Al Jupri, Ernawulan Syaodih


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


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

Full Text:



Ball, D. L., Hill, H.C, & Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide?, American Educator, 29(1), pp. 14-17, 20-22, 43-46.

Barrantes, M., & Blanco, L.J. (2006). A Study Of Prospective Primary Teachers’ Conceptions Of Teaching And Learning School Geometry, Journal of Mathematics Teach-er Education, 9 (5), 411–436.

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.

De Lange, J. (2006). Mathematical literacy for living from OECD-PISA perspective, Tsukuba Journal of Educational Study in Mathematics, 25,13–35.

Eli, J.A., Mohr-Schroeder, M.J., & Lee, C.W. (2013). Mathematical Connections and Their Relationship to Mathematics Knowledge for Teaching Geometry, School Science and Mathematics, 113(3), 120-134.

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.

Herbst, P.G. (2006). Teaching Geometry with Problems: Negotiating Instructional Situations and Mathematical Tasks, Journal for Research in Mathematics Education, 37(4), 313-347.

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 Van Hiele theory to instruction, Teaching Children Mathematics, 21(5), 305–313.

Indonesian Ministry of Education and Culture. (2013). Kurikulum 2013: Kompetensi Dasar Sekolah Dasar (SD)/ Madrasah Ibtidaiyah (MI). Jakarta: Indonesian Ministry of Education and Culture.

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

National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. Reston, Virginia: National Council of Teachers of Mathematics, Inc.

Ng, D. (2011). Indonesian primary teachers' mathematical knowledge for teaching geometry: implications for educational policy and teacher preparation programs, Asia-Pacific Journal of Teacher Education, 39(2), 151-164.

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.

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, 6, 310–316.



  • There are currently no refbacks.

Copyright (c) 2017 Jurnal Pengajaran MIPA

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

JPMIPA is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License

Jurnal Pengajaran Matematika dan Ilmu Pengetahuan Alam (JPMIPA) or Journal of Mathematics and Science Teaching 

All rights reserverd. pISSN 1412-0917 eISSN 2443-3616

Copyright © Faculty of Mathematics and Science Education (FPMIPA) Universitas Pendidikan Indonesia (UPI)


View My Stats