References
- Breidenbach D, Dubinsky E, Hawks J, et al. Development of the process conception of function. Educ Stud Math. 1992;23:247–285.
- Carlson M. A cross-sectional investigation of the development of the function concept. Research in collegiate mathematics education III. CBMS Issues Math Educ. 1998;7:114–163.
- Oehrtman M. Layers of abstraction: theory and design for the instruction of limit concepts. In: Carlson M, Rasmussen C, editors. Making the connection: research and teaching in undergraduate mathematics education. MAA notes. Vol. 73. Washington (DC): Mathematical Association of America; 2008; p. 65–80.
- Oehrtman M. Collapsing dimensions, physical limitation, and other student metaphors for limit concpets. J Res Math Educ. 2009;40(4):396–426.
- Orton A. Students' understanding of differentiation. Educ Stud Math. 1983;14:235–250.
- Zandieh M. A theoretical framework for analyzing student understanding of the concept of derivative. In: Dubinsky E, Schoenfeld A, Kaput J, editors. CBMS issues in mathematics education. Research in collegiate mathematics education, IV. Vol. 8. Providence (RI): American Mathematical Society; 2000. p. 103–127.
- Asiala M, Cottrill J, Dubinsky E, et al. The development of students' graphical understanding of the derivative. J Math Behav. 1997;16(4):399–431.
- Ferrini-Mundy J, Gaudard M. Secondary school calculus: preparation or pitfall in the study of college calculus? J Res Math Educ. 1992;23(1):56–71.
- Ferrini-Mundy J, Geuther-Graham K. An overview of the calculus curriculum reform effort: issues for learning, teaching, and curriculum development. Am Math Mon. 1991;98(7):627–635.
- Haciomeroglu ES, Aspinwall L, Presmeg NC. Contrasting cases of calculus students’ understanding of derivative graphs. Math Think Learn. 2010;12:152–176. DOI: 10.1080/10986060903480300.
- Yoon C, Thomas MOJ, Dreyfus T. Gestures and insight in advanced mathematical thinking. Int J Math Educ Sci Technol. 2011;42(7):891–901.
- Zandieh M, Knapp J. Exploring the role of metonymy in mathematical understanding and reasoning: the concept of derivative as an example. J Math Behav. 2006;25(1):1–17. DOI: 10.1016/j.jmathb.2005.11.002.
- Thompson PW. The development of the concept of speed and its relationship to concepts of rate. In: Harel G, Confrey J, editors. The development of multiplicative reasoning in the learning of mathematics. Albany (NY): SUNY Press; 1994. p. 179–234.
- Tall D. Functions and calculus. In: Bishop AJ, editor. International handbook of mathematics education. Vol. 4. Dordrecht: Kluwer; 1997. p. 289–325.
- Biza I. Students’ evolving meaning about tangent line with the mediation of a dynamic geometry environment and an instructional example space. Technol Knowl Learn. 2011;16(2):125–151. DOI: 10.1007/s10758-011-9180-3.
- Biza I, Christou C, Zachariades T. Student perspectives on the relationship between a curve and its tangent in the transition from Euclidean geometry to analysis. Res Math Educ. 2008;10(1):53–70. DOI: 10.1080/14794800801916457.
- Páez Murillo RE, Vivier L. Teachers’ conceptions of tangent line. J Math Behav. 2013;32(2):209–229. DOI: 10.1016/j.jmathb.2013.02.005.
- Kajander A, Lovric M. Mathematics textbooks and their potential role in supporting misconceptions. Int J Math Educ Sci Technol. 2009;40(2):173–181. DOI: 10.1080/00207390701691558.
- LaRue R, Vincent B, Sealey VL, et al., editors. Calculus students' early concept images of tangent lines. Seventeenth Annual Conference on Research in Undergraduate Mathematics Education; 2014 Feb 27–Mar 1; Denver, CO. 2014; p. 803–810.
- Vincent B, LaRue R, Sealey VL, et al. Calculus students' early concept images of tangent lines. Int J Math Educ Sci Technol. 2015;46(5):641–657. DOI: 10.1080/0020739X.2015.1005700.
- Vinner S. The role of definitions in the teaching and learning of mathematics. In: Tall D, editor. Advanced mathematical thinking. Dordrecht: Kluwer; 1991. p. 65–81.
- Vincent B. First semester calculus students’ concept definitions and concept images of the tangent line and how these relate to students’ understandings of the derivative [ dissertation]. Morgantown (WV): West Virginia University; 2016.
- Lithner J. Students' mathematical reasoning in university textbook exercises. Educ Stud Math. 2003;52:29–55.
- Lithner J. Mathematical reasoning in textbook exercises. J Math Behav. 2004;23(4):405–427.
- Silver EA, Marshall SP. Mathematical and scientific problem solving: findings, issues and instructional implications. In: Jones BF, Idol L, editors. Dimensions of thinking and cognitive instruction. Hillsdale (NJ): Erlbaum; 1989. p. 265–290.
- Hegarty M, Mayer RE, Monk CA. Comprehension of arithmetic word problems: a comparison of successful and unsuccessful problem solvers. J Educ Psychol. 1995;87(1):18–32.
- White P, Mitchelmore M. Conceptual knowledge in introductory calculus. J Res Math Educ. 1996;27(1):79–95.
- Watkins AE. The symbols and grammatical structures of mathematical English and the reading comprehension of college students. J Res Math Educ. 1979;10(3):216–218.
- Österholm M. Characterizing reading comprehension of mathematical texts. Educ Stud Math. 2006;63:325–346. DOI: 10.1007/s10649-005-9016-y.
- Osterholm M. Do students need to learn how to use their mathematics textbooks?: the case of reading comprehension. Nordisk matematikkdidaktikk. 2008;13(3):53–73.
- Shepherd MD, van de Sande C. Reading mathematics for understanding – from novice to expert. J Math Behav. 2014;35:74–86.
- Weinberg A, Wiesner E. Understanding mathematics textbooks through reader-oriented theory. Educ Stud Math. 2011;76(1):49–63. DOI: 10.1007/s10649-010-9264-3.
- Tall D, Vinner S. Concept image and concept definition in mathematics with particular reference to limits and continuity. Educ Stud Math. 1981;12(2):151–169.
- Vinner S, Dreyfus T. Images and definitions for the concept of function. J Res Math Educ. 1989;20:356–366.
- Vinner S. The pseudo-conceptual and the pseudo-analytical thought processes in mathematics learning. Res Stud Math. 1997;34:97–129.
- Anton H, Bivens I, Davis S. Calculus: early transcendentals. 10th ed. Hoboken (NJ): Wiley; 2012.
- Hughes-Hallett D, Gleason AM, McCallum WG, et al. Calculus. 5th ed. Hoboken (NJ): Wiley; 2009.
- Zill D, Wright W. Calculus: early transcendentals. 4th ed. Burlington (MA): Jones and Bartlett; 2011.
- Strauss A, Corbin J. Basics of qualitative research: techniques and procedures for developing grounded theory. 2nd ed. Thousand Oaks (CA): SAGE Publications; 1998.
- Braun V, Clarke V. Using thematic analysis in psychology. Qual Res Psychol. 2006;3(2):77–101. DOI: 10.1191/1478088706qp063oa.
- Sinclair N, Watson A, Zazkis R, et al. The structuring of personal example spaces. J Math Behav. 2011;30:291–303. DOI: 10.1016/j.jmathb.2011.04.001.