Main Article Content
Abstract
This study aims to investigate students’ prior knowledge as an obstacle when learning ratio and proportion concept. The study uses an interpretive paradigm which is part of Didactical Design Research. Eighth graders who had learned about ratio and proportion participated in this study. The analysis was carried out qualitatively based on the data from the students’ answers and interviews on their answers when solving ratio and proportion problems to identify learning obstacle, especially ontogenic obstacle regarding the students’ prior knowledge. The result of this study indicates that prior knowledge is one of the ontogenic obstacle in teaching and learning of ratio and proportion. It can be found from their learning experience in understanding the concept. In conclusion, investigating students' prior knowledge is essential for the effectiveness of teaching and learning of ratio and proportion. It is important to overcome ontogenic obstacles and to understand how to activate students’ prior knowledge using the right or appropriate methods when learning ratio and proportion.
Keywords
Article Details
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References
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- Anderson, J. R. (2015). Cognitive Psychology and Its Implications. Eighth Edition. USA: Worth Publisher.
- Andini, W., & Jupri, A. (2017). Student Obstacles in Ratio and Proportion Learning. Journal of Physics: Conference Series, 812 012048. https://doi.org/10.1088/1742-6596/812/1/012048
- Arican, M. (2016). Preservice Middle and High School Mathematics Teachers’ Strategies when Solving Proportion Problems. International Journal of Science and Mathematics Education, 16(2), 315–335. https://doi.org/10.1007/s10763-016-9775-1
- Ausubel, D. P., Novak, J. D., & Hanesian, H. (1978). Educational Psychology: A Cognitive View (Second Edition). New York: Holt, Rinehart and Winston.
- Ben-Chaim, D., Keret, Y., & Ilany, B. (2012). Ratio and Proportion, Research and Teaching in Mathematics Teachers’ Education (Pre- and In-service Mathematics Teachers of Elementary and Middle School Classes). Rotterdam: Sense Publisher.
- Bingolbali, E., Akkoc, H., Ozmantar, M. F., & Demir, S. (2011). Pre-service and In-service Teachers’ Views of the Sources of Students’ Mathematical Difficulties. International Electronic Journal of Mathematics Education, 6(1), 40–59. https://doi.org/https://doi.org/10.29333/iejme/260
- Bintara, I. A., & Suhendra. (2021). Analysis toward Learning Obstacles of Junior High School Students on the Topic of Direct and Inverse Proportion. Journal of Physics: Conference Series, 1882 01208. https://doi.org/10.1088/1742-6596/1882/1/012083
- Bock, D. D., Dooren, W. V., & Verschaffel, L. (2015). Students’ Understanding of Proportional, Inverse Proportional, and Affine Functions: Two Studies on the Role of External Representations. International Journal of Science and Mathematics Education, 13, 47–69. https://doi.org/10.1007/S10763-013-9475-Z
- Brousseau, G. (2002). Theory of Didactical Situations in Mathematics. Dordrecht: Kluwer Academic Publisher.
- Cesaria, A., & Herman, T. (2019). Learning Obstacle in Geometry. Journal of Engineering Science and Technology, 14(3), 1271–1280.
- Cetin, H., & Artekin, E. (2011). The Relationship between Eighth Grade Primary School Students’ Proportional Reasoning Skills and Success in Solving Equations. International Journal of Instruction, 4(1), 47–62.
- Cortina, J. L., Visnovska, J., & Zuniga, C. (2014). Equipartition as a Didactical Obstacle in Fraction Instruction. Acta Didactica Universitatis Comenianae Mathematics, 14(1), 1–18. https://doi.org/10.1007/s13394-013-0112-5
- Dochy, F. J. R. C., & Alexander, P. A. (1995). Mapping Prior Knowledge: A Framework for Discussion among Researchers. European Journal of Psychology of Education, 10(3), 225–242. https://doi.org/10.1007/BF03172918
- Glogger-Frey, I., Deutscher, M., & Renkl, A. (2018). Student Teachers’ Prior Knowledge as Prerequisite to Learn How to Assess Pupils’ Learning Strategies. Teaching and Teacher Education, 30, 227–241. https://doi.org/10.1016/j.tate.2018.01.012
- Hailikari, T., Katajavuori, N., & Lindblom-Ylanne, S. (2008). The Relevance of Prior Knowledge in Learning and Instructional Design. American Journal of Pharmaceutical Education, 72(5). https://doi.org/10.5688/aj7205113
- Hardi, J., Hudiono, B., & Mirza, A. (2013). Description of students' understanding of comparative problems and solution strategies in solving them [in Bahasa]. Jurnal Pendidikan Dan Pembelajaran Khatulistiwa, 2(5), 1–11. https://doi.org/http://dx.doi.org/10.26418/jppk.v2i5.1987
- Hutapea, M. L., Suryadi, D., & Nurlaelah, E. (2015). Analysis of Students’ Epistemological Obstacles on the Subject of Pythagorean Theorem. Jurnal Pengajaran Matematika Dan Ilmu Pengetahuan Alam, 20(1), 1–10. https://doi.org/10.18269/jpmipa.v20i1.555
- Jiang, C., Hwang, S., & Cai, J. (2014). Chinese and Singaporean Sixth-grade Students’ Strategies for Solving Problems about Speed. Educational Studies in Mathematics, 87(1), 27–50. https://doi.org/10.1007/s10649-014-9559-x
- Karli, M. G., & Yildiz, E. (2022). Incorrect Strategies Developed by Seventh- Grade Students to Solve Proportional Reasoning Problems. Journal of Qualitative Research in Education, 22(29), 111–148. https://doi.org/10.14689/enad.29.5
- Kivunja, C., & Kuyini, A. B. (2017). Understanding and Applying Research Paradigms in Educational Contexts. International Journal of Higher Education, 6(5), 26–41. https://doi.org/10.5430/ijhe.v6n5p26
- Lamon, S. J. (1993). Ratio and Proportion: Connecting Content and Children’s Thinking. Journal for Research in Mathematics Education, 24(1), 41–61. https://doi.org/10.2307/749385
- Ministry of Education and Culture. (2014). Regulation of the Minister of Education and Culture of the Republic of Indonesia Number 58 of 2014 concerning the 2013 Curriculum for Junior High Schools/Madrasah Tsanawiyah [in Bahasa].
- Misailidou, C., & Williams, J. (2003). Children’s Arguments in Discussion of a “Difficult” Ratio Problem: The Role of a Pictorial Representation. Proceedings of the 3rd Conference of the European Society for Research in Mathematics Education (CERME3). Bellaria, Italia.
- Ojose, B. (2015). Proportional Reasoning and Related Concepts: Analysis of Gaps and Understandings of Middle Grade Students. Universal Journal of Educational Research, 3(2), 104–112. https://doi.org/10.13189/ujer.2015.030206
- Pişkin-Tunç, M., & Sultan-Gündoğdu, N. (2022). Middle School Students’ Views about STEM Activities Used in Teaching Ratio and Proportion. Bartın University Journal of Faculty of Education, 10(3), 647–662. https://doi.org/10.14686/buefad.1095364
- Raharjanti, M., Nusantara, T., & Mulyati, S. (2016). Student Errors in Solving Problems of Comparison of Worth and Reverse Value [in Bahasa]. Proceedings of the Konferensi Nasional Penelitian Matematika Dan Pembelajarannya (KNPMP I) Universitas Muhammadiyah Surakarta, March, 312–319.
- Rittle-Johnson, B., Star, J. R., & Durkin, K. (2009). The Importance of Prior Knowledge When Comparing Examples: Influences on Conceptual and Procedural Knowledge of Equation Solving. Journal of Educational Psychology, 101(4), 836–852. https://doi.org/10.1037/a0016026
- Ruli, R. M., Priatna, N., Sufyani, P., & Endang, M. (2018). Analysis Learning Obstacle on Quadratic Function Topic. International Journal of Information and Education Technology, 8(9), 681–684. https://doi.org/10.18178/ijiet.2018.8.9.1122
- Shanty, N. O., Hartono, Y., Putri, R. I. I., & De Haan, D. (2011). Design Research on Mathematics Education: Investigating the Progress of Indonesian Fifth Grade Students’ Learning on Multiplication of Fractions with Natural Numbers. Journal on Mathematics Education, 2(2), 147–162. https://doi.org/10.22342/jme.2.2.749.147-162
- Sidik, G. S., Suryadi, D., & Turmudi, T. (2021). Learning Obstacle on Addition and Subtraction of Primary School Students: Analysis of Algebraic Thinking. Education Research International, 2021. https://doi.org/10.1155/2021/5935179
- Solomon, A. (1987). Proportion: Interraltions and Meaning in Mathematics. For the Learning of Mathematics, 7(1), 14–22.
- Suryadi, D. (2013). Didactical Design Research (DDR) in the Development of Mathematics Learning [in Bahasa]. Proceedings of the Seminar Nasional Pendidikan Matematika, Vol. 1. Cimahi: Program Studi Pendidikan Matematika, STKIP Siliwangi Bandung.
- Thanh, N. C., & Thanh, T. T. L. (2015). The Interconnection between Interpretivist Paradigm and Qualitative Methods in Education. American Journal of Educational Science, 1(2), 24–27.
- Thurn, C., Nussbaumer, D., Schumacher, R., & Stern, E. (2022). The Role of Prior Knowledge and Intelligence in Gaining from a Training on Proportional Reasoning. Journal of Intelligence, 10(2), 1–27. https://doi.org/10.3390/jintelligence10020031
- Ültanır, E. (2012). An Epistemological Glance at the Constructivist Approach: Constructivist Learning in Dewey, Piaget, and Montessori. International Journal of Instruction, 5(2), 195–212.
- Valverde, G., & Castro, E. (2012). Prospective Elementary School Teachers’ Proportional Reasoning. PNA, 7(1).
- Van de Walle, J. A. (2008). Elementary and Middle School Mathematics, Volume 2, Sixth Edition [in Bahasa]. Jakarta: Erlangga.
- Wahyuningrum, A. S., Suryadi, D., & Turmudi. (2017). Epistemological Obstacles on the Topic of Ratio and Proportion among Junior High School Students. Journal of Physics: Conference Series, 895 012066. https://doi.org/10.1088/1742-6596/895/1/012066
- Wahyuningrum, A. S., Suryadi, D., & Turmudi, T. (2019). Learning Obstacles among Indonesian Eighth Graders on Ratio and Proportion. Journal of Physics: Conference Series, 1320 01204. https://doi.org/10.1088/1742-6596/1320/1/012046
- Wijaya, A. (2017). The relationships between Indonesian fourth graders’ difficulties in fractions and the opportunity to learn fractions: A snapshot of TIMSS results. International Journal of Instruction, 10(4), 221–236. https://doi.org/10.12973/iji.2017.10413a
- Yee, L. P. (2007). Teaching Primary School Mathematics: A Resource Book. Singapore: McGrawHill education.
- Yuksel, I. (2012). Activating Students’ Prior Knowledge: The Core Strategies. World Applied Sciences Journal, 20(8), 1197–1201. https://doi.org/10.5829/idosi.wasj.2012.20.08.473
References
Ahl, L. M. (2019). Designing a Research-based Detection Test for Eliciting Students’ Prior Understanding on Proportional Reasoning. Adults Learning Mathematics: An International Journal, 14(1), 6–22. https://files.eric.ed.gov/fulltext/EJ1232385.pdf
Anderson, J. R. (2015). Cognitive Psychology and Its Implications. Eighth Edition. USA: Worth Publisher.
Andini, W., & Jupri, A. (2017). Student Obstacles in Ratio and Proportion Learning. Journal of Physics: Conference Series, 812 012048. https://doi.org/10.1088/1742-6596/812/1/012048
Arican, M. (2016). Preservice Middle and High School Mathematics Teachers’ Strategies when Solving Proportion Problems. International Journal of Science and Mathematics Education, 16(2), 315–335. https://doi.org/10.1007/s10763-016-9775-1
Ausubel, D. P., Novak, J. D., & Hanesian, H. (1978). Educational Psychology: A Cognitive View (Second Edition). New York: Holt, Rinehart and Winston.
Ben-Chaim, D., Keret, Y., & Ilany, B. (2012). Ratio and Proportion, Research and Teaching in Mathematics Teachers’ Education (Pre- and In-service Mathematics Teachers of Elementary and Middle School Classes). Rotterdam: Sense Publisher.
Bingolbali, E., Akkoc, H., Ozmantar, M. F., & Demir, S. (2011). Pre-service and In-service Teachers’ Views of the Sources of Students’ Mathematical Difficulties. International Electronic Journal of Mathematics Education, 6(1), 40–59. https://doi.org/https://doi.org/10.29333/iejme/260
Bintara, I. A., & Suhendra. (2021). Analysis toward Learning Obstacles of Junior High School Students on the Topic of Direct and Inverse Proportion. Journal of Physics: Conference Series, 1882 01208. https://doi.org/10.1088/1742-6596/1882/1/012083
Bock, D. D., Dooren, W. V., & Verschaffel, L. (2015). Students’ Understanding of Proportional, Inverse Proportional, and Affine Functions: Two Studies on the Role of External Representations. International Journal of Science and Mathematics Education, 13, 47–69. https://doi.org/10.1007/S10763-013-9475-Z
Brousseau, G. (2002). Theory of Didactical Situations in Mathematics. Dordrecht: Kluwer Academic Publisher.
Cesaria, A., & Herman, T. (2019). Learning Obstacle in Geometry. Journal of Engineering Science and Technology, 14(3), 1271–1280.
Cetin, H., & Artekin, E. (2011). The Relationship between Eighth Grade Primary School Students’ Proportional Reasoning Skills and Success in Solving Equations. International Journal of Instruction, 4(1), 47–62.
Cortina, J. L., Visnovska, J., & Zuniga, C. (2014). Equipartition as a Didactical Obstacle in Fraction Instruction. Acta Didactica Universitatis Comenianae Mathematics, 14(1), 1–18. https://doi.org/10.1007/s13394-013-0112-5
Dochy, F. J. R. C., & Alexander, P. A. (1995). Mapping Prior Knowledge: A Framework for Discussion among Researchers. European Journal of Psychology of Education, 10(3), 225–242. https://doi.org/10.1007/BF03172918
Glogger-Frey, I., Deutscher, M., & Renkl, A. (2018). Student Teachers’ Prior Knowledge as Prerequisite to Learn How to Assess Pupils’ Learning Strategies. Teaching and Teacher Education, 30, 227–241. https://doi.org/10.1016/j.tate.2018.01.012
Hailikari, T., Katajavuori, N., & Lindblom-Ylanne, S. (2008). The Relevance of Prior Knowledge in Learning and Instructional Design. American Journal of Pharmaceutical Education, 72(5). https://doi.org/10.5688/aj7205113
Hardi, J., Hudiono, B., & Mirza, A. (2013). Description of students' understanding of comparative problems and solution strategies in solving them [in Bahasa]. Jurnal Pendidikan Dan Pembelajaran Khatulistiwa, 2(5), 1–11. https://doi.org/http://dx.doi.org/10.26418/jppk.v2i5.1987
Hutapea, M. L., Suryadi, D., & Nurlaelah, E. (2015). Analysis of Students’ Epistemological Obstacles on the Subject of Pythagorean Theorem. Jurnal Pengajaran Matematika Dan Ilmu Pengetahuan Alam, 20(1), 1–10. https://doi.org/10.18269/jpmipa.v20i1.555
Jiang, C., Hwang, S., & Cai, J. (2014). Chinese and Singaporean Sixth-grade Students’ Strategies for Solving Problems about Speed. Educational Studies in Mathematics, 87(1), 27–50. https://doi.org/10.1007/s10649-014-9559-x
Karli, M. G., & Yildiz, E. (2022). Incorrect Strategies Developed by Seventh- Grade Students to Solve Proportional Reasoning Problems. Journal of Qualitative Research in Education, 22(29), 111–148. https://doi.org/10.14689/enad.29.5
Kivunja, C., & Kuyini, A. B. (2017). Understanding and Applying Research Paradigms in Educational Contexts. International Journal of Higher Education, 6(5), 26–41. https://doi.org/10.5430/ijhe.v6n5p26
Lamon, S. J. (1993). Ratio and Proportion: Connecting Content and Children’s Thinking. Journal for Research in Mathematics Education, 24(1), 41–61. https://doi.org/10.2307/749385
Ministry of Education and Culture. (2014). Regulation of the Minister of Education and Culture of the Republic of Indonesia Number 58 of 2014 concerning the 2013 Curriculum for Junior High Schools/Madrasah Tsanawiyah [in Bahasa].
Misailidou, C., & Williams, J. (2003). Children’s Arguments in Discussion of a “Difficult” Ratio Problem: The Role of a Pictorial Representation. Proceedings of the 3rd Conference of the European Society for Research in Mathematics Education (CERME3). Bellaria, Italia.
Ojose, B. (2015). Proportional Reasoning and Related Concepts: Analysis of Gaps and Understandings of Middle Grade Students. Universal Journal of Educational Research, 3(2), 104–112. https://doi.org/10.13189/ujer.2015.030206
Pişkin-Tunç, M., & Sultan-Gündoğdu, N. (2022). Middle School Students’ Views about STEM Activities Used in Teaching Ratio and Proportion. Bartın University Journal of Faculty of Education, 10(3), 647–662. https://doi.org/10.14686/buefad.1095364
Raharjanti, M., Nusantara, T., & Mulyati, S. (2016). Student Errors in Solving Problems of Comparison of Worth and Reverse Value [in Bahasa]. Proceedings of the Konferensi Nasional Penelitian Matematika Dan Pembelajarannya (KNPMP I) Universitas Muhammadiyah Surakarta, March, 312–319.
Rittle-Johnson, B., Star, J. R., & Durkin, K. (2009). The Importance of Prior Knowledge When Comparing Examples: Influences on Conceptual and Procedural Knowledge of Equation Solving. Journal of Educational Psychology, 101(4), 836–852. https://doi.org/10.1037/a0016026
Ruli, R. M., Priatna, N., Sufyani, P., & Endang, M. (2018). Analysis Learning Obstacle on Quadratic Function Topic. International Journal of Information and Education Technology, 8(9), 681–684. https://doi.org/10.18178/ijiet.2018.8.9.1122
Shanty, N. O., Hartono, Y., Putri, R. I. I., & De Haan, D. (2011). Design Research on Mathematics Education: Investigating the Progress of Indonesian Fifth Grade Students’ Learning on Multiplication of Fractions with Natural Numbers. Journal on Mathematics Education, 2(2), 147–162. https://doi.org/10.22342/jme.2.2.749.147-162
Sidik, G. S., Suryadi, D., & Turmudi, T. (2021). Learning Obstacle on Addition and Subtraction of Primary School Students: Analysis of Algebraic Thinking. Education Research International, 2021. https://doi.org/10.1155/2021/5935179
Solomon, A. (1987). Proportion: Interraltions and Meaning in Mathematics. For the Learning of Mathematics, 7(1), 14–22.
Suryadi, D. (2013). Didactical Design Research (DDR) in the Development of Mathematics Learning [in Bahasa]. Proceedings of the Seminar Nasional Pendidikan Matematika, Vol. 1. Cimahi: Program Studi Pendidikan Matematika, STKIP Siliwangi Bandung.
Thanh, N. C., & Thanh, T. T. L. (2015). The Interconnection between Interpretivist Paradigm and Qualitative Methods in Education. American Journal of Educational Science, 1(2), 24–27.
Thurn, C., Nussbaumer, D., Schumacher, R., & Stern, E. (2022). The Role of Prior Knowledge and Intelligence in Gaining from a Training on Proportional Reasoning. Journal of Intelligence, 10(2), 1–27. https://doi.org/10.3390/jintelligence10020031
Ültanır, E. (2012). An Epistemological Glance at the Constructivist Approach: Constructivist Learning in Dewey, Piaget, and Montessori. International Journal of Instruction, 5(2), 195–212.
Valverde, G., & Castro, E. (2012). Prospective Elementary School Teachers’ Proportional Reasoning. PNA, 7(1).
Van de Walle, J. A. (2008). Elementary and Middle School Mathematics, Volume 2, Sixth Edition [in Bahasa]. Jakarta: Erlangga.
Wahyuningrum, A. S., Suryadi, D., & Turmudi. (2017). Epistemological Obstacles on the Topic of Ratio and Proportion among Junior High School Students. Journal of Physics: Conference Series, 895 012066. https://doi.org/10.1088/1742-6596/895/1/012066
Wahyuningrum, A. S., Suryadi, D., & Turmudi, T. (2019). Learning Obstacles among Indonesian Eighth Graders on Ratio and Proportion. Journal of Physics: Conference Series, 1320 01204. https://doi.org/10.1088/1742-6596/1320/1/012046
Wijaya, A. (2017). The relationships between Indonesian fourth graders’ difficulties in fractions and the opportunity to learn fractions: A snapshot of TIMSS results. International Journal of Instruction, 10(4), 221–236. https://doi.org/10.12973/iji.2017.10413a
Yee, L. P. (2007). Teaching Primary School Mathematics: A Resource Book. Singapore: McGrawHill education.
Yuksel, I. (2012). Activating Students’ Prior Knowledge: The Core Strategies. World Applied Sciences Journal, 20(8), 1197–1201. https://doi.org/10.5829/idosi.wasj.2012.20.08.473