Modern scientific view has been shaped from calculus concepts, mainly derivative which is the core of calculus. Derivative  lies at the foundation of the scientific world view (Bressoud, 1992). Providing a basis for the modern sciences, derivative constitutes an important factor for the development of many branches of science. Without regard to specific details, derivative can be thought of as how much one quantity is changing in reaction to changes in some other quantity. The concept has various definitions like; the limit of the difference quotient, the slope of the tangent line, instantaneous rate of change, or velocity (Boyer, 1949).

There is considerable variation in the applications of derivative not only in academic life but also in real life. Rate of change in position and velocity are some examples of the real life applications. The derivative is an important concept in the branches of both mathematics and physics. Mastery in derivative is profitable for the students all along their lives.

Studies dealing with the achievement of derivative in both high school and university levels exist in the literature. These studies make it clear that derivative is a relatively abstract and difficult concept (e.g. Kieran, 1992; Orton, 1983). Students' low achievements in derivative have been proved to be a universal case by the previous research studies (Dunham & Osborne, 1991; Ferrini-Mundy & Graham, 1994; Orton, 1983; Selden, Mason, & Selden, 1989; Viholainen, 2006). Students who take calculus course, even in the university level have difficulties to cope with this connections (Parameswaran, 2007).

On the other hand, students have difficulties to connect the multiple definitions (Ferrini-Mundy & Graham, 1994) and multiple representations (Dunham & Osborne, 1991) of the derivative. Research studies conducted about the use of multiple representations indicated that students have considerable difficulties in connecting different representations effectively and generally have mastery in only one representation (Habre & Abboud, 2006; Morgan, 1990; Ferrini-Mundy & Lauten, 1994). Because of the above mentioned considerable factors, the teaching of derivative is very important in the high school and university.

For teaching any subject, teachers need more than content knowledge. The idea of pedagogical content knowledge (PCK)  was inserted by Schulman (1986) and brougt much interest with fruitful applications in teacher education. In its most general terms, pedagogical content knowledge is the knowledge in the intersection of content and pedagogical knowledge (Shulman, 1986). There have been many applications of PCK in many branches (e.g., Ball, Thames &Phelps, 2008; Van Driel, Verloop, & de Vos, 1998). Moreover, the positive effects of teachers with PCK on student achievement were determined by the literature (e.g., Hill, Rowan, Ball, 2005; Lange, Kleickmann, & Möller, 2012). In mathematics there are studies of PCK in elementary level (Hill, Ball & Schilling, 2008; Hill, Rowan, Ball, 2005). However there can be fund no measure of teachers’ PCK of derivative to conduct studies in higher mathematics. This study aims to develop the measure of teachers’ PCK of derivative.

The Research questions:

1. How can items for a PCK-test be developed on the basis of literature to measure teachers’ PCK of derivative?
2. Are these PCK-items reliable and valid for assessing teachers’ PCK of derivative?

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