The Spatial Thinking Process of the Field-Independent Students based on Action-Process-Object-Schema Theory
Spatial thinking has roles to facilitate learners to remember, understand, reason, and communicate objects and the connections among objects that are .
- Pub. date: October 15, 2021
- Pages: 1807-1823
- 676 Downloads
- 1192 Views
- 4 Citations
Spatial thinking has roles to facilitate learners to remember, understand, reason, and communicate objects and the connections among objects that are represented in space. This research aims to analyze the spatial thinking process of students in constructing new knowledge seen from the field-independent cognitive style learners based on Action-Process-Object-Schema (APOS) theory. APOS theory is used to explore spatial thinking processes which consist of mental structures of action, process, object, and schema. This research is qualitative research with an exploratory method. It provided the students' opportunity to solve problems alternately until the method found the most appropriate subjects for the research objectives. The subjects were 2 students of Mathematics Education in the fourth semester of Universitas Muria Kudus Indonesia. The data collection techniques were started by distributing the validated and reliable spatial thinking questions, the cognitive style question, and the interview. The applied data analysis consisted of data reduction, presentation, and conclusion. The findings showed (1) spatial thinking process of holistic-external representation typed learners were indicated by the representative thinking element, abstract-illustrative figure expression to communicate and complete the tasks correctly, (2) spatial thinking process of the holistic-internal representation typed learners were indicated by the representative means, having ideas, connecting with the previous knowledge in the forms of symbols and numbers, and finding the final results correctly although incomplete.
Keywords: APOS theory, cognitive style, field-independent, spatial thinking.
References
Arnon, I., Cottrill, J., Dubinsky, E., Oktaç, A., Fuentes, S. R., Trigueros, M., & Weller, K. (2014). APOS Theory. Springer. https://doi.org/10.1007/978-1-4614-7966-6
Atit, K., Uttal, D. H., & Stieff, M. (2020). Situating space: Using a discipline-focused lens to examine spatial thinking skills. Cognitive Research: Principles and Implications, 5(19), 1-16. https://doi.org/10.1186/s41235-020-00210-z
Aziz, T. A., & Kurniasih, M. D. (2019). External representation flexibility of domain and range of function. Journal on Mathematics Education, 10(1), 143–155. https://doi.org/10.22342/jme.10.1.5257.143-156
Bintoro, H. S., Zaenuri, & Wardono. (2021). Application of information technology and communication-based lesson study on mathematics problem-solving ability. In D. R. Indriyanti (Ed.), Journal of Physics: Conference Series, The 7th International Conference on Mathematics, Science and Education (pp. 1-6). Universitas Negeri Semarang. Indonesia. https://doi.org/10.1088/1742-6596/1918/4/04210 5
Boccia, M., Vecchione, F., Piccardi, L., & Guariglia, C. (2017). Effect of cognitive style on learning and retrieval of navigational environments. Frontiers in Pharmacology, 8(496), 1–10. https://doi.org/10.3389/fphar.2017.00496
Cataloglu, E., & Ates, S. (2014). The effects of cognitive styles on naïve impetus theory application degrees of pre-service science teachers. International Journal of Science and Mathematics Education, 12(4), 699–719. https://doi.org/10.1007/s10763-013-9430-z
Chasanah, C., Riyadi, & Usodo, B. (2020). The effectiveness of learning models on written mathematical communication skills viewed from students’ cognitive styles. European Journal of Educational Research, 9(3), 979–994. https://doi.org/10.12973/eu-jer.9.3.979
Chen, X., Zhao, S., & Li, W. (2019). Opinion dynamics model based on cognitive styles: field-dependence and field-independence. Complexity, 2019(1), 1-12. https://doi.org/10.1155/2019/2864124
Cheng, Y. L., & Mix, K. S. (2014). Spatial training improves children’s mathematics ability. Journal of Cognition and Development, 15(1), 2–11. https://doi.org/10.1080/15248372.2012.725186
Crollen, V., Albouy, G., Lepore, F., & Collignon, O. (2017). How visual experience impacts the internal and external spatial mapping of sensorimotor functions. Scientific Reports, 7(1), 1–9. https://doi.org/10.1038/s41598-017-01158-9
Erkan Yazici, Y. (2017). İlk yıl mimarlık öğrencilerinin bilişsel stilleri ile görsel uzamsal zekaları arasındaki ilişki [The relationship between cognitive style and visual spatial intelligence of first year architectural students]. Kastamonu Eğitim Dergisi/ Kastamonu Education Journal, 25(2), 805–820.
Fiantika, F. R. (2016). Representation elements of spatial thinking. In M. Rahayuningsih (Ed.), Journal of Physics: Conference Series, (IOP Publishing Ltd), The 3rd International Conference on Mathematics, Science and Education (pp. 1-4). Universitas Negeri Semarang. Indonesia. https://doi.org/10.1088/1742-6596/824/1/012056
Fiantika, F. R. (2021). Mathematical and mental rotation skill in internal representation of elementary students. In N. Ishartono (Eds.), Journal of Physics: Conference Series, (IOP Publishing Ltd), National Conference on Mathematics Research and Mathematics Learning/ Konferensi Nasional Penelitian Matematika dan Pembelajarannya (KNPMP) V (pp. 1-5). Universitas Muhammadiyah Surakarta. Indonesia. https://doi.org/10.1088/1742-6596/1776/1/012011
Gal, H. (2019). When the use of cognitive conflict is ineffective—problematic learning situations in geometry. Educational Studies in Mathematics, 102(2), 239–256. https://doi.org/10.1007/s10649-019-09904-8
Handhika, J., Cari, Suparmi, & Sunarno, W. (2015). Exsternal representation to overcome misconception in physics. In Sutikno, A. Widiyatmoko, Masturi, A. Purwinarko (Eds.), International Conference on Mathematics, Science, and Education 2015 (pp. 34–37). Universitas Negeri Semarang. Indonesia.
Hanifah, U., Juniati, D., & Siswono, T. Y. E. (2018). Students’ spatial performance: cognitive style and sex differences. In Y. S. Rahayu, R. Ekawati, A. B. D. Nandiyanto, A. Lukito, S. C. Wibawa (Eds.), Journal of Physics: Conference Series, (IOP Publishing Ltd), Mathematics, Informatics, Science and Education International Conference (MISEIC 2017) (pp. 1-7). Universitas Negeri Surabaya. Indonesia. https://doi.org/10.1088/1742-6596/947/1/012014
Ijirana, I., & Mansyur, J. (2020). Patterns of metacognitive skills and external representation of students in chemistry problem solving. Journal of Educational Science/ Jurnal Ilmu Pendidikan, 25(2), 58-65. https://doi.org/10.17977/um048v25i2p58-65
Inglis, M. (2015). Review of APOS theory: A framework for research and curriculum development in mathematics education, Arnon et al. (2014). New York, NY, USA: Springer-Verlag New York. eBook ISBN: 978-1-4614-7966-6, Hardcover ISBN: 978-1-4614-7965-9. International Journal of Research in Undergraduate Mathematics Education, 1(3), 413–417. https://doi.org/10.1007/s40753-015-0015-9
Junarti, Sukestiyarno, Y. L., Mulyono, & Dwidayati, N. K. (2020). The process of structure sense of group prerequisite material: A case in indonesian context. European Journal of Educational Research, 9(3), 1047–1061. https://doi.org/10.12973/eu-jer.9.3.1047
Khodadady, E., & Zeynali, S. (2012). Field-dependence/independence cognitive style and performance on the IELTS listening comprehension. International Journal of Linguistics, 4(3), 622–635. https://doi.org/10.5296/ijl.v4i3.2389
Khusna, A. H. (2020). Analytical thinking process of student in proving mathematical argument. International Journal of Scientific and Technology Research, 9(1), 1248–1251.
Maier, P. H. (1998). Spatial geometry and spatial ability - How to make solid geometry solid?. In E. Cohors-Fresenborg, K. Reiss, G. Toener & H.-G. Weigand (Eds.), Selected Papers from the Annual Conference of Didactics of Mathematics (pp. 63-75). Osnabrueck University.
Masalimova, A. R., Mikhaylovsky, M. N., Grinenko, A. V., Smirnova, M. E., Andryushchenko, L. B., Kochkina, M. A., & Kochetkov, I. G. (2019). The interrelation between cognitive styles and copying strategies among student youth. Eurasia Journal of Mathematics, Science and Technology Education, 15(4), 1–7. https://doi.org/10.29333/ejmste/103565
Michel, E., & Hof, A. (2013). Promoting spatial thinking and learning with mobile field trips and eGeo-Riddles. In T. Jekel, A. Car, J. Strobl, G. Griesebner (Eds.), GI forum 2013 creating the GISociety conference proccedings (pp. 378–387). Wichmann-Verlag. https://doi.org/10.1553/giscience2013s378
Motahari, M. S., & Norouzi, M. (2015). The difference between field independent and field dependent cognitive styles regarding translation quality. Theory and Practice in Language Studies, 5(11), 2373-2381. https://doi.org/10.17507/tpls.0511.23
Muhammad, T., Daniel, E. G. S., & Abdurauf, R. A. (2015). Cognitive styles field dependence / independence and scientific achievement of male and female students of zamfara state college of education maru, Nigeria. Journal of Education and Practice, 6(10), 58–64.
Muhtarom, Murtianto, Y. H., & Sutrisno. (2017). Thinking process of students with high-mathematics ability: A study on QSR NVivo 11-assisted data analysis. International Journal of Applied Engineering Research, 12(17), 6934–6940.
National Research Council. (2005). Learning to think spatially. The National Academies Press. https://doi.org/10.17226/11019
Naurzalina, D., Karimova, A., Sarkulov, M., Tolegenova, A., Zholamanova, A., & Almurzayeva, B. (2015). Cognitive style and gender differencies in spatial abilities. In A. G. Welch, K. Köiv, A. Belusova, J. A. Kumar (Eds.), The European Proceedings of Social & Behavioural Sciences (pp. 95-105). Future Academy. https://doi.org/10.15405/epsbs.2015.01.11
Nori, R., & Giusberti, F. (2006). Predicting cognitive styles from spatial abilities. American Journal of Psychology, 119(1), 67–86. https://doi.org/10.2307/20445319
Patahuddin, S. M., Rokhmah, S., & Ramful, A. (2020). What does teaching of spatial visualisation skills incur: an exploration through the visualise-predict-check heuristic. Mathematics Education Research Journal, 32(2), 307–329. https://doi.org/10.1007/s13394-020-00321-2
Putri, S. K., Hasratuddin, H., & Syahputra, E. (2019). Development of learning devices based on realistic mathematics education to improve students’ spatial ability and motivation. International Electronic Journal of Mathematics Education, 14(2), 393–400. https://doi.org/10.29333/iejme/5729
Ramful, A., Lowrie, T., & Logan, T. (2017). Measurement of spatial ability: Construction and validation of the spatial reasoning instrument for middle school students. Journal of Psychoeducational Assessment, 35(7), 709–727. https://doi.org/10.1177/0734282916659207
Sapti, M., Purwanto, Irawan, E. B., As’ari, A. R., Sa’dijah, C., Susiswo, & Wijaya, A. (2019). Comparing model-building process: A model prospective teachers used in interpreting students’ mathematical thinking. Journal on Mathematics Education, 10(2), 171–184. https://doi.org/10.22342/jme.10.2.7351.171-184
Schindler, M., & Lilienthal, A. J. (2019). Domain-specific interpretation of eye tracking data: towards a refined use of the eye-mind hypothesis for the field of geometry. Educational Studies in Mathematics, 101(1), 123–139. https://doi.org/10.1007/s10649-019-9878-z
Seah, R. T. K., & Horne, M. (2020). The influence of spatial reasoning on analysing about measurement situations. Mathematics Education Research Journal, 32(2), 365–386. https://doi.org/10.1007/s13394-020-00327-w
Shawky, A., Elbiblawy, E., & Maresch, G. (2020). Spatial ability differences between students with a math learning disability and their other normal colleagues. Journal of Humanities and Applied Social Sciences, Advance online publication. https://doi.org/10.1108/jhass-01-2020-0016
Singer, F. M., Voica, C., & Pelczer, I. (2017). Cognitive styles in posing geometry problems: implications for assessment of mathematical creativity. ZDM - Mathematics Education, 49(1), 37–52. https://doi.org/10.1007/s11858-016-0820-x
Tikhomirova, T. (2017). Spatial thinking and memory in russian high school students with different levels of mathematical fluency. Procedia - Social and Behavioral Sciences, 237, 1260–1264. https://doi.org/10.1016/j.sbspro.2017.02.204
Yilmaz, H. B. (2009). On the development and measurement of spatial ability. International Electronic Journal of Elementary Education, 1(2), 83–96.
Yuda, M. (2011). Effectiveness of digital educational materials for developing spatial thinking of elementary school students. Procedia - Social and Behavioral Sciences (pp. 116–119). Elsevier. https://doi.org/10.1016/j.sbspro.2011.07.045
Zhang, J., & Wang, H. (2005). The effect of external representations on numeric tasks. The Quarterly Journal of Experimental Psychology Section A, 58(5), 817–838. https://doi.org/10.1080/02724980443000340
Zuliana, E., Oktavianti, I., Ratnasari, Y., & Bintoro, H. S. (2020). Design and application of marionette tangram: An educational teaching media for mathematics and social science learning process in elementary schools. Universal Journal of Educational Research, 8(3), 931–935. https://doi.org/10.13189/ujer.2020.080326
Zwartjes, L. (2018). Developing geospatial thinking learning lines in secondary education: The GI learner project. European Journal of Geography, 9(4), 138–151.