills Training and Entrepreneurial Development (AAMUSTED). The van Hiele Geometry Test (VHGT) was administered to measure participants’ levels of geometric thinking. The results revealed that 8.8% of participants attained van Hiele Level 1 (visualization), 30.0% reached Level 2 (analysis), and 32.4% achieved Level 3 (abstraction). However, only 15.9% and 12.9% of prospective teachers reached Levels 4 (deduction) and 5 (rigor), respectively. These findings indicate a significant gap between the current geometric thinking skills of prospective teachers and the expectations of the Ghanaian mathematics curriculum, which anticipates higher-order thinking skills. The study concludes that the current undergraduate mathematics education programs in Ghanaian universities may not be adequately preparing future teachers to teach senior high school geometry effectively. It is recommended that these programs be revised to include more focus on developing higher-order geometric thinking skills, with an emphasis on deductive reasoning, formal proof-based learning and rigor in geometry thinking. Enhancing the curriculum and teaching methods could narrow this gap and improve the overall quality of geometry education in Ghana.
},
 year = {2024}
}

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TY  - JOUR
T1  - Geometric Thinking of Prospective Mathematics Teachers: Assessing the Foundation Built by University Undergraduate Education in Ghana

AU  - Robert Benjamin Armah
Y1  - 2024/07/23
PY  - 2024
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DO  - 10.11648/j.tecs.20240902.12
T2  - Teacher Education and Curriculum Studies
JF  - Teacher Education and Curriculum Studies
JO  - Teacher Education and Curriculum Studies
SP  - 40
EP  - 51
PB  - Science Publishing Group
SN  - 2575-4971
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AB  - This study investigates the geometric thinking levels of final year prospective mathematics teachers in Ghana, utilizing the van Hiele model to evaluate their proficiency. The main purpose was to assess whether university undergraduate mathematics education provides a sufficiently strong foundation for teaching senior high school geometry. A descriptive survey design was employed, involving 1,255 prospective mathematics teachers from three universities: University of Education Winneba (UEW), University of Cape Coast (UCC), and Akenten Appiah-Menka University of Skills Training and Entrepreneurial Development (AAMUSTED). The van Hiele Geometry Test (VHGT) was administered to measure participants’ levels of geometric thinking. The results revealed that 8.8% of participants attained van Hiele Level 1 (visualization), 30.0% reached Level 2 (analysis), and 32.4% achieved Level 3 (abstraction). However, only 15.9% and 12.9% of prospective teachers reached Levels 4 (deduction) and 5 (rigor), respectively. These findings indicate a significant gap between the current geometric thinking skills of prospective teachers and the expectations of the Ghanaian mathematics curriculum, which anticipates higher-order thinking skills. The study concludes that the current undergraduate mathematics education programs in Ghanaian universities may not be adequately preparing future teachers to teach senior high school geometry effectively. It is recommended that these programs be revised to include more focus on developing higher-order geometric thinking skills, with an emphasis on deductive reasoning, formal proof-based learning and rigor in geometry thinking. Enhancing the curriculum and teaching methods could narrow this gap and improve the overall quality of geometry education in Ghana.

VL  - 9
IS  - 2
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Author Information

Robert Benjamin Armah

Department of Mathematics Education, University of Education, Winneba, Ghana

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http://orcid.org/0000-0002-7426-7299

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APA Style

Armah, R. B. (2024). Geometric Thinking of Prospective Mathematics Teachers: Assessing the Foundation Built by University Undergraduate Education in Ghana. Teacher Education and Curriculum Studies, 9(2), 40-51. https://doi.org/10.11648/j.tecs.20240902.12

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ACS Style

Armah, R. B. Geometric Thinking of Prospective Mathematics Teachers: Assessing the Foundation Built by University Undergraduate Education in Ghana. Teach. Educ. Curric. Stud. 2024, 9(2), 40-51. doi: 10.11648/j.tecs.20240902.12

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AMA Style

Armah RB. Geometric Thinking of Prospective Mathematics Teachers: Assessing the Foundation Built by University Undergraduate Education in Ghana. Teach Educ Curric Stud. 2024;9(2):40-51. doi: 10.11648/j.tecs.20240902.12

Copy | Download

@article{10.11648/j.tecs.20240902.12,
  author = {Robert Benjamin Armah},
  title = {Geometric Thinking of Prospective Mathematics Teachers: Assessing the Foundation Built by University Undergraduate Education in Ghana
},
  journal = {Teacher Education and Curriculum Studies},
  volume = {9},
  number = {2},
  pages = {40-51},
  doi = {10.11648/j.tecs.20240902.12},
  url = {https://doi.org/10.11648/j.tecs.20240902.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.tecs.20240902.12},
  abstract = {This study investigates the geometric thinking levels of final year prospective mathematics teachers in Ghana, utilizing the van Hiele model to evaluate their proficiency. The main purpose was to assess whether university undergraduate mathematics education provides a sufficiently strong foundation for teaching senior high school geometry. A descriptive survey design was employed, involving 1,255 prospective mathematics teachers from three universities: University of Education Winneba (UEW), University of Cape Coast (UCC), and Akenten Appiah-Menka University of Skills Training and Entrepreneurial Development (AAMUSTED). The van Hiele Geometry Test (VHGT) was administered to measure participants’ levels of geometric thinking. The results revealed that 8.8% of participants attained van Hiele Level 1 (visualization), 30.0% reached Level 2 (analysis), and 32.4% achieved Level 3 (abstraction). However, only 15.9% and 12.9% of prospective teachers reached Levels 4 (deduction) and 5 (rigor), respectively. These findings indicate a significant gap between the current geometric thinking skills of prospective teachers and the expectations of the Ghanaian mathematics curriculum, which anticipates higher-order thinking skills. The study concludes that the current undergraduate mathematics education programs in Ghanaian universities may not be adequately preparing future teachers to teach senior high school geometry effectively. It is recommended that these programs be revised to include more focus on developing higher-order geometric thinking skills, with an emphasis on deductive reasoning, formal proof-based learning and rigor in geometry thinking. Enhancing the curriculum and teaching methods could narrow this gap and improve the overall quality of geometry education in Ghana.
},
 year = {2024}
}

Copy | Download

TY  - JOUR
T1  - Geometric Thinking of Prospective Mathematics Teachers: Assessing the Foundation Built by University Undergraduate Education in Ghana

AU  - Robert Benjamin Armah
Y1  - 2024/07/23
PY  - 2024
N1  - https://doi.org/10.11648/j.tecs.20240902.12
DO  - 10.11648/j.tecs.20240902.12
T2  - Teacher Education and Curriculum Studies
JF  - Teacher Education and Curriculum Studies
JO  - Teacher Education and Curriculum Studies
SP  - 40
EP  - 51
PB  - Science Publishing Group
SN  - 2575-4971
UR  - https://doi.org/10.11648/j.tecs.20240902.12
AB  - This study investigates the geometric thinking levels of final year prospective mathematics teachers in Ghana, utilizing the van Hiele model to evaluate their proficiency. The main purpose was to assess whether university undergraduate mathematics education provides a sufficiently strong foundation for teaching senior high school geometry. A descriptive survey design was employed, involving 1,255 prospective mathematics teachers from three universities: University of Education Winneba (UEW), University of Cape Coast (UCC), and Akenten Appiah-Menka University of Skills Training and Entrepreneurial Development (AAMUSTED). The van Hiele Geometry Test (VHGT) was administered to measure participants’ levels of geometric thinking. The results revealed that 8.8% of participants attained van Hiele Level 1 (visualization), 30.0% reached Level 2 (analysis), and 32.4% achieved Level 3 (abstraction). However, only 15.9% and 12.9% of prospective teachers reached Levels 4 (deduction) and 5 (rigor), respectively. These findings indicate a significant gap between the current geometric thinking skills of prospective teachers and the expectations of the Ghanaian mathematics curriculum, which anticipates higher-order thinking skills. The study concludes that the current undergraduate mathematics education programs in Ghanaian universities may not be adequately preparing future teachers to teach senior high school geometry effectively. It is recommended that these programs be revised to include more focus on developing higher-order geometric thinking skills, with an emphasis on deductive reasoning, formal proof-based learning and rigor in geometry thinking. Enhancing the curriculum and teaching methods could narrow this gap and improve the overall quality of geometry education in Ghana.

VL  - 9
IS  - 2
ER  -

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