Authors retain the copyright without restrictions for their published content in this journal. HSSR is a SHERPA ROMEO Green Journal.
Publishing License
This is an open-access article distributed under the terms of
ALTERATION REPRESENTATION IN THE PROCESS OF TRANSLATION GRAPHIC TO GRAPHIC
Corresponding Author(s) : Galuh Tyasing Swastika
Humanities & Social Sciences Reviews,
Vol. 8 No. 1 (2020): January
Abstract
Purpose of the study: This research aims to analyze the alteration representation in the process of translation graphic to graphic where students were asked to solve derivative and integral graphics problems.
Methodology: This research used a pseudo-experimental study with Pretest-posttest nonequivalent Group Design. This research was conducted on 24 mathematics education students. Students were asked to solve derivative and integral graphics problems. Some samples of students were interviewed to determine the translation process.
Main Findings: The results of the study showed that the subject used two different methods to carry out the translation process. Thus, all students perform the process of translating the graphic representation into graphs with two different methods, namely the interval and the symbolic.
Applications of this study: The implications of this study indicated that the translation process can help students solve problems, especially problems with graphs and algebra, also revealed activity in the translation process different from that of other researchers before.
Novelty/Originality of this study: Researchers express a new activity to the translation by calling the conversion Intermediary In the stages of Preliminary Coordination (PC) and Objective Construction (CT), S1 and S2 show different forms.
Keywords
Download Citation
Endnote/Zotero/Mendeley (RIS)BibTeX
- Abrahamson, D. (2006). Mathematical representations as conceptual composites: Implications for design. The Twenty-Eighth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, 2, 464–466.
- Aduâ€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. https://doi.org/10.1111/j.1949-8594.2011.00129.x DOI: https://doi.org/10.1111/j.1949-8594.2011.00129.x
- 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 DOI: https://doi.org/10.1016/j.sbspro.2015.07.197
- Bossé, M. J., Adu-Gyamfi, K., & Cheetham, M. (2011). Translations Among Mathematical Representations: Teacher Beliefs and Practices. International Journal for Mathematics Teaching & Learning, (June), 1–23.
- Bossé, Michael J, Adu-Gyamfi, K., & Chandler, K. (2014). Students ’ Differentiated Translation Processes. International Journal for Mathematics Teaching and Learning, (828), 1–28.
- Bruner, J. S. (1966). Toward a theory of instruction (Vol. 59). Harvard University Press.
- Cangelosi, R., Madrid, S., Cooper, S., Olson, J., & Hartter, B. (2013). The negative sign and exponential expressions: Unveiling students’ persistent errors and misconceptions. Journal of Mathematical Behavior, 32(1), 69–82. https://doi.org/10.1016/j.jmathb.2012.10.002 DOI: https://doi.org/10.1016/j.jmathb.2012.10.002
- ÇELİK, D., & SAĞLAM-ARSLAN, A. (2012). The Analysis of Teacher Candidates’ Translating Skills in Multiple Representations. Elementary Education Online, 11(1), 239–250.
- Clark, J. M., & Paivio, A. (1991). Dual Coding Theory and Education. Educational Psychology Review, 3(3), 149–210. https://doi.org/10.1007/BF01320076 DOI: https://doi.org/10.1007/BF01320076
- Dubinsky, E., & McDonald, M. (2001). APOS: a constructivist theory of learning. (pp. 275–282). : In In D. Holton (Ed.), The teaching and learning of mathematics at university level: An ICMI study (pp. 275–282). Dordrecht, The Netherlands: Kluwer Academic Publishers.
- Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, Vol. 61, pp. 103–131. https://doi.org/10.1007/s10649-006-0400-z DOI: https://doi.org/10.1007/s10649-006-0400-z
- Flanders, S. T. (2015). Investigating flexibility, reversibility, and multiple representations in a calculus environment. (Doctoral dissertation, University of Pittsburgh).
- Gagatsis, A., & Shiakalli, M. (2004). Ability to translate from one representation of the concept of function to another and mathematical problem-solving. Educational Psychology, 24(5), 645–657. https://doi.org/10.1080/0144341042000262953 DOI: https://doi.org/10.1080/0144341042000262953
- Goldin, G. A. (2002). Representation in mathematical learning and problem-solving. In In L. D. English (Ed.), Handbook of international research in mathematics education (pp. 197–218). Mahwah, NJ: Lawrence Erlbaum Associates, Publishers.
- Goldin, G., & Shteingold, N. (2001). Systems of Representations and the Development of Mathematical Concepts. In The Roles of Representation in School Mathematics (pp. 1–23).
- Hjalmarson, M. (2007). Mathematical Representations. https://doi.org/10.1007/978-94-007-4978-8_103 DOI: https://doi.org/10.1007/978-94-007-4978-8_103
- Hong, Y. Y., & Thomas, M. O. J. (2015). Graphical construction of a local perspective on differentiation and integration. Mathematics Education Research Journal, 27(2), 183–200. https://doi.org/10.1007/s13394-014-0135-6 DOI: https://doi.org/10.1007/s13394-014-0135-6
- İpek, A. S., & Okumuş, S. (2012). İlköğretim matematik öğretmen adaylarının matematiksel problem çözmede kullandıkları temsiller. Gaziantep University Journal of Social Sciences, 11(3), 681-700.
- Janvier, C. (1987). Problems of Representation in the Teaching and Learning of Mathematics. London: Lawrence Erlbaum Associates Publishers.
- Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. https://doi.org/10.17226/9822 DOI: https://doi.org/10.17226/9822
- 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.
- Marzano, R. J. (2004). Building background knowledge for academic achievement: Research on what works in schools. Alexandria, VA: Association for Supervision and Curriculum Development.
- Marzano, R. J., Pickering, D. J., & Pollock, J. E. (2001). Classroom instruction that works: Research-based strategies for increasing student achievement. Alexandria, VA: Association for Supervision and Curriculum Development.
- NCTM. (2000). Principles and Standards for School Mathematics. Reston: VA: NCTM.
- Pape, S., & Tchoshanow, M. (2001). The role of representation (s) in developing mathematical understanding. Theory into Practice, 40(2), 118–127. https://doi.org/10.1207/s15430421tip4002_6 DOI: https://doi.org/10.1207/s15430421tip4002_6
- Rahmawati, D., Purwanto, P., Subanji, S., Hidayanto, E., & Anwar, R. B. (2017). Process of mathematical representation translation from verbal into graphic. International Electronic Journal of Mathematics Education, 12(4), 367–381.
- Ramful, A. (2009). REVERSIBLE REASONING IN MULTIPLICATIVE SITUATIONS: CONCEPTUAL ANALYSIS, AFFORDANCES AND CONSTRA1NTS. Dissertation of University of Georgia.
- Ramful, A. (2014). The Journal of Mathematical Behavior Reversible reasoning in fractional situations : Theorems-in-action and constraints. Journal of Mathematical Behavior, 33, 119–130. https://doi.org/10.1016/j.jmathb.2013.11.002 DOI: https://doi.org/10.1016/j.jmathb.2013.11.002
- Tall, D. (1992). Students ’ Difficulties in Calculus. Proceedings of Working Group 3 on Students’ Difficulties in Calculus, ICME-7, (August 1992), 13–28. Quebec, Canada.
- Tripathi, P. N. (2013). Developing Mathematical Understanding through Multiple Representations. In Mathematics Teaching in the Middle School (Vol. 13, pp. 438–445). National Council of Teachers of Mathematics. DOI: https://doi.org/10.5951/MTMS.13.8.0438
- Van de Walle, J. A. (2007). Elementary and Middle School Mathematics: Teaching Developmentally, 6th edition (6th ed.). Boston: Pearson Education, Inc.
References
Abrahamson, D. (2006). Mathematical representations as conceptual composites: Implications for design. The Twenty-Eighth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, 2, 464–466.
Aduâ€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. https://doi.org/10.1111/j.1949-8594.2011.00129.x DOI: https://doi.org/10.1111/j.1949-8594.2011.00129.x
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 DOI: https://doi.org/10.1016/j.sbspro.2015.07.197
Bossé, M. J., Adu-Gyamfi, K., & Cheetham, M. (2011). Translations Among Mathematical Representations: Teacher Beliefs and Practices. International Journal for Mathematics Teaching & Learning, (June), 1–23.
Bossé, Michael J, Adu-Gyamfi, K., & Chandler, K. (2014). Students ’ Differentiated Translation Processes. International Journal for Mathematics Teaching and Learning, (828), 1–28.
Bruner, J. S. (1966). Toward a theory of instruction (Vol. 59). Harvard University Press.
Cangelosi, R., Madrid, S., Cooper, S., Olson, J., & Hartter, B. (2013). The negative sign and exponential expressions: Unveiling students’ persistent errors and misconceptions. Journal of Mathematical Behavior, 32(1), 69–82. https://doi.org/10.1016/j.jmathb.2012.10.002 DOI: https://doi.org/10.1016/j.jmathb.2012.10.002
ÇELİK, D., & SAĞLAM-ARSLAN, A. (2012). The Analysis of Teacher Candidates’ Translating Skills in Multiple Representations. Elementary Education Online, 11(1), 239–250.
Clark, J. M., & Paivio, A. (1991). Dual Coding Theory and Education. Educational Psychology Review, 3(3), 149–210. https://doi.org/10.1007/BF01320076 DOI: https://doi.org/10.1007/BF01320076
Dubinsky, E., & McDonald, M. (2001). APOS: a constructivist theory of learning. (pp. 275–282). : In In D. Holton (Ed.), The teaching and learning of mathematics at university level: An ICMI study (pp. 275–282). Dordrecht, The Netherlands: Kluwer Academic Publishers.
Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, Vol. 61, pp. 103–131. https://doi.org/10.1007/s10649-006-0400-z DOI: https://doi.org/10.1007/s10649-006-0400-z
Flanders, S. T. (2015). Investigating flexibility, reversibility, and multiple representations in a calculus environment. (Doctoral dissertation, University of Pittsburgh).
Gagatsis, A., & Shiakalli, M. (2004). Ability to translate from one representation of the concept of function to another and mathematical problem-solving. Educational Psychology, 24(5), 645–657. https://doi.org/10.1080/0144341042000262953 DOI: https://doi.org/10.1080/0144341042000262953
Goldin, G. A. (2002). Representation in mathematical learning and problem-solving. In In L. D. English (Ed.), Handbook of international research in mathematics education (pp. 197–218). Mahwah, NJ: Lawrence Erlbaum Associates, Publishers.
Goldin, G., & Shteingold, N. (2001). Systems of Representations and the Development of Mathematical Concepts. In The Roles of Representation in School Mathematics (pp. 1–23).
Hjalmarson, M. (2007). Mathematical Representations. https://doi.org/10.1007/978-94-007-4978-8_103 DOI: https://doi.org/10.1007/978-94-007-4978-8_103
Hong, Y. Y., & Thomas, M. O. J. (2015). Graphical construction of a local perspective on differentiation and integration. Mathematics Education Research Journal, 27(2), 183–200. https://doi.org/10.1007/s13394-014-0135-6 DOI: https://doi.org/10.1007/s13394-014-0135-6
İpek, A. S., & Okumuş, S. (2012). İlköğretim matematik öğretmen adaylarının matematiksel problem çözmede kullandıkları temsiller. Gaziantep University Journal of Social Sciences, 11(3), 681-700.
Janvier, C. (1987). Problems of Representation in the Teaching and Learning of Mathematics. London: Lawrence Erlbaum Associates Publishers.
Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. https://doi.org/10.17226/9822 DOI: https://doi.org/10.17226/9822
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.
Marzano, R. J. (2004). Building background knowledge for academic achievement: Research on what works in schools. Alexandria, VA: Association for Supervision and Curriculum Development.
Marzano, R. J., Pickering, D. J., & Pollock, J. E. (2001). Classroom instruction that works: Research-based strategies for increasing student achievement. Alexandria, VA: Association for Supervision and Curriculum Development.
NCTM. (2000). Principles and Standards for School Mathematics. Reston: VA: NCTM.
Pape, S., & Tchoshanow, M. (2001). The role of representation (s) in developing mathematical understanding. Theory into Practice, 40(2), 118–127. https://doi.org/10.1207/s15430421tip4002_6 DOI: https://doi.org/10.1207/s15430421tip4002_6
Rahmawati, D., Purwanto, P., Subanji, S., Hidayanto, E., & Anwar, R. B. (2017). Process of mathematical representation translation from verbal into graphic. International Electronic Journal of Mathematics Education, 12(4), 367–381.
Ramful, A. (2009). REVERSIBLE REASONING IN MULTIPLICATIVE SITUATIONS: CONCEPTUAL ANALYSIS, AFFORDANCES AND CONSTRA1NTS. Dissertation of University of Georgia.
Ramful, A. (2014). The Journal of Mathematical Behavior Reversible reasoning in fractional situations : Theorems-in-action and constraints. Journal of Mathematical Behavior, 33, 119–130. https://doi.org/10.1016/j.jmathb.2013.11.002 DOI: https://doi.org/10.1016/j.jmathb.2013.11.002
Tall, D. (1992). Students ’ Difficulties in Calculus. Proceedings of Working Group 3 on Students’ Difficulties in Calculus, ICME-7, (August 1992), 13–28. Quebec, Canada.
Tripathi, P. N. (2013). Developing Mathematical Understanding through Multiple Representations. In Mathematics Teaching in the Middle School (Vol. 13, pp. 438–445). National Council of Teachers of Mathematics. DOI: https://doi.org/10.5951/MTMS.13.8.0438
Van de Walle, J. A. (2007). Elementary and Middle School Mathematics: Teaching Developmentally, 6th edition (6th ed.). Boston: Pearson Education, Inc.