Defining the “belief” construct

Extensive academic debates attempting to define a precise universal conceptual definition on the belief construct has yet to be established within the research literature. Possibly as a result of researchers assuming that readers already know what beliefs are (Thompson, 1992) or the flexibility of the belief construct is accommodating to many (Goldin, Rosken & Torner, 2009). Alternatively, Leder & Forgasz (2002) contend that it is not easy to produce a precise definition because the belief concept is not directly observable and is inferred. However, Fives & Buehl (2012) argue that the difficulty lies not in the definition since several authors have provided so but instead encouraging researchers to consistently define and use such terms within and across interrelated fields. Nevertheless, a mosaic of overlapping constructs populated within a densely and uncertain world of interchangeable conceptualisations exist. Though Wilson & Cooney (2002) advise that it is more germane to be acquainted with the influence of teacher beliefs rather than seeking harmony on a definition. McLeod & McLeod (2002, p. 120) propose “there is no single definition of the term “belief” that is correct and true, but several types of definitions that are illuminative in different situations”. For example, Pajares (1992) expresses the view that beliefs include:

attitudes, values, judgments, opinions, ideology, perceptions, conceptions, conceptual systems, preconceptions, dispositions, implicit theories, explicit theories, personal theories, internal mental processes, action strategies, rules of practice, practical principles, perspectives, repertoires of understanding, and social strategy (p. 309).

According to Hermans, van Braak & Van Keer (2008, p. 128), beliefs are “a set of conceptual representations which store general knowledge of objects, people and events, and their characteristic relationships”. Cross (2015, p. 175) maintains that beliefs are “embodied conscious and unconscious ideas and thoughts about oneself, the world, and one’s position in it developed through membership in various social groups, which are considered by the individual to be true”. Tillema (1994) avows that beliefs serve as filters which screen new information and ultimately determine which elements are accepted and integrated in their knowledge base. Similarly, Clark & Peterson (1986) advocate beliefs act as a monitor which practitioners make their decisions rather than just relying on their pedagogical knowledge or curriculum guidelines. What is notable about this definition is that is recognises that teachers’ beliefs can influence classroom practice irrespective of the written curriculum. In contrast, Perry, Wong & Howard (2006) warn that beliefs are rooted and constrained by the culture of the society and educational systems in which the teachers are living and working.

Unsurprisingly, with so many different perspectives, Mason (2004, p. 347) calls for the research community “to work out what beliefs actually are, and where they fit into an entire alphabet of associated terms”. Skott (2013, p. 548) notes that belief research is notorious for its conceptual and methodological problems and laments that the “notion of beliefs, however, is still somewhat underspecified, and the discussion continues on how to distinguish it from knowledge, conceptions, emotions, and values”. For instance, in their study of American primary teachers’ pedagogical content beliefs, Peterson et al. (1989) describe practitioners as individuals who rely on their knowledge and beliefs to understand and interpret the rapid flow of events in a classroom, make decisions and act on their interpretations. Peterson et al. (1989) employ the term ‘knowledge’ which relates to ‘pedagogical content knowledge’ as illustrated by Shulman (1986) but appear to attempt to coalesce knowledge and beliefs into a common construct. While some support remains for this conception (e.g. Pajares, 1992; Calderhead, 1996) other researchers have at least attempted to distinguish between beliefs and other suppositions such as knowledge, affect, values, emotions, etc. (e.g. Nespor, 1987; Kagan, 1992; Thompson, 1992; Calderhead, 1996; Richardson, 1996; Handel, 2003; Philipp, 2007).

Beliefs have been extensively portrayed from a mathematical perspective. Goldin, Rosken & Torner (2009) argue that beliefs are fundamental to the discussion of problem solving

approaches in mathematics education and are necessary components in the psychology of how mathematical problems are solved. Schoenfeld (1992, p. 358) interprets beliefs “as an individual’s understandings and feelings that shape the ways that the individual conceptualizes and engages in mathematical behavior”. It is important to consider that the nature of the classroom environment that the teacher creates can shape learners beliefs about the nature of mathematics (Schoenfeld, 1992). Likewise, Lester, Garofalo & Kroll (1989, p. 77) articulate that “beliefs constitute the individuals subjective knowledge about self, mathematics, problem solving, and the topics dealt with in problem statements”. In the same vein, Hersh (1986, p. 13) invites us to examine our mathematical pedagogy and alludes to the critical nature of a philosophy of mathematics when he questions: “The issue, then, is not, what is the best way to teach? But, what is mathematics really all about?”.

In sum up, Skott (2015) in his analysis of the conceptualisation of teachers’ beliefs concluded that there appears to be four key aspects. First, beliefs are used to describe individual mental constructs that are subjectively true for the person in question. Second, there are cognitive as well as affective aspects to beliefs. Third, beliefs are considered stable and may stem from schooling, life experiences, teacher education programmes and collaborations with colleagues. They tend to be resistant to change. Fourth, beliefs are expected to significantly influence classroom practice.