Academic journal article The Mathematics Enthusiast

Cognition and Affect in Mathematics Problem Solving with Prospective Teachers

Academic journal article The Mathematics Enthusiast

Cognition and Affect in Mathematics Problem Solving with Prospective Teachers

Article excerpt

Abstract: Recent studies relating the affective domain with the teaching and learning of mathematics, and more specifically with mathematics problem solving, have focused on teacher education. The authors of these studies have been ever more insistently pointing to the need to design educational programs that take an integrated cognitive and affective approach to mathematics education. Given this context, we have designed and implemented a program of intervention on mathematics problem solving for prospective primary teachers. We here describe some results of that program.

Keywords: Mathematics Teaching, Problem Solving, and the Affective Domain

Problem solving (PS) has always been regarded as a focal point of mathematics, and in the last 30 years its presence in curricula has increased notably (Castro, 2008; Santos, 2007). It is regarded as the methodological backbone to approach mathematics content since it both requires and helps develop skills in analysis, comprehension, reasoning, and application. At the same time, it is now being proposed as an item of curricular content in its own right as a core competence that students need to acquire. Castro (2008) and Santos (2008) recognize that attempts to teach students general PS strategies have been unsuccessful. Also, it seems important to emphasize the lack of attention in textbooks to learning heuristic problem solving strategies (Schoenfeld, 2007; Pino & Blanco, 2008).

The results of the Programme for International students Assessment (PISA) of 2003, 2006, and 2009 have highlighted the importance of mathematics problem solving (MPS) in compulsory education. One of the aspects tacitly accepted in the curricula at this educational level is the influence of affect on the teaching and learning of mathematics in general, and of MPS in particular. Already in the 1980s, Charles & Lester (1982) were observing that: "Theproblem solver must have sufficient motivation and lack of stress and/or anxiety to allow progress towards a solution" (p. 10). In their work, they recognized that factors involving cognition, experience, and affect influence the MPS process. Among the affective factors that they explicitly noted were interest, motivation, pressure, anxiety, stress, perseverance, and resistance to premature closure. It is currently accepted that the cognitive processes involved in PS are susceptible to the influence of the affective domain in its three fundamental areas: beliefs, attitudes, and emotions (Sriraman, 2003).

Initial Primary Teacher Education, the Affective Domain (Beliefs, Attitudes, and Emotions), and Problem Solving

Research on the affective domain has also expanded to the field of initial teacher education and the professional development of in-service teachers. It is considered that, in their actions in the classroom, teachers cannot dissociate affect from content when faced with a specific activity for pupils at a specific level.

Influence of beliefs

" When prospective primary teachers enter an Initial Education Centre they bring with them the educational baggage of many years in school. They thus naturally have conceptions and beliefs concerning Mathematics and the teaching/learning of Mathematics that derive from their own learning experience" (Blanco, 2004, p.40). Furthermore: "Few apparent changes in their beliefs were affected as a result of traditional mathematics method courses" (Chapman, 2000, p. 188).

It is important to distinguish the beliefs of prospective primary teachers (PPTs) about mathematics as an object - about its teaching and learning, beliefs which depend on affect - and their beliefs about themselves as learners - beliefs related to their selfconcept, self-confidence, expectations of control, etc.

Beliefs about mathematics and problem solving

According to Llinares and Sánchez (1996), prospective teachers acquire a technical school culture that conditions their approach to mathematics tasks and learning as future teachers. …

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