A Comparison of Pedagogical Practices and Beliefs in International and Domestic Mathematics Teaching Assistants

Since the late 1800s, mathematics teaching assistants (MTAs) have significantly influenced undergraduate education because of a wide variety of their roles in universities and their potential effect on education (McGivney-Burelle, DeFranco, Vinsonhaler, & Santucci, 2001; Speer, Gutmann, & Murphy, 2005). Because of spending a number of times interacting with students through grading students' assignments and exams, providing tutoring services and office hours, and teaching classes (Hendrix, 1995; Speer, Gutmann & Murphy, 2005), MTAs' pedagogical practices directly influence their students' perspective on mathematics and achievement in mathematics education (Commander, Hart, & Singer, 2000; Speer, Gutmann, & Murphy, 2005). In the last two decades, the number of international mathematics teaching assistants (IMTAs) has been increased in mathematics departments in the U.S. because of the globalization of research institutions. Through the increased number of IMTAs, students in research universities have more opportunities to be taught by IMTAs than to be taught by domestic mathematics teaching assistants (DMTAs) (Twale, Shannon, & Moore, 1997). Because of MTAs' vital roles in mathematics departments, mathematics departments have provided and developed training programs such as short- or long-term orientations in order to improve their pedagogical practices and knowledge. Despite of these supports, the majority of MTAs have taught classes based on their personal knowledge derived from their mathematics learning experiences as students because of their first priority goal, studying their fields, and their resistance to new methods of teaching (Chae, Lim, & Fisher, 2009; Baiocco & De Waters, 1998; McGivney-Burelle, DeFranco, Vinsonhaler, & Santucci, 2001).Even though researchers indicate that a wide range of factors influence teachers' practices, in particular, Speer (2005) and Thompson (1992) assert that there are significant relationships between teachers' beliefs and their teaching practices. In addition, educational experiences and philosophies influence the formation of MTAs' beliefs and teaching practices (McGivney-Burelle, DeFranco, Vinsonhaler, & Santucci, 2001; Twale, Shannon, and Moore, 1997). Researchers have been interested in MTAs regarding MTAs' knowledge and beliefs, difficulties, aspects of their experience, curriculum development for MTAs; however, a limited number of studies have conducted MTAs' teaching practices. There is little literature that provides IMTAs' pedagogical knowledge, different practices, and beliefs in detail. In addition, there are few studies about comparisons between IMTAs and DMTAs among pedagogical knowledge, practices, experiences, and challenges. From this case study as a qualitative research project, faculty in mathematics departments has opportunities to understand different IMTAs' and DMTAs' pedagogical practices regarding their beliefs. Mathematics departments and developer of training programs are able to have insight into the appropriate support for IMTAs and DMTAs. The purposes of this study are to explore different beliefs and pedagogical practices between international and domestic MTAs and sought to answer the following two research questions: "What are the differences in beliefs and pedagogical practices between international and domestic MTAs?" and "How are MTAs' different teaching practices shaped by their beliefs?"Literature ReviewDefinitions and Categorizations of BeliefsEven if researchers have studied definitions of beliefs for several decades, the definitions have been vague. Several researchers have been interested in beliefs because factors of making teachers' instructional decisions were not enough to explain the nature of teachers' instruction without teachers' beliefs. Because of raising concerns of beliefs, several researchers in mathematics education defined beliefs as personal philosophical conceptions, ideologies, worldviews and values that shape practice and orient knowledge (Aguirre & Speer, 1999; Ernest, 1989; Speer, 2005). …