Students’ mental construction in cube and cuboid concepts based on mathematical ability differences

Imam Rofiki, Ahmad Choirul Anam, Putri Eka Sari, Wahyu Henky Irawan, Ika Santia

Abstract


Understanding of cube and cuboid concepts is one of the essential goals of solid geometry learning. Most studies of students’ understanding of these concepts have posited a gap between the students’ surface area and volume conceptions of its and students’ understanding. The study aims to describe the students’ mental constructions in APOS (Action, Process, Object, and Schema) theory framework. This study used analysis of students as subject to three junior high school students who have differences in mathematical abilities with a qualitative approach. Data were collected by the task sheet and interview. The result of this study evidences that subject who has high mathematical ability could solve problems about cube and cuboid concepts correctly in the action stage. In the process and object stage, subject could provide detailed explanations of how steps to assess the surface area and volume of cube and cuboid. She compared two shapes with different sizes of cube and cuboid. In the schema stage, she made systematic understanding related to the concepts of surface area and volume of cube and cuboid. The subject who has medium mathematical ability explained her mental construction in action and process stage well, despite the error in the process stage. Next stage, she had compared two different shapes of cube and cuboid to found their ratio. The last stage, she had not completed her explanation. The subject has low mathematical ability could solve the problems about cube and cuboid concepts. At the process, object, and schema stage, she had not completed its indicators to show cube and cuboid concepts.


Keywords


Understanding Concepts; Mental Construction; APOS Theory; Mathematical Ability

Full Text:

PDF

References


Altieri, M., & Schirmer, E. (2019). Learning the concept of eigenvalues and eigenvectors: a comparative analysis of achieved concept construction in linear algebra using APOS theory among students from different educational backgrounds. ZDM, 51(7), 1125-1140.

Anam, A. C., Juniati, D., & Wijayanti, P. (2019). Understanding the quadrilateral concept of junior high school students based on APOS theory in terms of differences in cognitive styles, Proceedings on Mathematics, Informatics, Science, and Education International Conference (MISEIC 2019). Atlantis Press.

Anwar, & Rofiki, I. (2018). Investigating students’ learning trajectory: A case on triangle. Journal of Physics: Conference Series, 1088(1), 012021. https://doi.org/10.1088/1742-6596/1088/1/012021

Arnon, I., Cottrill, J., Dubinsky, E., Oktaç, A., Fuentes, S. R., Trigueros, M., & Weller, K. (2014). The APOS paradigm for research and curriculum development. In APOS Theory (pp. 93-108). New York: Springer.

Bansilal, S., Deonarain B., & Maria T. (2017). An APOS study on pre-service teachers’ understanding of injections and surjections. Journal of Mathematical Behavior, 48, 22-37.

Barmby, P., Harries T., Higgins S., & Suggate. (2007). How can we assess mathematical understanding. Proceedings on the 31stof the International Group for the Psychology of Mathematics Education. 41-48. Seoul: PME.

Barody, A. J., Feil Y., & Johson A. R. (2007). An alternative reconceptualization of procedural and conceptual knowledge. Journal for Research in Mathematics Education, 38, 115-131.

Borji, V., Alamolhodaei, H., & Radmehr, F. (2018). Application of the APOS-ACE theory to improve students’ graphical understanding of derivative. EURASIA Journal of Mathematics, Science and Technology Education, 14(7), 2947-2967.

Dubinsky, E. (2002). Reflective abstraction in advanced mathematical thinking. In Advanced mathematical thinking (pp. 95-126). Springer, Dordrecht.

Dubinsky, E., & Wilson, T. R. (2001). High school students’ understanding of the function concept. Journal of Mathematical Behavior, 32(1), 83-101.

Figueroa, A. P., Possani, E., & Trigueros, M. (2018). Matrix multiplication and transformations: An APOS approach. The Journal of Mathematical Behavior, 52, 77-91.

García, M., I., & Parraguez, M. (2017). The basis step in the construction of the principle of mathematical induction based on APOS theory. The Journal of Mathematical Behavior, 46, 128-143.

Haylock, D., & Cockburn, A. D. (2008). Understanding mathematics for young children: A guide for foundation stage and lower primary teachers. United Kingdom: SAGE Publication.

Kurniawan, A. P., Anam, A. C., Abdussakir, & Rofiki, I. (2019). Integrasi etnomatematika dengan model pembelajaran probing-prompting untuk melatih komunikasi matematis siswa. Mapan: Jurnal Matematika dan Pembelajaran, 7(1), 1-15.

Martínez-Planell, R., & Delgado, A. C. (2016). The unit circle approach to the construction of the sine and cosine functions and their inverses: An application of APOS theory. The Journal of Mathematical Behavior, 43, 111-133.

Mena-Lorca, A., & Parraguez, A. M. M. (2016). Mental constructions for the group isomorphism theorem. International Electronic Journal of Mathematics Education, 11(2), 377-393.

Ndlovu, Z., & Brijlall, D. (2016). Pre-service mathematics teachers’ mental constructions of the determinant concept. International Journal of Educational Sciences, 14(1-2), 145-156.

Priss, U. (2018). Combining and contrasting formal concept analysis and APOS theory. In International Conference on Conceptual Structures (pp. 96-104). Springer, Cham.

Puloo, M. M. L., Juniati, D., & Wijayanti, P. (2018). Visualization profile of junior high school students in solving geometry problems viewed from gender differences. Journal of Physics: Conference Series, 1108(1), 012063.

Rofiki, I., Nusantara, T., Subanji, S., & Chandra, T. D. (2017). Reflective plausible reasoning in solving inequality problem. IOSR Journal of Research & Method in Education (IOSRJRME), 7(1), 101–112. https://doi.org/10.9790/7388-070101101112

Suryani, A. I., Anwar, Hajidin, & Rofiki, I. (2020). The practicality of mathematics learning module on triangles using GeoGebra. Journal of Physics: Conference Series, 1470(1), 012079. https://doi.org/10.1088/1742-6596/1470/1/012079

Vidakovic, D., Dubinsky, E., & Weller, K. (2018). APOS theory: Use of computer programs to foster mental constructions and student’s creativity. In Creativity and Technology in Mathematics Education (pp. 441-477). Springer, Cham.




DOI: http://dx.doi.org/10.24042/ajpm.v11i1.5946

Refbacks

  • There are currently no refbacks.


 

Creative Commons License
Al-Jabar : Jurnal Pendidikan Matematika is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.