Jackson Pasini Mairing


Problem solving is important for mathematical learning because it enables students to enhance high thinking skills and positive attitudes. This research aimed at describing and comparing the abilities of junior high school students in grade VIII from one of the regencies/cities in Central Kalimantan (Indonesia) in solving mathematical problems based on schools’ accreditations (A, B, C, and unaccredited), and schools’ status (public and private). The researcher gave three mathematical problems to the students from 20 samples of schools. The schools were randomly selected from the population consisting of 62 junior high schools. Each student’s solution was scored using a holistic rubric. The scores were summarized using some statistics represented in tables and graphics and were analyzed using a Kruskal-Wallis nonparametric test because the data were not normally distributed. The finding indicated that the average scores of the public and private schools’ students were 4.71 and 3.49 (scale 0-12), respectively. Based on the percentages, namely 1.91% and 39.66%, the students were classified as good and naive problem solvers, respectively. Further test revealed that the students from the A-accredited public schools significantly achieved the highest score for problem solving skills. Meanwhile, the students in the A-accredited and the unaccredited private schools did not show a significant difference in the skills. Similar result was also found in the public schools which were accredited B and C, and unaccredited.


Accreditation levels; good problem solvers; mathematical problems; naive problem solvers; problem solving

Full Text:



Badan Akreditasi Nasional Sekolah/Madrasah. (2010). Kebijakan dan pedoman akreditasi sekolah/madrasah [Policy and accreditation manual of schools]. Jakarta, Indonesia: BAN S/M.

Bush. W. S., & Greer, A.S. (Eds). (1999). Mathematics assessment. A practical handbook for grade 9–12. Reston, VA: The National Council of Teachers of Mathematics Inc.

Carlson, M. P., & Bloom, I. (2005). The cyclic nature of problem solving: an emergent multidimensional problem solving framework. Educational Studies in Mathematics, 58, 45–75. doi:10.1007/s10649-005-0808-x.

Charles, R., Lester. F., & O’Daffer, P. (1997). How to evaluate progress in problem solving. Reston, VA: The National Council of Teachers of Mathematics, Inc.

Cohen, L., Manion, L., & Morrison, K. (2007). Research methods in education (6th ed.). New York, NY: Routledge.

Daniel, W. W. (1989). Statistika nonparametrik terapan [Applied nonparametric statistics]. Jakarta, Indonesia: Gramedia.

Hannula, M. S. (2002). Attitude Toward Mathematics: Emotions, Expectations and Values. Educational Studies in Mathematics, 49, 25–46. doi:10.1023/A:1016048823497.

Ho, K. F., & Hedberg, J. G. (2005). Teachers’ pedagogies and their impact on students’ mathematical problem solving. Journal of Mathematical Behaviour, 24: 238–252. doi:10.1016/ j.jmathb.2005.09.006.

Kadir. (2010). Statistika untuk penelitian ilmu-ilmu sosial [Statistics for social science]. Jakarta, Indonesia: Rosemata Sempurna.

King, F. J., Goodson, L., & Rohani, F. (2016). Higher order thinking skills. Retrieved from

Krulik, S., Rudnik, J., & Milou, E. (2003). Teaching mathematics in middle schools. A practical guide. Boston, MA: Pearson Education Inc.

Lerch, C. M. (2004). Control decisions and personal beliefs: Their affect on solving mathematics problem. Journal of Mathematical Behaviour, 23, 21–36. doi:10.1016/j.jmathb.2003.12.002.

Lodico, M. G., Spaulding, D. T., & Voegtle, K. H. (2006). Method in educational research: From theory to practice. San Francisco, CA: John Willey & Sons, Inc.

Lonsdale, M. (2003). Impact of school libraries on student achievement: A review of the research. Camberwell Victoria, Australia: Australian Council for Educational Research.

Mairing, J. P. (2014). Student’s difficulties in solving problem of real analysis. In H. Sutrisno, W. S. Dwandaru, & K. P. Krisnawan (Ed.), International Conference on Research, Implementation and Education of Mathematics and Sciences (ICRIEMS) (pp. ME 321 – 330). Yogyakarta, Indonesia: Universitas Negeri Yogyakarta.

Mairing, J. P. (2017). Thinking process of naive problem solvers to solve mathematical problems. International Educational Studies, 10(1), 1 – 10. doi:10.5539/ies.v10n1p1

Mairing, J. P., Budayasa, I. K., & Juniaiti, D. (2011). Profil pemecahan masalah peraih medali OSN [Problem solving profile of national mathematics olympiad medalists]. Jurnal Pendidikan dan Pembelajaran, 18(1), 65–71. Retrieved from

Mairing, J. P., Budayasa, I. K., & Juniaiti, D. (2012). Perbedaan profil pemecahan masalah peraih medali OSN matematika berdasarkan jenis kelamin [The difference of problem solving profile of national mathematics olympiad medalists according to gender]. Jurnal Ilmu Pendidikan, 18(2), 125 – 134. doi:10.17977/jip.v18i2.3612

Marzano, R. J., Pickering, D., & McTighe, J. (1993). Assessing student outcomes. Alexandria, VA: Association for Supervision and Curriculum Development.

Matlin, M. W. (1994). Cognition (4th ed.). Orlando, FL: Harcourt Brace & Company.

Muir, T., Beswick, K., & Williamson, J. (2008). I am not very good at solving problems: An exploration of student’s problem solving behaviours. The Journal of Mathematical Behaviour, 27, 228–241. doi:10.1016/j.jmathb.2008.04.003.

Musser, G. L., Burger, W. F., & Peterson, B. E. (2011). Mathematics for elementary teachers, a contemporary approach (9th ed.). Hoboken, NJ: John Wiley & Sons, Inc.

National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: The National Council of Teachers of Mathematics, Inc.

Ontario Ministry of Education. (2006). A guide to effective instruction in mathematics kindergarten to grade 6, volume two: Problem solving and communication. Toronto, Canada: Ontario Ministry of Education.

Pape, S. J. (2004). Middle school children’s problem solving behavior: A cognitive analysis from a reading comprehension perspective. Journal for Research in Mathematics Education, 35, 187-219. doi:10.2307/30034912.

Parke, C. S., Lane, S., Silver, E. A., & Magone, M. E. (2003). Using assessment to improve middle–grades mathematics teaching & learning. Reston, VA: The National Council of Teachers of Mathematics, Inc.

Pimta, S., Tayruakham, S., & Nuangchalerm, P. (2009). Factors influencing mathematics problem solving ability of sixth grade students. Journal of Social Sciences, 5(4), 381–385. Retrieved from

Polya, G. (1973). How to solve it (2nd ed.). Princeton, NJ: Princeton University Press.

Polya, G. (1981). Mathematical discovery: On understanding, learning and teaching problem solving. New York, NY: John Wiley & Sons, Inc.

Posamentier, A. S., & Krulik, S. (2009). Problem solving in mathematics grades 3–6, powerful strategies to deepen understanding. Thousand Oaks, CA: Corwin A SAGE Company.

Reys, R., Lindquist, M. M., Lambdin, D. V., & Smith, N. L. (2009). Helping children learn mathematics (9th ed.). Hoboken, NJ: John Wiley & Sons, Inc.

Ruffel, M., Mason, J. and Allen, B. (1998). Studying attitude to mathematics. Educational Studies in Mathematics, 35, 1–18. doi:10.1023/A:1003019020131.

Sa’dijah, C., & Sukoriyanto. (2015). Asesmen pembelajaran matematika [Mathematical learning assessments]. Malang, Indonesia: UM Press.

Skemp, R. R. (1982). The psychology of learning mathematics. Middlesex, England: Pinguin Books, Ltd.

Solso, R. L. (1995). Cognitive psychology (4th ed.). Needham Heights, MA: Allyn & Bacon.

Sternberg, R. J., & Sternberg, K. (2012). Cognitive psychology (6th ed.). Belmont, CA: Wadsworth Cengage Learning.

Tambychik, T., & Meerah, T. S. M. (2010). Students’ difficulties in mathematical problem solving: What do they say? Procedia Social and Behavioral Sciences, 8, 142–151. doi:10.1016/ j.sbspro.2010.12.020.

Tiurma, L., & Ratnawati, H. (2015). Keefektifan pembelajaran multimedia materi dimensi tiga ditinjau dari prestasi dan minat belajar matematika di SMA [The effectiveness of learning solid concept with multimedia towards senior high school students’ achievement and motivation of learning mathematics]. Jurnal Kependidikan, 44(2), 175–187. Retrieved from

Utami, I. B., Sutama, & Subadi, T. (2012). Kontribusi fasilitas belajar, lingkungan belajar, dan motivasi berpretasi terhadap hasil belajar matematika sekolah berbasis ISO di SMK Negeri 1 Purwodadi [The effect of school facilities, learning environment, and motivation towards achievement of students from ISO-based vocational schools in Purwodadi]. Retrieved from _PUBLIKASI.pdf.

Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2010). Elementary and middle school mathematics: Teaching developmentally (7th ed.). Boston, MA: Ally & Bacon.

Woodward, J., Beckmann, S., Driscoll, M., Franke, M., Herzig, P., Jitendra, A., Koedinger, K. R., & Ogbuehi, P. (2012). Improving mathematical problem solving in grade 4 through 8. Washington, DC: National Center for Education Evaluation and Regional Assistance, Institut of Educational Science, US Department of Education.

Zeitz, P. (2009). The art and craft of problem solving (2nd ed.). Hoboken, NJ: John Wiley & Sons, Inc.



  • There are currently no refbacks.

Copyright (c) 2017 Jackson Pasini Mairing

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