Araştırma Makalesi

Yıl 2021,
Cilt: 8 Sayı: 1, 16 - 26, 08.03.2021
### Öz

### Anahtar Kelimeler

### Destekleyen Kurum

### Proje Numarası

### Teşekkür

### Kaynakça

The purpose of studying geometry is for the development of student thinking, able to abstract and reason, against concepts in the object. Note on some study results that the combination of the student's conceptualization process and knowledge of geometry are a source of barriers to their learning. This study aims to investigate how students actualize their geometry knowledge for the development of thinking to the level of abstraction. Investigations on input, internal processing, and output. This study was conducted on high school students use questions regarding object and product of thought in geometry thinking at analysis and abstraction level. Based on study findings, students actualize their knowledge through figural aspects then developed into the conceptual aspect, and the two aspects are integrated with the relationship between properties. There is a mathematical connection to the integration process. However, because most students' understanding of geometry knowledge is still prototypical figural concepts, so there is an interaction issue between figural and conceptual aspects, namely the validity of relationship between properties. Therefore, students learn geometry in order to investigate the connections between objects and properties as a whole.

abstraction actualization conceptual encapsulation figural aspect

Indonesian Ministry of Research, Technology, and Higher Education

ID Proposal: 8f667415-62b5-4097-ae25-f2f2c9ffdb5b

Indonesian Ministry of Research, Technology, and Higher Education

- Abdullah, A. H., & Zakaria, E. (2013). The effects of Van Hiele's phases of learning geometry on students’ degree of acquisition of Van Hiele levels. Procedia-Social and Behavioral Sciences, 102, 251-266.
- Alghadari, F., & Herman, T. (2018). The obstacles of geometric problem-solving on solid with vector and triangle approach. Journal of Physics: Conference Series, 1132 (1), 012046.
- Cesaria, A., & Herman, T. (2019). Learning Obstacle in Geometry. Journal of Engineering Science and Technology, 14(3), 1271-1280.
- Fiantika, F. R., Budayasa, I. K., & Lukito, A. (2018). Internal process: what is abstraction and distortion process. J. Phys. Ser, 983, 012086.
- Fischbein, E. (1993). The theory of figural concepts. Educational studies in mathematics, 24(2), 139-162.
- Fitriani, N., Suryadi, D., & Darhim, D. (2018a). The Students’mathematical Abstraction Ability through Realistic Mathematics Education with VBA-Microsoft Excel. Infinity Journal, 7(2), 123-132.
- Fitriani, N., Suryadi, D., & Darhim, D. (2018b). Analysis of mathematical abstraction on concept of a three dimensional figure with curved surfaces of junior high school students. Journal of Physics: Conference Series, 1132 (1), 012037.
- Fitriyani, H., Widodo, S. A., & Hendroanto, A. (2018). Students’geometric Thinking Based on Van Hiele’s Theory. Infinity Journal, 7(1), 55-60.
- Fujita, T., Kondo, Y., Kumakura, H., & Kunimune, S. (2017). Students’ geometric thinking with cube representations: Assessment framework and empirical evidence. The Journal of Mathematical Behavior, 46, 96-111.
- Giannakopoulos, A. (2017). An alternative way of solving geometry riders in grade 12: back to synthesis and analysis. In T Penlington & C Chikiwa (Eds.) Proceedings of the 23rd Annual National Congress of the Association for Mathematics Education of South Africa, 19-27.
- Gray, E., & Tall, D. (2007). Abstraction as a natural process of mental compression. Mathematics Education Research Journal, 19(2), 23-40.
- Hakim, L. L., & Nurlaelah, E. (2018). Mathematical mindsets: the abstraction in mathematical problem solving. Journal of Physics: Conference Series, 1132, 012048.
- Herbst, P., Fujita, T., Halverscheid, S., & Weiss, M. (2017). The Learning and Teaching of Geometry in Secondary Schools: A Modeling Perspective. NY: Routledge.
- Luneta, K. (2015). Understanding students' misconceptions: an analysis of final Grade 12 examination questions in geometry. Pythagoras, 36(1), 1-11.
- Mariotti, M. A. (1995). Images and concepts in geometrical reasoning. In Exploiting mental imagery with computers in mathematics education, 97-116. Berlin, Heidelberg: Springer.
- Radmehr, F., & Drake, M. (2018). An assessment-based model for exploring the solving of mathematical problems: Utilizing revised bloom’s taxonomy and facets of metacognition. Studies in Educational Evaluation, 59, 41-51.
- Rahayu, T., & Alghadari, F. (2019). Identitas Bayangan Konsep Limas: Analisis Terhadap Konsepsi Matematis Siswa. INOMATIKA, 1(1), 17-30.
- Rosilawati, R., & Alghadari, F. (2018). Konsepsi Siswa pada Suatu Bentuk Bangun Ruang Terkait dengan Rusuk dan Diagonal Sisi. Prisma, 7(2), 164-176.
- Scheiner, T., & Pinto, M. M. (2014). Cognitive processes underlying mathematical concept construction: The missing process of structural abstraction. In Nicol, C., Oesterle, S., Liljedahl, P., & Allan, D. (Eds.) Proceedings of the Joint Meeting of PME 38 and PME-NA, 36(5), 105-112. Vancouver, Canada: PME.
- Seah, R., & Horne, M. (2019). The construction and validation of a geometric reasoning test item to support the development of learning progression. Mathematics Education Research Journal, 1-22.
- Sharma, S. (2019). Use of theories and models in geometry education research: A critical review. Waikato Journal of Education, 24(1), 43-54.
- Silfverberg, H. (2019). Geometrical Conceptualization. In A Fritz, V Haase & P Räsänen (Eds.) International Handbook of Mathematical Learning Difficulties: From the Laboratory to the Classroom, pp. 611-630. Switzerland: Springer, Cham.
- Sulistiowati, D. L., Herman, T., & Jupri, A. (2019). Student Difficulties in Solving Geometry Problem Based on Van Hiele Thinking Level. Journal of Physics: Conference Series, 1157(4), 042118.
- Tall, D. (2004a). Introducing three worlds of mathematics. For the Learning of Mathematics, 23(3), 29-33.
- Tall, D. (2004b). Building theories: The three worlds of mathematics. For the learning of mathematics, 24(1), 29-32.
- Tall, D. (2013). How Humans Learn To Think Mathematically: Exploring the Three Worlds of Mathematics. USA: Cambridge University Press.
- Tall, D. (2020). Making Sense of Mathematical Thinking over the Long Term: The Framework of Three Worlds of Mathematics and New Developments. MINTUS: Beiträge zur mathematischen, naturwissenschaftlichen und technischen Bildung. Wiesbaden: Springer.
- Tan, T. H., Tarmizi, R. A., Yunus, A. S. M., & Ayub, A. F. M. (2015). Understanding the primary school students’ van Hiele levels of geometry thinking in learning shapes and spaces: A Q-methodology. Eurasia Journal of Mathematics, Science and Technology Education, 11(4), 793-802.
- Utami, D. N., Kusmanto, B., & Widodo, S. A. (2019). Analisis Kesalahan dalam Mengerjakan Soal Geometri. Jurnal Edukasi Matematika dan Sains, 7(1), 37-44.
- Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2017). Elementary and Middle School Mathematics: Teaching Developmentally. United States: Pearson Education.
- Widodo, S. A., Pangesti, A. D., Istiqomah, I., Kuncoro, K. S., & Arigiyati, T. A. (2020). Thinking Process of Concrete Student in Solving Two-Dimensional Problems. Jurnal Pendidikan Matematika, 14(2), 117-128.
- Yi, M., Flores, R., & Wang, J. (2020). Examining the influence of van Hiele theory-based instructional activities on elementary preservice teachers’ geometry knowledge for teaching 2-D shapes. Teaching and Teacher Education, 91, 103038.

Yıl 2021,
Cilt: 8 Sayı: 1, 16 - 26, 08.03.2021
### Öz

### Anahtar Kelimeler

### Proje Numarası

### Kaynakça

The purpose of studying geometry is for the development of student thinking, able to abstract and reason, against concepts in the object. Note on some study results that the combination of the student's conceptualization process and knowledge of geometry are a source of barriers to their learning. This study aims to investigate how students actualize their geometry knowledge for the development of thinking to the level of abstraction. Investigations on input, internal processing, and output. This study was conducted on high school students use questions regarding object and product of thought in geometry thinking at analysis and abstraction level. Based on study findings, students actualize their knowledge through figural aspects then developed into the conceptual aspect, and the two aspects are integrated with the relationship between properties. There is a mathematical connection to the integration process. However, because most students' understanding of geometry knowledge is still prototypical figural concepts, so there is an interaction issue between figural and conceptual aspects, namely the validity of relationship between properties. Therefore, students learn geometry in order to investigate the connections between objects and properties as a whole.

abstraction actualization conceptual encapsulation figural aspect

ID Proposal: 8f667415-62b5-4097-ae25-f2f2c9ffdb5b

- Abdullah, A. H., & Zakaria, E. (2013). The effects of Van Hiele's phases of learning geometry on students’ degree of acquisition of Van Hiele levels. Procedia-Social and Behavioral Sciences, 102, 251-266.
- Alghadari, F., & Herman, T. (2018). The obstacles of geometric problem-solving on solid with vector and triangle approach. Journal of Physics: Conference Series, 1132 (1), 012046.
- Cesaria, A., & Herman, T. (2019). Learning Obstacle in Geometry. Journal of Engineering Science and Technology, 14(3), 1271-1280.
- Fiantika, F. R., Budayasa, I. K., & Lukito, A. (2018). Internal process: what is abstraction and distortion process. J. Phys. Ser, 983, 012086.
- Fischbein, E. (1993). The theory of figural concepts. Educational studies in mathematics, 24(2), 139-162.
- Fitriani, N., Suryadi, D., & Darhim, D. (2018a). The Students’mathematical Abstraction Ability through Realistic Mathematics Education with VBA-Microsoft Excel. Infinity Journal, 7(2), 123-132.
- Fitriani, N., Suryadi, D., & Darhim, D. (2018b). Analysis of mathematical abstraction on concept of a three dimensional figure with curved surfaces of junior high school students. Journal of Physics: Conference Series, 1132 (1), 012037.
- Fitriyani, H., Widodo, S. A., & Hendroanto, A. (2018). Students’geometric Thinking Based on Van Hiele’s Theory. Infinity Journal, 7(1), 55-60.
- Fujita, T., Kondo, Y., Kumakura, H., & Kunimune, S. (2017). Students’ geometric thinking with cube representations: Assessment framework and empirical evidence. The Journal of Mathematical Behavior, 46, 96-111.
- Giannakopoulos, A. (2017). An alternative way of solving geometry riders in grade 12: back to synthesis and analysis. In T Penlington & C Chikiwa (Eds.) Proceedings of the 23rd Annual National Congress of the Association for Mathematics Education of South Africa, 19-27.
- Gray, E., & Tall, D. (2007). Abstraction as a natural process of mental compression. Mathematics Education Research Journal, 19(2), 23-40.
- Hakim, L. L., & Nurlaelah, E. (2018). Mathematical mindsets: the abstraction in mathematical problem solving. Journal of Physics: Conference Series, 1132, 012048.
- Herbst, P., Fujita, T., Halverscheid, S., & Weiss, M. (2017). The Learning and Teaching of Geometry in Secondary Schools: A Modeling Perspective. NY: Routledge.
- Luneta, K. (2015). Understanding students' misconceptions: an analysis of final Grade 12 examination questions in geometry. Pythagoras, 36(1), 1-11.
- Mariotti, M. A. (1995). Images and concepts in geometrical reasoning. In Exploiting mental imagery with computers in mathematics education, 97-116. Berlin, Heidelberg: Springer.
- Radmehr, F., & Drake, M. (2018). An assessment-based model for exploring the solving of mathematical problems: Utilizing revised bloom’s taxonomy and facets of metacognition. Studies in Educational Evaluation, 59, 41-51.
- Rahayu, T., & Alghadari, F. (2019). Identitas Bayangan Konsep Limas: Analisis Terhadap Konsepsi Matematis Siswa. INOMATIKA, 1(1), 17-30.
- Rosilawati, R., & Alghadari, F. (2018). Konsepsi Siswa pada Suatu Bentuk Bangun Ruang Terkait dengan Rusuk dan Diagonal Sisi. Prisma, 7(2), 164-176.
- Scheiner, T., & Pinto, M. M. (2014). Cognitive processes underlying mathematical concept construction: The missing process of structural abstraction. In Nicol, C., Oesterle, S., Liljedahl, P., & Allan, D. (Eds.) Proceedings of the Joint Meeting of PME 38 and PME-NA, 36(5), 105-112. Vancouver, Canada: PME.
- Seah, R., & Horne, M. (2019). The construction and validation of a geometric reasoning test item to support the development of learning progression. Mathematics Education Research Journal, 1-22.
- Sharma, S. (2019). Use of theories and models in geometry education research: A critical review. Waikato Journal of Education, 24(1), 43-54.
- Silfverberg, H. (2019). Geometrical Conceptualization. In A Fritz, V Haase & P Räsänen (Eds.) International Handbook of Mathematical Learning Difficulties: From the Laboratory to the Classroom, pp. 611-630. Switzerland: Springer, Cham.
- Sulistiowati, D. L., Herman, T., & Jupri, A. (2019). Student Difficulties in Solving Geometry Problem Based on Van Hiele Thinking Level. Journal of Physics: Conference Series, 1157(4), 042118.
- Tall, D. (2004a). Introducing three worlds of mathematics. For the Learning of Mathematics, 23(3), 29-33.
- Tall, D. (2004b). Building theories: The three worlds of mathematics. For the learning of mathematics, 24(1), 29-32.
- Tall, D. (2013). How Humans Learn To Think Mathematically: Exploring the Three Worlds of Mathematics. USA: Cambridge University Press.
- Tall, D. (2020). Making Sense of Mathematical Thinking over the Long Term: The Framework of Three Worlds of Mathematics and New Developments. MINTUS: Beiträge zur mathematischen, naturwissenschaftlichen und technischen Bildung. Wiesbaden: Springer.
- Tan, T. H., Tarmizi, R. A., Yunus, A. S. M., & Ayub, A. F. M. (2015). Understanding the primary school students’ van Hiele levels of geometry thinking in learning shapes and spaces: A Q-methodology. Eurasia Journal of Mathematics, Science and Technology Education, 11(4), 793-802.
- Utami, D. N., Kusmanto, B., & Widodo, S. A. (2019). Analisis Kesalahan dalam Mengerjakan Soal Geometri. Jurnal Edukasi Matematika dan Sains, 7(1), 37-44.
- Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2017). Elementary and Middle School Mathematics: Teaching Developmentally. United States: Pearson Education.
- Widodo, S. A., Pangesti, A. D., Istiqomah, I., Kuncoro, K. S., & Arigiyati, T. A. (2020). Thinking Process of Concrete Student in Solving Two-Dimensional Problems. Jurnal Pendidikan Matematika, 14(2), 117-128.
- Yi, M., Flores, R., & Wang, J. (2020). Examining the influence of van Hiele theory-based instructional activities on elementary preservice teachers’ geometry knowledge for teaching 2-D shapes. Teaching and Teacher Education, 91, 103038.

Toplam 32 adet kaynakça vardır.

Birincil Dil | İngilizce |
---|---|

Konular | Alan Eğitimleri |

Bölüm | Araştırma Makalesi |

Yazarlar | |

Proje Numarası | ID Proposal: 8f667415-62b5-4097-ae25-f2f2c9ffdb5b |

Yayımlanma Tarihi | 8 Mart 2021 |

Yayımlandığı Sayı | Yıl 2021 Cilt: 8 Sayı: 1 |