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References
- Breive, S. (2022). Abstraction and Embodiment: Exploring the Process of Grasping a General. Educational Studies in Mathematics, 110(2), 313–329. https://doi.org/10.1007/s10649-021-10137-x
- Budiarto, M. T., Khabibah, S., & Setianingsih, R. (2017). Construction of High School Students’ Abstraction Levels in Understanding the Concept of Quadrilaterals. International Education Studies, 10(2), 148. https://doi.org/10.5539/ies.v10n2p148
- Bueno, R. W. da S., Henriques, A., & Galle, L. A. V. (2023). Mathematics Preservice Teachers ’ Perceptions Regarding ICT Use in Teaching and Learning Practices. Acta Scientiae, 25(5), 227–249. https://doi.org/10.17648/acta.scientiae.7633
- Centina, A. Del. (2016). On Kepler ’ s System of Conics in Astronomiae Pars Optica. Archive for History of Exact Sciences, 70, 567–589. https://doi.org/10.1007/s00407-016-0175-2
- Dewi, I., Siregar, N., & Andriani, A. (2018). The analysis of junior high school students’ mathematical abstraction ability based on local cultural wisdom. Journal of Physics: Conference Series, 1088(1), 012076. https://doi.org/10.1088/1742-6596/1088/1/012076
- Dintarini, M., & Zukhrufurrohmah. (2021). Analisis Pemberian Scaffolding Melalui Online Form untuk Mengatasi Kesulitan Berpikir Spasial. ẟELT∆ Jurnal Ilmiah Pendidikan Matematika, 9(2), 221–232. http://dx.doi.org/10.31941/delta.v9i2.1414
- Dreyfus, T., Hershkowitz, R., & Schwarz, B. (2015). The Nested Epistemic Actions Model for Abstraction in Context: Theory as Methodological Tool and Methodological Tool as Theory. In A. B.-A. et Al. (Ed.), Approaches to Qualitative Research in Mathematics Education, Advances in Mathematics Education (pp. 185–2017). Springer Science+Business Media Dordrecht. https://doi.org/10.1007/978-94-017-9181-6_8
- Dubinsky, E., & Tall, D. (1991). Advanced mathematical thinking and the computer. Advanced Mathematical Thinking, 8, 231–248. https://doi.org/10.1007/0-306-47203-1_14
- Elgrably, H., & Leikin, R. (2021). Creativity as a function of problem-solving expertise: posing new problems through investigations. ZDM - Mathematics Education, 53(4), 891–904. https://doi.org/10.1007/s11858-021-01228-3
- Florio, E. (2021). Claude Mydorge Reader and Interpreter of Apollonius ’ Conics. Mathematics, 9, 261. https://doi.org/10.3390/math9030261
- Florio, E. (2022). The Parabola: Section of a Cone or Locus of Points of a Plane? Tips for Teaching of Geometry from Some Writings by Mydorge and Wallis. Mathematics, 10(6), 974–992. https://doi.org/10.3390/math10060974
- Fried, M. N. (2003). The Use of Analogy in Book VII of Apollonius ’ Conica The Use of Analogy in Book VII of Apollonius ’ Conica. Science in Context, 16(3), 349–365. https://doi.org/10.1017/S026988970300084X
- Fried, M. N. (2022). Edmond Halley and Apollonius : second ‑ order historical knowledge in mathematics education. ZDM – Mathematics Education, 0123456789. https://doi.org/10.1007/s11858-022-01391-1
- Glaister, E. M., & Glaister, P. (2006). Introducing conics without eccentricity. International Journal of Mathematical Education in Science and Technology, 37(2), 235–245. https://doi.org/10.1080/00207390500285800
- Gray, E. M., & Tall, D. O. (1992). Success and Failure in Mathematics: Procept and Procedure 1. A Primary Perspective. Workshop on Mathematics Education and Computers, April, 216–221.
- Gray, E. M., & Tall, D. O. (2007). Abstraction as a natural process of mental compression. Mathematics Education Research Journal, 19(2), 23–40. https://doi.org/10.1007/BF03217454
- Hartinah, S., Suherman, S., Syazali, M., Efendi, H., Junaidi, R., Jermsittiparsert, K., & Umam, R. (2019). Probing-prompting based on ethnomathematics learning model: The effect on mathematical communication skills. Journal for the Education of Gifted Young Scientists, 7(4), 799–814. https://doi.org/10.17478/jegys.574275
- Heath, T. (1896). Apollonius of Perga: Treatise on Conic Sections. C. J. CLAY AND SONS.
- Hershkowitz, R., Hadas, N., Dreyfus, T., & Schwarz, B. B. (2007). Abstracting Processes, from Individuals’ Constructing of Knowledge to a Group’s “Shared Knowledge.” Mathematics Education Research Journal, 19(2), 41–68. https://doi.org/10.1007/BF03217455
- Hershkowitz, R., Schwarz, B. B., & Dreyfus, T. (2001). Abstraction in Context: Epistemic Actions. Journal for Research in Mathematics Education, 32(2), 195–222. https://doi.org/10.1093/ojls/14.2.255
- Hodiyanto, Budiarto, M. T., Ekawati, R., Susanti, G., Kim, J., & Bonyah, E. (2024). How abstraction of a pre-service teacher in constructing relationships among quadrilaterals. Journal on Mathematics Education, 15(2), 339–362. https://doi.org/10.22342/jme.v15i2.pp339-362
- Hollebrands, K., & Stohl Lee, H. (2011). Introduction to dynamic geometry environments. Kendall Hunt Online, 1–22.
- Jupri, A. (2017). From geometry to algebra and vice versa: Realistic mathematics education principles for analyzing geometry tasks. AIP Conference Proceedings, 1830. https://doi.org/10.1063/1.4980938
- Jupri, Al, & Drijvers, P. (2016). Student Difficulties in Mathematizing Word Problems in Algebra. Eurasia Journal of Mathematics, Science & Technology Education, 12(9), 2481–2502. https://doi.org/10.12973/eurasia.2016.1299a
- Komala, E. (2018). Analysis of Students’ Mathematical Abstraction Ability By Using Discursive Approach Integrated Peer Instruction of Structure Algebra Ii. Infinity Journal, 7(1), 25-34. https://doi.org/10.22460/infinity.v7i1.p25-34
- Kouropatov, A., & Dreyfus, T. (2014). Learning the integral concept by constructing knowledge about accumulation. ZDM - Mathematics Education, 46(4), 533–548. https://doi.org/10.1007/s11858-014-0571-5
- Memnun, D. S., Aydın, B., Özbilen, Ö., & Erdoğan, G. (2017). The abstraction process of limit knowledge. Kuram ve Uygulamada Egitim Bilimleri, 17(2), 345–371. https://doi.org/10.12738/estp.2017.2.0404
- Memnun, D. S., Sevindik, F., Beklen, C., & Dinç, E. (2019). Analysis of the Abstraction Process of Continuity Knowledge. World Journal of Education, 9(2), 141. https://doi.org/10.5430/wje.v9n2p141
- Mitchelmore, M. C., & White, P. (2004). Abstraction in mathematics learning. Mathematics Education Research Journal, 19(2), 1–9. https://doi.org/10.1007/BF03217452
- Munson, J. (2019). After eliciting : Variation in elementary mathematics teachers ’ discursive pathways during collaborative problem solving. Journal of Mathematical Behavior, August, 100736. https://doi.org/10.1016/j.jmathb.2019.100736
- Ng, O. L., Shi, L., & Ting, F. (2020). Exploring differences in primary students’ geometry learning outcomes in two technology-enhanced environments: dynamic geometry and 3D printing. International Journal of STEM Education, 7(1), 1–13. https://doi.org/10.1186/s40594-020-00244-1
- Nurhasanah, F., Kusumah, Y. S., Sabandar, J., & Suryadi, D. (2017). Mathematical Abstraction: Constructing Concept of Parallel Coordinates. Journal of Physics: Conference Series, 895(1), 012076. https://doi.org/10.1088/1742-6596/895/1/012076
- Ozmantar, M. F. (2005). An investigation of the formation of mathematical abstractions through scaffolding. Univeristy of Leeds, July.
- Ozmantar, M. F., & Monaghan, J. (2007). A Dialectical Approach to the Formation of Mathematical Abstractions. Mathematics Education Research Journal, 19(2), 89–112. https://doi.org/10.1007/BF03217457
- Pegg, J., & Tall, D. (2005). The fundamental cycle of concept construction underlying various theoretical frameworks. ZDM - International Journal on Mathematics Education, 37(6), 468–475. https://doi.org/10.1007/BF02655855
- Priatna, N., Martadiputra, B. A. P., & Wibisono, Y. (2018). Developing geogebra-assisted reciprocal teaching strategy to improve junior high school students’ abstraction ability, lateral thinking and mathematical persistence. Journal of Physics: Conference Series, 1013(1), 012142. https://doi.org/10.1088/1742-6596/1013/1/012142
- Putra, Z. H., Afrillia, Y. M., Dahnilsyah, & Tjoe, H. (2023). Prospective elementary teachers ’ informal mathematical proof using GeoGebra : The case of 3D shapes. Journal on Mathematics Education, 14(3), 449–468. https://doi.org/10.22342/jme.v14i3.pp449-468
- Rich, K. M., & Yadav, A. (2020). Applying Levels of Abstraction to Mathematics Word Problems. TechTrends, 64(3), 395–403. https://doi.org/10.1007/s11528-020-00479-3
- Rich, K. M., Yadav, A., & Zhu, M. (2019). Levels of abstraction in students’ mathematics strategies: What can applying computer science ideas about abstraction bring to elementary mathematics ? Journal of Computers in Mathematics and Science Teaching, 38(3), 267–298. https://www.learntechlib.org/p/210229/
- Ron, G., Dreyfus, T., & Hershkowitz, R. (2010). Partially correct constructs illuminate students ’ inconsistent answers. Educational Studies in Mathematics, 75, 65–87. https://doi.org/10.1007/s10649-010-9241-x
- Ron, G., Dreyfus, T., & Hershkowitz, R. (2017). Looking back to the roots of partially correct constructs: The case of the area model in probability. Journal of Mathematical Behavior, 45, 15–34. https://doi.org/10.1016/j.jmathb.2016.10.004
- Salinas, P., & Pulido, R. (2017). Understanding the Conics through Augmented Reality. Eurasia Journal of Mathematics, Science and Technology Education, 13(2), 341–354. https://doi.org/10.12973/eurasia.2017.00620a
- Sfard, A. (1991). On the Dual Nature of Mathematical Conceptions: Reflections on Processes and Objects as Different Sides of the Same Coin. Educational Studies in Mathematics, 22(1), 1–36. https://doi.org/10.1007/BF00302715
- Skemp, R. R. (1987). The Psychology of learning mathematics. In The Psychology of Learning Mathematics: Expanded American Edition (pp. 1–218). Lawrence Erlbaum Associates. https://doi.org/10.4324/9780203396391
- Turgut, M. (2019). Sense-Making Regarding Matrix Representation of Geometric Transformations in R2 : A semiotic mediation perspective in a dynamic geometry environment. ZDM - Mathematics Education, 51(7), 1199–1214. https://doi.org/10.1007/s11858-019-01032-0
- Yao, X., & Manouchehri, A. (2019). Middle school students’ generalizations about properties of geometric transformations in a dynamic geometry environment. Journal of Mathematical Behavior, 55(September 2018), 100703. https://doi.org/10.1016/j.jmathb.2019.04.002
References
Breive, S. (2022). Abstraction and Embodiment: Exploring the Process of Grasping a General. Educational Studies in Mathematics, 110(2), 313–329. https://doi.org/10.1007/s10649-021-10137-x
Budiarto, M. T., Khabibah, S., & Setianingsih, R. (2017). Construction of High School Students’ Abstraction Levels in Understanding the Concept of Quadrilaterals. International Education Studies, 10(2), 148. https://doi.org/10.5539/ies.v10n2p148
Bueno, R. W. da S., Henriques, A., & Galle, L. A. V. (2023). Mathematics Preservice Teachers ’ Perceptions Regarding ICT Use in Teaching and Learning Practices. Acta Scientiae, 25(5), 227–249. https://doi.org/10.17648/acta.scientiae.7633
Centina, A. Del. (2016). On Kepler ’ s System of Conics in Astronomiae Pars Optica. Archive for History of Exact Sciences, 70, 567–589. https://doi.org/10.1007/s00407-016-0175-2
Dewi, I., Siregar, N., & Andriani, A. (2018). The analysis of junior high school students’ mathematical abstraction ability based on local cultural wisdom. Journal of Physics: Conference Series, 1088(1), 012076. https://doi.org/10.1088/1742-6596/1088/1/012076
Dintarini, M., & Zukhrufurrohmah. (2021). Analisis Pemberian Scaffolding Melalui Online Form untuk Mengatasi Kesulitan Berpikir Spasial. ẟELT∆ Jurnal Ilmiah Pendidikan Matematika, 9(2), 221–232. http://dx.doi.org/10.31941/delta.v9i2.1414
Dreyfus, T., Hershkowitz, R., & Schwarz, B. (2015). The Nested Epistemic Actions Model for Abstraction in Context: Theory as Methodological Tool and Methodological Tool as Theory. In A. B.-A. et Al. (Ed.), Approaches to Qualitative Research in Mathematics Education, Advances in Mathematics Education (pp. 185–2017). Springer Science+Business Media Dordrecht. https://doi.org/10.1007/978-94-017-9181-6_8
Dubinsky, E., & Tall, D. (1991). Advanced mathematical thinking and the computer. Advanced Mathematical Thinking, 8, 231–248. https://doi.org/10.1007/0-306-47203-1_14
Elgrably, H., & Leikin, R. (2021). Creativity as a function of problem-solving expertise: posing new problems through investigations. ZDM - Mathematics Education, 53(4), 891–904. https://doi.org/10.1007/s11858-021-01228-3
Florio, E. (2021). Claude Mydorge Reader and Interpreter of Apollonius ’ Conics. Mathematics, 9, 261. https://doi.org/10.3390/math9030261
Florio, E. (2022). The Parabola: Section of a Cone or Locus of Points of a Plane? Tips for Teaching of Geometry from Some Writings by Mydorge and Wallis. Mathematics, 10(6), 974–992. https://doi.org/10.3390/math10060974
Fried, M. N. (2003). The Use of Analogy in Book VII of Apollonius ’ Conica The Use of Analogy in Book VII of Apollonius ’ Conica. Science in Context, 16(3), 349–365. https://doi.org/10.1017/S026988970300084X
Fried, M. N. (2022). Edmond Halley and Apollonius : second ‑ order historical knowledge in mathematics education. ZDM – Mathematics Education, 0123456789. https://doi.org/10.1007/s11858-022-01391-1
Glaister, E. M., & Glaister, P. (2006). Introducing conics without eccentricity. International Journal of Mathematical Education in Science and Technology, 37(2), 235–245. https://doi.org/10.1080/00207390500285800
Gray, E. M., & Tall, D. O. (1992). Success and Failure in Mathematics: Procept and Procedure 1. A Primary Perspective. Workshop on Mathematics Education and Computers, April, 216–221.
Gray, E. M., & Tall, D. O. (2007). Abstraction as a natural process of mental compression. Mathematics Education Research Journal, 19(2), 23–40. https://doi.org/10.1007/BF03217454
Hartinah, S., Suherman, S., Syazali, M., Efendi, H., Junaidi, R., Jermsittiparsert, K., & Umam, R. (2019). Probing-prompting based on ethnomathematics learning model: The effect on mathematical communication skills. Journal for the Education of Gifted Young Scientists, 7(4), 799–814. https://doi.org/10.17478/jegys.574275
Heath, T. (1896). Apollonius of Perga: Treatise on Conic Sections. C. J. CLAY AND SONS.
Hershkowitz, R., Hadas, N., Dreyfus, T., & Schwarz, B. B. (2007). Abstracting Processes, from Individuals’ Constructing of Knowledge to a Group’s “Shared Knowledge.” Mathematics Education Research Journal, 19(2), 41–68. https://doi.org/10.1007/BF03217455
Hershkowitz, R., Schwarz, B. B., & Dreyfus, T. (2001). Abstraction in Context: Epistemic Actions. Journal for Research in Mathematics Education, 32(2), 195–222. https://doi.org/10.1093/ojls/14.2.255
Hodiyanto, Budiarto, M. T., Ekawati, R., Susanti, G., Kim, J., & Bonyah, E. (2024). How abstraction of a pre-service teacher in constructing relationships among quadrilaterals. Journal on Mathematics Education, 15(2), 339–362. https://doi.org/10.22342/jme.v15i2.pp339-362
Hollebrands, K., & Stohl Lee, H. (2011). Introduction to dynamic geometry environments. Kendall Hunt Online, 1–22.
Jupri, A. (2017). From geometry to algebra and vice versa: Realistic mathematics education principles for analyzing geometry tasks. AIP Conference Proceedings, 1830. https://doi.org/10.1063/1.4980938
Jupri, Al, & Drijvers, P. (2016). Student Difficulties in Mathematizing Word Problems in Algebra. Eurasia Journal of Mathematics, Science & Technology Education, 12(9), 2481–2502. https://doi.org/10.12973/eurasia.2016.1299a
Komala, E. (2018). Analysis of Students’ Mathematical Abstraction Ability By Using Discursive Approach Integrated Peer Instruction of Structure Algebra Ii. Infinity Journal, 7(1), 25-34. https://doi.org/10.22460/infinity.v7i1.p25-34
Kouropatov, A., & Dreyfus, T. (2014). Learning the integral concept by constructing knowledge about accumulation. ZDM - Mathematics Education, 46(4), 533–548. https://doi.org/10.1007/s11858-014-0571-5
Memnun, D. S., Aydın, B., Özbilen, Ö., & Erdoğan, G. (2017). The abstraction process of limit knowledge. Kuram ve Uygulamada Egitim Bilimleri, 17(2), 345–371. https://doi.org/10.12738/estp.2017.2.0404
Memnun, D. S., Sevindik, F., Beklen, C., & Dinç, E. (2019). Analysis of the Abstraction Process of Continuity Knowledge. World Journal of Education, 9(2), 141. https://doi.org/10.5430/wje.v9n2p141
Mitchelmore, M. C., & White, P. (2004). Abstraction in mathematics learning. Mathematics Education Research Journal, 19(2), 1–9. https://doi.org/10.1007/BF03217452
Munson, J. (2019). After eliciting : Variation in elementary mathematics teachers ’ discursive pathways during collaborative problem solving. Journal of Mathematical Behavior, August, 100736. https://doi.org/10.1016/j.jmathb.2019.100736
Ng, O. L., Shi, L., & Ting, F. (2020). Exploring differences in primary students’ geometry learning outcomes in two technology-enhanced environments: dynamic geometry and 3D printing. International Journal of STEM Education, 7(1), 1–13. https://doi.org/10.1186/s40594-020-00244-1
Nurhasanah, F., Kusumah, Y. S., Sabandar, J., & Suryadi, D. (2017). Mathematical Abstraction: Constructing Concept of Parallel Coordinates. Journal of Physics: Conference Series, 895(1), 012076. https://doi.org/10.1088/1742-6596/895/1/012076
Ozmantar, M. F. (2005). An investigation of the formation of mathematical abstractions through scaffolding. Univeristy of Leeds, July.
Ozmantar, M. F., & Monaghan, J. (2007). A Dialectical Approach to the Formation of Mathematical Abstractions. Mathematics Education Research Journal, 19(2), 89–112. https://doi.org/10.1007/BF03217457
Pegg, J., & Tall, D. (2005). The fundamental cycle of concept construction underlying various theoretical frameworks. ZDM - International Journal on Mathematics Education, 37(6), 468–475. https://doi.org/10.1007/BF02655855
Priatna, N., Martadiputra, B. A. P., & Wibisono, Y. (2018). Developing geogebra-assisted reciprocal teaching strategy to improve junior high school students’ abstraction ability, lateral thinking and mathematical persistence. Journal of Physics: Conference Series, 1013(1), 012142. https://doi.org/10.1088/1742-6596/1013/1/012142
Putra, Z. H., Afrillia, Y. M., Dahnilsyah, & Tjoe, H. (2023). Prospective elementary teachers ’ informal mathematical proof using GeoGebra : The case of 3D shapes. Journal on Mathematics Education, 14(3), 449–468. https://doi.org/10.22342/jme.v14i3.pp449-468
Rich, K. M., & Yadav, A. (2020). Applying Levels of Abstraction to Mathematics Word Problems. TechTrends, 64(3), 395–403. https://doi.org/10.1007/s11528-020-00479-3
Rich, K. M., Yadav, A., & Zhu, M. (2019). Levels of abstraction in students’ mathematics strategies: What can applying computer science ideas about abstraction bring to elementary mathematics ? Journal of Computers in Mathematics and Science Teaching, 38(3), 267–298. https://www.learntechlib.org/p/210229/
Ron, G., Dreyfus, T., & Hershkowitz, R. (2010). Partially correct constructs illuminate students ’ inconsistent answers. Educational Studies in Mathematics, 75, 65–87. https://doi.org/10.1007/s10649-010-9241-x
Ron, G., Dreyfus, T., & Hershkowitz, R. (2017). Looking back to the roots of partially correct constructs: The case of the area model in probability. Journal of Mathematical Behavior, 45, 15–34. https://doi.org/10.1016/j.jmathb.2016.10.004
Salinas, P., & Pulido, R. (2017). Understanding the Conics through Augmented Reality. Eurasia Journal of Mathematics, Science and Technology Education, 13(2), 341–354. https://doi.org/10.12973/eurasia.2017.00620a
Sfard, A. (1991). On the Dual Nature of Mathematical Conceptions: Reflections on Processes and Objects as Different Sides of the Same Coin. Educational Studies in Mathematics, 22(1), 1–36. https://doi.org/10.1007/BF00302715
Skemp, R. R. (1987). The Psychology of learning mathematics. In The Psychology of Learning Mathematics: Expanded American Edition (pp. 1–218). Lawrence Erlbaum Associates. https://doi.org/10.4324/9780203396391
Turgut, M. (2019). Sense-Making Regarding Matrix Representation of Geometric Transformations in R2 : A semiotic mediation perspective in a dynamic geometry environment. ZDM - Mathematics Education, 51(7), 1199–1214. https://doi.org/10.1007/s11858-019-01032-0
Yao, X., & Manouchehri, A. (2019). Middle school students’ generalizations about properties of geometric transformations in a dynamic geometry environment. Journal of Mathematical Behavior, 55(September 2018), 100703. https://doi.org/10.1016/j.jmathb.2019.04.002