GAMTE 2015 Officers,GAMTE 2015 Conference Committee, GAMTE 2015 Proceeding Committee, Purposes and Goals of GAMTE, Letter from the President, Table of Contents

College students often ask questions such as, “Why do I have to take this class? Is there a point to it?” For Early Childhood Education (ECE) majors these questions may often take on a slightly different form, wondering, “How can I incorporate this information into my classroom?” or “Do I understand this well enough to teach this to my students?” It is especially important for pre- service teachers to feel confident working with the mathematical content that they are learning and for them to believe that they can successfully teach that same information to a group of students. Swackhamer, Koellner, Basile, and Kimbrough (2009) have called for additional research concerning “how content knowledge can support teacher efficacy along with increasing the knowledge of students” (page 75). The number of mathematics content courses provided to support the development of early childhood education majors understanding of mathematics varies across universities. Some wonder whether it is necessary to have a series of four mathematics content courses or if a fewer number of courses would suffice. This study is intended to determine if there is a significant difference in how pre-service teachers think about teaching mathematics at each stage of a progression of four-course content courses, as well as to determine if there seems to be a ceiling effect when students no longer feel these courses are continuing to improve their content knowledge and subsequent teaching ability. Cohen and Hill (2001) describe teacher beliefs as, “Teachers’ ideas about mathematics teaching and learning” and note that these beliefs may shape their teaching. One aspect of a teacher’s beliefs includes her sense of self-efficacy. Researchers have recognized teacher’s sense of self-efficacy as an important attribute of effective teaching which is related to positive teacher and student outcomes (Tschannen-Moran, Woolfolk Hoy, & Hoy; 1998). In this study we explore the effects of a series of four mathematics content courses on pre-service teachers’ beliefs about teaching mathematics and their own self efficacy beliefs. These classes were designed to improve understanding and self-efficacy in a subject that many students have the most difficulty with. Our study provides a snapshot of students from each of the four content courses in the series by exploring their beliefs about teaching mathematics and their own self-efficacy and beliefs they hold at the end of each course.

Many teachers have trouble transitioning their students between natural recursive thinking about the data and algebraic notation for representing linear functions (Zazkis & Liljedahl, 2002).

The availability and familiarity of online discussion tools create new instructional options that teacher educators can use to foster prospective teachers’ understanding of mathematics. In particular, online discussion blogs provide an avenue through which teacher educators can press prospective teachers to explore mathematical concepts and share their mathematical reasoning with peers. Furthermore, by incorporating visual stimulations as a design component of these discussion blogs, prospective teachers can make sense of and respond to others’ ideas about mathematical concepts with greater clarity. This paper shares preliminary findings of a research study that examined the extent to which the design of a series of visually-aided online discussion prompts facilitated prospective elementary teachers’ (PSTs) use of mathematical reasoning in a geometry and measurement course. Results suggest that (a) the wording of discussion prompts influences the nature of mathematical justifications that PSTs focus on in their responses and (b) social norms for communicating in online forums may influence the ways in which PSTs interact with peers in an online discussion blog about their mathematical reasoning.