Prescriptions Guiding Prospective Teachers in Teaching Mathematics

Abstract

(ProQuest: ... denotes formulae omitted.)Relevant LiteratureProspective teachers go through teacher training programs and take many courses that partially or mostly address teacher knowledge categories (as detailed later in the article) at different universities in the world. Thus, they gain experience in contentspecific and generic knowledge types and in pedagogical reasoning that will shape their future teaching. prospective teachers bring to those courses or to their programs is as important as what they are taught in those courses (Ball, 1988; Goulding, Rowland, & Barber, 2002) and the experiences they gain from their programs. they bring to courses is crucial because of the two following reasons: (1) They are likely to operate from that knowledge in their future classrooms, which may not be parallel to the type of teaching that is expected of them when they graduate from those programs and enter the teaching practice. (2) This factor is also important to inform the field about the needs of teachers and teacher education programs. Such information may help us to revise and enhance teacher education programs and the teaching of those future teachers.As Ball (1988, p. 46) mentioned,How can teacher educators productively challenge, change, and extend what teacher education students bring? Knowing more about what teachers bring and what they learn from different components of and approaches to professional preparation is one more critical piece to the puzzle of improving the impact of mathematics teacher education on what goes on in elementary mathematics classrooms.Related information on this matter can be obtained through analyses of teachers' knowledge levels as they go through the programs using certain measurement instruments (e.g., Hill, Schilling, & Ball, 2004; Toluk Ucar, 2011; Turnuklu, 2005) or through analyses of teachers' actual teaching approach (e.g., Rowland, Turner, Thwaites, & Huckstep, 2009; Haciomeroglu, 2012). Our study falls into the latter category because we also believe that an investigation of teacher knowledge as they teach is informative in identifying teachers'needs and the nature of teaching knowledge. Such information can be obtained through investigations of in-service or prospective teachers. The current study strictly focuses on actual teaching of prospective teachers and deliberates the methods/ways of teaching, which we call prescriptions that guide these teachers' mathematics teaching. We pursued the following research question: teaching methods (prescriptions) guide prospective middle school mathematics teachers in their teaching of mathematics? The relevant literature that oriented us in pursuing this question and the rationale for the study is detailed below.The relevant literature suggests that mathematics teachers draw on various resources in teaching mathematics. One of these resources is mathematics teacher knowledge (Ball & Forzani, 2009), which has a special feature specific to mathematics teaching (Ball, Thames, & Phelps, 2008). Identification of the core of (mathematics) teacher knowledge is pursued extensively in mathematics education literature (e.g., Hill et al., 2004; Rowland, Huckstep, & Thwaites, 2005; Shulman, 1986). Revealing how and in what ways teacher knowledge guides, limits, or shapes teachers' teaching approach is as important as understanding the nature of teacher knowledge. An articulation of the factors that affect the teaching of mathematics teachers may inform decisions as to what should be focused on in teacher education programs and policy development. The current study aims to contribute to such knowledge base through investigating prospective teachers' teaching.Our search in the relevant literature also reveals the following questions that many researchers have struggled with for the last few decades: What kind of knowledge do teachers need to teach effectively? is the nature of the knowledge that is specific to teaching? …