Indirect Analogical Reasoning Components

K Kristayulita

Abstract


If using different instruments obtained a different analogical reasoning component. With use  people-piece analogies, verbal analogies, and geometric analogies, have analogical reasoning component consists of encoding, inferring, mapping, and application. Meanwhile,  with use analogical problems (algebra, source problem and target problem is equal), have analogical reasoning components consist of structuring, mapping, applying, and verifying. The instrument used was analogical problems consisting of two problems where the source problem was symbolic quadratic equation problem and the target problems were trigonometric equation problem and a word problem. This study aims to provide information analogical reasoning process in solving indirect analogical problems. in addition, to identify the analogical reasoning components in solving indirect analogical problems. Using a qualitative design approach, the study was conducted at two schools in Mataram city of Nusa Tenggara Barat, Indonesia. The results of the study provide an overview of analogical reasoning of the students in solving indirect analogical problems and there is a component the representation and mathematical model in solving indirect analogical problems.  So the analogical reasoning component in solving indirect analogical problems is the representation and mathematical modeling, structuring, mapping, applying, and verifying. This means that there are additional components of analogical reasoning developed by Ruppert. Analogical reasoning components in problem-solving depend on the analogical problem is given.


Keywords


analogical reasoning; component; indirect analogical problems;

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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.

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

Bernardo, A. B. I. (2001). Analogical Problem Construction and Transfer in Mathematical Problem Solving. Educational Psychology, 21(2), 137–150. https://doi.org/10.1080/01443410020043841

Duit, R. (1991). On the role of analogies and metaphors in learning science. Science Education, 75(6), 649–672.

Eliasmith, C., & Thagard, P. (2001). Integrating structure and meaning: A distributed model of analogical mapping. Cognitive Science, 25(2), 245–286.

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

Gentner, D. (1983). Structure-mapping: A theoretical framework for analogy. Cognitive Science, 7(2), 155–170.

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. Language, Literacy, and Cognitive Development: The Development and Consequences of Symbolic Communication, 87–120.

Holyoak, K. J., & Hummel, J. E. (2001). Toward an understanding of analogy within a biological symbol system. The Analogical Mind: Perspectives from Cognitive Science, 161–195.

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. In Journal of Physics: Conference Series (Vol. 1028, p. 012154). IOP Publishing.

Magdas, I. (2015). Analogical Reasoning in Geometry Education. Acta Didactica Napocensia, 8(1), 57–65.

Melis, E., & Veloso, M. (1998). Analogy in problem solving. In Handbook of practical reasoning: Computational and theoretical aspects. Citeseer. Retrieved from http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.51.8553

O’Donoghue, J. (2004). Finding Novel Analogies. University College Dublin. Retrieved from http://www.cs.nuim.ie/~dod/pubs/05-thesis.pdf

Richland, L. E., Holyoak, K. J., & Stigler, J. W. (2004). Analogy use in eighth-grade mathematics classrooms. Cognition and Instruction, 22(1), 37–60.

Ruppert, M. (2013). Ways of analogical reasoning–thought processes in an example based learning environment. Erscheint in: Proceedings of the CERME, 8. Retrieved from http://cerme8.metu.edu.tr/wgpapers/WG1/WG1_Ruppert.pdf

Sternberg, R. J. (1977). Component processes in analogical reasoning. Psychological Review, 84(4), 353.

Thagard, P. (2005). Mind: introduction to cognitive science (2nd ed). Cambridge, Mass: MIT Press.

Whitten, S., & Graesser, A. C. (2003). Comprehension of text in problem solving. The Psychology of Problem Solving, 207–229.




DOI: https://doi.org/10.29103/mjml.v4i1.2939

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