### EXTERNAL REPRESENTATION FLEXIBILITY OF DOMAIN AND RANGE OF FUNCTION

#### Abstract

#### Keywords

#### Full Text:

PDF#### References

Abdullah, S. A. S. (2010). Comprehending the concept of functions. Procedia-Social and Behavioral Sciences, 8, 281–287).

Almog, N., & Ilany, B. S. (2012). Absolute value inequalities: High school students’ solutions and misconceptions. Educational Studies in Mathematics, 81(3), 347–364.

Arnold, S. (2004). Investigating functions: Domains and ranges. Australian Senior Mathematics Journal, 18(1), 59–64.

Aziz, T. A., Pramudiani, P., & Purnomo, Y. W. (2017). How do college students solve logarithm questions? International Journal on Emerging Mathematics Education, 1(1), 25–40.

Bannister, V. R. P. (2014). Flexible conceptions of perspectives and representations: An examination of pre-service mathematics teachers’ knowledge. International Journal of Education in Mathematics, Science and Technology, 2(3), 223–233.

Cho, P., & Moore-Russo, D. (2014). How students come to understand the domain and range for the graphs of functions. Proceedings of the Joint Meeting of the PME 38 and PME-NA 36 (Vol. 2, pp. 281–288). Vancouver: International Group for the Psychology of Mathematics Education.

Cho, Y. D. (2013). College Students’ Understanding of the Domain and Range of Functions on Graphs. Buffalo: State University of New York at Buffalo.

Clement, L. L. (2001). What do students really know about functions? Mathematics Teacher, 94(9), 745–748.

Cuoco, A. A., & Curcio, F. R. (2001). The Roles of Representation in School Mathematics. Reston: National Council of Teachers of Mathematics.

Dorko, A., & Weber, E. (2014). Generalising calculus ideas from two dimensions to three: How multivariable calculus students think about domain and range. Research in Mathematics Education, 16(3), 269–287.

Downing, D. (2009). Dictionary of Mathematics Terms (3rd ed.). New York: Barron’s.

Drlik, D. I. (2015). Student Understanding of Function and Success in Calculus. Boise: Boise State University.

Dufour-Janvier, B., Bednarz, N., & Belanger, M. (1987). Pedagogical considerations concerning the problem of representation. Problems of Representation in the Teaching and Learning of Mathematics, 109–122.

Eisenberg, T., & Dreyfus, T. (1994). On understanding how students learn to visualize function transformations. Research in Collegiate Mathematics Education, 1, 45–68.

Elia, I., Panaoura, A., Eracleous, A., & Gagatsis, A. (2007). Relations between secondary pupils’ conceptions about functions and problem solving in different representations. International Journal of Science and Mathematics Education, 5(3), 533–556.

Elia, I., & Spyrou, P. (2006). How students conceive function: A triarchic conceptual-semiotic model of the understanding of a complex concept. The Montana Mathematics Enthusiast, 3(2), 256–272.

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.

Goldin, G., & Steingold, N. (2001). Systems of Representations and the Development of Mathematical Concepts. The Roles of Representation in School Mathematics, 1–23.

Gür, H. (2009). Trigonometry learning. New Horizons in Education, 57(1), 67–80.

Kamber, D., & Takaci, D. (2018). On problematic aspects in learning trigonometry. International Journal of Mathematical Education in Science and Technology, 49(2), 161–175.

Keating, D. P., & Crane, L. L. (1990). Domain-general and domain-specific processes in proportional reasoning: A commentary on the “Merrill-Palmer Quarterly” special issue on cognitive development. Merrill-Palmer Quarterly, 36(3), 411–424.

Martínez-Planell, R., Gaisman, M. T., & McGee, D. (2015). On students’ understanding of the differential calculus of functions of two variables. The Journal of Mathematical Behavior, 38, 57–86.

Martínez-Planell, R., & Gaisman, M. T. (2009). Students’ ideas on functions of two variables: Domain, range, and representations. Proceedings of the 31st PME-NA (Vol. 5, pp. 73–80). Vancouver: International Group for the Psychology of Mathematics Education.

Martínez-Planell, R., & Gaisman, M. T. (2012). Students’ understanding of the general notion of a function of two variables. Educational Studies in Mathematics, 81(3), 365–384.

Moschkovich, J., Schoenfeld, A. H., & Arcavi, A. (1993). Aspects of understanding: On multiple perspectives and representations of linear relations and connections among them. Integrating Research on the Graphical Representation of Functions, 69–100.

Neger, N., & Frame, M. (2005). Visualizing the domain and range of the composition of functions. Mathematics Teacher, 98(5), 306–311.

Orhun, N. (2001). Students’ mistakes and misconceptions on teaching of trigonometry. Journal of Curriculum Studies, 32(6), 797–820.

Özkan, E. M., & Ünal, H. (2009). Misconception in Calculus-I: Engineering students’ misconceptions in the process of finding domain of functions. Procedia - Social and Behavioral Sciences, 1(1), 1792–1796.

Rockswold, G. (2012). Essentials of College Algebra with Modeling and Visualization (4th ed.). Boston, MA: Pearson Education, Inc.

Sajka, M. (2003). A secondary school student’s understanding of the concept of function - A case study. Educational Studies in Mathematics, 53(3), 229–254.

Sierpinska, A. (1992). On understanding the notion of function. The Concept of Function: Aspects of Epistemology and Pedagogy, 25, 23–58.

Yilmaz, Y., Durmus, S., & Yaman, H. (2018). An investigation of pattern problems posed by middle school mathematics preservice teachers using multiple representation. International Journal of Research in Education and Science, 4(1), 148–164.

DOI: https://doi.org/10.22342/jme.10.1.5257.143-156

### Refbacks

- There are currently no refbacks.

**Journal on Mathematics Education**

Kampus FKIP Bukit Besar

Jl. Srijaya Negara, Bukit Besar

Palembang - 30139

p-ISSN: 2087-8885 | e-ISSN: 2407-0610

Journal on Mathematics Education is licensed under a Creative Commons Attribution 4.0 International License

View My Stats

**Indexed by**: