[1] A. Ariza, S. Llinares, and J. Valls, Students’ understanding of the function-derivative relationship when learning economic concepts, Math. Educ. Res. J. 27 (2015), no. 4, 615–635.
[2] I. Arnon, J. Cottrill, E. Dubinsky, A. Okta,c, S.R. Fuentes, M. Trigueros, and K. Weller, APOS Theory: A Framework for Research and Curriculum Development in Mathematics Education, New York, Heidelberg, Dordrecht, London, Springer, 2014.
[3] M. Asiala, A. Brown, D.J. DeVries, E. Dubinsky, D. Mathews, and K. Thomas, A framework for research and development in undergraduate mathematics education, Res. Colleg. Math. Educ. 6 (1996), no. 2, 1–32.
[4] M. Asiala, J. Cottrill, E. Dubinsky, and K.E. Schwingendorf, The development of students’ graphical understanding of the derivative, J. Math. Behav. 16 (1997), no. 4, 399–430.
[5] M. Berger, Making mathematical meaning: from preconcepts to pseudoconcepts to concepts, Pythagoras 63 (2006), 14–21.
[6] V. Borji and R. Mart´ınez-Planell, What does ‘y is defined as an implicit function of x’ mean?: An application of APOS-ACE, J. Math. Behav. 56 (2019), 100739.
[7] D. Breidenbach, E. Dubinsky, J. Hawks, and D. Nichols, Development of the process conception of function, Educ. Stud. Math. 23 (1999), 247–285.
[8] I. Cetin, Students’ understanding of loops and nested loops in computer programming: An APOS theory perspective, Canad. J. Sci. Math. Technol. Educ. 15 (2015), 155–170.
[9] I. Cetin, Students’ understanding of limit concept: An APOS perspective, Doctoral Thesis, Middle East Technical University, Turkey, 2009.
[10] J.M. Clark, F. Cordero, J. Cottrill, B. Czarnocha, D.J. DeVries, D. St. John, T. Tolias, and D. Vidakovic, Constructing a schema: The case of the chain rule, J. Math. Behav. 16 (1999), no. 4, 345–364.
[11] E. Dubinsky and M. McDonald, APOS: A constructivist theory of learning in undergraduate mathematics education research, New ICMI Stud. Ser. 7 (2001), 275–282.
[12] A. Dominguez, P. Barniol, and G. Zavala, Test of understanding graphs in calculus: Test of students’ interpretation of calculus graphs, EURASIA J. Math. Sci. Technol. Educ. 13 (2017), no. 10, 6507-6531.
[13] T. Eisenherg, On the development of a sense for functions, The Concept of Function: Aspects of Epistemology and Pedagogy, Mathematical Association of America, Washington, 1999, pp. 153-174.
[14] J. Garcıa -Garcıa and C. Dolores-Flores, Pre-university students’ mathematical connections when sketching the graph of derivative and antiderivative functions, Math. Educ. Res. J. 33 (2019), no. 1, 1–22.
[15] V. Giraldo, L. M. Carvalho and D. Tall, Descriptions and definitions in the teaching of elementary calculus, Int. Group Psycho. Math. Educ. 2 (2003), 445–452.
[16] R. Martınez-Planell, M. Trigueros, and D. McGee, Student understanding of directional derivatives of functions of two variables, Proc. 37th Ann. Meet. North Amer. Chapter Int. Group Psycho. Math. Educ., East Lansing, MI: Michigan State University, 2015.
[17] A. Orton, Student’s understanding of differentiation, Educ. Stud. Math. 14 (1983), 235–250.
[18] D. Tall, Students’ difficulties in calculus, plenary address, Proc. ICME 7 (1993), 13–28.
[19] M. Thomas and S. Stewart, Eigenvalues and eigenvectors: Embodied, symbolic and formal thinking, Math. Educ. Res. J. 23 (2011), no. 3, 275–296.
[20] T. Uygur and A. Ozdas, Misconceptions and difficulties with the chain rule, The Mathematics Education into the 21st Century Project, University of Technology, Malaysia, 2015, pp. 209-213.
[21] H.D. Weigand, A discrete approach to the concept of derivative, ZDM Math. Educ. 46 (2014), 603–619.
[22] K. Weller, I. Arnon, and E. Dubinsky, Preservice teachers’ understanding of the relation between a fraction or integer and its decimal expansion, Canad. J. Sci., Math. Technol. Educ. 9 (2009), 5–28.
[23] K. Weller, I. Arnon, and E. Dubinsky, Preservice teachers’ understandings of the relation between a fraction or integer and its decimal expansion: Strength and stability of belief, Canad. J. Sci., Math. Technol. Educ. 11 (2011), 129–159.
[24] M. Zandieh, A theoretical framework for analyzing student understanding of the concept of derivative, CBMS Issues Math. Educ. 8 (2000), 103–127.