Research Article
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Year 2020, Volume: 20 Issue: 88, 87 - 104, 20.07.2020

Abstract

References

  • Amir-Mofidi, S., Amiripour, P., & Bijan-Zadeh, M. H. (2012). Instruction of mathematical concepts through analogical reasoning skills. Indian Journal of Science and Technology, 5(6), 2916–2922. Retrieved from https://doi.org/10.17485/ijst/2012/v5i6.12
  • Assmus, D., Forster, F., & Fritzlar, T. (2014). Analogizing during mathematical problem solving-theoretical and empirical considerations. In Proceeding of the Joint Meeting of PME (Vol. 38, pp. 73–80). Retrieved from https://iris.unito.it/retrieve/handle/2318/1620514/285455/PME38-2014%20Vancouver%202.pdf#page=83
  • Bassok, M. (2001). Semantic alignments in mathematical word problems. The Analogical Mind: Perspectives from Cognitive Science, 401–433.
  • Bernardo, A. B. I. (2001). Analogical Problem Construction and Transfer in Mathematical Problem Solving. Educational Psychology, 21(2), 137–150. Retrieved from https://doi.org/10.1080/01443410020043841
  • Creswell, J. W. (2013). Research design: Qualitative, quantitative, and mixed methods approaches. Sage publications. Retrieved from https://www.google.com/books?hl=en&lr=&id=EbogAQAAQBAJ&oi=fnd&pg=PP1&dq=Reseach+Design:+Qualitative,+Quantitative,+and+Mixed+Methods+Approaches.&ots=cbaQvRMzE3&sig=noU93mpCThgY41T49ShXjBVvouo
  • DiMaggio, P. (1997). Culture and cognition. Annual Review of Sociology, 23(1), 263–287. Retrieved from https://doi.org/10.1146/annurev.soc.23.1.263
  • English, L. D. (2004). Mathematical and analogical reasoning of young learners. Routledge. Retrieved from https://www.google.com/books?hl=en&lr=&id=GCqRAgAAQBAJ&oi=fnd&pg=PP1&dq=Mathematical+and+analogical+reasoning+of+young+learners&ots=oXoAt3Ad_U&sig=DVbtiQwggdS6COnnz916j6iqZF4
  • Eveleth, D. M. (2016). Analogical reasoning: When a non-expert reasons like an expert. Journal of Behavioral and Applied Management, 1(1), 28-40. Retrieved from https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&cad=rja&uact=8&ved=2ahUKEwjk55T9jvTqAhWZFzQIHa2rDegQFjANegQIBhAB&url=https%3A%2F%2Fjbam.scholasticahq.com%2Fapi%2Fv1%2Fattachments%2F1959%2Fdownload&usg=AOvVaw31bXCwTjRSPP7Z6UUOiPWj
  • Gentner, D. (1983). Structure-mapping: A theoretical framework for analogy. Cognitive Science, 7(2), 155–170. Retrieved from https://doi.org/10.1207/s15516709c0g0702_3
  • Gentner, D., & Holyoak, K. J. (1997). Reasoning and learning by analogy: Introduction. American Psychologist, 52, 32–34. Retrieved from https://doi.org/10.1037/0003-066X.52.1.32
  • Gentner, D., Holyoak, K. J., & Kokinov, B. N. (Eds.). (2001). The analogical mind: perspectives from cognitive science. Cambridge, Mass: MIT Press.
  • Gentner, D., & Loewenstein, J. (2002). Relational language and relational thought. Amsel, Eric (Ed); Byrnes, James P. (Ed). Language, Literacy, and Cognitive Development: The Development and Consequences of Symbolic Communication, 87–120, Erlbaum. Retrieved from https://loewenstein.web.illinois.edu/papers/GentnerLoewenstein02.pdf
  • Gentner, D., & Markman, A. B. (1997). Structure mapping in analogy and similarity. American Psychologist, 52(1), 45. Retrieved from https://doi.org/10.1037/0003-066X.52.1.45
  • Gust, H., Krumnack, U., Kühnberger, K.-U., & Schwering, A. (2008). Analogical Reasoning: A Core of Cognition. KI, 22(1), 8–12. Retrieved from http://schwering.staff.ifgi.de/gust_KIThemenheft.pdf
  • Holyoak, K. J., & Hummel, J. E. (2001). Toward an understanding of analogy within a biological symbol system. In D. Gentner, K. J. Holyoak, & B. N. Kokinov (Eds.), The analogical mind: Perspectives from cognitive science (161–195). The MIT Press.
  • Krawczyk, D. C. (2012). The cognition and neuroscience of relational reasoning. Brain Research, 1428, 13–23. Retrieved from https://doi.org/10.1016/j.brainres.2010.11.080
  • Kristayulita, K., Nusantara, T., As’ari, A. R., & Sa’dijah, C. (2018). Identification of Students Errors in Solving Indirect Analogical Problems Based on Analogical Reasoning Components. Journal of Physics: Conference Series, 1028, 012154. Retrieved from https://doi.org/10.1088/1742-6596/1028/1/012154
  • Magdas, I. (2015). Analogical Reasoning in Geometry Education. Acta Didactica Napocensia, 8(1), 57–65. Retrieved from https://files.eric.ed.gov/fulltext/EJ1064450.pdf Markman, A. B., & Gentner, D. (2000). Structure mapping in the comparison process. The American Journal of Psychology, 113(4), 501. Retrieved from https://doi.org/10.2307/1423470
  • Saleh, K., Yuwono, I., As’ ari, A. R., & Sa’dijah, C. (2017). Errors analysis solving problems analogies by Newman procedure using analogical reasoning. International Journal of Humanities and Social Sciences, 9(1), 17-26. Retrieved from https://ijhss.net/index.php/ijhss/article/view/253/89
  • Thagard, P. (2005). Mind: introduction to cognitive science (2nd ed). Cambridge, Mass: MIT Press.
  • Trench, M., Oberholzer, N., & Minervino, R. (2009). Dissolving the analogical paradox: Retrieval under a production paradigm is highly constrained by superficial similarity. New Frontiers in Analogy Research, 443–452. Retrieved from https://www.researchgate.net/publication/215991952_Dissolving_the_analogical_paradox_retrieval_under_a_production_paradigm_is_highly_constrained_by_superficial_similarity/link/0deec5263081c8c74f000000/download
  • Voskoglou, M. G. (2012). Mathematizing the Process of Analogical Reasoning. Journal of Mathematical Modelling and Application, 1(7), 58–69. Retrieved from https://proxy.furb.br/ojs/index.php/modelling/article/view/2836/2204

Schema of Analogical Reasoning - Thinking Process in Example Analogies Problem

Year 2020, Volume: 20 Issue: 88, 87 - 104, 20.07.2020

Abstract

Purpose: Analogical reasoning has been studied using a variety of tasks that generally required consideration of the relationship between the object and its integration to conclude an analog schema. The aim of this study was to describe the model of analogical reasoning schema based on some analogical problems.


Research Method:
In this study used a qualitative research approach with design research is the case study. Data were taken from 16-year-old high school students, West Nusa Tenggara Indonesia. The researcher selected 4 students who answered two analogical problems correctly and used in analyzing qualitative data.

Findings: The findings showed that there is a difference in the schema. The first type is that students can directly map between target problem and source problem, followed by structuring, applying, and verifying. The second type is that the student can not directly map between the target problem with the source problem, but the student needs to do a representation of the target problem so as to find a form of problem that has similarities with the source problem. Then the student can map between target problem with source problem, followed by doing the process as the first schema type.

The Implication for Research and Practice: Findings of this study may have an impact on the way teachers teach mathematics on the analogical problems they use. Teachers can consider mathematical problems used in learning so that students easily understand the theory from the concepts being taught. And then, teachers need to develop an analogical problem that can develop critical and creative thinking to enhance the creativity of high school students with their analogical reasoning.

References

  • Amir-Mofidi, S., Amiripour, P., & Bijan-Zadeh, M. H. (2012). Instruction of mathematical concepts through analogical reasoning skills. Indian Journal of Science and Technology, 5(6), 2916–2922. Retrieved from https://doi.org/10.17485/ijst/2012/v5i6.12
  • Assmus, D., Forster, F., & Fritzlar, T. (2014). Analogizing during mathematical problem solving-theoretical and empirical considerations. In Proceeding of the Joint Meeting of PME (Vol. 38, pp. 73–80). Retrieved from https://iris.unito.it/retrieve/handle/2318/1620514/285455/PME38-2014%20Vancouver%202.pdf#page=83
  • Bassok, M. (2001). Semantic alignments in mathematical word problems. The Analogical Mind: Perspectives from Cognitive Science, 401–433.
  • Bernardo, A. B. I. (2001). Analogical Problem Construction and Transfer in Mathematical Problem Solving. Educational Psychology, 21(2), 137–150. Retrieved from https://doi.org/10.1080/01443410020043841
  • Creswell, J. W. (2013). Research design: Qualitative, quantitative, and mixed methods approaches. Sage publications. Retrieved from https://www.google.com/books?hl=en&lr=&id=EbogAQAAQBAJ&oi=fnd&pg=PP1&dq=Reseach+Design:+Qualitative,+Quantitative,+and+Mixed+Methods+Approaches.&ots=cbaQvRMzE3&sig=noU93mpCThgY41T49ShXjBVvouo
  • DiMaggio, P. (1997). Culture and cognition. Annual Review of Sociology, 23(1), 263–287. Retrieved from https://doi.org/10.1146/annurev.soc.23.1.263
  • English, L. D. (2004). Mathematical and analogical reasoning of young learners. Routledge. Retrieved from https://www.google.com/books?hl=en&lr=&id=GCqRAgAAQBAJ&oi=fnd&pg=PP1&dq=Mathematical+and+analogical+reasoning+of+young+learners&ots=oXoAt3Ad_U&sig=DVbtiQwggdS6COnnz916j6iqZF4
  • Eveleth, D. M. (2016). Analogical reasoning: When a non-expert reasons like an expert. Journal of Behavioral and Applied Management, 1(1), 28-40. Retrieved from https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&cad=rja&uact=8&ved=2ahUKEwjk55T9jvTqAhWZFzQIHa2rDegQFjANegQIBhAB&url=https%3A%2F%2Fjbam.scholasticahq.com%2Fapi%2Fv1%2Fattachments%2F1959%2Fdownload&usg=AOvVaw31bXCwTjRSPP7Z6UUOiPWj
  • Gentner, D. (1983). Structure-mapping: A theoretical framework for analogy. Cognitive Science, 7(2), 155–170. Retrieved from https://doi.org/10.1207/s15516709c0g0702_3
  • Gentner, D., & Holyoak, K. J. (1997). Reasoning and learning by analogy: Introduction. American Psychologist, 52, 32–34. Retrieved from https://doi.org/10.1037/0003-066X.52.1.32
  • Gentner, D., Holyoak, K. J., & Kokinov, B. N. (Eds.). (2001). The analogical mind: perspectives from cognitive science. Cambridge, Mass: MIT Press.
  • Gentner, D., & Loewenstein, J. (2002). Relational language and relational thought. Amsel, Eric (Ed); Byrnes, James P. (Ed). Language, Literacy, and Cognitive Development: The Development and Consequences of Symbolic Communication, 87–120, Erlbaum. Retrieved from https://loewenstein.web.illinois.edu/papers/GentnerLoewenstein02.pdf
  • Gentner, D., & Markman, A. B. (1997). Structure mapping in analogy and similarity. American Psychologist, 52(1), 45. Retrieved from https://doi.org/10.1037/0003-066X.52.1.45
  • Gust, H., Krumnack, U., Kühnberger, K.-U., & Schwering, A. (2008). Analogical Reasoning: A Core of Cognition. KI, 22(1), 8–12. Retrieved from http://schwering.staff.ifgi.de/gust_KIThemenheft.pdf
  • Holyoak, K. J., & Hummel, J. E. (2001). Toward an understanding of analogy within a biological symbol system. In D. Gentner, K. J. Holyoak, & B. N. Kokinov (Eds.), The analogical mind: Perspectives from cognitive science (161–195). The MIT Press.
  • Krawczyk, D. C. (2012). The cognition and neuroscience of relational reasoning. Brain Research, 1428, 13–23. Retrieved from https://doi.org/10.1016/j.brainres.2010.11.080
  • Kristayulita, K., Nusantara, T., As’ari, A. R., & Sa’dijah, C. (2018). Identification of Students Errors in Solving Indirect Analogical Problems Based on Analogical Reasoning Components. Journal of Physics: Conference Series, 1028, 012154. Retrieved from https://doi.org/10.1088/1742-6596/1028/1/012154
  • Magdas, I. (2015). Analogical Reasoning in Geometry Education. Acta Didactica Napocensia, 8(1), 57–65. Retrieved from https://files.eric.ed.gov/fulltext/EJ1064450.pdf Markman, A. B., & Gentner, D. (2000). Structure mapping in the comparison process. The American Journal of Psychology, 113(4), 501. Retrieved from https://doi.org/10.2307/1423470
  • Saleh, K., Yuwono, I., As’ ari, A. R., & Sa’dijah, C. (2017). Errors analysis solving problems analogies by Newman procedure using analogical reasoning. International Journal of Humanities and Social Sciences, 9(1), 17-26. Retrieved from https://ijhss.net/index.php/ijhss/article/view/253/89
  • Thagard, P. (2005). Mind: introduction to cognitive science (2nd ed). Cambridge, Mass: MIT Press.
  • Trench, M., Oberholzer, N., & Minervino, R. (2009). Dissolving the analogical paradox: Retrieval under a production paradigm is highly constrained by superficial similarity. New Frontiers in Analogy Research, 443–452. Retrieved from https://www.researchgate.net/publication/215991952_Dissolving_the_analogical_paradox_retrieval_under_a_production_paradigm_is_highly_constrained_by_superficial_similarity/link/0deec5263081c8c74f000000/download
  • Voskoglou, M. G. (2012). Mathematizing the Process of Analogical Reasoning. Journal of Mathematical Modelling and Application, 1(7), 58–69. Retrieved from https://proxy.furb.br/ojs/index.php/modelling/article/view/2836/2204
There are 22 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Kristayulita Krıstayulıta This is me 0000-0001-7066-8063

Toto Nusantara This is me 0000-0003-1116-9023

Abdur Rahman As’arı This is me 0000-0002-4959-0043

Cholis Sa’dıjah This is me 0000-0002-0264-8578

Publication Date July 20, 2020
Published in Issue Year 2020 Volume: 20 Issue: 88

Cite

APA Krıstayulıta, K., Nusantara, T., As’arı, A. R., Sa’dıjah, C. (2020). Schema of Analogical Reasoning - Thinking Process in Example Analogies Problem. Eurasian Journal of Educational Research, 20(88), 87-104.
AMA Krıstayulıta K, Nusantara T, As’arı AR, Sa’dıjah C. Schema of Analogical Reasoning - Thinking Process in Example Analogies Problem. Eurasian Journal of Educational Research. July 2020;20(88):87-104.
Chicago Krıstayulıta, Kristayulita, Toto Nusantara, Abdur Rahman As’arı, and Cholis Sa’dıjah. “Schema of Analogical Reasoning - Thinking Process in Example Analogies Problem”. Eurasian Journal of Educational Research 20, no. 88 (July 2020): 87-104.
EndNote Krıstayulıta K, Nusantara T, As’arı AR, Sa’dıjah C (July 1, 2020) Schema of Analogical Reasoning - Thinking Process in Example Analogies Problem. Eurasian Journal of Educational Research 20 88 87–104.
IEEE K. Krıstayulıta, T. Nusantara, A. R. As’arı, and C. Sa’dıjah, “Schema of Analogical Reasoning - Thinking Process in Example Analogies Problem”, Eurasian Journal of Educational Research, vol. 20, no. 88, pp. 87–104, 2020.
ISNAD Krıstayulıta, Kristayulita et al. “Schema of Analogical Reasoning - Thinking Process in Example Analogies Problem”. Eurasian Journal of Educational Research 20/88 (July 2020), 87-104.
JAMA Krıstayulıta K, Nusantara T, As’arı AR, Sa’dıjah C. Schema of Analogical Reasoning - Thinking Process in Example Analogies Problem. Eurasian Journal of Educational Research. 2020;20:87–104.
MLA Krıstayulıta, Kristayulita et al. “Schema of Analogical Reasoning - Thinking Process in Example Analogies Problem”. Eurasian Journal of Educational Research, vol. 20, no. 88, 2020, pp. 87-104.
Vancouver Krıstayulıta K, Nusantara T, As’arı AR, Sa’dıjah C. Schema of Analogical Reasoning - Thinking Process in Example Analogies Problem. Eurasian Journal of Educational Research. 2020;20(88):87-104.