Inés Mª Gómez-Chacón

Meta-emotion and Mathematical Modeling Processes in Computerized Environments

Integrating technology into teaching mathematics is a complex issue whose inter-related components must be addressed holistically. The research on the interaction between affect and cognition proposed in this chapter focuses on a number of understudied areas in problem-solving: visualization, affect, meta-emotion and the identification of students’ affective pathways. The two studies described revealed the existence of several emotional phenomena associated with technology-assisted learning: (a) an initially positive attitude toward computer-aided mathematics learning and a preference for visual reasoning; (b) instrumental genesis associated with social and contextual dimensions of emotion and cognition; and (c) the effect of meta-emotion on task performance and the development of visual processes.

Mathematics Attitudes in Computerized Environments

In the last few decades, research on technology-assisted teaching and learning has identified a variety of factors that are involved in the effective integration of such methods. Focusing on one such factor, attitudes, this paper reports on research on attitudes and technology in the context of secondary school mathematics (15- and 16-year-old students). The results reveal significant aspects of attitudes toward mathematics and technology as well as of certain underlying cognitive-emotional processes (inductive attitude, accuracy and rigour, perseverance, critical thinking) that may be useful for teachers integrating software such as GeoGebra into their class curriculum.

Hidden Connections and Double Meanings: A Mathematical Viewpoint of Affective and Cognitive Interactions in Learning

This paper poses methodological questions concerning the evaluation of emotion in the process of mathematical learning where the interaction between emotion and cognition occurs. These methodological aspects are considered not only from the perspective of educational psychology but from that of mathematics education. Some epistemological and ontological aspects, which are considered central to the cognition-affect interplay, are noted. Special attention is given to the notion of cognitive-affective structure as a dynamic system. The interplay between cognition and affect in mathematics is viewed through the concepts of local and global affect and using a mathematical working space model. A model of this interplay is illustrated with research examples, enabling us to move from descriptions of cognition-affect at an individual level to the explanation of the tendency of a group. The non-linear modelling of emotion is reflected in the affect-cognition local structure.

Appraising Emotion in Mathematical Knowledge: Reflections on Methodology

Abstract In the affect research, a need has recently been identified for a more accurate description of the interplay among the cultural, social, and personal realms. This chapter deals with ways to combine the various methodologies used in empirical research on affect to obtain a fuller understanding of the interaction between cognitive and emotional/motivational variables. Theoretical and methodological issues are also discussed and an account is given of specific research, in which the methodology deployed included qualitative microethnographic techniques and case studies. Significant relationships between cognition and emotion at different levels and in the local and global structures of affect are described in the context of learning mathematics. The importance of social and cultural identity is reviewed as a vehicle for understanding the effect of the emotional dimension on mathematical knowledge.