Teachers’ beliefs have been considered a significant area of study because of their perceived influence on teachers’ actions and subsequently how the learning context is shaped and organized (Nespor, 1987; Pajares, 1992; Philipp, 2007; Raymond, 1997; Thompson, 1992; Wilson & Cooney, 2002). Much of the research on beliefs in mathematics education documents the inconsistency between teachers’ beliefs and their classroom practices (e.g. Cooney, 1985; Raymond, 1997; Thompson, 1984). We would like to move beyond simply acknowledging and providing evidence of these inconsistencies by applying ‘a sensible systems’ perspective to our study of beliefs (Leatham, 2006). This framework holds as a basic assumption that “teachers are inherently sensible rather than inconsistent beings” (p. 92). Therefore, an individual’s beliefs are organized in ways that make sense to them. So it is possible that the beliefs that are most central to teachers’ decision-making on the part of the teacher are not math-related (Leatham, 2006), or there are intervening contextual factors that are of significant influence (Herbel-Eisenmann et al., 2006). We consider situations where there are perceived inconsistencies, opportunities for exploration into the nature of teachers’ beliefs and how they are held. In our work with an elementary teacher over the course of three years, we sought to explain her belief system and how our work with her served as a catalyst for reorganization of her beliefs.

Methodology

            This case study involved a first-grade teacher, Ms. Wyatt, who taught in an urban, high-needs school in the Midwest. She is African-American and had taught elementary school for over 5 years. Data sources included eight interviews, videotaped classroom observations, email communications, and researcher memos. We employed generic thematic analysis by reducing the extensive text of the interviews into core themes (LeCompte & Preissle, 1993) that reflected the teacher’s beliefs about mathematics, mathematics teaching and student learning, and thoughts about the professional development activities. The themes and findings were compiled, summarized, and reported in narrative form.
Professional Development

            The three-year PD programme had three main activities:     

Math-Science PBL. Ms. Wyatt worked on project-based units to explore mathematical ideas in authentic contexts and to gain first-hand knowledge of inquiry-based methods.

            Video Lesson Analysis. As Sherin and van Es (2009) suggested, ‘‘watching and reflecting on video… has the potential to foster teacher learning’’ (p. 20). Ms. Wyatt videotaped her classes 3-4 times per week during year 2; then we met bi-weekly to discuss selected videoclips.

            Math-content sessions. Ms. Wyatt participated in monthly workshops to expand her mathematics content knowledge.

Findings

Observed inconsistencies between beliefs and practice

In response to questions about her views on mathematics and mathematics teaching, Ms. Wyatt responded,

“… it’s about problem solving, it’s more than formulas. You need to understand why the formula makes sense and where it comes from….you know [teaching is] not just giving directions, more facilitating…making sure that they [the students] are thinking.”

Ms. Wyatt considered mathematics to be problem-solving, where students navigate their way through problem situations rather than memorizing formulas. She also believed teachers should serve as facilitators, encouraging students to think.  However, her practices did not always reflect these views. During classroom observations, students had few opportunities to problem solve and her teaching style tended to diminish the cognitive demand of the few tasks implemented that were conceptually-rich. Worksheets were also fairly commonplace; students completed them during the latter half reinforcing content covered during the first half.       

Seeking explanations for inconsistencies

Initially Ms. Wyatt’s beliefs aligned with reform-based mathematics; however, her practices were fairly traditional. Seeking resolution, we explored further. Describing her long-term professional goals, she stated,

I would just like to be fearless… you're under so many constraints like parent expectations...they look for worksheets all the time. I want to tell a parent “I'm not sitting here doing worksheets all day!”

Regarding inquiry-based teaching, she stated, “I’ve attempted it! I think it’s very hard with primary students… there just comes a point when you have to give them the information... .” The above examples show that in addition to parental expectations, there were non math-related beliefs that took precedence in certain classroom situations; for example, beliefs about the abilities of her first-grade students (young students can’t handle inquiry)

Resolving Inconsistencies and Foregrounding Desirable Beliefs

At the end of the 3-year program we observed that Ms. Wyatt’s constructivist-based beliefs had greater influence on her instructional decision-making.

In reference to the video lesson analysis, she stated 

…I am learning to learn from the students…like my lesson today, I had that experience where I had to stop, reflect and make changes, and they caught on. I probably would have never changed my thought process so it is important to reflect and think about what they are doing

Reflecting on an inquiry-based lesson, she described skills the students had developed,

At first it was really hard for me because I’m used to the old fashion way …now I’ve found that before they would just give me answers, now they know how to ask a question.

By the end of the program, Ms. Wyatt’s practices cohered with beliefs associated with student-centered pedagogy. She had expressed similar beliefs at the beginning of the program but they were not the most influential to her practices leading us to initially conclude that there were belief-practice inconsistencies. Further exploration showed that there were contextual factors and other belief clusters that were more influential to pedagogical decisions. However, engagement in a series of PD activities appeared to support reorganization of Ms. Wyatt’s belief system to foreground constructivist-based beliefs.

Significance of the Study

The process of exploring apparent inconsistencies rather than simply describing these inconsistencies supports a deeper understanding of the nature of beliefs and how they are organized, which is of great methodological and practical significance. With the insights garnered from these explorations, we can determine whether belief change is warranted or if the situation requires a ‘power-shift’ within the belief clusters so that desired math-related beliefs are foregrounded in instructional decision-making. As such, we can design PD to better support teachers in their work.