Exponents include some certain rules related to power and base. This situation leads to some problems in which students get confused to remember the rules of exponents. For this reason, students perceive exponents as challenging, unnecessary and complicated concepts and also they think that exponents have no connection with everyday life (Şenay, 2002; Van-de Walle, 2007). In the literature, there have been a few studies focused on students’ conceptions and misconceptions of exponents (Cengiz, 2006; Crider, 1998; Orhun, 1998; Şenay, 2002). They especially focused on what type of difficulties and misconceptions that students commonly made with exponents and its’ operations. For instance, Orhun (1998) examined 249 eighth and ninth grade students’ misconceptions about exponents and root numbers by using ten open-ended items. One of the results of the study showed that students couldn't understand the difference between (-a)² and -a². Similarly, Şenay (2002) conducted a master thesis to investigate 729 ninth grade students’ errors and misconceptions about exponents and root numbers. Researcher concluded that students both did not define exponents and root numbers and made error in calculation because of their inadequate knowledge of the properties and rules of these numbers. Different from these studies, Avcu (2010) searched eighth grade students’ understanding in comparing exponents with the use of an exponent achievement test comprised of 20 open ended items. He found that students’ answers in comparing exponents changed according to the case of being decimal number or natural number of base and power. Furthermore, Crider (1998) designed a research with introductory algebra students at university. He mentioned that students were not able to place integer exponents on number line due to the difficulty in determining the magnitude of a given exponent.

Related literature indicates that there are a few studies related exponents that were specifically focused on determination of students’ misconceptions and difficulties. On the other hand, there is no research about exponents in which participants are pre-service or in-service teachers. However, teachers’ inadequate content knowledge or pedagogical content knowledge about mathematical concepts may cause some misconceptions and difficulties in students’ mind. Many studies conducted in recent years have emphasized that teachers have not got enough proficiency to teach mathematical concepts in elementary level (Ball, 1990, Even, 1993; Ma, 1999; Tirosh, 2000; Toluk Uçar, 2009, 2011). The results of these studies showed that pre-service and in-service teachers use mathematical expressions based on memorized rules in their lessons instead of supporting conceptual knowledge. In this regard, it is important to examine pre-service teachers’ knowledge about exponent in order to contribute to literature in teacher education. As a result, the aim of this research is to investigate pre-service teachers’ knowledge about eight grade students’ possible errors in exponents.  Research question of this study is given below:

What is pre-service mathematics teachers’ knowledge about eight grade students’ possible errors in exponents?

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