Research Article
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The relationship between multiple representations and thinking structures: example of the integral concept

Year 2022, Volume 10, Issue 4, 563 - 571, 30.12.2022
https://doi.org/10.17478/jegys.1213997

Abstract

In this study, the effect of teaching the concept of integral with multiple representations on the concept definitions of teacher candidates was examined. And also, the effect of teacher candidates ‘ thinking structures on their use of multiple representations was investigated. In this study, algebraic, graphical and numerical representations were used together in teaching the concept of integral at university level. Since the course content was designed by supporting multiple representations, a quasi-experimental research-experimental research design was used in the research. In this study, quasi-experimental research experimental research design was used because the course content was designed by supporting multiple representations. In this study, the study group consisted of secondary school mathematics teacher candidates. Within the scope of the research, Mathematical Process and Integral Concept Test were used. These scales were analyzed by quantitative and qualitative methods. Regardless of the thinking structures of the pre-service teachers, it has been determined that concept definitions include different representations depending on the teaching style supported by multiple representations in the course. It has been observed that the thinking structures of the pre-service teachers affect their representation preferences slightly, if not too much, while defining the concept. However, it has been determined that there are no sharp boundaries in the types of representation used by participants with different thinking structures. Even though the pre-service teachers had different thinking structures, they used multiple representations in their concept recognition. It can be concluded that this situation has a connection with the use of multiple representations in the lesson in addition to the thinking structures of the participants. It can be concluded that this situation has a connection with the use of multiple representations in the lesson in addition to the thinking structures of the participants. According to this result, the use of more than one representation in teaching a concept enables students to learn the concept in a versatile way. For this reason, it can be said that the use of multiple representations in teaching the concept of integral provides a higher level and deeper learning. This situation can be generalized to other concepts as well.

References

  • Aspinwall. L., & Shaw, K. L. (2002). Representations in Calculus: Two contrasting cases. The Mathematics Teacher, 95(6), 434-439.
  • Barnett, R. A., Ziegler, M. R., Sobecki, D., & Byleen, K. E. (2008). Precalculus: Graphs and models. McGraw-Hill Higher Education.
  • Budak, S., & Roy, G. (2013). A case study investigating the effects of technology on visual and nonvisual thinking preferences in mathematics. Technology, Instruction, Cognition & Learning, 9(3). 217-236.
  • Clements, M. A. (1982). Careless errors made by sixth-grade children on written mathematical tasks. Journal for Research in Mathematics Education, 13(2), 136-144.
  • Cobb, P., Yackel, E., & Wood, T. (1992). A constructivist alternative to the representational view of mind in mathematics education. Journal for Research in Mathematics Education, 23(1), 2–33.
  • Cuoco, A., & Curcio, F. (2001). The roles of representation in school mathematics: 2001 NCTM yearbook. Reston: NCTM.
  • Edwards, C. H., & Penney, D. E. (1994). Multivariable calculus with analytic geometry. Prentice Hall.
  • Girard, N. R. (2002). Students' representational approaches to solving calculus problems: Examining the role of graphing calculators. Unpublished EdD, Pittsburg: University of Pittsburg.
  • Goldin, G. A. (2004). Problem solving heuristics, affect, and discrete mathematics. ZDM, 36(2), 56-60.
  • Hacıomeroglu, E. S., Chicken, E., & Dixon, J. K. (2013). Relationships between gender, cognitive ability, preference, and calculus performance. Mathematical Thinking and Learning, 15(3), 175-189,
  • Hallet, D. H. (1991). Visualization and calculus reform. In Visualization in teaching and learning mathematics , 121-126.
  • Keller, B. A., & Hirsch, C. R. (1998). Student preferences for representations of functions. International Journal of Mathematical Education in Science and Technology, 29(1), 1-17.
  • Kendal, M., & Stacey, K. (2003). Tracing learning of three representations with the differentiation competency framework. Mathematics Education Research Journal, 15(1), 22-41.
  • Krutetskii, V. A. (1976). The psychology of mathematical abilities in schoolchildren. University Of Chicago Press.
  • Lesh, R., Post, T. R., & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. In Problems of representations in the teaching and learning of mathematics, 33-40.
  • Ostebee, A., & Zorn, P. (1997). Pro choice. The American Mathematical Monthly, 104(8), 728-730.
  • Presmeg, N. C. (1986). Visualization in high school mathematics. For the Learning of Mathematics, 6(3), 42-46.
  • Rasslan, S. ve Tall, D. (2002). Definitions and images for the definite integral concept. Proceedings of the 26th Conference of the International Group for the Psychology of Mathematics Education, (July 21-26), Vol. 4, 89-96, Norwich: England.
  • Thompson, P. W., & Silverman, J. (2008). The concept of accumulation in calculus. Making The Connection: Research And Teaching In Undergraduate Mathematics, 73, 43-52.

Year 2022, Volume 10, Issue 4, 563 - 571, 30.12.2022
https://doi.org/10.17478/jegys.1213997

Abstract

References

  • Aspinwall. L., & Shaw, K. L. (2002). Representations in Calculus: Two contrasting cases. The Mathematics Teacher, 95(6), 434-439.
  • Barnett, R. A., Ziegler, M. R., Sobecki, D., & Byleen, K. E. (2008). Precalculus: Graphs and models. McGraw-Hill Higher Education.
  • Budak, S., & Roy, G. (2013). A case study investigating the effects of technology on visual and nonvisual thinking preferences in mathematics. Technology, Instruction, Cognition & Learning, 9(3). 217-236.
  • Clements, M. A. (1982). Careless errors made by sixth-grade children on written mathematical tasks. Journal for Research in Mathematics Education, 13(2), 136-144.
  • Cobb, P., Yackel, E., & Wood, T. (1992). A constructivist alternative to the representational view of mind in mathematics education. Journal for Research in Mathematics Education, 23(1), 2–33.
  • Cuoco, A., & Curcio, F. (2001). The roles of representation in school mathematics: 2001 NCTM yearbook. Reston: NCTM.
  • Edwards, C. H., & Penney, D. E. (1994). Multivariable calculus with analytic geometry. Prentice Hall.
  • Girard, N. R. (2002). Students' representational approaches to solving calculus problems: Examining the role of graphing calculators. Unpublished EdD, Pittsburg: University of Pittsburg.
  • Goldin, G. A. (2004). Problem solving heuristics, affect, and discrete mathematics. ZDM, 36(2), 56-60.
  • Hacıomeroglu, E. S., Chicken, E., & Dixon, J. K. (2013). Relationships between gender, cognitive ability, preference, and calculus performance. Mathematical Thinking and Learning, 15(3), 175-189,
  • Hallet, D. H. (1991). Visualization and calculus reform. In Visualization in teaching and learning mathematics , 121-126.
  • Keller, B. A., & Hirsch, C. R. (1998). Student preferences for representations of functions. International Journal of Mathematical Education in Science and Technology, 29(1), 1-17.
  • Kendal, M., & Stacey, K. (2003). Tracing learning of three representations with the differentiation competency framework. Mathematics Education Research Journal, 15(1), 22-41.
  • Krutetskii, V. A. (1976). The psychology of mathematical abilities in schoolchildren. University Of Chicago Press.
  • Lesh, R., Post, T. R., & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. In Problems of representations in the teaching and learning of mathematics, 33-40.
  • Ostebee, A., & Zorn, P. (1997). Pro choice. The American Mathematical Monthly, 104(8), 728-730.
  • Presmeg, N. C. (1986). Visualization in high school mathematics. For the Learning of Mathematics, 6(3), 42-46.
  • Rasslan, S. ve Tall, D. (2002). Definitions and images for the definite integral concept. Proceedings of the 26th Conference of the International Group for the Psychology of Mathematics Education, (July 21-26), Vol. 4, 89-96, Norwich: England.
  • Thompson, P. W., & Silverman, J. (2008). The concept of accumulation in calculus. Making The Connection: Research And Teaching In Undergraduate Mathematics, 73, 43-52.

Details

Primary Language English
Subjects Education and Educational Research
Journal Section Thinking Skills
Authors

Bahar DİNÇER> (Primary Author)
İZMİR DEMOKRASİ ÜNİVERSİTESİ
0000-0003-4767-7791
Türkiye

Publication Date December 30, 2022
Published in Issue Year 2022, Volume 10, Issue 4

Cite

Bibtex @research article { jegys1213997, journal = {Journal for the Education of Gifted Young Scientists}, eissn = {2149-360X}, address = {editorjegys@gmail.com}, publisher = {Genç Bilge Yayıncılık}, year = {2022}, volume = {10}, number = {4}, pages = {563 - 571}, doi = {10.17478/jegys.1213997}, title = {The relationship between multiple representations and thinking structures: example of the integral concept}, key = {cite}, author = {Dinçer, Bahar} }
APA Dinçer, B. (2022). The relationship between multiple representations and thinking structures: example of the integral concept . Journal for the Education of Gifted Young Scientists , 10 (4) , 563-571 . DOI: 10.17478/jegys.1213997
MLA Dinçer, B. "The relationship between multiple representations and thinking structures: example of the integral concept" . Journal for the Education of Gifted Young Scientists 10 (2022 ): 563-571 <https://dergipark.org.tr/en/pub/jegys/issue/73113/1213997>
Chicago Dinçer, B. "The relationship between multiple representations and thinking structures: example of the integral concept". Journal for the Education of Gifted Young Scientists 10 (2022 ): 563-571
RIS TY - JOUR T1 - The relationship between multiple representations and thinking structures: example of the integral concept AU - BaharDinçer Y1 - 2022 PY - 2022 N1 - doi: 10.17478/jegys.1213997 DO - 10.17478/jegys.1213997 T2 - Journal for the Education of Gifted Young Scientists JF - Journal JO - JOR SP - 563 EP - 571 VL - 10 IS - 4 SN - -2149-360X M3 - doi: 10.17478/jegys.1213997 UR - https://doi.org/10.17478/jegys.1213997 Y2 - 2022 ER -
EndNote %0 Journal for the Education of Gifted Young Scientists The relationship between multiple representations and thinking structures: example of the integral concept %A Bahar Dinçer %T The relationship between multiple representations and thinking structures: example of the integral concept %D 2022 %J Journal for the Education of Gifted Young Scientists %P -2149-360X %V 10 %N 4 %R doi: 10.17478/jegys.1213997 %U 10.17478/jegys.1213997
ISNAD Dinçer, Bahar . "The relationship between multiple representations and thinking structures: example of the integral concept". Journal for the Education of Gifted Young Scientists 10 / 4 (December 2022): 563-571 . https://doi.org/10.17478/jegys.1213997
AMA Dinçer B. The relationship between multiple representations and thinking structures: example of the integral concept. JEGYS. 2022; 10(4): 563-571.
Vancouver Dinçer B. The relationship between multiple representations and thinking structures: example of the integral concept. Journal for the Education of Gifted Young Scientists. 2022; 10(4): 563-571.
IEEE B. Dinçer , "The relationship between multiple representations and thinking structures: example of the integral concept", Journal for the Education of Gifted Young Scientists, vol. 10, no. 4, pp. 563-571, Dec. 2022, doi:10.17478/jegys.1213997

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