THE EFFECT OF METACOGNITIVE STRATEGIES ON SPATIAL VISUALIZATION PERFORMANCE IN GEOMETRY

David Koomson

Abstract


Visualization is pivotal in geometric cognition, comprising three levels ranging from plane-level visualization to spatial visualization. It is at the spatial visualization level that learners demonstrate the capability to accurately translate two-dimensional images into three-dimensional objects and understand the relationships between the two dimensions. This study investigates the effect of metacognitive instruction on spatial visualization performance (SVP) among senior high school students. Through a post-test only control and experimental group design, three spatial visualization strategies (cognitive modeling, self-questioning, and reciprocal teaching) were assigned to three groups of students, while no instructions were given to a control group; all groups comprised 88 students. The findings challenge traditional stereotypes about gender differences in spatial abilities by revealing no significant performance difference between males and females in terms of enhancing spatial visualization using metacognitive approaches. Furthermore, the study found that the effect of metacognitive strategies in enhancing spatial visualization performance is positive, demonstrating that teaching students to be aware of and regulate their cognitive processes leads to improved performance across all experimental groups. The research also finds no significant differences among the metacognitive instructional strategies, suggesting that the core strategies of metacognition are universally effective. The findings emphasize the need for educational reforms that promote gender equity and the integration of metacognitive instruction into curricula.

 

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geometry; spatial visualization; metacognitive strategies; senior high school; Ghana

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References


Aboagye, K. O., Ke, Y. D., & Mante, D. A. (2021). Factors influencing students’ perceived difficulties in studying geometry: A case of Konogo-Odumasi, Ghana. Open Journal of Social Sciences, 9(9), 526-540. http://dx.doi.org/10.4236/jss.2021.99038

Acquah, S., & Alhassan, M. N. (2018). Assessing the Challenges of Ghanaian Pre-Service Teachers in Their Learning of Geometric Transformation Concepts and Perception of Factors Inhibiting the Development of Their Mathematical Knowledge for Teaching. International Journal of Innovative Research and Development, 7(4). http://dx.doi.org/10.24940/ijird/2018/v7/i4/APR18042

Akayuure, Peter. (2019). The spatial ability effect on pre-service teachers’ basic geometry content knowledge in relation to verbal reasoning (Doctoral dissertation, University of Education, Winneba (UEW). Retrieved from https://ir.uew.edu.gh/handle/123456789/1659

Alghadari, F., Herman, T., & Prabawanto, S. (2020). Factors affecting senior high school students to solve three-dimensional geometry problems. International Electronic Journal of Mathematics Education, 15(3). Retrieved from https://www.iejme.com/article/factors-affecting-senior-high-school-students-to-solve-three-dimensional-geometry-problems-8234

Altan, R. Y., & Temel, Z. F. (2023). The Effect of Metacognitive Strategy-Based Geometry Education on Young Childrens’ Metacognitive and Executive Functions Skills. Pegem Journal of Education and Instruction, 13(2), 297-313. https://doi.org/10.47750/pegegog.13.02.34

Ampadu, E. (2012). Teachers’ perceptions of students’ mathematics performance in Ghana: The case of selected junior high schools in Cape Coast metropolis. African Journal of Educational Studies in Mathematics and Sciences, 10, 11-27. http://dx.doi.org/10.47963/toe.v13i.220

Anamuah-Mensah, J., Mereku, D. K., & Ghartey-Ampiah, J. (2015). TIMSS 2007 Ghana report: Findings from IEA's trends in international mathematics and science study at the eighth grade. Ghana Ministry of Education.

Anif, S., Prayitno, H. J., & Sari, D. P. (2019, April). Metacognitive knowledge of mathematics education students in analytical geometry of space. In Journal of Physics: Conference Series (Vol. 1211, No. 1, p. 012056). IOP Publishing. Retrieved from http://dx.doi.org/10.1088/1742-6596/1211/1/012056

Arcavi, A. (2003). The role of visual representations in the learning of mathematics. Educational studies in mathematics, 52(3), 215-241. http://dx.doi.org/10.1023/A:1024312321077

Arıcı, S., & Aslan-Tutak, F. (2015). The effect of origami-based instruction on spatial visualization, geometry achievement, and geometric reasoning. International Journal of Science and Mathematics Education, 13, 179-200. https://doi.org/10.1007/s10763-013-9487-8

Armah, R. B., & Kissi, P. S. (2019). Use of the van Hiele theory in investigating teaching strategies used by the college of education geometry tutors. EURASIA Journal of Mathematics, Science and Technology Education, 15(4). http://dx.doi.org/10.29333/ejmste/103562

Artzt, A. F., & Armour-Thomas, E. (1992). Development of a cognitive-metacognitive framework for protocol analysis of mathematical problem solving in small groups. Cognition and Instruction, 9(2), 137-175. Retrieved from https://www.jstor.org/stable/3233531

Asemani, E., Asiedu-Addo, S. K., & Oppong, R. A. (2017). The geometric thinking level of senior high school students in Ghana. International Journal of Mathematics and Statistics Studies, 5(3), 1-8. Retrieved from https://www.researchgate.net/publication/317570630_THE_GEOMETRIC_THINKING_LEVELS_OF_SENIOR_HIGH_SCHOOL_STUDENTS_IN_GHANA

Aydın, U., & Ubuz, B. (2010). Structural model of metacognition and knowledge of geometry. Learning and Individual Differences, 20(5), 436-445. https://doi.org/10.1016/j.lindif.2010.06.002

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, 6(3), 103-124. http://dx.doi.org/10.31695/IJASRE.2020.33766

Baenninger, M., & Newcombe, N. (1989). The role of experience in spatial test performance: A meta-analysis. Sex Roles, 20(5-6), 327-344. https://doi.org/10.1007/BF00287729

Baffoe, E., & Mereku, D. K. (2011). The van Hiele levels of understanding of students entering senior high school in Ghana. African Journal of Educational Studies in Mathematics and Sciences, 8, 51-62. http://dx.doi.org/10.4314/ajesms.v8i1.69103

Baki, A., Kosa, T., & Guven, B. (2011). A comparative study of the effects of using dynamic geometry software and physical manipulatives on the spatial visualisation skills of pre‐service mathematics teachers. British Journal of Educational Technology, 42(2), 291-310. https://doi.org/10.1111/j.1467-8535.2009.01012.x

Baltes, P. B., & Lindenberger, U. (1997). Emergence of a powerful connection between sensory and cognitive functions across the adult life span: A new window to the study of cognitive aging? Psychology and Aging, 12(1), 12-21. Retrieved from https://www.semanticscholar.org/paper/Emergence-of-a-powerful-connection-between-sensory-Baltes-Lindenberger/0f8603032cd78ca42ab35e7f28430015f48ae826

Bandoh, S. O., Akweittey, E., Lotey, E. K., Gordon, J. F., & Appiagyei, E. (2024). Using UTAUT model to assess the factors influencing the use of ICT in Ghanaian pre-tertiary mathematics education. Journal of Digital Educational Technology, 4(1). https://doi.org/10.30935/jdet/14297

Bransford, J. D., Brown, A. L., & Cocking, R. R. (Eds.). (2000). How people learn: Brain, mind, experience, and school. National Academies Press. Retrieved from https://cradall.org/sites/default/files/How%20People%20Learn-Brain_Mind_Experience_and%20School%20-%20Expanded%20Edition.pdf

Brown, B., & Doe, A. (2018). Factors contributing to difficulties in geometry among Ghanaian students. Educational Psychology Review, 42(1), 78-91.

Bülbül, B. Ö., & Güler, M. (2023). Examining the effect of dynamic geometry software on supporting geometric habits of mind: A qualitative inquiry. E-Learning and Digital Media, 20(2), 138-161. https://doi.org/10.1177/20427530221107776

Ceci, S. J., & Williams, W. M. (2010). Sex differences in math-intensive fields. Current Directions in Psychological Science, 19(5), 275-279. https://doi.org/10.1177/0963721410383241

Clements, D. H. (2004). Geometric and spatial thinking in early childhood education. Engaging young children in mathematics: Standards for early childhood mathematics education, 267-297. http://dx.doi.org/10.4324/9781410609236

Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2018). Applied multiple regression/correlation analysis for the behavioral sciences. Routledge. Retrieved from https://eli.johogo.com/Class/CCU/SEM/_Applied%20Multiple%20Regression-Correlation%20Analysis%20for%20the%20Behavioral%20Sciences_Cohen.pdf

Colcombe, S., & Kramer, A. F. (2003). Fitness effects on the cognitive function of older adults: A meta-analytic study. Psychological Science, 14(2), 125-130. https://doi.org/10.1111/1467-9280.t01-1-01430

Contero, M., Naya, F., Company, P., Saorín, J. L., & Pastor, J. (2005). Improving visualization skills in engineering education. IEEE Computer Graphics and Applications, 25, 24-31. https://doi.org/10.1109/MCG.2005.107

Contreras, M. J., Escrig, R., Prieto, G., & Elosúa, M. R. (2018). Spatial visualization ability improves with and without studying technical drawing. Cognitive processing, 19, 387-397. https://doi.org/10.1007/s10339-018-0859-4

Creswell, J. W., & Creswell, J. D. (2017). Research design: Qualitative, quantitative, and mixed methods approaches. Sage Publications. Retrieved from https://us.sagepub.com/en-us/nam/research-design/book270550

Creswell, J. W., & Plano Clark, V. L. (2018). Designing and conducting mixed methods research. Sage Publications. Retrieved from https://collegepublishing.sagepub.com/products/designing-and-conducting-mixed-methods-research-3-241842

Denbel, Dejene Girma. (2015). Students' Learning Experiences When Using a Dynamic Geometry Software Tool in a Geometry Lesson at Secondary School in Ethiopia. Journal of education and practice 6.1 23-38. Retrieved from https://files.eric.ed.gov/fulltext/EJ1083857.pdf

Desoete, A., & Veenman, M. (2010). Metacognition in mathematics education. ZDM, 42, 263-265. http://dx.doi.org/10.1007/s11858-010-0243-z

Doe, A., & Brown, B. (2019). Understanding the fear of mathematics among Ghanaian students. International Journal of Mathematics Education, 31(4), 567-580.

Eastman, P. M., & Barnett, J. C. (1979). The interaction between spatial visualization abilities and the use of manipulative materials in the enactive and iconic modes for preservice elementary teachers. International Journal of Mathematical Educational in Science and Technology, 10(4), 517-524. https://doi.org/10.1080/0020739790100405

Efklides, A. (2008). Metacognition: Defining its facets and levels of functioning about self-regulation and co-regulation. European Psychologist, 13(4), 277–287. https://doi.org/10.1027/1016-9040.13.4.277

English, L. D., & King, D. T. (2015). STEM learning through engineering design: Fourth-grade students’ investigations in aerospace. International journal of stem education, 2, 1-18. Retrieved from https://eric.ed.gov/?id=EJ1181778

Enki, K. (2014). Effects of using manipulatives on seventh grade students' achievement in transformation geometry and orthogonal views of geometric figures (Master's thesis, Middle East Technical University). Retrieved from https://etd.lib.metu.edu.tr/upload/12617286/index.pdf

Erdenechimeg, S., & Danaa, G. (2023). Some results and evaluation of training for the development of students’ spatial visualization. Embedded Selforganising Systems, 10. http://dx.doi.org/10.14464/ess.v10i7.630

Eryılmaz Çevirgen, A. (2012). Casual relations among 12th grade students' geometry knowledge, spatial ability, gender and school type. Retrieved from https://etd.lib.metu.edu.tr/upload/12614970/index.pdf

Flavell, J. H. (1979). Metacognition and cognitive monitoring: A new area of cognitive-developmental inquiry. American Psychologist, 34(10), 906-911. https://doi.org/10.1037/0003-066X.34.10.906

Garrity, C. (1998). Does the Use of Hands-On Learning, with Manipulatives, Improve the Test Scores of Secondary Education Geometry Students?. Retrieved from https://eric.ed.gov/?id=ED422179

Ghosh, A., & Mitra, S. (2020). Statistics for Research. CRC Press.

Giardino, V. (2010). Intuition and visualization in mathematical problem solving. Topoi, 29(1), 29-39. http://dx.doi.org/10.1007/s11245-009-9064-5

Gilligan‐Lee, K. A., Hawes, Z. C., Williams, A. Y., Farran, E. K., & Mix, K. S. (2023). Hands‐On: Investigating the role of physical manipulatives in spatial training. Child development, 94(5), 1205-1221. https://doi.org/10.1111/cdev.13963

Goldsmith, L. T., Hetland, L., Hoyle, C., & Winner, E. (2016). Visual-spatial thinking in geometry and the visual arts. Psychology of aesthetics, creativity, and the arts, 10(1), 56. https://doi.org/10.1037/aca0000027

Gourgey, A. F. (1998). Metacognition in basic skills instruction. Instructional Science, 26, 81-96. https://doi.org/10.1023/A:1003092414893

Guay, R. B., & McDaniel, E. D. (1977). The relationship between mathematics achievement and spatial abilities among elementary school children. Journal for Research in Mathematics Education, 8(3), 211-215. Retrieved from https://www.jstor.org/stable/748522

Gulkilik, H. (2016). The Role of Virtual Manipulatives in High School Students’ Understanding of Geometric Transformations. http://dx.doi.org/10.1007/978-3-319-32718-1_10

Ha, O., & Fang, N. (2018). Interactive virtual and physical manipulatives for improving students’ spatial skills. Journal of Educational Computing Research, 55(8), 1088-1110. https://doi.org/10.1177/0735633117697730

Haciomeroglu, E. S. (2016). Object-Spatial Visualization and Verbal Cognitive Styles, and Their Relation to Cognitive Abilities and Mathematical Performance. Educational Sciences: Theory and Practice, 16(3), 987-1003. Retrieved from https://files.eric.ed.gov/fulltext/EJ1115147.pdf

Hair, J. F., Black, W. C., Babin, B. J., Anderson, R. E., & Tatham, R. L. (2010). Multivariate Data Analysis (7th ed.). Pearson. Retrieved from https://books.google.ro/books/about/Multivariate_Data_Analysis.html?id=VvXZnQEACAAJ&redir_esc=y

Hannafin, R. D., Truxaw, M. P., Vermillion, J. R., & Liu, Y. (2008). Effects of spatial ability and instructional program on geometry achievement. The Journal of Educational Research, 101(3), 148-157. http://dx.doi.org/10.3200/JOER.101.3.148-157

Hattie, J., & Timperley, H. (2007). The power of feedback. Review of Educational Research, 77(1), 81-112. https://doi.org/10.3102/003465430298487

Hawes, Z., Moss, J., Caswell, B., Seo, J., & Ansari, D. (2019). Relations between numerical, spatial, and executive function skills and mathematics achievement: A latent-variable approach. Cognitive Psychology, 109, 68-90. https://doi.org/10.1016/j.cogpsych.2018.12.002

Hegarty, M. (2011). The cognitive science of visual‐spatial displays: Implications for design. Topics in cognitive science, 3(3), 446-474. https://doi.org/10.1111/j.1756-8765.2011.01150.x

Hegarty, M., & Kozhevnikov, M. (1999). Types of visual-spatial representations and mathematical problem solving. Journal of Educational Psychology, 91(4), 684-689. https://doi.org/10.1037/0022-0663.91.4.684

Hegarty, M., & Tarampi, M. R. (2015). Teaching Spatial Thinking: Perspectives from Cognitive Psychology. In TSTIP@ COSIT (pp. 36-44). Retrieved from https://ceur-ws.org/Vol-1557/paper8.pdf

Hegarty, M., & Waller, D. (2004). A dissociation between mental rotation and perspective-taking spatial abilities. Intelligence, 32(2), 175-191. https://doi.org/10.1016/j.intell.2003.12.001

Hegarty, M., & Waller, D. (2005). Individual differences in spatial abilities. The Cambridge handbook of visuospatial thinking, 121-169. https://doi.org/10.1017/CBO9780511610448.005

Hershkowitz, R., Duval, R., Bussi, M. G. B., Boero, P., Lehrer, R., Romberg, T., ... & Jones, K. (1998). Reasoning in geometry. In Perspectives on the Teaching of Geometry for the 21st Century: An ICMI Study (pp. 29-83). Dordrecht: Springer Netherlands. Retrieved from https://link.springer.com/book/10.1007/978-94-011-5226-6

Hidayah, I., & Istiandaru, A. (2018). Manipulatives and Question Series for Elementary School Mathematics Teaching on Solid Geometry. International Journal of Instruction, 11(3), 649-662. http://dx.doi.org/10.12973/iji.2018.11344a

Hidayah, I., Dwijanto, D., & Istiandaru, A. (2018). Manipulatives and Question Series for Elementary School Mathematics Teaching on Solid Geometry. International Journal of Instruction, 11, 649-662. http://dx.doi.org/10.12973/iji.2018.11344a

Horn, J. L., & Cattell, R. B. (1966). Refinement and test of the theory of fluid and crystallized general intelligences. Journal of Educational Psychology, 57(5), 253-270. https://doi.org/10.1037/h0023816

Hwang, W. Y., Su, J. H., Huang, Y. M., & Dong, J. J. (2009). A study of multi-representation of geometry problem solving with virtual manipulatives and a whiteboard system. Journal of Educational Technology & Society, 12(3), 229-247. Retrieved from https://www.researchgate.net/publication/220374659_A_Study_of_Multi-Representation_of_Geometry_Problem_Solving_with_Virtual_Manipulatives_and_Whiteboard_System

Hyde, J. S. (2005). The gender similarities hypothesis. American Psychologist, 60(6), 581-592. Retrieved from https://www.apa.org/pubs/journals/releases/amp-606581.pdf

İbili, E. (2019). The use of dynamic geometry software from a pedagogical perspective: current status and prospects. Journal of Computer and Education Research, 7(14), 337-355. http://dx.doi.org/10.18009/jcer.579517

Johnson, R. B., & Christensen, L. (2014). Educational research: Quantitative, qualitative, and mixed approaches. Sage Publications. Retrieved from https://us.sagepub.com/en-us/nam/educational-research/book259335

Johnson, R. B., & Onwuegbuzie, A. J. (2004). Mixed methods research: A research paradigm whose time has come. Educational Researcher, 33(7), 14-26. https://doi.org/10.3102/0013189X033007014

Jones, C., & Smith, J. (2020). Challenges in integrating geometric concepts and axioms among Ghanaian students. Mathematics Teaching, 55(3), 210-225.

Jones, K. (2010). The Value of Using Manipulatives in Teaching Geometry. Mathematics in School, 29, 16-18.

Jones, K., & Tzekaki, M. (2016). Research on the teaching and learning of geometry. The second handbook of research on the psychology of mathematics education, 109-149. Retrieved from https://eprints.soton.ac.uk/400610/1/Jones_Tzekaki_PME_2nd_research_handbook_geometry_2016.pdf

Kaufmann, H., Steinbügl, K., Dünser, A., & Glück, J. (2005). General training of spatial abilities by geometry education in augmented reality. Annual Review of CyberTherapy and Telemedicine: A Decade of VR, 3, 65-76. Retrieved from https://www.researchgate.net/publication/216867613_General_Training_of_Spatial_Abilities_by_Geometry_Education_in_Augmented_Reality

Komala, K., & Haqq, A. A. (2021). Development of Geometry Test Based on Van Hiele's Theory in Exploration Profile of Student's Spatial Reasoning Ability Level. EduMa: Mathematics education learning and teaching‏‏‎, 10(1), 83-97. http://dx.doi.org/10.24235/eduma.v10i1.8518

Koomson, D., Boateng, F. O., & Lotey, E. K. (2024). Investigating the Level of Mathematics Anxiety among Junior High School Pupils. Mathematics Education Journal, 8(2), 147–158. http://dx.doi.org/10.22219/mej.v8i2.33693

Kospentaris, G., Spyrou, P., & Lappas, D. (2011). Exploring students’ strategies in area conservation geometrical tasks. Educational Studies in Mathematics, 77, 105-127. https://doi.org/10.1007/s10649-011-9303-8

Krampe, R. T., & Ericsson, K. A. (1996). Maintaining excellence: Deliberate practice and elite performance in young and older pianists. Journal of Experimental Psychology: General, 125(4), 331-359. https://doi.org/10.1037//0096-3445.125.4.331

Kruskal, W. H., & Wallis, W. A. (1952). Use of ranks in one-criterion variance analysis. Journal of the American Statistical Association, 47(260), 583-621. https://doi.org/10.1080/01621459.1952.10483441

Kuzle, A. (2013). Patterns of metacognitive behavior during mathematics problem-solving in a dynamic geometry environment. International Electronic Journal of Mathematics Education, 8(1), 20-40. Retrieved from https://www.iejme.com/download/patterns-of-metacognitive-behavior-during-mathematics-problem-solving-in-a-dynamic-geometry.pdf

Kyeremeh, P., Awuah, F. K., & Dorwu, E. (2023). Integration of Ethnomathematics in Teaching Geometry: A Systematic Review and Bibliometric Report. Journal of Urban Mathematics Education, 16(2), 68-89. https://doi.org/10.21423/jume-v16i2a519

Lee, C. Y., & Chen, M. J. (2014). The impacts of virtual manipulatives and prior knowledge on geometry learning performance in junior high school. Journal of Educational Computing Research, 50(2), 179-201. http://dx.doi.org/10.2190/EC.50.2.b

Lee, N. H., Ng, K. E. D., & Yeo, J. B. W. (2019). Metacognition in the teaching and learning of mathematics. In Mathematics Education in Singapore. https://doi.org/10.1007/978-981-13-3573-0_11

Leopold, C. (2005). Geometry education for developing spatial visualisation abilities of engineering students. Journal Biuletyn of Polish Society for Geometry and Engineering Graphics, 15. Retrieved from https://www.researchgate.net/publication/228908412_Geometry_education_for_developing_spatial_visualisation_abilities_of_engineering_students

Lestari, W., & Jailani. (2018, September). Enhancing an ability mathematical reasoning through metacognitive strategies. In Journal of Physics: Conference Series (Vol. 1097, p. 012117). IOP Publishing. http://dx.doi.org/10.1088/1742-6596/1097/1/012117

Linn, M. C., & Petersen, A. C. (1985). Emergence and characterization of sex differences in spatial ability: A meta-analysis. Child Development, 56(6), 1479-1498. Retrieved from https://pubmed.ncbi.nlm.nih.gov/4075870/

Lohman, D. F. (1996). Spatial abilities as traits, processes, and knowledge. In R. J. Sternberg & J. E. Davidson (Eds.), Conceptions of giftedness (2nd ed., pp. 97–116). Cambridge University Press. Retrieved from https://psycnet.apa.org/record/1987-98828-006

Lohman, D. F. (2012). Spatial abilities and instructional methods in secondary school mathematics: Some explorations. In K. F. Sawyer (Ed.), Handbook of Education and Training in Professional Psychology (pp. 97-108). American Psychological Association.

Lotey, E. K., Boateng, F. O., Arthur, Y. D., Adu-Obeng, B., & Gordon, J. F. (2025). Exploring GeoGebra acceptance: an implication for pre-service mathematics teachers’ professional development. Cogent Education, 12(1), 2514980. https://doi.org/10.1080/2331186X.2025.2514980

Lowrie, T., Logan, T., & Hegarty, M. (2019). The influence of spatial visualization training on students’ spatial reasoning and mathematics performance. Journal of Cognition and Development, 20(5), 729-751. https://doi.org/10.1080/15248372.2019.1653298

Lowrie, T., Resnick, I., Harris, D., & Logan, T. (2020). In search of the mechanisms that enable transfer from spatial reasoning to mathematics understanding. Mathematics Education Research Journal, 32, 175-188. https://doi.org/10.1007/s13394-020-00336-9

Luneta, K. (2015). Understanding students' misconceptions: an analysis of final Grade 12 examination questions in geometry. Pythagoras, 36(1), 1-11. https://doi.org/10.4102/pythagoras.v36i1.261

Mann, H. B., & Whitney, D. R. (1947). On a test of whether one of two random variables is stochastically larger than the other. The Annals of Mathematical Statistics, 18(1), 50-60. https://doi.org/10.1214/aoms/1177730491

Markey, S. M. (2009). The relationship between visual-spatial reasoning ability and math and geometry problem-solving. American International College. https://eric.ed.gov/?id=ED532420

Mathewson, J. H. (1999). Visual‐spatial thinking: An aspect of science overlooked by educators. Science education, 83(1), 33-54. https://doi.org/10.1002/(SICI)1098-237X(199901)83:1%3C33::AID-SCE2%3E3.0.CO;2-Z

Mevarech, Z. R., & Kramarski, B. (1997). IMPROVE: A multidimensional method for teaching mathematics in heterogeneous classrooms. American Educational Research Journal, 34, 365-394. http://dx.doi.org/10.3102/00028312034002365

Mevarech, Z. R., & Kramarski, B. (2003). The effects of metacognitive training versus worked-out examples on students' mathematical reasoning. British Journal of Educational Psychology, 73(3), 449-471. https://doi.org/10.1348/000709903322591181

Mjenda, M., Mutarutinya, V., & Owiti, D. (2023). Assessing the Effectiveness of Computer-Aided Instructional Techniques in Enhancing Students’ 3D Geometry Spatial Visualization Skills Among Secondary School Students in Tanzania. International Journal of Learning, Teaching and Educational Research. https://doi.org/10.26803/ijlter.22.6.31

Muftirah, L., Nugroho, P. B., & Shinta, M. (2023). Developing Geometric Visualization Skills through Interactive Teaching Methods. Journal of Mathematics Education, 15, 45-60.

Nahmias, E., & Teicher, M. (2021). Incorporating a Metacognitive Learning Model to Improve Geometric Thinking in High-School Students. Journal of Education and Learning, 10(5), 102-108. https://doi.org/10.5539/jel.v10n5p102

Naufal, M. A., Abdullah, A. H., Osman, S., Abu, M. S., & Ihsan, H. (2021). The Effectiveness of Infusion of Metacognition in van Hiele Model on Secondary School Students' Geometry Thinking Level. International Journal of Instruction, 14(3), 535-546. http://dx.doi.org/10.29333/iji.2021.14331a

Newcombe, N. S. (2010). Picture this: Increasing math and science learning by improving spatial thinking. American Educator, 34(2), 29-35. Retrieved from https://www.aft.org/sites/default/files/Newcombe_1.pdf

Oladosu, L. O. (2014). Secondary school students’ meaning and learning of circle geometry (Doctoral dissertation, University of Calgary). Retrieved from https://ucalgary.scholaris.ca/bitstreams/af1fdc8b-1e8a-4b30-898e-6add4be49c63/download

Onyancha, R. M., Derov, M., & Kinsey, B. L. (2009). Improvements in spatial ability as a result of targeted training and computer‐aided design software use: Analyses of object geometries and rotation types. Journal of Engineering Education, 98(2), 157-167. https://doi.org/10.1002/j.2168-9830.2009.tb01014.x

Owens, K., & Outhred, L. (2006). The complexity of learning geometry and measurement. In Handbook of research on the psychology of mathematics education (pp. 83-115). Brill. http://dx.doi.org/10.1163/9789087901127_005

Özerem, A. (2012). Misconceptions in geometry and suggested solutions for seventh-grade students. Procedia-Social and Behavioral Sciences, 55, 720-729. http://dx.doi.org/10.1016/j.sbspro.2012.09.557

Özsoy, G. (2011). An investigation of the relationship between metacognition and mathematics achievement. Asia Pacific Education Review, 12, 227-235. Retrieved from http://dx.doi.org/10.1007/s12564-010-9129-6

Palincsar, A. S., & Brown, A. L. (1984). Reciprocal teaching of comprehension-fostering and comprehension-monitoring activities. Cognition and Instruction, 1(2), 117-175. http://dx.doi.org/10.1207/s1532690xci0102_1

Panaoura, G., Gagatsis, A., & Lemonides, C. (2007). Spatial abilities about performance in geometry tasks. Retrieved from https://www.researchgate.net/publication/247211162_Panaoura_G_Gagatsis_A_Lemonides_Ch_2007_Spatial_abilities_in_relation_to_performance_in_geometry_tasks_5th_CERME_Congress_of_ERME_the_European_Society_for_Research_in_Mathematics_Education_22nd_of_Feb

Paris, S. G., & Winograd, P. (1990). How metacognition can promote academic learning and instruction. In B. F. Jones & L. Idol (Eds.), Dimensions of thinking and cognitive instruction (pp. 15-51). Routledge. Retrieved from https://www.taylorfrancis.com/chapters/edit/10.4324/9780203771686-2/metacognition-promote-academic-learning-instruction-scott-paris-peter-winograd

Park, H. Y., Jung, S. M., & Kim, Y. (2014). Metacognitive Learning Methods to Improve Mathematical Thinking. Journal of the Korean School Mathematics Society, 17(4), 717-746.

Park, J., Kim, D. E., & Sohn, M. (2011). 3D simulation technology as an effective instructional tool for enhancing spatial visualization skills in apparel design. International Journal of Technology and Design Education, 21, 505-517. https://doi.org/10.1007/s10798-010-9127-3

Pedrosa, C. M., Barbero, B. R., & Miguel, A. R. (2014). Spatial visualization learning in engineering: Traditional methods vs. a web-based tool. Journal of Educational Technology & Society, 17(2), 142-157. Retrieved from https://www.jstor.org/stable/jeductechsoci.17.2.142

Pressley, M., & Afflerbach, P. (1995). Verbal protocols of reading: The nature of constructively responsive reading. Routledge. Retrieved from https://www.routledge.com/Verbal-Protocols-of-Reading-The-Nature-of-Constructively-Responsive-Reading/Pressley-Afflerbach/p/book/9780805817645

Purnomo, M. E. R., & Machromah, I. U. (2018, January). Major difficulty in solid geometry learning for university students: Developing visual spatial skills. In University of Muhammadiyah Malang's 1st International Conference of Mathematics Education (INCOMED 2017) (pp. 143-146). Atlantis Press. Retrieved from http://dx.doi.org/10.2991/incomed-17.2018.31

Purnomo, Y. W., & Machromah, U. (2018). Visualizing Solid Geometry: A Significant Step in Tackling Geometry Problems. International Journal of Educational Research, 92, 10-20.

Rafi, A., Samsudin, K., & Said, C. S. (2008). Training in Spatial Visualization: The Effects of Training Method and Gender. Journal of Educational Technology and Society, 11, 127-140. Retrieved from https://www.researchgate.net/publication/220374788_Training_in_Spatial_Visualization_The_Effects_of_Training_Method_and_Gender

Rosenshine, B., & Meister, C. (1992). The use of scaffolds for teaching higher-level cognitive strategies. Educational Leadership, 49(7), 26-33. Retrieved from https://formapex.com/telechargementpublic/rosenshine1992a.pdf?616d13afc6835dd26137b409becc9f87=0f8596400454ea1d4810973bafd79e9b

Sahin, S. M., & Kendir, F. (2013). The effect of using metacognitive strategies for solving geometry problems on students' achievement and attitude. Educational Research and Reviews, 8(19), 1777. Retrieved from https://academicjournals.org/article/article1382341949_Sahin%20and%20Kendir.pdf

Sala, G., & Gobet, F. (2017). Working memory training in typically developing children: A meta-analysis of the available evidence. Developmental Psychology, 53(4), 671–685. https://doi.org/10.3758/s13423-019-01681-y

Salthouse, T. A. (1996). The processing-speed theory of adult age differences in cognition. Psychological Review, 103(3), 403-428. https://doi.org/10.1037/0033-295x.103.3.403

Salthouse, T. A. (2004). What and when of cognitive aging. Current Directions in Psychological Science, 13(4), 140-144. https://doi.org/10.1111/j.0963-7214.2004.00293.x

Schneider, W., & Artelt, C. (2010). Metacognition and mathematics education. ZDM, 42, 149-161. http://dx.doi.org/10.1007/s11858-010-0240-2

Schraw, G., & Dennison, R. S. (1994). Assessing metacognitive awareness. Contemporary Educational Psychology, 19(4), 460-475. https://doi.org/10.1006/ceps.1994.1033

Schraw, G., & Dennison, R. S. (1994). The role of metacognition in problem solving. In J. Metcalfe & A. P. Shimamura (Eds.), Metacognition: Knowing about knowing (pp. 207–226). MIT Press. https://doi.org/10.7551/mitpress/4561.001.0001

Schraw, G., & Moshman, D. (1995). Metacognitive theories. Educational Psychology Review, 7(4), 351-371. http://dx.doi.org/10.1007/BF02212307

Schunk, D. H., & Ertmer, P. A. (2000). Self-regulation and academic learning: Self-efficacy enhancing interventions. In M. Boekaerts, P. R. Pintrich, & M. Zeidner (Eds.), Handbook of self-regulation (pp. 631-649). Academic Press. https://doi.org/10.1016/B978-012109890-2/50048-2

Schunk, D. H., & Zimmerman, B. J. (2007). Influencing children’s self-efficacy and self-regulation of reading and writing through modeling. Reading & Writing Quarterly, 23(1), 7-25. http://dx.doi.org/10.1080/10573560600837578

Sercenia, J. C., & Prudente, M. S. (2023). Effectiveness of the Metacognitive-based Pedagogical Intervention on Mathematics Achievement: A Meta-Analysis. International Journal of Instruction 16(4). http://dx.doi.org/10.29333/iji.2023.16432a

Shelton, B. E., & Hedley, N. R. (2004). Exploring a cognitive basis for learning spatial relationships with augmented reality. Technology, Instruction, Cognition and Learning, 1(4), 323. Retrieved from https://www.researchgate.net/publication/43952613_Exploring_a_Cognitive_Basis_for_Learning_Spatial_Relationships_with_Augmented_Reality

Sinclair, N., Bartolini Bussi, M. G., de Villiers, M., Jones, K., Kortenkamp, U., Leung, A., & Owens, K. (2016). Recent research on geometry education: An ICME-13 survey team report. ZDM, 48, 691-719. https://doi.org/10.1007/s11858-016-0796-6

Smith, J. (2017). Core Mathematics as a Prerequisite for Higher Education Admission. Educational Research and Reviews, 12, 287-295.

Smith, J. (2017). The importance of core mathematics proficiency in Ghanaian higher education institutions. Journal of Education, 45(2), 123-135.

Sorby, S. (2009). Developing spatial cognitive skills among middle school students. Cognitive Processing, 10(2), 312-315. https://doi.org/10.1007/s10339-009-0310-y

Sorby, S. A. (2009). Educational research in developing 3-D spatial skills for engineering students. International Journal of Science Education, 31(3), 459-480. https://doi.org/10.1080/09500690802595839

Sorby, S. A. (2009). Spatial visualization in engineering graphics and STEM disciplines. Engineering Design Graphics Journal, 73(3), 1-14.

Spelke, E. S. (2005). Sex differences in intrinsic aptitude for mathematics and science?: A critical review. American Psychologist, 60(9), 950-958. Retrieved from https://www.harvardlds.org/wp-content/uploads/2017/01/spelke2005-1.pdf

Steen, K., Brooks, D., & Lyon, T. (2006). The impact of virtual manipulatives on first grade geometry instruction and learning. Journal of Computers in Mathematics and Science Teaching, 25(4), 373-391. Retrieved from https://eric.ed.gov/?id=EJ752423

Stillman, G., & Mevarech, Z. (2010). Metacognition research in mathematics education: from hot topic to mature field. ZDM, 42, 145-148. http://dx.doi.org/10.1007/s11858-010-0245-x

Strutchens, M. E., Harris, K. A., & Martin, W. G. (2001). Take time for action: assessing geometric and measurement understanding using manipulatives. Mathematics Teaching in the Middle School, 6(7), 402-405. https://doi.org/10.5951/MTMS.6.7.0402

Tay, M. K. (2023). Enhancing High School Students’ Spatial Reasoning Through Geometry Transformation Instruction in Ghana. Retrieved from https://www.researchgate.net/publication/373142344_ENHANCING_SPATIAL_REASONING_THROUGH_GEOMETRY_TRANSFORMATION_INSTRUCTION_IN_GHANA

Titus, S., & Horsman, E. (2009). Characterizing and improving spatial visualization skills. Journal of Geoscience Education, 57(4), 242-254. Retrieved from https://files.eric.ed.gov/fulltext/EJ1164746.pdf

Uttal, D. H., Meadow, N. G., Tipton, E., Hand, L. L., Alden, A. R., Warren, C., & Newcombe, N. S. (2013). The malleability of spatial skills: A meta-analysis of training studies. Psychological Bulletin, 139(2), 352–402. https://doi.org/10.1037/a0028446

Uttal, D. H., Meadow, N. G., Tipton, E., Hand, L. L., Alden, A. R., Warren, C., & Newcombe, N. S. (2013). The malleability of spatial skills: A meta-analysis of training studies. Psychological Bulletin, 139(2), 352-402. Retrieved from https://doi.org/10.1037/a0028446

Van der Walt, M. S., Maree, J. G., & Ellis, S. M. (2008). Metacognition in the learning of mathematics in the senior phase: Some implications for the curriculum. International Journal of Adolescence and Youth, 14(3), 205-235. http://dx.doi.org/10.1080/02673843.2008.9748004

Van Hiele, P. M. (1959). The child’s thought and geometry. English translation of selected writings of Dina van Hiele-Geldof and Pierre M. van Hiele, 243-252. Retrieved from https://eric.ed.gov/?id=ED287697

Van Meter, P., & Garner, J. (2005). The promise and practice of learner-generated drawing: Literature review and synthesis. Educational Psychology Review, 17(4), 285-325. https://doi.org/10.1007/s10648-005-8136-3

Veenman, M. V. (2015). Metacognition. In Handbook of individual differences in reading (pp. 26-40). Routledge. Retrieved from https://www.taylorfrancis.com/chapters/edit/10.4324/9780203075562-3/metacognition-marcel-veenman

Vorhölter, K. (2023). Metacognition in mathematical modeling: the connection between metacognitive individual strategies, metacognitive group strategies and modeling competencies. Mathematical Thinking and Learning, 25(3), 317-334. https://doi.org/10.1080/10986065.2021.2012740

Voyer, D., Voyer, S., & Bryden, M. P. (1995). Magnitude of sex differences in spatial abilities: A meta-analysis and consideration of critical variables. Psychological Bulletin, 117(2), 250-270. https://doi.org/10.1037/0033-2909.117.2.250

Wahab, R. A., Abdullah, A. H., Abu, M. S., Atan, N. A., & Mokhtar, M. (2018). A learning 3d geometry through SketchUp Make (SPPD-SUM) to enhance visual spatial skills and the level of geometric thinking. Journal of Fundamental and Applied Sciences, 10, 1005-1039. http://dx.doi.org/10.4314/jfas.v10i6s.50

Wai, J., Lubinski, D., & Benbow, C. P. (2009). Spatial ability for STEM domains: Aligning over 50 years of cumulative psychological knowledge solidifies its importance. Journal of Educational Psychology, 101(4), 817-835. http://dx.doi.org/10.1037/a0016127

Wang, H. C., Chang, C. Y., & Li, T. Y. (2007). The comparative efficacy of 2D-versus 3D-based media design for influencing spatial visualization skills. Computers in Human Behavior, 23(4), 1943-1957. https://doi.org/10.1016/j.chb.2006.02.004

Wang, S., Hu, B. Y., & Zhang, X. (2021). Kindergarteners’ spatial skills and their reading and math achievement in second grade. Early Childhood Research Quarterly, 57, 156-166. https://doi.org/10.1016/j.ecresq.2021.06.002

West African Examinations Council (WAEC). (2017). Chief Examiner’s Report for the WASSCE. Ghana Education Service.

West African Examinations Council (WAEC). (2021). Chief Examiner’s Report for the WASSCE. Ghana Education Service.

West African Examinations Council (WAEC). (2023). Chief Examiner’s Report for the WASSCE. Ghana Education Service.

Williams, C. B., Gero, J., Lee, Y., & Paretti, M. (2010, January). Exploring spatial reasoning ability and design cognition in undergraduate engineering students. In International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (Vol. 44144, pp. 669-676). Retrieved from http://dx.doi.org/10.1115/DETC2010-28925

Willis, S. L., Tennstedt, S. L., Marsiske, M., Ball, K., Elias, J., Koepke, K. M., ... & Wright, E. (2006). Long-term effects of cognitive training on everyday functional outcomes in older adults. JAMA, 296(23), 2805-2814. https://doi.org/10.1001/jama.296.23.2805

Wilson, J., & Clarke, D. (2004). Towards the modelling of mathematical metacognition. Mathematics Education Research Journal, 16, 25-48. http://dx.doi.org/10.1007/BF03217394

Yalley, E., Armah, G., & Ansah, R. K. (2021). Effect of the VAN Hiele Instructional Model on Students’ Achievement in Geometry. Education Research International, 2021, 1-10. http://dx.doi.org/10.1155/2021/6993668

Yang, K. L. (2012). Structures of cognitive and metacognitive reading strategy use for reading comprehension of geometry proof. Educational Studies in Mathematics, 80, 307-326. https://doi.org/10.1007/s10649-011-9350-1

Zhong, J., Li, W., Zhuang, Z., & Dai, L. (2019). Metacognitive processes enhance spatial cognitive ability: Evidence from eye movements and behavior. Journal of Experimental Psychology: General, 148(2), 316–328.

Zimmerman, B. J. (2002). Becoming a self-regulated learner: An overview. Theory into Practice, 41(2), 64-70. https://doi.org/10.1207/s15430421tip4102_2




DOI: http://dx.doi.org/10.46827/ejes.v12i10.6226

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