Main Article Content


Functional analysis has been of interest and the thinking of students should be prepared.  Analyzing the process of conceptualizing geometric function problem solving based on the dimensions of cognitive processes and knowledge was the purpose of this study. The subjects of this study were three students selected purposively from one of the secondary schools in Indonesia. Exploration of these studies with constant comparative techniques. The results of the data analysis show that the cognitive processes that operate and the knowledge applied by students focus on the conceptualization of algebraic representations. Based on the conceptualization process, students' conceptual systems are still fragmented because of the problem of the relationship between the concept and the basis of its relationship. As a result, procedural knowledge is more dominant.


Bloom Taxonomy Cognitive Process Conceptualization Geometric-Function Knowledge Dimension

Article Details


  1. Alghadari, F., & Kusuma, A. P. (2018). Pendekatan analogi untuk memahami konsep dan definisi dari pemecahan masalah. In Prosiding Seminar Nasional Matematika dan Pendidikan Matematika (SNMPM), Cirebon.

  2. Alghadari, F., Yuni, Y., & Wulandari, A. (2019). Conceptualization in solving a geometric-function problem: an effective and efficient process. Journal of Physics: Conference Series, 1315(1), 012004.

  3. Bartholomew, S. R., & Strimel, G. J. (2018). Factors influencing student success on open-ended design problems. International Journal of Technology and Design Education, 28(3), 753-770.

  4. Borji, V., Font, V., Alamolhodaei, H., & Sánchez, A. (2018). Application of the complementarities of two theories, APOS and OSA, for the analysis of the university students’ understanding on the graph of the function and its derivative. Eurasia Journal of Mathematics, Science and Technology Education, 14(6), 2301-2315.

  5. Choi, Y. J., & Hong, J. K. (2014). On the students' thinking of the properties of derivatives. The Mathematical Education, 53(1), 25-40.

  6. Clancey, W. (2001). Is abstraction a kind of idea or how conceptualization works? Cognitive Science Quarterly, 1(3-4), 389-421.

  7. Dossey, J. A. (2017). Problem solving from a mathematical standpoint. In B. Csapó & J. Funke (Eds.), The Nature of Problem Solving: Using Research to Inspire 21st Century Learning (pp. 59-72). OECD Publishing.

  8. Glaser, B. G. (2002). Conceptualization: On theory and theorizing using grounded theory. International journal of qualitative methods, 1(2), 23-38.

  9. Hendriana, H., & Fadhillah, F. M. (2019). The students’ mathematical creative thinking ability of junior high school through problem-solving approach. Infinity Journal, 8(1), 11-20.

  10. Hendriana, H., Prahmana, R. C. I., & Hidayat, W. (2018). Students’ performance skills in creative mathematical reasoning. Infinity Journal, 7(2), 83-96.

  11. Hong, Y. Y., & Thomas, M. O. (2015). Graphical construction of a local perspective on differentiation and integration. Mathematics Education Research Journal, 27(2), 183-200.

  12. Iskandar, S. M. (2016). Pendekatan keterampilan metakognitif dalam pembelajaran sains di kelas [Approach of metacognitive skills in science learning in the classroom]. Erudio Journal of Educational Innovation, 2(2), 13-20.

  13. Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. The National Academies Press.

  14. Kop, P. M., Janssen, F. J., Drijvers, P. H., Veenman, M. V., & van Driel, J. H. (2015). Identifying a framework for graphing formulas from expert strategies. The Journal of Mathematical Behavior, 39, 121-134.

  15. Mumu, J., Prahmana, R. C. I., & Tanujaya, B. (2017). Construction and reconstruction concept in mathematics instruction. Journal of Physics: Conference Series, 943(1), 012011.

  16. Nagle, C., Moore-Russo, D., Viglietti, J., & Martin, K. (2013). Calculus students’ and instructors’conceptualizations of slope: A comparison across academic levels. International Journal of Science and Mathematics Education, 11(6), 1491-1515.

  17. Oberle, D., Volz, R., Staab, S., & Motik, B. (2004). An extensible ontology software environment. In S. Staab & R. Studer (Eds.), Handbook on ontologies (pp. 299-319). Springer.

  18. Österman, T., & Bråting, K. (2019). Dewey and mathematical practice: revisiting the distinction between procedural and conceptual knowledge. Journal of Curriculum Studies, 51(4), 457-470.

  19. Polya, G. (1981). Mathematical Discovery on Understanding, Learning and Teaching Problem Solving, Volumes I and II. John Wiley & Sons.

  20. Radmehr, F., & Drake, M. (2017). Revised Bloom's taxonomy and integral calculus: unpacking the knowledge dimension. International Journal of Mathematical Education in Science and Technology, 48(8), 1206-1224.

  21. Radmehr, F., & Drake, M. (2018). An assessment-based model for exploring the solving of mathematical problems: Utilizing revised bloom’s taxonomy and facets of metacognition. Studies in Educational Evaluation, 59, 41-51.

  22. Rittle-Johnson, B., & Schneider, M. (2015). Developing conceptual and procedural knowledge of mathematics. In R. C. Kadosh & A. Dowker (Eds.), Oxford handbook of numerical cognition (pp. 1118-1134). Oxford University Press.

  23. Sahin, Z., Yenmez, A. A., & Erbas, A. K. (2015). Relational understanding of the derivative concept through mathematical modeling: A case study. Eurasia Journal of Mathematics, Science and Technology Education, 11(1), 177-188.

  24. Setyawan, F., Prahmana, R. C. I., Istiandaru, A., & Hendroanto, A. (2017). Visualizer’s representation in functions. Journal of Physics: Conference Series, 943(1), 012004.

  25. Tobin, P. (2012). Mathematics Standard Level: For Use with the International Baccalaureate Diploma Programme (IB Mathematics) (F. Cirrito, Ed.). IBID Press.

  26. Tokgoz, E., & Gualpa, G. C. (2015). STEM majors’ cognitive calculus ability to sketch a function graph. In 2015 ASEE Annual Conference & Exposition, Seattle, Washington.

  27. Usman, A. I. (2017). Geometric error analysis in applied calculus problem solving. European Journal of Science and Mathematics Education, 5(2), 119-133.

  28. Wagner, J., & Sharp, J. (2017). A calculus activity with foundations in geometric learning. The Mathematics Teacher, 110(8), 618-623.

  29. Widodo, S. A., Nayazik, A., & Prahmana, R. (2019). Formal student thinking in mathematical problem-solving. Journal of Physics: Conference Series, 1188(1), 012087.