Research Article
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Year 2020, Volume: 8 Issue: 3, 991 - 1003, 15.09.2020
https://doi.org/10.17478/jegys.704984

Abstract

References

  • 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

Number pattern generalization process by provincial mathematics olympiad winner students

Year 2020, Volume: 8 Issue: 3, 991 - 1003, 15.09.2020
https://doi.org/10.17478/jegys.704984

Abstract

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.

References

  • 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
There are 23 citations in total.

Details

Primary Language English
Subjects Other Fields of Education
Journal Section Gifted Education
Authors

Andi Mulawakkan Firdaus 0000-0002-4551-1643

Dwi Junıatı 0000-0002-5352-3708

Pradnyo Wijayanti This is me 0000-0003-4935-3838

Publication Date September 15, 2020
Published in Issue Year 2020 Volume: 8 Issue: 3

Cite

APA Firdaus, A. M., Junıatı, D., & Wijayanti, P. (2020). Number pattern generalization process by provincial mathematics olympiad winner students. Journal for the Education of Gifted Young Scientists, 8(3), 991-1003. https://doi.org/10.17478/jegys.704984
AMA Firdaus AM, Junıatı D, Wijayanti P. Number pattern generalization process by provincial mathematics olympiad winner students. JEGYS. September 2020;8(3):991-1003. doi:10.17478/jegys.704984
Chicago Firdaus, Andi Mulawakkan, Dwi Junıatı, and Pradnyo Wijayanti. “Number Pattern Generalization Process by Provincial Mathematics Olympiad Winner Students”. Journal for the Education of Gifted Young Scientists 8, no. 3 (September 2020): 991-1003. https://doi.org/10.17478/jegys.704984.
EndNote Firdaus AM, Junıatı D, Wijayanti P (September 1, 2020) Number pattern generalization process by provincial mathematics olympiad winner students. Journal for the Education of Gifted Young Scientists 8 3 991–1003.
IEEE A. M. Firdaus, D. Junıatı, and P. Wijayanti, “Number pattern generalization process by provincial mathematics olympiad winner students”, JEGYS, vol. 8, no. 3, pp. 991–1003, 2020, doi: 10.17478/jegys.704984.
ISNAD Firdaus, Andi Mulawakkan et al. “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.
JAMA Firdaus AM, Junıatı D, Wijayanti P. Number pattern generalization process by provincial mathematics olympiad winner students. JEGYS. 2020;8:991–1003.
MLA Firdaus, Andi Mulawakkan et al. “Number Pattern Generalization Process by Provincial Mathematics Olympiad Winner Students”. Journal for the Education of Gifted Young Scientists, vol. 8, no. 3, 2020, pp. 991-1003, doi:10.17478/jegys.704984.
Vancouver Firdaus AM, Junıatı D, Wijayanti P. Number pattern generalization process by provincial mathematics olympiad winner students. JEGYS. 2020;8(3):991-1003.
By introducing the concept of the "Gifted Young Scientist," JEGYS has initiated a new research trend at the intersection of science-field education and gifted education.