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Examining Senior High School Girls’ Thinking Levels in Solving Problems on Circle Theorems

Received: 17 September 2022     Accepted: 4 October 2022     Published: 17 October 2022
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Abstract

The learning of Circle theorems is frequently highlighted as one challenging geometric content area for students at Senior High Schools (SHS). However, it remain unclear how students, especially girls are reasoning when dealing with problems in circle theorems. This descriptive study examined students’ ability and reasoning in solving problems involving Circle theorems. Two objectives were set to guide the study, focusing on SHS students’ levels of thinking in problem solving involving Circle theorems. A test, covering four basic theorems of geometry of circles in SHS curriculum, was designed and used to collect data from a purposive sample of 80 3rd-year students of Mfantsiman Girls’ SHS. The results showed that students’ thinking in Circle theorems follows the taxonomy of Uni-structural, Multi-structural, Relational and Extended abstract thinking levels. The study also found that about two-fifth of the students could not cope with problems involving relational and extended abstract reasoning, drawing of conclusions or even stating the four circle theorems. The study concludes that SHS mathematics teachers should reconsider how to teach deductively to improve the relational and abstract thinking levels of the 3rd-year students before they write the SHS final examinations. This could be facilitated through the use of SOLO taxonomy with super-item model as a diagnostic tool to ensure the growth of the students’ problem solving and reasoning skills in circle theorems.

Published in International Journal of Secondary Education (Volume 10, Issue 4)
DOI 10.11648/j.ijsedu.20221004.11
Page(s) 127-135
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), 2022. Published by Science Publishing Group

Keywords

Circle Theorems, Geometric Thinking, Senior High School Girls, SOLO

References
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[2] Diana, N., Suryadi, D., & Dahlan, J. A. (2020). Analysis of students’ mathematical connection abilities in solving problem of circle material: transposition study. Journal for the Education of Gifted Young Scientists, 8 (2), 829-842. http://dx.doi.org/10.17478/jegys/
[3] Basarear, T. (2012). Mathematics for elementary school teachers (5th ed). Brooks/Cole.
[4] Fabiyi, T. R. (2017). Geometry concepts in mathematics perceived difficult to learn by senior secondary school students in Ekiti State Nigeria. IOSR Journal of Research & Method in Education, 7 (1), 83-90.
[5] Ministry of Education (2012). Teaching Syllabus for core mathematics (Senior High School). CRDD, Ministry of Education.
[6] National Research Council (2005). Introduction. National Research Council. How students learn mathematics in the classroom.
[7] Baah-Duodu, S., Osei-Buabeng, V., Cornelius, E. F., Hegan, J. E., & Nabie, M. J. (2020). Review of literature on teaching and learning geometry and measurement: a case of Ghanaian standards based mathematics curriculum. International Journal of Advances in Scientific Research and Engineering (IJASRE), 6 (3), 103-123.
[8] Tay, M. K., & Wonkyi, T. M. (2018). Effect of using Geogebra on senior high school students’ performance in circle theorems. African Journal of Educational Studies in Mathematics and Sciences, 14, 1-18.
[9] Sharma, S. (2019). Use of theories and models in geometry education research: A critical review. Waikato Journal of Education, 24 (1), 43-54. https://doi.org/10.15663/wje.v24i1.644.
[10] Chimuka, A. (2017). The effect of integration of GeoGebra software in the teaching of circle geometry on grade 11 students’ achievement. Unpublished master’s thesis, University of South Africa. https://core.ac.uk/download/pdf/129899181.pdf.
[11] Biggs, J. & Tang, C. (2011). Teaching for Quality Learning at University. Open University Press.
[12] Kusmaryono, I. Suyitno, H., Dwijanto, D. & Dwidayati., N. (2018). Analysis of Abstract Reasoning from Grade 8 students in mathematical problem solving with SOLO Taxonomy Guide. Infinity 7 (2), 69-82.
[13] Gagani, R. F. M., & Misa, R. O. (2017). Solo based-cognition levels of inductive reasoning in Geometry. Alberta Journal of Educational Research, 63 (4), 344-356.
[14] Özdemir, A. Ş., & Yildiz, S. G. (2015). The examination of elementary mathematics pre-service teachers’ spatial abilities. Procedia-Social and Behavioral Sciences, 174, 594-601.
[15] Korkmaz, F., & Unsal, S. (2017). Analysis of attainments and evaluation questions in sociology curriculum according to the SOLO taxonomy. Eurasian Journal of Educational Research, 17 (69), 75-92.
[16] Adeniji, S. M., Baker, P., & Schmude, M. (2022). Structure of the Observed Learning Outcomes (SOLO) model: A mixed-method systematic review of research in mathematics education. Eurasia Journal of Mathematics, Science and Technology Education, 18 (6), em 2119. https://doi.org/10.29333/ejmste/12087
[17] Maftuh, M. K., & Hidayat, D. (2018). The Effect of Super-item Learning Model on Increasing Students Learning Achievements. (JIML) Journal of Innovative Mathematics Learning, 1 (4), 282-288.
[18] Apawu, J., Owusu-Ansah, N. A., & Akayuure, P. (2018). A Study on the Algebraic Working Processes of Senior High School Students in Ghana. European Journal of Science and Mathematics Education, 6 (2), 62-68.
[19] Yulian, V. N. (2019, November). Enhancing students’ mathematical synthesis ability by superitem learning model. In Journal of Physics: Conference Series (Vol. 1280, No. 4, p. 042030). IOP Publishing.
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  • APA Style

    Victoria Felicia Aidoo Bervell, Peter Akayuure. (2022). Examining Senior High School Girls’ Thinking Levels in Solving Problems on Circle Theorems. International Journal of Secondary Education, 10(4), 127-135. https://doi.org/10.11648/j.ijsedu.20221004.11

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    ACS Style

    Victoria Felicia Aidoo Bervell; Peter Akayuure. Examining Senior High School Girls’ Thinking Levels in Solving Problems on Circle Theorems. Int. J. Second. Educ. 2022, 10(4), 127-135. doi: 10.11648/j.ijsedu.20221004.11

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    AMA Style

    Victoria Felicia Aidoo Bervell, Peter Akayuure. Examining Senior High School Girls’ Thinking Levels in Solving Problems on Circle Theorems. Int J Second Educ. 2022;10(4):127-135. doi: 10.11648/j.ijsedu.20221004.11

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  • @article{10.11648/j.ijsedu.20221004.11,
      author = {Victoria Felicia Aidoo Bervell and Peter Akayuure},
      title = {Examining Senior High School Girls’ Thinking Levels in Solving Problems on Circle Theorems},
      journal = {International Journal of Secondary Education},
      volume = {10},
      number = {4},
      pages = {127-135},
      doi = {10.11648/j.ijsedu.20221004.11},
      url = {https://doi.org/10.11648/j.ijsedu.20221004.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsedu.20221004.11},
      abstract = {The learning of Circle theorems is frequently highlighted as one challenging geometric content area for students at Senior High Schools (SHS). However, it remain unclear how students, especially girls are reasoning when dealing with problems in circle theorems. This descriptive study examined students’ ability and reasoning in solving problems involving Circle theorems. Two objectives were set to guide the study, focusing on SHS students’ levels of thinking in problem solving involving Circle theorems. A test, covering four basic theorems of geometry of circles in SHS curriculum, was designed and used to collect data from a purposive sample of 80 3rd-year students of Mfantsiman Girls’ SHS. The results showed that students’ thinking in Circle theorems follows the taxonomy of Uni-structural, Multi-structural, Relational and Extended abstract thinking levels. The study also found that about two-fifth of the students could not cope with problems involving relational and extended abstract reasoning, drawing of conclusions or even stating the four circle theorems. The study concludes that SHS mathematics teachers should reconsider how to teach deductively to improve the relational and abstract thinking levels of the 3rd-year students before they write the SHS final examinations. This could be facilitated through the use of SOLO taxonomy with super-item model as a diagnostic tool to ensure the growth of the students’ problem solving and reasoning skills in circle theorems.},
     year = {2022}
    }
    

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    T1  - Examining Senior High School Girls’ Thinking Levels in Solving Problems on Circle Theorems
    AU  - Victoria Felicia Aidoo Bervell
    AU  - Peter Akayuure
    Y1  - 2022/10/17
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    N1  - https://doi.org/10.11648/j.ijsedu.20221004.11
    DO  - 10.11648/j.ijsedu.20221004.11
    T2  - International Journal of Secondary Education
    JF  - International Journal of Secondary Education
    JO  - International Journal of Secondary Education
    SP  - 127
    EP  - 135
    PB  - Science Publishing Group
    SN  - 2376-7472
    UR  - https://doi.org/10.11648/j.ijsedu.20221004.11
    AB  - The learning of Circle theorems is frequently highlighted as one challenging geometric content area for students at Senior High Schools (SHS). However, it remain unclear how students, especially girls are reasoning when dealing with problems in circle theorems. This descriptive study examined students’ ability and reasoning in solving problems involving Circle theorems. Two objectives were set to guide the study, focusing on SHS students’ levels of thinking in problem solving involving Circle theorems. A test, covering four basic theorems of geometry of circles in SHS curriculum, was designed and used to collect data from a purposive sample of 80 3rd-year students of Mfantsiman Girls’ SHS. The results showed that students’ thinking in Circle theorems follows the taxonomy of Uni-structural, Multi-structural, Relational and Extended abstract thinking levels. The study also found that about two-fifth of the students could not cope with problems involving relational and extended abstract reasoning, drawing of conclusions or even stating the four circle theorems. The study concludes that SHS mathematics teachers should reconsider how to teach deductively to improve the relational and abstract thinking levels of the 3rd-year students before they write the SHS final examinations. This could be facilitated through the use of SOLO taxonomy with super-item model as a diagnostic tool to ensure the growth of the students’ problem solving and reasoning skills in circle theorems.
    VL  - 10
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    ER  - 

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Author Information
  • Department of Mathematics, Mfantsiman Girls’ Senior High School, Mankessim, Ghana

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

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