How Do Assimilation and Accommodation Occur in The Translation Process of Representation?

Galuh Swastika; Toto Nusantara; Subanji Subanji; Santi Irawati

doi:10.17275/per.23.50.10.3

EN

How Do Assimilation and Accommodation Occur in The Translation Process of Representation?

Abstract

This study aims to describe the translation process of representation in mathematics education students’ solving of mathematical problems in the form of graphs. The translation process involves four activities: unpacking the source, preliminary coordination, constructing the target, and determining equivalence. The study was conducted on 65 students who took Calculus at three different universities in East Java Province, Indonesia. Research data in the form of answers to mathematical problems, video recordings, and interviews were analyzed based on the activity of the translation process within the accommodation and assimilation framework. Based on data analysis, the characteristics of the representation translation process are obtained in three categories, namely the symbolic-algebraic translation process (SA), the verbal translation process (V), and the symbolic-conceptual translation process (SC). When “unpacking the source” and “preliminary coordination,” SA looks difficult, so it changes the equations and graphs for completion several times. V verbally smoothly performs four translational process activities. However, subject V has doubts about the graph made after reading the question back. SC uses graph equations until it finds a solution in the form of a graph. However, after reflection, SC resolves the problem with the theory of monotony. It is important for the future teacher to understand the translation process of representation, especially given the difficulty students have solving mathematical problems. Prospective teachers are expected to be able to develop meaningful learning with various forms of representation so that students can connect their concepts to problem solving.

Keywords

translation representation;, assimilation, accomodation

Supporting Institution

Universitas Nahdlatul Ulama Blitar

Thanks

The researchers would like to express their gratitude to the Ministry of the Research, Technology, and Higher Education of Republic of Indonesia, Universitas Negeri Malang, and Universitas Nahdlatul Ulama Blitar.

References

Adu-Gyamfi, K., Bossé, M. J., & Chandler, K. (2016). Student Connections between Algebraic and Graphical Polynomial Representations in the Context of a Polynomial Relation. International Journal of Science and Mathematics Education, 15(5), 915–938. https://doi.org/10.1007/s10763-016-9730-1
Adu-Gyamfi, K., Stiff, L. V, & Bossé, M. J. (2012). Lost in Translation: Examining Translation Errors Associated With Mathematical Representations. School Science and Mathematics, 112(3), 159–170.
Ainsworth, S. (1999). The functions of multiple representations. Computers & Education, 33(2–3), 131–152.
Bal, A. P. (2014). The Examination of Representations used by Classroom Teacher Candidates in Solving Mathematical Problems. Educational Sciences: Theory & Practice, 14, 6. https://doi.org/10.12738/estp.2014.6.2189
Bal, A. P. (2015). Skills Of Using And Transform Multiple Representations Of The Prospective Teachers. Procedia - Social and Behavioral Sciences, 197(February), 582–588. https://doi.org/10.1016/j.sbspro.2015.07.197
Biber, A. Ç. (2014). Mathematics teacher candidates skills of using multiple representations for division of fractions. Educational Research and Reviews, 9(8), 237–244. https://doi.org/10.5897/ERR2013.1703
Bossé, M. J., Adu-Gyamfi, K., & Chandler, K. (2014). Students ’ Differentiated Translation Processes. International Journal for Mathematics Teaching and Learning, 828, 1–28.
Bossé, M. J., Adu-Gyamfi, K., & Cheetham, M. (2011). Translations Among Mathematical Representations: Teacher Beliefs and Practices. International Journal for Mathematics Teaching & Learning, June.
Çelik, D., & Saglam-Arslan, A. (2012). The Analysis of Teacher Candidates’ Translating Skills in Multiple Representations. Elementary Education Online, 11(1), 239–250.
Creswell, J. W. (2015). Educational research: Planning, conducting, and evaluating quantitative and qualitative research (Fifth edition). Pearson.

Delice, A., & Sevimli, E. (2010). An investigation of the pre-services teachers' ability of using multiple representations in problem-solving success: The case of definite integral. Educational Sciences: Theory & Practice, 10(1), 111-149.
Dündar, S. (2015). Mathematics Teacher-Candidates’ Performance in Solving Problems with Different Representation Styles: The Trigonometry Example. EURASIA Journal of Mathematics, Science and Technology Education, 11(6). https://doi.org/10.12973/eurasia.2015.1396a
Duval, R. (1999). Representation, Vision and Visualization: Cognitive Functions in Mathematical Thinking. Basic Issues for Learning. Proceedings of the Twenty First Annual Meeting of the North American Chapter of the International Groupfor the Psychology of Mathematics Education, 3–26.
Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics (Vol. 61). https://doi.org/10.1007/s10649-006-0400-z
Gagatsis, A., Christou, C., & Elia, I. (2004). The Nature of Multiple Representations in Developing Mathematical Relationships. Quaderni Di Ricerca in Didattica, 10.
Gagatsis, A., & Shiakalli, M. (2004). An Ability to Translate from One Representation of the Concept of Function to Another and Mathematical Problem Solving. Educational Psychology, 24(5), 37–41. https://doi.org/10.1080/0144341042000262953
Hiebert, J., & Carpenter, T. P. (1992). Learning and teaching with understanding. In Handbook of research on mathematics teaching and learning (pp. 65–97). Macmillan Publishing Company.
İpek, A. S., & Okumuş, S. (2012). The Representations of Pre-service Elementary Mathematics Teachers Used in Solving Mathematical Problems. Gaziantep Un. Journal of Social Science, 11(3), 681–700.
Jao, L. (2013). From sailing ships to subtraction symbols: Multiple representations to support abstraction. International Journal for Mathematics Teaching & Learning, 33, 49–64.
Kaput, J. J. (1989). Linking representations in the symbol systems of algebra. In: Wagner, S. and Kieran, C. Editors, Research Issues in the Learning and Teaching of Algebra Erlbaum, Hillsdale, NJ., 167–194.
Leinhardt, G., Zaslavsky, O., & Stein, M. K. (1990). Functions, Graphs, and Graphing: Tasks, Learning, and Teaching. Review of Educational Research, 60(1), 1–64. https://doi.org/10.3102/00346543060001001
Lesh, R., Post, T., & Behr, M. (1987). Representations and Translations among Representations in Mathematics Learning and Problem Solving. Problems of Representation in the Teaching and Learning of Mathematics, 33–40.
Mhlolo, M. K., Venkat, H., & Schäfer, M. (2012). The nature and quality of the mathematical connections teachers make. Pythagoras, 33(1), 9 pages. https://doi.org/10.4102/pythagoras.v33i1.22
NCTM. (2000). Principles and Standards for School Mathematics. VA: NCTM.
Pape, S. J. (2004). Middle School Children’s Problem-Solving Behavior: A Cognitive Analysis from a Reading Comprehension Perspective. Journal for Research in Mathematics Education, 35(3), 187. https://doi.org/10.2307/30034912
Pape, S. J., & Tchoshanov, M. A. (2001). The role of representation (s) in developing mathematical understanding. Theory into Practice, 40(2), 118–127.
Porzio, D. T. (1994). The effects of differing technological approaches to calculus on students’ use and understanding of multiple representations when solving problems [Dissertation Abstracts International, 55(10), 3128A]. University Microfilms No. AAI 9505274.
Rahmawati, D. (2019). Translation Between Mathematical Representation: How Students Unpack Source Representation? Matematika Dan Pembelajaran, 7(1), 50–64.
Rahmawati, D., & Anwar, R. B. (2020). Translation of mathematical representation: Characteristics of verbal representation unpacking. Journal of Education and Learning (EduLearn), 14(2), 162–167. https://doi.org/10.11591/edulearn.v14i2.9538
Rahmawati, D., Purwanto, S., Hidayanto, E., & Anwar, R. B. (2017). Process of Mathematical Representation Translation from Verbal into Graphic. IEJME-Mathematics Education, 12(4), 367–381.
Rahmawati, D., Purwanto, Subanji, Hidayanto, E., & Anwar, B. (2017). Process of Mathematical Representation Translation from Verbal into Graphic. International Electronic Journal of Mathematics Education, 12(3), 367–381.
Rodgers, C. (2002). Defining Reflection: Another Look at John Dewey and Reflective Thinking. 25.
Shiakalli, M., & Gagatsis, A. (2006). Compartmentalization of representation in tasks related to addition and subtraction using the number line. PME CONFERENCE, 5, 5-105-5–112.
Skemp, R. R. (1987). The psychology of learning mathematics (Expanded American Edition). Lawrence Erlbaum Associates Publishers.
Sternberg, R. J., & Sternberg, K. (2012). Cognitive Psychology (Sixth Edition). Wadsworth: Cengage Learning.
Subanji. (2007). Pseudo Covariational Reasoning Thinking Process in Constructing Graphs of Inverse Dynamics Event Functions. Universitas Negeri Surabaya.
Subanji. (2011). Covariational Reasoning Pseudo Theory. Universitas Negeri Malang (UM PRESS).
Swastika, G. T., Abdurahman, A., Irawan, E. B., Nusantara, T., Subanji, & Irawati, S. (2018). REPRESENTATION TRANSLATION ANALYSIS OF JUNIOR HIGH SCHOOL STUDENTS IN SOLVING MATHEMATICS PROBLEMS. International Journal of Insights for Mathematics Teaching, 01(2), 115–129.
Swastika, G. T., Nusantara, T., Subanji, & Irawati, S. (2020). Alteration Representation In The Process Of Translation Graphic To Graphic. Humanities & Social Sciences Reviews, 8(1), 334–343. https://doi.org/10.18510/hssr.2020.8144
Villegas, J. L., Castro, E., & Gutiérrez, J. (2009). Representations in problem solving: A case study with optimization problems. 7(17), 279–308.

Details

Primary Language

English

Subjects

Educational Psychology

Journal Section

Research Article

Authors

Galuh Swastika ^*
0000-0001-9069-0508
Indonesia

Toto Nusantara
0000-0003-1116-9023
Indonesia

Subanji Subanji
0000-0002-4281-1923
Türkiye

Santi Irawati
0000-0003-0516-6723
Indonesia

Early Pub Date

May 13, 2023

Publication Date

May 1, 2023

Submission Date

November 26, 2022

Acceptance Date

March 27, 2023

Published in Issue

Year 2023 Volume: 10 Number: 3

DOI

https://doi.org/10.17275/per.23.50.10.3

IZ

https://izlik.org/JA27CA28ZZ

APA

Swastika, G., Nusantara, T., Subanji, S., & Irawati, S. (2023). How Do Assimilation and Accommodation Occur in The Translation Process of Representation? Participatory Educational Research, 10(3), 167-190. https://doi.org/10.17275/per.23.50.10.3

AMA

1.Swastika G, Nusantara T, Subanji S, Irawati S. How Do Assimilation and Accommodation Occur in The Translation Process of Representation? PER. 2023;10(3):167-190. doi:10.17275/per.23.50.10.3

Chicago

Swastika, Galuh, Toto Nusantara, Subanji Subanji, and Santi Irawati. 2023. “How Do Assimilation and Accommodation Occur in The Translation Process of Representation?”. Participatory Educational Research 10 (3): 167-90. https://doi.org/10.17275/per.23.50.10.3.

EndNote

Swastika G, Nusantara T, Subanji S, Irawati S (May 1, 2023) How Do Assimilation and Accommodation Occur in The Translation Process of Representation? Participatory Educational Research 10 3 167–190.

IEEE

[1]G. Swastika, T. Nusantara, S. Subanji, and S. Irawati, “How Do Assimilation and Accommodation Occur in The Translation Process of Representation?”, PER, vol. 10, no. 3, pp. 167–190, May 2023, doi: 10.17275/per.23.50.10.3.

ISNAD

Swastika, Galuh - Nusantara, Toto - Subanji, Subanji - Irawati, Santi. “How Do Assimilation and Accommodation Occur in The Translation Process of Representation?”. Participatory Educational Research 10/3 (May 1, 2023): 167-190. https://doi.org/10.17275/per.23.50.10.3.

JAMA

1.Swastika G, Nusantara T, Subanji S, Irawati S. How Do Assimilation and Accommodation Occur in The Translation Process of Representation? PER. 2023;10:167–190.

MLA

Swastika, Galuh, et al. “How Do Assimilation and Accommodation Occur in The Translation Process of Representation?”. Participatory Educational Research, vol. 10, no. 3, May 2023, pp. 167-90, doi:10.17275/per.23.50.10.3.

Vancouver

1.Galuh Swastika, Toto Nusantara, Subanji Subanji, Santi Irawati. How Do Assimilation and Accommodation Occur in The Translation Process of Representation? PER. 2023 May 1;10(3):167-90. doi:10.17275/per.23.50.10.3