An Exploration of the Effects of a Practicum-Based Mathematics Methods Course on the Beliefs of Elementary Preservice Teachers

Effects of a practicum-based elementary mathematics methods course on the beliefs of preservice teachers regarding conceptual knowledge in school mathematics were explored using a pre-post design. The intensity of those beliefs was assessed before and after the methods course using the IMAP Web-Based Beliefs Survey, an instrument constructed by the “Integrating Mathematics and Pedagogy” (IMAP) research group at San Diego State University. The IMAP Beliefs Survey assesses belief intensity by asking respondents to react to and analyze written and video cases (Ambrose, Clement, Philipp, & Chauvot, 2004; Philipp, Ambrose, Clement, Sowder, Schappelle, Sowder, Chauvot, & Thanheiser, 2005). Its use with preservice teachers enrolled in mathematics content courses for elementary education majors has been previously reported (Ambrose et al., 2004). In the current study, significant pre-post effects regarding belief changes were obtained in the desired direction, thus suggesting the appropriateness of conducting a future, more extensive experimental investigation of the effects of a practicum-based methods course on teacher beliefs. Practicum-Based Methods Course Effects 3 An Exploration of the Effects of a Practicum-Based Mathematics Methods Course on the Beliefs of Elementary Preservice Teachers Introduction Mathematics teacher educators in the United States face critical challenges related to the preparation of future teachers of mathematics. Data from the 2003 Trends in International Mathematics and Science Study (National Center for Education Statistics, n.d.) reveal that, despite some recent gains, American students continue to lag behind many of their international counterparts in mathematics competency at both the fourth and eighth grade levels. Ma, in Knowing and Teaching Elementary Mathematics (1999), suggested one possible reason for the plethora of troubling data regarding student achievement in mathematics. She described “the vicious circle formed by low-quality mathematics education and low-quality teacher knowledge of school mathematics” (p. 149). In other words, teachers of mathematics, especially those who teach at the elementary level, generally do not possess the knowledge necessary to help empower future generations of adults mathematically. Therefore, without some sort of ongoing, widespread, and powerfully effective intervention, U.S. students appear destined to continued mediocrity in mathematics performance. Ma (1999) further postulated that teacher preparation might be the force needed to break the above-mentioned “vicious circle” (p. 149). This emphasis on the role of preservice teacher preparation is in some ways rather ironic. Preservice teacher preparation is viewed as a vehicle for improving inservice teacher performance. However, overwhelming evidence from multiple disciplines, including mathematics education, indicates that preservice preparation is significantly enhanced by strong and consistent preservice/inservice teacher partnerships (e.g., Kagan, 1992; Richardson, 1996). In other words, to break the vicious circle that characterizes Practicum-Based Methods Course Effects 4 inservice teacher performance, those same inservice teachers need to provide laboratories for preservice teachers to explore, investigate, and make sense of conceptual mathematics methodology. Promoting teacher change is complicated at best. Investigators have emphasized the role of beliefs as an important consideration in encouraging change (e.g., Civil, 1993; Vacc & Bright, 1999). In a review of research regarding teachers’ beliefs, Pajares (1992) suggested that teacher change research be conducted from a perspective that focuses on “the things and ways that teachers believe” because “beliefs are the best indicators of the decisions individuals make throughout their lives” (p. 307). Hersh (1986) stated that “one’s conception of what mathematics is affects one’s conception of how it should be presented” (p. 13). Fullan (2001) emphasized the central role of beliefs in bringing about educational change: “Changes in beliefs and understanding . are the foundation [for] achieving lasting reform” (p. 45). Changing beliefs is generally considered to be challenging in teacher education settings; there is much empirical evidence to support the long-standing assumption that teachers’ belief systems tend to be deeply entrenched (Pajares, 1992). Changes in beliefs “challenge the core values held by individuals regarding the purposes of education; moreover, beliefs are often not explicit, discussed, or understood, but rather are buried at the level of unstated assumptions” (Fullan, 2001, p. 44). According to Mewborn (2002), teacher beliefs about mathematics teaching and learning may be embedded within “wider beliefs about education, human relationships, and a person’s role in society” (p. 27). Teachers’ prior experiences as students may be particularly influential. Unlike most students choosing to major in other disciplines, potential teachers enter their chosen field with many years of experience as learners in the context in which they will work. Their experience as Practicum-Based Methods Course Effects 5 students in mathematics classrooms influences their perceptions of what mathematics is, what it means to “do” mathematics, and the role school mathematics plays in society. Thus, the nature of their beliefs regarding how mathematics should be taught may be deeply influenced as well. The difficulty of changing beliefs is further illustrated by the findings of Steinberg, Empson, and Carpenter (2004), who noted that even when teachers embrace new beliefs, they may not necessarily sustain that change or continue to change. Ernest’s (1989) landmark study demonstrated that the following beliefs commonly possessed by preservice teachers have powerful effects on the decisions they make while teaching mathematics: 1. Mathematics is a set of rules to be learned rather than a body of interrelated and connected concepts. 2. Teaching mathematics consists of telling students how to follow procedures rather than supporting students as they attempt to understand. 3. Learning mathematics is a process of practicing and memorizing rather than a process of reasoning and sensemaking. These beliefs, which are widely held even today, still shape mathematics education in many classrooms (Fuson, Kalchman, & Bransford, 2005). Pajares (1992) suggested that teachers are unlikely to change their beliefs unless they find them to be unsatisfactory when challenged. In his review of research on professional growth among preservice and beginning teachers, Kagan (1992) concluded that extensive interaction with school-age students enables preservice teachers to confront their own beliefs and acknowledge the need for change. Wilcox, Schram, Lappan, and Lanier (1991) also reached similar conclusions as they implemented a content and methods course sequence, with Practicum-Based Methods Course Effects 6 accompanying field experiences, designed to help prospective teachers change their knowledge and beliefs about mathematics and mathematics education. This line of reasoning leads to the implications of Ma’s conclusion stated previously. That is, preservice teachers are unlikely to make significant changes in their classroom practice relative to the teaching of mathematics unless they are challenged to confront their own beliefs within the context of extensive field practicum experiences. Philipp, Thanheiser, and Clement (2002), along with other investigators of the NSFfunded Integrating Mathematics and Pedagogy (IMAP) Project at San Diego State University, promoted significant improvements in preservice teachers’ beliefs regarding conceptual mathematics teaching. Their approach paired participation in a math-for-elementary-teachers content course with field practicum experiences in a public school setting. They assessed the intensity of those beliefs using the IMAP Web-Based Beliefs Survey. (This instrument is described in greater detail in the following section.) We wondered if a similar approach might also promote belief changes in elementary mathematics methods students as measured by the same instrument. Therefore, we designed this study to explore the effects of a three-credit-hour methods course with a practicum-based component upon the beliefs of preservice elementary education majors regarding conceptual approaches to teaching mathematics. The results should help us determine the viability of conducting future research in which we plan to use an experimental model to investigate more thoroughly possible causal relationships between methods-related field practica and belief changes. Practicum-Based Methods Course Effects 7 The Study We used a simple pre-post design to conduct our exploratory study. We considered using a Likert-type instrument because such instruments have been commonly used to measure teachers’ beliefs, but Hoffman and Kugle (1982) suggested that results gained from the use of such instruments may not reveal actual beliefs. In essence, such scales may assess a teachers’ ability to “talk the talk” but not necessarily “walk the walk” in terms of applying conceptual teaching approaches as a result of changing beliefs. More recently, researchers have used a variety of means to ascertain preservice teachers’ beliefs, including interviews, classroom observations, journals, written reflections, and surveys. Most of this research has been qualitative in nature and typically has involved small samples. Although the sample size for this particular study was not large, we plan to conduct other investigations regarding changing beliefs with larger samples, so our first challenge was to obtain an instrument capable of providing quantitative data on a sizeable scale. The aforementioned IMAP research group developed an online survey instrument that requires respondents to interpret descriptions of classroom situations or actual videotaped cases. The