Year 2020, Volume 8 , Issue 3, Pages 973 - 989 2020-09-15

Eighth-grades students’ mental models in solving a number pattern problem

Novi PRAYEKTİ [1] , Toto NUSANTARA [2] , Sudirman SUDİRMAN [3] , Hery SUSANTO [4]


This study aims to explore all the types of students' mental models of number patterns. The study used a qualitative approach with an explorative type. The subjects used to characterize the student's mental models in this study were 46 eighth grade students in Indonesia. To reveal the subjects’ mental model, they were asked to solve the number pattern problem and were interviewed. For ensuring the validity and reliability of the research results, triangulation technique was used by comparing the results of video recording interviews and written test results. The study showed that in solving the problem of number patterns given, there were 4 types of mental models. They were formal direct mental model, formal indirect mental model, synthetic direct mental model, and synthetic indirect mental model. What we found in this study shows that some students have different mental models to solve the problem. Hence, in future teachers must introduce various strategies to solve the problem and conduct learning that can enrich students' mental models.
mental model, problem solving, students characterization, number pattern
  • Allen, L. G. (2001). Teaching mathematical induction: An alternative approach. Mathematics Teacher, 94(6), 500-504.
  • 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
  • Bofferding, L. (2014). Negative integer understanding: Characterizing first graders’ mental models. Journal for Research in Mathematics Education, 45(2), 194–245. https://doi.org/10.5951/jresematheduc.45.2.0194
  • Botzer, G., & Yerushalmy, M. (2008). Embodied semiotic activities and their role in the construction of mathematical meaning of motion graphs. International Journal of Computers for Mathematical Learning, 13(3), 1-12. https://doi.org/10.1007/s10758-008-9133-7
  • Carifio, J. (2015). Updating, modernizing, and testing Polya’s theory of [mathematical] problem solving in terms of current cognitive, affective, and information processing theories of learning, emotions, and complex performances. Journal of Education and Human Development, 4(3), 105–117. https://doi.org/10.15640/jehd.v4n3a12
  • Chiou, G. L. (2013). Reappraising the relationships between physics students’ mental models and predictions: An example of heat convection. Physical Review Special Topics-Physics Education Research, 9(1), 010119. https://doi.org/10.1103/PhysRevSTPER.9.010119
  • Chittleborough, G. (2004). The role of teaching models and chemical representations in developing students' mental models of chemical phenomena (Doctoral dissertation). Curtin University.
  • Dubinsky, E., & McDonald, M. A. (2001). APOS: A constructivist theory of learning in undergraduate mathematics education research. In the Teaching and Learning of Mathematics at University Level (pp. 275-282). Springer, Dordrecht.
  • Fazio, C., Battaglia, O. R., & Di Paola, B. (2013). Investigating the quality of mental models deployed by undergraduate engineering students in creating explanations: The case of thermally activated phenomena. Physical Review Special Topics-Physics Education Research, 9(2), 020101. https://doi.org/10.1103/PhysRevSTPER.9.020101
  • Font, V., Trigueros, M., Badillo, E., & Rubio, N. (2016). Mathematical objects through the lens of two different theoretical perspectives: APOS and OSA. Educational Studies in Mathematics, 91(1), 107–122. https://doi.org/10.1007/s10649-015-9639-6
  • Golfashani, N. (2003). Understanding reliability and validity in qualitative research. The Qualitative Report, 8(4), 597–607. https://nsuworks.nova.edu/tqr/vol8/iss4/6
  • Goodnough, K. C., & Hung, W. (2008). Engaging teachers’ pedagogical content knowledge: Adopting a nine-step problem-based learning model. Interdisciplinary Journal of Problem-Based Learning, 2(2), 10–13. https://doi.org/10.7771/1541-5015.1082
  • Greca, I. M., & Moreira, M. A. (2002). Mental, physical, and mathematical models in the teaching and learning of physics. Science Education, 86(1), 106–121. https://doi.org/10.1002/sce.10013
  • Halim, N. D. A., Ali, M. B., Yahaya, N., & Said, M. N. H. M. (2013). Mental model in learning chemical bonding: A preliminary study. Procedia-Social and Behavioral Sciences, 97, 224–228. https://doi.org/10.1016/j.sbspro.2013.10.226
  • Hartikainen, S., Rintala, H., Pylväs, L., & Nokelainen, P. (2019). The concept of active learning and the measurement of learning outcomes: A review of research in engineering higher education. Education Sciences, 9(4), 9–12. https://doi.org/10.3390/educsci9040276
  • Hidayah, I., Pujiastuti, E., & Chrisna, J. E. (2017). Teacher’s stimulus helps students achieve mathematics reasoning and problem solving competences. Journal of Physics: Conference Series, 824(1), 012042. https://doi.org/10.1088/1742-6596/755/1/011001
  • Hillman, W. (2003). Learning how to learn: Problem based learning. Australian Journal of Teacher Education, 28(2), 1-10. https://doi.org/10.14221/ajte.2003v28n2.1
  • Jansoon, N., Coll, R. K., & Somsook, E. (2009). Understanding mental models of dilution in Thai students. International Journal of Environmental and Science Education, 4(2), 147–168.
  • Kusdinar, U., Sukestiyarno, Isnarto, & Istiandaru, A. (2017). Krulik and Rudnik model heuristic strategy in mathematics problem solving. International Journal on Emerging Mathematics Education, 1(2), 205-210. https://doi.org/10.12928/ijeme.v1i2.5708
  • Lindblom, S. (2019). The role of research-based evidence in cultivating quality of teaching and learning in higher education. Uniped, 42(01), 106-110. https://doi.org/10.18261/issn.1893-8981-2019-01-08
  • Mathison, S. (1988). Why Triangulate. Educational researcher, 17(2), 13-17.
  • Ministry of Education and Culture. (2016). The management of national education in Year 2014/2015 at a Glance. http://publikasi.data.kemdikbud.go.id/uploadDir/isi_6549DA84-7A7F-44B5-AD22-829B1F002A4F_.pdf
  • Mulligan, J. T., Mitchelmore, M. C., English, L. D., & Robertson, G. (2010). Implementing a Pattern and Structure Mathematics Awareness Program (PASMAP) in Kindergarten. In L. Sparrow, B. Kissane, & C. Hurst (Eds.), Shaping the future of mathematics education: Proceedings of the 33rd annual conference of the Mathematics Education Research Group of Australasia (pp.793-803). MERGA.
  • NCTM. (2000). Principles and standards for school mathematics. National Council of Teachers of Mathematics.
  • Nite, S. (2017). Using Polya’s problem solving process in the mathematics classroom to prepare for taks. In G. D. Allen, & A. Ross. (Eds), Pedagogy and Content in Middle and High School Mathematics (pp.233-235). SensePublishers, Rotterdam. https://doi.org/10.1007/978-94-6351-137-7_51
  • Rogers, M. A. P., Cross, D. I., Gresalfi, M. S., Trauth-Nare, A. E., & Buck, G. A. (2011). First year implementation of a project-based learning approach: The need for addressing teachers’ orientations in the era of reform. International Journal of Science and Mathematics Education, 9(4), 893-917.
  • Prayekti, N., Nusantara, T., Sudirman, & Susanto, H. (2019). Students ’ mental model in solving the patterns of generalization problem. IOP Conf. Series: Earth and Environmental Science, 243. https://doi.org/10.1088/1755-1315/243/1/012144
  • Putra, H. D., Herman, T., & Sumarmo, U. (2017). Development of student worksheets to improve the ability of mathematical problem posing. International Journal on Emerging Mathematics Education, 1(1), 1-10. https://doi.org/10.12928/ijeme.v1i1.5507
  • Radford, L. (2003). Gestures, speech, and the sprouting of signs: A semiotic-cultural approach to students’ types of generalization. Mathematical Thinking and Learning, 5(1), 37–70. https://doi.org/10.1207/s15327833mtl0501_02
  • Radford, L., & Peirce, C. S. (2006, March). Algebraic thinking and the generalization of patterns: A semiotic perspective. In Proceedings of the 28th conference of the international group for the psychology of mathematics education, North American chapter (Vol. 1, pp. 2-21).
  • Resnik, M. D. (1997). Mathematics as a Science of Patterns. Oxford University Press.
  • Rofiki, I., & Santia, I. (2018). Describing the phenomena of students’ representation in solving ill-posed and well-posed problems. International Journal on Teaching and Learning Mathematics, 1(1), 39–50. https://doi.org/https://doi.org/10.18860/ijtlm.v1i1.5713
  • 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
  • Tikekar, V. G. (2009). Deceptive patterns in mathematics. International Journal Mathematic Science Education, 2(1), 13-21.
  • Vogel, R. (2005). Patterns - a fundamental idea of mathematical thinking and learning. ZDM - International Journal on Mathematics Education, 37(5), 445–449. https://doi.org/10.1007/s11858-005-0035-z
  • Vosniadou, S. (1994). Capturing and modeling the process of conceptual change. Learning and Instruction, 4, 4–9. https://doi.org/10.1016/0959-4752(94)90018-3
  • Vosniadou, S., & Brewer, W. F. (1992). Mental models of the earth: A study of conceptual change in childhood. Cognitive psychology, 24(4), 535-585.
  • Wenglinsky, H. (2002). How schools matter: The link between teacher classroom practices and students academic performance. Education Policy Analysis Archives, 10(12), 1–30.
  • Widodo, S. A., Darhim, D., & Ikhwanudin, T. (2018). Improving mathematical problem solving skills through visual media. Journal of Physics: Conference Series, 948(1), 012004. https://doi.org/10.1088/1742-6596/948/1/012004
Primary Language en
Subjects Education and Educational Research
Published Date September 2020
Journal Section Differentiated Instruction
Authors

Orcid: 0000-0001-6629-3166
Author: Novi PRAYEKTİ (Primary Author)
Institution: Universitas PGRI Banyuwangi
Country: Indonesia


Orcid: 0000-0003-1116-9023
Author: Toto NUSANTARA
Institution: Universitas Negeri Malang
Country: Indonesia


Orcid: 0000-0003-3548-3367
Author: Sudirman SUDİRMAN
Institution: Universitas Negeri Malang
Country: Indonesia


Orcid: 0000-0002-1424-444X
Author: Hery SUSANTO
Institution: Universitas Negeri Malang
Country: Indonesia


Supporting Institution Universitas PGRI Banyuwangi
Project Number 3
Thanks thanks to Universitas Negeri Malang
Dates

Publication Date : September 15, 2020

Bibtex @research article { jegys708044, journal = {Journal for the Education of Gifted Young Scientists}, issn = {}, eissn = {2149-360X}, address = {editorjegys@gmail.com}, publisher = {Genç Bilge Yayıncılık}, year = {2020}, volume = {8}, pages = {973 - 989}, doi = {10.17478/jegys.708044}, title = {Eighth-grades students’ mental models in solving a number pattern problem}, key = {cite}, author = {Prayekti̇, Novi and Nusantara, Toto and Sudi̇rman, Sudirman and Susanto, Hery} }
APA Prayekti̇, N , Nusantara, T , Sudi̇rman, S , Susanto, H . (2020). Eighth-grades students’ mental models in solving a number pattern problem . Journal for the Education of Gifted Young Scientists , 8 (3) , 973-989 . DOI: 10.17478/jegys.708044
MLA Prayekti̇, N , Nusantara, T , Sudi̇rman, S , Susanto, H . "Eighth-grades students’ mental models in solving a number pattern problem" . Journal for the Education of Gifted Young Scientists 8 (2020 ): 973-989 <https://dergipark.org.tr/en/pub/jegys/issue/55332/708044>
Chicago Prayekti̇, N , Nusantara, T , Sudi̇rman, S , Susanto, H . "Eighth-grades students’ mental models in solving a number pattern problem". Journal for the Education of Gifted Young Scientists 8 (2020 ): 973-989
RIS TY - JOUR T1 - Eighth-grades students’ mental models in solving a number pattern problem AU - Novi Prayekti̇ , Toto Nusantara , Sudirman Sudi̇rman , Hery Susanto Y1 - 2020 PY - 2020 N1 - doi: 10.17478/jegys.708044 DO - 10.17478/jegys.708044 T2 - Journal for the Education of Gifted Young Scientists JF - Journal JO - JOR SP - 973 EP - 989 VL - 8 IS - 3 SN - -2149-360X M3 - doi: 10.17478/jegys.708044 UR - https://doi.org/10.17478/jegys.708044 Y2 - 2020 ER -
EndNote %0 Journal for the Education of Gifted Young Scientists Eighth-grades students’ mental models in solving a number pattern problem %A Novi Prayekti̇ , Toto Nusantara , Sudirman Sudi̇rman , Hery Susanto %T Eighth-grades students’ mental models in solving a number pattern problem %D 2020 %J Journal for the Education of Gifted Young Scientists %P -2149-360X %V 8 %N 3 %R doi: 10.17478/jegys.708044 %U 10.17478/jegys.708044
ISNAD Prayekti̇, Novi , Nusantara, Toto , Sudi̇rman, Sudirman , Susanto, Hery . "Eighth-grades students’ mental models in solving a number pattern problem". Journal for the Education of Gifted Young Scientists 8 / 3 (September 2020): 973-989 . https://doi.org/10.17478/jegys.708044
AMA Prayekti̇ N , Nusantara T , Sudi̇rman S , Susanto H . Eighth-grades students’ mental models in solving a number pattern problem. JEGYS. 2020; 8(3): 973-989.
Vancouver Prayekti̇ N , Nusantara T , Sudi̇rman S , Susanto H . Eighth-grades students’ mental models in solving a number pattern problem. Journal for the Education of Gifted Young Scientists. 2020; 8(3): 973-989.