Year 2020, Volume 8 , Issue 3, Pages 991 - 1003 2020-09-15

Number pattern generalization process by provincial mathematics olympiad winner students

Andi Mulawakkan FİRDAUS [1] , Dwi JUNIATI [2] , Pradnyo WİJAYANTİ [3]


This research aims to explore the Number Generalization Process of the winner students of Mathematics Olympiad. The Number Generalization Process in this study is based on APOS theory. This research is explorative research with a qualitative approach. The subjects of the study were the junior high school students who won the provincial mathematics Olympiad in South Sulawesi, Indonesia. Subjects were given instruments that had been developed, namely the number patterns generalization test. Data collection of this study is the number patterns generalization test and in-depth interviews. The data analysis process was reducing, describing, validating, and concluding. The results showed that the students who won the Olympics in the action stage determine the next term, if given a sequence by using a number pattern. At the stage of the process, action interiorizing by calculating the value of the next term repeatedly and explaining the process of determining the next term. At the object stage, encapsulating the process by showing that a number pattern has certain characteristics, de-encapsulating by assessing the observed pattern, and checking the number pattern found. At the schema stage, explaining the generalization properties of number sequence patterns by linking the actions, processes, objects of a concept with other concepts, doing thematization by linking the existing concept patterns to the general sequence.
Pattern Generalization, APOS Theory, Number sequence, Mathematics olympiad
  • Asiala, M., Brown, A., DeVries, D. J., Dubinsky, E., Mathews, D., & Thomas, K. (1997). A framework for research and curriculum development in undergraduate mathematics education. Maa Notes, 37–54.
  • Barbosa, A. N. A., Vale, I., & Palhares, P. (2012). PATTERN TASKS: THINKING PROCESSES USED Ve rs ió Cl a m e Ve rs ió Cl a. Revista Latinoamericana de Investigación En Matemática Educativa, 15(3), 273–293.
  • Barbosa, A., & Vale, I. (2015). Visualization in pattern generalization : Potential and Challenges. Journal of the European Teacher Education Network, 10(1), 57–70.
  • DeVries, D. J. (2001). RUMEC/ APOS Theory Glossary.
  • Dindyal, J. (2007). High school students’ use of patterns and generalisations. Proceedings of the 30th Annual Conferences of the Mathematics Education Research Group of Australasia, 1(July), 236–245.
  • Dubinsky, E. (2001). Using a Theory of Learning in College. TaLUM, 12, 10–15.
  • Dubinsky, E., & McDonald, M. A. (2001). APOS: A constructivist theory of learning in undergraduate mathematics education research. The Teaching and Learning of Mathematics at …, 1–22. https://doi.org/10.1007/0-306-47231-7_25
  • Dubinsky, E., Weller, K., McDonald, M. A., & Brown, A. (2005). Some historical issues and paradoxes regarding the concept of infinity: An APOS-based analysis: Part 1. Educational Studies in Mathematics, 58(3), 335–359. https://doi.org/10.1007/s10649-005-2531-z
  • Firdaus, A. M., Juniati, D., & Wijayanti, P. (2019a). Generalization Pattern ’ s Strategy of Junior High School students based on Gender Generalization Pattern ’ s Strategy of Junior High School students based on Gender. Journal of Physics: Conference Series, 1417(1). https://doi.org/10.1088/1742-6596/1417/1/012045
  • Firdaus, A. M., Juniati, D., & Wijayanti, P. (2019b). The characteristics of junior high school students in pattern generalization. Journal of Physics: Conference Series, 1157(4). https://doi.org/10.1088/1742-6596/1157/4/042080
  • Lannin, J. K., Barker, D. D., & Townsend, B. E. (2006). Recursive and explicit rules: How can we build student algebraic understanding? Journal of Mathematical Behavior, 25(4), 299–317. https://doi.org/10.1016/j.jmathb.2006.11.004
  • Maf’ulah, S., Juniati, D., & Siswono, T. Y. E. (2017). The aspects of reversible thinking in solving algebraic problems by an elementary student winning national Olympiad medals in science. World Transactions on Engineering and Technology Education, 15(2), 189–194.
  • Moleong, L. J. (2012). Metode Penelitian Kualitatif (Edisi Revisi). PT. Remaja Rosdakarya.
  • Mulligan, J., & Mitchelmore, M. (2009). Awareness of pattern and structure in early mathematical development . Mathematics Education Research ... Awareness of Pattern and Structure in Early Mathematical Development. Mathematics Education Research Journal, 21(May), 33–49. https://doi.org/10.1007/BF03217544
  • Murtafiah, W., Sa’dijah, C., Chandra, T. D., & Susiswo, S. (2019). Decision making of the winner of the national student creativity program in designing ICT-based learning media. TEM Journal, 8(3), 1039–1045. https://doi.org/10.18421/TEM83-49
  • Muzaini, M., Juniati, D., & Siswono, T. Y. E. (2019). Profiles quantitative reasoning and students’ generalization ability on topic of direct proportion. Journal of Physics: Conference Series, 1188(1). https://doi.org/10.1088/1742-6596/1188/1/012034
  • Pound, L. (2008). Thinking and learning about mathematics in the early years. routledge.
  • Rivera, F. (2013). Teaching and Learning Patterns in School Mathematics. https://doi.org/10.1007/978-94-007-2712-0
  • Setyosari, P. (2016). Metode Penelitian Pendidikan dan Pengembangan. Jakarta: Kencana.
  • Tikekar, V. G. (2009). Deceptive patterns in mathematics [2. International Journal of Mathematical Science Education, 2(1), 13–21.
  • van de Grift, W. (2007). Quality of Teaching in Four European Countries: A Review of The Literature and Application of an Assessment Instrument. Educational Research, 49(2), 127–152. https://doi.org/10.1080/00131880701369651
  • van der Lans, R. M., van de Grift, W. J. C. M., & van Veen, K. (2017). Developing an Instrument for Teacher Feedback: Using the Rasch Model to Explore Teachers’ Development of Effective Teaching Strategies and Behaviors. Journal of Experimental Education, 0(0), 1–18. https://doi.org/10.1080/00220973.2016.1268086
  • Zazkis, R., & Campbell, S. (1996). Divisibility and multiplicative structure of natural numbers: Preservice teachers’ understanding. Journal for Research in Mathematics Education, 27(5), 540–563. https://doi.org/10.2307/749847
Primary Language en
Subjects Education and Educational Research
Published Date September 2020
Journal Section Gifted Education
Authors

Orcid: 0000-0002-4551-1643
Author: Andi Mulawakkan FİRDAUS (Primary Author)
Institution: Universitas Muhammadiyah Makassar
Country: Indonesia


Orcid: 0000-0002-5352-3708
Author: Dwi JUNIATI
Institution: Universitas Negeri Surabaya
Country: Indonesia


Orcid: 0000-0003-4935-3838
Author: Pradnyo WİJAYANTİ
Institution: Universitas Negeri Surabaya
Country: Indonesia


Dates

Publication Date : September 15, 2020

Bibtex @research article { jegys704984, 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 = {991 - 1003}, doi = {10.17478/jegys.704984}, title = {Number pattern generalization process by provincial mathematics olympiad winner students}, key = {cite}, author = {Fi̇rdaus, Andi Mulawakkan and Junıatı, Dwi and Wi̇jayanti̇, Pradnyo} }
APA Fi̇rdaus, A , Junıatı, D , Wi̇jayanti̇, P . (2020). Number pattern generalization process by provincial mathematics olympiad winner students . Journal for the Education of Gifted Young Scientists , 8 (3) , 991-1003 . DOI: 10.17478/jegys.704984
MLA Fi̇rdaus, A , Junıatı, D , Wi̇jayanti̇, P . "Number pattern generalization process by provincial mathematics olympiad winner students" . Journal for the Education of Gifted Young Scientists 8 (2020 ): 991-1003 <https://dergipark.org.tr/en/pub/jegys/issue/55332/704984>
Chicago Fi̇rdaus, A , Junıatı, D , Wi̇jayanti̇, P . "Number pattern generalization process by provincial mathematics olympiad winner students". Journal for the Education of Gifted Young Scientists 8 (2020 ): 991-1003
RIS TY - JOUR T1 - Number pattern generalization process by provincial mathematics olympiad winner students AU - Andi Mulawakkan Fi̇rdaus , Dwi Junıatı , Pradnyo Wi̇jayanti̇ Y1 - 2020 PY - 2020 N1 - doi: 10.17478/jegys.704984 DO - 10.17478/jegys.704984 T2 - Journal for the Education of Gifted Young Scientists JF - Journal JO - JOR SP - 991 EP - 1003 VL - 8 IS - 3 SN - -2149-360X M3 - doi: 10.17478/jegys.704984 UR - https://doi.org/10.17478/jegys.704984 Y2 - 2020 ER -
EndNote %0 Journal for the Education of Gifted Young Scientists Number pattern generalization process by provincial mathematics olympiad winner students %A Andi Mulawakkan Fi̇rdaus , Dwi Junıatı , Pradnyo Wi̇jayanti̇ %T Number pattern generalization process by provincial mathematics olympiad winner students %D 2020 %J Journal for the Education of Gifted Young Scientists %P -2149-360X %V 8 %N 3 %R doi: 10.17478/jegys.704984 %U 10.17478/jegys.704984
ISNAD Fi̇rdaus, Andi Mulawakkan , Junıatı, Dwi , Wi̇jayanti̇, Pradnyo . "Number pattern generalization process by provincial mathematics olympiad winner students". Journal for the Education of Gifted Young Scientists 8 / 3 (September 2020): 991-1003 . https://doi.org/10.17478/jegys.704984
AMA Fi̇rdaus A , Junıatı D , Wi̇jayanti̇ P . Number pattern generalization process by provincial mathematics olympiad winner students. JEGYS. 2020; 8(3): 991-1003.
Vancouver Fi̇rdaus A , Junıatı D , Wi̇jayanti̇ P . Number pattern generalization process by provincial mathematics olympiad winner students. Journal for the Education of Gifted Young Scientists. 2020; 8(3): 991-1003.