Mathematics-Related Beliefs and Affect

Abstract

Influential approaches to the definition and operationalization of beliefs and other affective dimensions are described in this chapter. Snapshots of research findings are presented, commonly used measures are listed, and some technologically enhanced approaches to the measurement of beliefs and affect are discussed. Contributions, both theoretical and practical, to research on the affective domain by those concerned with gender issues are also referenced. Keywords Affect • Beliefs • Gender • Mathematics • Measuring affect 2.1 About Beliefs, Affect, and Mathematics-Introduction 2.1.1 Setting the Context Why, it could be asked, are both beliefs and affect in the title of this contribution? The inclusion of both terms warrants a special comment. In his influential and frequently cited article Pajares (1992) argued convincingly that, within the field of educational psychology, defining beliefs is at best a game of player's choice. They travel in disguise and often under alias-attitudes, values, judgments, axioms, 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, repertories of understanding, and social strategy, to name but a few that can be found in the literature. (p. 309) Mason (2004) similarly argued that it is often difficult to work out what beliefs actually cover and illustrated this by producing "an entire alphabet of associated interlinked terms":

Relationship between pre-service mathematics teachers’ knowledge, beliefs and instructional practices in China

“…Teachers' beliefs have been one of the most broadly investigated topics in the field of mathematics teacher education. However, so far, no agreed definition of beliefs has been developed (Leder 2019). One common trend is to define teacher beliefs as "psychologically held understandings, premises, or propositions about the world that are thought to be true" (Philipp 2007, p. 259).…”

Cultural values and prospective teachers’ beliefs about success in mathematics and in its teaching

“…There is a wide consensus in educational research that it is almost impossible to define teachers' beliefs consistently (e.g., Fives & Buehl, 2012;Leder, 2019;Schoen & LaVenia, 2019). However, it is possible to provide a specific understanding of teachers' beliefs, and apply this understanding to the body of research on teachers' beliefs (Fives & Buehl, 2012;Hannula, 2012).…”

Middle school students’ beliefs about mathematics as a discipline

“…However, the concept of beliefs is ambiguous. Its definition as well as its relation to other cognitive and affective aspects of mathematics learning and teaching are the subjects of currently ongoing discussions (e.g., Furinghetti & Pehkonen, 2002;Leder, 2022;Pajares, 1992), and various frameworks exist and emerge (e.g., Hannula, 2012;Op't Eynde et al, 2002). Empirical research on students' mathematics-related beliefs is for a large part addressed through descriptive studies, seeking to identify their character and content (e.g., Grootenboer & Marshman, 2016;Rolka & Halverscheid, 2011).…”

“…Generally, the literature points to the ambiguous use of the concept of beliefs (e.g., Furinghetti & Pehkonen, 2002;Goldin et al, 2009;Leder, 2022;Rolka & Roesken-Winter, 2015). This diversity in the understanding and application of the concept can be quite consequential in relation to the research in the field and how research results are received (Di Martino & Zan, 2011).…”

“…So how, then, does one proceed in the investigation and measuring of students' beliefs in a manner that is as reliable as possible? Turning to the literature, Leder (2019) finds that self-report measures (e.g., questionnaires) are widely used, which makes the consideration mentioned above highly relevant. Thompson (1992) states that research on beliefs employs qualitative methods such as interviews, classroom observations, linguistic analysis and responses to stimulation materials-often in combination, as in this study.…”