Research Article
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Multi-representation raised by prospective teachers in expressing algebra

Year 2020, , 857 - 870, 15.06.2020
https://doi.org/10.17478/jegys.688710

Abstract

This study investigates multi-representations raised by prospective teachers in expressing algebra. Through a case study approach, as many as 112 prospective mathematics education teachers from Universitas Negeri Malang of Indonesia participated in this research. researchers use test, interview and research sheet instruments as data collection tools. Then an analysis is carried out so that the following categories are obtained: subjects that symbolically express algebra, pictorial, and geometric. The results obtained that some subjects express symbolically algebra (83 of 112 subjects), while some subjects expressed pictorially (17 of 112 subjects), and geometrically (12 of 112 subjects). The research findings show that there are three forms of representation raised by the subject in expressing algebra, namely the representation of algebraic symbols, image representations, and geometric representations. Most of the participants produced algebraic symbolic representations and some of them experienced obstacles in producing pictorial representations and geometric representations, also researcher found similar patterns in producing geometric representation namely, perception, appearance, strategy, and re-examination. Researchers recommend geometric representations for further research because they tend to be done by subjects with high mathematical abilities and rarely found research that produces geometrical representations when solving algebraic problems.

Supporting Institution

Universitas Negeri Malang and Universitas Muhammadiyah Makassar

References

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  • Beckmann, S., & Izsák, A. (2015). Two perspectives on proportional relationships: Extending complementary origins of multiplication in terms of quantities. Journal for Research in Mathematics Education, 46(1), 17–38. https://doi.org/10.5951/jresematheduc.46.1.0017
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  • Papadopoulos, I. (2019). Using mobile puzzles to exhibit certain algebraic habits of mind and demonstrate symbol-sense in primary school students. Journal of Mathematical Behavior, 53(July), 210–227. https://doi.org/10.1016/j.jmathb.2018.07.001
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  • Powell, S. R., Gilbert, J. K., & Fuchs, L. S. (2019). Variables influencing algebra performance: Understanding rational numbers is essential. Learning and Individual Differences, 74(July), 101758. https://doi.org/10.1016/j.lindif.2019.101758
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Year 2020, , 857 - 870, 15.06.2020
https://doi.org/10.17478/jegys.688710

Abstract

References

  • Addition, I. (2015). National Council of Teachers of Mathematics a proposed instructional theory for integer addition and subtraction a proposed instructional theory for integer addition and subtraction. National Council of Teachers of Mathematics, 43(4), 428–464.
  • Adu-gyamfi & Bosse. (2013). Processes and reasoning in representations of linear functions, (March). https://doi.org/10.1007/s10763-013-9416-x
  • Afriyani, D., Sa’Dijah, C., Subanji, S., & Muksar, M. (2019). Students’ construction error in translation among mathematical representations. Journal of Physics: Conference Series, 1157(3), 0–6. https://doi.org/10.1088/1742-6596/1157/3/032098
  • Amir, M. F., Mufarikhah, I. A., Wahyuni, A., Nasrun, & Rudyanto, H. E. (2019). Developing ‘Fort Defending’ Game as a Learning Design for Mathematical Literacy Integrated to Primary School Curriculum in Indonesia. Elementary Education Online, 18(3), 1081–1092.
  • Baek, J. M., Wickstrom, M. H., Tobias, J. M., Miller, A. L., Safak, E., Wessman-Enzinger, N., & Kirwan, J. V. (2017). Preservice teachers’ pictorial strategies for a multistep multiplicative fraction problem. Journal of Mathematical Behavior, 45, 1–14. https://doi.org/10.1016/j.jmathb.2016.10.005
  • Beckmann, S., & Izsák, A. (2015). Two perspectives on proportional relationships: Extending complementary origins of multiplication in terms of quantities. Journal for Research in Mathematics Education, 46(1), 17–38. https://doi.org/10.5951/jresematheduc.46.1.0017
  • Blanton, M., Stephens, A., Knuth, E., Gardiner, A. M., Isler, I., Kim, J., … Kim, J. (2015). The development of children’s algebraic thinking: The impact of a comprehensive early algebra intervention in third grade, Journal for Research in Mathematics Education, 46(1), 39–87.
  • Boonen, A. J. H., Van Wesel, F., Jolles, J., & Van der Schoot, M. (2014). The role of visual representation type, spatial ability, and reading comprehension in word problem solving: An item-level analysis in elementary school children. International Journal of Educational Research, 68, 15–26. https://doi.org/10.1016/j.ijer.2014.08.001
  • Bruce, C. D., Davis, B., Sinclair, N., McGarvey, L., Hallowell, D., Drefs, M., … Woolcott, G. (2017). Understanding gaps in research networks: using “spatial reasoning” as a window into the importance of networked educational research. Educational Studies in Mathematics, 95(2), 143–161. https://doi.org/10.1007/s10649-016-9743-2
  • Cankoy, O., & Özder, H. (2011). The influence of visual representations and context on mathematical word problem solving bağlam ve görsel anlatımların matematiksel sözel problem çözümüne etkisi (The influence of visual representations and context on mathematical word problem solving), Pamukkale University Faculty of Education Journal , 30, 91–100.
  • Chang, B. L., Cromley, J. G., & Tran, N. (2016). Coordinating multiple representations in a reform calculus textbook. International Journal of Science and Mathematics Education, 14(8), 1475–1497. https://doi.org/10.1007/s10763-015-9652-3
  • Covington, A. C., Sheppard, P., Flint, T. K., & Tackie, N. A. (2019). To what extent does hands-on exposure to algebraic thinking predict mathematics achievement for urban middle schoolers? Journal of Educational Issues, 5(1), 118. https://doi.org/10.5296/jei.v5i1.14460
  • Creswell, J. W. (2012). Educational Research: planning, conducting, and evaluating quantitative and qualitative research. Boston, United States of America: Pearson Education.
  • David, M. M., Tomaz, V. S., & Ferreira, M. C. C. (2014). How visual representations participate in algebra classes’ mathematical activity. ZDM - International Journal on Mathematics Education, 46, 95–107. https://doi.org/10.1007/s11858-013-0550-2
  • de la Fuente & Deulofeu. (2016). Translation between language representation in problem solving as a tool to construct algebraic. 13th International Congress on Mathematical Education Hamburg , 24-31 July 2016, (July), 1–4.
  • Dogan-dunlap, H. (2010). Linear algebra students ’ modes of reasoning : Geometric representations. Linear Algebra and Its Applications, 432(8), 2141–2159. https://doi.org/10.1016/j.laa.2009.08.037
  • Fujita, T., Kondo, Y., Kumakura, H., & Kunimune, S. (2017). Students’ geometric thinking with cube representations: Assessment framework and empirical evidence. Journal of Mathematical Behavior, 46, 96–111. https://doi.org/10.1016/j.jmathb.2017.03.003
  • Garnelo, M., & Shanahan, M. (2019). Reconciling deep learning with symbolic artificial intelligence: representing objects and relations. Current Opinion in Behavioral Sciences, 29, 17–23. https://doi.org/10.1016/j.cobeha.2018.12.010
  • Haciomeroglu, E. S., & LaVenia, M. (2017). Object-spatial imagery and verbal cognitive styles in high school students. Perceptual and Motor Skills, 124(3), 689–702. https://doi.org/10.1177/0031512517698555
  • Herbst, P., & Kosko, K. W. (2013). Using representations of practice to elicit mathematics teachers ’ tacit knowledge of practice : a comparison of responses to animations and videos. Journal of Mathematics Teacher Education, 17, 515–537. https://doi.org/10.1007/s10857-013-9267-y
  • Huang, R., & Kulm, G. (2012). Prospective middle grade mathematics teachers’ knowledge of algebra for teaching. Journal of Mathematical Behavior, 31(4), 417–430. https://doi.org/10.1016/j.jmathb.2012.06.001
  • Ina V.S. Mullis, Michael O. Martin, Pierre Foy, & Arora. A. (2012). Timss 2011 International Results in Mathematics. TIMSS & PIRLS International Study Center (Vol. 2012).
  • Jacobs, V. R., Franke, M. L., Carpenter, T. P., Levi, L., Jacobs, R., Franke, M. L., … Battey, D. (2015). Professional Development Focused on Children ’ s Algebraic Reasoning in Elementary School of, 38(3), 258–288.
  • Jupri, A., Drijvers, P., & van den Heuvel-Panhuizen, M. (2014). Difficulties in initial algebra learning in Indonesia. Mathematics Education Research Journal, 26(4), 683–710. https://doi.org/10.1007/s13394-013-0097-0
  • Karakok, G. (2019). Making connections among representations of eigenvector: what sort of a beast is it? ZDM - Mathematics Education, (0123456789). https://doi.org/10.1007/s11858-019-01061-9
  • Karakok, G., Stephenie, H. S., & Dyben, A. (2014). Secondary teachers ’ conception of various forms of complex numbers. Journal of Mathematics Teacher Education, 18, 327–351. https://doi.org/10.1007/s10857-014-9288-1
  • Kidron, I., & Tall, D. (2015). The roles of visualization and symbolism in the potential and actual infinity of the limit process, Educational Studies in Mathematics, 183–199. https://doi.org/10.1007/s10649-014-9567-x
  • Kospentaris, G., Vosniadou, S., Kazi, S., & Thanou, E. (2016). Visual and analytic strategies in geometry. Frontline Learning Research 4(1), 40-57. http://doi.org/10.14786/flr.v4i1.226
  • Kotsopoulos, D., Zambrzycka, J., & Makosz, S. (2017). Gender differences in toddlers’ visual-spatial skills. Mathematical Thinking and Learning, 19(3), 167–180. https://doi.org/10.1080/10986065.2017.1328634
  • Lailiyah, S., Nusantara, T., Sa’Dijah, C., Irawan, E. B., Kusaeri, & Asyhar, A. H. (2018). Structuring students’ analogical reasoning in solving algebra problem. IOP Conference Series: Materials Science and Engineering, 296(1), 1-6. https://doi.org/10.1088/1757-899X/296/1/012029
  • Leikin, R., Leikin, M., Waisman, I., & Shaul, S. (2013). Effect of the presence of external representations on accuracy and reaction time in solving mathematical double-choice problems by students of different levels of instruction. International Journal of Science and Mathematics Education, 11(5), 1049–1066. https://doi.org/10.1007/s10763-012-9389-1
  • Lepak, J. R., Wernet, J. L. W., & Ayieko, R. A. (2018). Capturing and characterizing students ’ strategic algebraic reasoning through cognitively demanding tasks with focus on representations. Journal of Mathematical Behavior, (October 2017), 0–1. https://doi.org/10.1016/j.jmathb.2018.01.003
  • Levenberg, I. (2014). Formulation of word problems in geometry by gifted pupils. Journal for the Education of the Young Scientist and Giftedness, 2(2), 28–28. https://doi.org/10.17478/jeysg.201429019
  • Llinares, S., & Clemente, F. (2014). Characteristics of pre-service primary school teachers’ configural reasoning. Mathematical Thinking and Learning, 16(3), 234–250. https://doi.org/10.1080/10986065.2014.921133
  • Lutaif, B., Gabriel, B., Lima, L. De, & Gomes, E. (2019). Linear algebra in engineering : an analysis of Latin American studies. ZDM, (0123456789). https://doi.org/10.1007/s11858-019-01081-5
  • Mamolo, A., Ruttenberg-Rozen, R., & Whiteley, W. (2015). Developing a network of and for geometric reasoning. ZDM Mathematics Education, 47, 483-496. https://doi.org/10.1007/s11858-014-0654-3
  • Máté, I. (2019). The foundation of the romany students’ algebra knowledge through text-based problems, 12(1), 191–199. https://doi.org/10.24193/adn.12.1.14.192
  • Mcgee, E. O. (2016). Robust and Fragile Mathematical Identities : A Framework for Exploring Racialized Experiences and High Achievement Among Black College Students, 46(5), 599–625. http://doi.org/10.5951/jresematheduc.46.5.0599
  • Montenegro, P., Costa, C., & Lopes, B. (2018). Transformations in the Visual Representation of a Figural Pattern Transformations in the Visual Representation of a Figural Pattern. Mathematical Thinking and Learning, 20(2), 91–107. https://doi.org/10.1080/10986065.2018.1441599
  • Natsheh, I., & Karsenty, R. (2014). Exploring the potential role of visual reasoning tasks among inexperienced solvers. ZDM - International Journal on Mathematics Education, 46(1), 109–122. https://doi.org/10.1007/s11858-013-0551-1
  • Ott, N., Brünken, R., Vogel, M., & Malone, S. (2018). Multiple symbolic representations: The combination of formula and text supports problem solving in the mathematical field of propositional logic. Learning and Instruction, 58(April), 88–105. https://doi.org/10.1016/j.learninstruc.2018.04.010
  • Papadopoulos, I. (2019). Using mobile puzzles to exhibit certain algebraic habits of mind and demonstrate symbol-sense in primary school students. Journal of Mathematical Behavior, 53(July), 210–227. https://doi.org/10.1016/j.jmathb.2018.07.001
  • Pitta-pantazi, D., & Christou, C. (2010). Spatial versus object visualisation: The case of mathematical understanding in three-dimensional arrays of cubes and nets. International Journal of Educational Research, 49(2–3), 102–114. https://doi.org/10.1016/j.ijer.2010.10.001
  • Powell, S. R., Gilbert, J. K., & Fuchs, L. S. (2019). Variables influencing algebra performance: Understanding rational numbers is essential. Learning and Individual Differences, 74(July), 101758. https://doi.org/10.1016/j.lindif.2019.101758
  • Presmeg, N. (2014). Contemplating visualization as an epistemological learning tool in mathematics, ZDM-Mathematics Education, 46, 151–157. https://doi.org/10.1007/s11858-013-0561-z
  • Sa’dijah, C., Afriyani, D., Subanji, S., & Muksar, M. (2018). Characteristics of students’ mathematical understanding in solving multiple representation task based on Solo Taxonomy. International Electronic Journal of Mathematics Education, 13(3), 281–287. https://doi.org/10.12973/iejme/3920
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There are 59 citations in total.

Details

Primary Language English
Subjects Other Fields of Education
Journal Section Teacher Education
Authors

Sirajuddin Sirajuddin 0000-0003-3275-9815

Cholis Sa'dıjah 0000-0002-0264-8578

Nengah Parta 0000-0003-4255-9323

Sukorıyanto - This is me 0000-0003-1700-6735

Publication Date June 15, 2020
Published in Issue Year 2020

Cite

APA Sirajuddin, S., Sa’dıjah, C., Parta, N., -, S. (2020). Multi-representation raised by prospective teachers in expressing algebra. Journal for the Education of Gifted Young Scientists, 8(2), 857-870. https://doi.org/10.17478/jegys.688710
AMA Sirajuddin S, Sa’dıjah C, Parta N, - S. Multi-representation raised by prospective teachers in expressing algebra. JEGYS. June 2020;8(2):857-870. doi:10.17478/jegys.688710
Chicago Sirajuddin, Sirajuddin, Cholis Sa’dıjah, Nengah Parta, and Sukorıyanto -. “Multi-Representation Raised by Prospective Teachers in Expressing Algebra”. Journal for the Education of Gifted Young Scientists 8, no. 2 (June 2020): 857-70. https://doi.org/10.17478/jegys.688710.
EndNote Sirajuddin S, Sa’dıjah C, Parta N, - S (June 1, 2020) Multi-representation raised by prospective teachers in expressing algebra. Journal for the Education of Gifted Young Scientists 8 2 857–870.
IEEE S. Sirajuddin, C. Sa’dıjah, N. Parta, and S. -, “Multi-representation raised by prospective teachers in expressing algebra”, JEGYS, vol. 8, no. 2, pp. 857–870, 2020, doi: 10.17478/jegys.688710.
ISNAD Sirajuddin, Sirajuddin et al. “Multi-Representation Raised by Prospective Teachers in Expressing Algebra”. Journal for the Education of Gifted Young Scientists 8/2 (June 2020), 857-870. https://doi.org/10.17478/jegys.688710.
JAMA Sirajuddin S, Sa’dıjah C, Parta N, - S. Multi-representation raised by prospective teachers in expressing algebra. JEGYS. 2020;8:857–870.
MLA Sirajuddin, Sirajuddin et al. “Multi-Representation Raised by Prospective Teachers in Expressing Algebra”. Journal for the Education of Gifted Young Scientists, vol. 8, no. 2, 2020, pp. 857-70, doi:10.17478/jegys.688710.
Vancouver Sirajuddin S, Sa’dıjah C, Parta N, - S. Multi-representation raised by prospective teachers in expressing algebra. JEGYS. 2020;8(2):857-70.
By introducing the concept of the "Gifted Young Scientist," JEGYS has initiated a new research trend at the intersection of science-field education and gifted education.