Al Jupri, Ernawulan Syaodih


This study investigated master students’ problem-solving strategies and also interpreted their formal and informal thinking when dealing with geometry problems inviting the use of algebra in the solution processes. In order to do so, an explorative study through individual written test, observation, and field notes, involving 47 master students of the primary education program, was carried out. The perspective of Van Hiele theory on the development of geometric thought was used to interpret student formal and informal thinking when dealing with geometry problems. The results showed that more than half of the participated students used informal rather than formal algebraic strategies in solving geometry problems; when students used algebraic strategies, their works were imperfect as they still made mistakes in applying the strategies. In the light of Van Hiele theory, we concluded that participated students’ thinking ability were still in between formal and informal thinking when dealing with geometry problems.


algebra, geometry, formal and informal thinking,Van Hiele theory


Breyfogle, M. L., & Lynch, C. M. (2010). Van Hiele revisited. Mathematics Teaching in The Middle School, 16(4), 233–238.

Burger, W. F., & Shaughnessy, J. M. (1986). Characterizing the van Hiele levels of development in geometry. Journal for Research in Mathematics Education, 17(1), 31–48.

Clements, D. H. (1985). Perspective on “the child’s thought and geometry”. Classic in Mathematics Education Research, pp. 60, State University of New York at Buffalo.

Crowley, M. L. (1987). The Van Hiele model of the development of geometric thought. In Learning and Teaching Geometry, K-12, 1987 Yearbook of the National Council of Teachers of Mathematics, edited by M. M. Lindquist, pp. 1–16, Reston Va: National Council of Teachers of Mathematics.

De Lange, J. (1987). Mathematics insight and meaning. Dissertation. Utrecht, the Netherlands: OW & OC.

De Lange, J. (2006). Mathematical literacy for living from OECD-PISA perspective. Tsukuba Journal of Educational Study in Mathematics. Vol. 25. Special Issue on The APEC-TSUKUBA International Conference “Innovative Teaching Mathematics through Lesson Study” (pp. 13–15). Tokyo, Japan: University of Tsukuba.

Gutierrez, A., Jaime, A., & Fortuny, J. M. (1991). An alternative paradigm to evaluate the acquisition of the Van Hiele levels. Journal for Research in Mathematics Education, 22(3), 237–251.

Herskowitz, R. (1998). About reasoning in geometry. In C. Mammana, & V. Villani (Eds.), Perspective on the teaching of geometry for the 21st century (pp. 29–36). Dordrecht, Boston, London: Kluwer Academic Publishers.

Howse, T. D., & Howse, M. E. (2015). Linking the Van Hiele theory to instruction. Teaching Children Mathematics, 21(5), 305–313.

Jupri, A., & Drijvers, P. (2016). Student difficulties in mathematizing word problems in algebra. Eurasia Journal of Mathematics, Science & Technology Education, 12(9), 2481–2502.

Mammana, C., & Villani, V. (1998). Perspectives on the teaching of geometry for the 21st century: An ICMI study. Dordrect, Boston, London: Kluwer Academic Publishers.

Sanjaya, D., & Wijaya, S. (2007). Strategi penyelesaian soal-soal matematika yang mengasyikan untuk SD/MI dan SMP/MTS. Jakarta: Kandel.

Szetela, W., & Nicol, C. (1992). Evaluating problem solving in mathematics. Educational Leadership, 49(8), 42–45.

Tampomas, H., & Saputra, R. H. (2006). Olimpiade matematika untuk Sekolah Dasar. Jakarta: Grasindo.

Teppo, A. (1991). Van Hiele levels of geometric thought revisited. The Mathematics Teacher, 84(3), 210–221.

Treffers, A. (1987). Three dimensions. A model of goal and theory description in mathematics instruction-The Wiskobas project. Dordrecht, the Netherlands: Kluwer Academic Publishers.

Van den Heuvel-Panhuizen, M. (2003). The didactical use of models in realistic mathematics education: An example from a longitudinal trajectory on percentage. Educational Studies in Mathematics, 54(1), 9–35.

Van Hiele, P. M. (1986). Structure and insight. Orlando, Fla: Academic Press.

Van Hiele, P. M. (1999). Developing geometric thinking through activities that begin with play. Teaching Children Mathematics, 5(6), 310–316.

Wiworo. (2004). Olimpiade Matematika dan IPA Sekolah Dasar/Madrasah Ibtidaiyah. Makalah yang disampaikan dalam Diklat Instruktur/Pengembang Matematika SD Jenjang lanjut di PPPG Matematika, 6–19 Agustus 2004.



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