Markku S. Hannula

This paper will review theoretical approaches for research on mathematics-related affect from the 1990s until today. In order to organise this field, a metatheory of the affective domain is developed, based on distinctions along three dimensions: 1) cognitive, motivational and emotional aspects of affect; 2) rapidly changing affective states versus relatively stable affective traits; and 3) the social, psychological and physiological nature of affect. Using ideas from enactivism and other system theories, the third dimension is elaborated. The embodied perspective brings forth on the one hand the evolutionary basis of human affect, and on the other the individual developmental perspective. Classroom microculture and cross-cutting social variables (e.g., gender and ethnicity) are identified as two different ways of theorising the social dimension of mathematics-related affect.

Since 1990's there has developed a strong cluster of research around affect in mathematics in Finland. This review highlights some outcome of this work. It is argued that both theoretically and methodologically there has been a tendency to incorporate influences from several sources, which has provided a fertile ground for innovative research. Some of the empirical findings are also reviewed.

Students in a mathematics classroom are motivated to do many things, not only the ones we expect them to do. In order to understand student behaviour in classrooms we need to increase our understanding of what motivation is and how it is regulated. Two issues relevant to a critique of mainstream motivation research need consideration: (a) the importance of the unconscious in motivation and (b) focusing on motivational states and processes rather than traits. In the present paper, motivation is conceptualised as a potential to direct behaviour through the mechanisms that control emotion. As a potential, motivation cannot be directly observed. It is observable only as it manifests itself in affect and cognition, for example as beliefs, values and emotional reactions. This potential is structured through needs and goals. Based on this view of motivation and the author’s earlier studies, three aspects of motivation regulation are discussed. Primarily, goals are derived from needs: in learning situations, the psychological needs for autonomy, competence, and social belonging
are the most significant determinants of goal choices. As a second aspect, this view accepts the influence of students’ beliefs about the accessibility of different goals. As a third aspect, the influence of automatic emotional reactions for goal regulation will be discussed. The case of Frank will be used 1) to illustrate how motivation can be inferred from different
kinds of data and 2) as an example of how conflicting goals lead to non-straightforward self-regulation.

Affect has been studied from different perspectives: as subjective experience, as physiological process and as social communication. In mathematics education the main concepts that have been used are emotion, attitude, beliefs, values, and motivation. The aim of this research has been to increase the coherence of the theoretical foundation for the role of affect in mathematical thinking and learning. A special emphasis has been placed on understanding the dynamic aspects of affect: how affect influences the different learning processes and how different experiences influence the development of affect.
The theoretical background of the analyses is based on cognition, emotion, and motivation, which are seen within a framework of self-regulation. Cognition is seen to be connectionist and embodied, motivation is conceptualised as a structure of needs and goals, and emotion is seen to have three readouts: physiology, subjective experience and expressive behaviour. The approach acknowledges the importance of unconscious regulation and the existence of multiple regulative mechanisms.
The thesis is a combination of theoretical and empirical work. The empirical work is based on a qualitative longitudinal study in two classrooms.
The main results of this work are the following:
1) A conceptualisation of the metalevel of affect-cognition interaction (metacognition, emotional cognition, cognitive emotion, and metaemotion).
2) A critical reconceptualisation of the concept attitude, which is seen as an amalgam of several evaluative processes: situational emotions, automated emotions, expected outcomes, and the value of the relevant goals.
3) Identification of cognitive intimacy – a kind of shared ‘flow’ – as an important aspect of the social dimension of affect in learning.
4) Elaboration of the use of fiction writing as a method of analysis and reporting in qualitative studies.
Key words: mathematics, affect, emotion, attitude, beliefs, motivation, meta-affect, fiction writing.

This article suggests a new framework for analysing attitude and changes in attitude. After reviewing relevant findings in the field of psychology of emotions, the author will provide a new conceptualisation for attitude. Four different evaluative processes are identified as aspects of attitude: emotions aroused in the situation, emotions associated with the stimuli, expected consequences, and relating the situation to personal values. The usefulness of this analytical framework will be illustrated with an exemplary case study. An ethnographic case study of Rita, a lower secondary school student, will be analysed. The case study will describe her negative attitude towards mathematics, and then examine how negative emotions developed during problem solving situations. Within half a year her attitude towards mathematics changed dramatically to more positive.
KEYWORDS: attitude, emotion, expectation, value, change, case study.

The focus of this paper is in the building of theory; more specifically, the meta-level of emotion and cognition. Several authors have presented different, overlapping concepts that parallel metacognition, and extend the idea of meta-level of mental processes onto the affective domain. Based on a literature review, the metalevel is in this paper reconceptualised by dividing it into four domains. The four domains are 1) metacognition (cognitions about cognitions), 2) emotional cognition (cognitions about emotions), 3) cognitive emotions (emotions about cognitions), and 4) meta-emotions (emotions about emotions).

This article consists of two parts. First, a model of interacting representational systems will be presented. Model combines the cognitive and affective domains under a common framework of representations. This model will be used for describing the interplay between beliefs, scripts, values, emotions, and actions. The second part of the article will present a case study of two girls who attended the same class, but experienced this quite differently. The case will be interpreted using the created model.

Using the theoretical framework of self-regulated learning as a starting point, this article will elaborate students’ self-regulation of goals. Three aspects of goal regulation will be discussed within the context of mathematics classrooms. 1) Goals are seen as elements of a needs-goals structure, and goal choices may be derived from needs values. 2) Self-efficacy beliefs are interpreted as beliefs about accessibility of goals. Goal accessibility belief is seen as a necessary, but not sufficient condition for adoption of a new goal. 3) Automated emotional reactions are seen as a possible inertia force. Some qualitative data of a three-year longitudinal study will be presented to illustrate the presented conclusions.

This paper is an exploration into the social dimension of emotions. It is based on protocols of student problem-solving sessions and comments from student interviews that are part of a three-year longitudinal ethnographic study of one school class. Focusing on the role of emotions in social coordination of problem solving behaviour, this research extends into an area that has not received enough attention in previous research. Specifically, it provides some insight into the shared cognitive intimacy, which was occasionally experienced by students who constructed together a solution for a problem.  Shared cognitive intimacy is an example of a situation where students can simultaneously fulfil both cognitive and social needs. Another phenomenon that was observed was how some students used defensive strategies to hide their lack of competency. These defensive strategies are often counterproductive in achieving the cognitive goals but they are functional in the service of social goals

This article will combine three different approaches used by the author before. One case study will be analysed from the point of view of different aspects of attitude influencing the student’s behaviour (Hannula 2002a; 2002c), and, at the same time, from the point of view of students’ goal regulation in the situation (Hannula, 2002b; In print). With fiction writing techniques, an effort is made to make it possible for the reader to immerse into the inner worlds of the students and into the feelings they experienced (Hannula, Submitted).

Abstract. Here we report some results of a two-year study for grades 5-6 and 7-8 (dur-ing the academic years 2001–03). The study included a quantitative survey for ap-proximately 150 Finnish mathematics classes out of which 10 classes were selected to a longitudinal part of the ...

In this presentation, I will review the development of research on affect in mathematics education since the late 1990s and forecast some directions for future development. One trend in the development has been the elaboration of the theoretical foundation. I will suggest that a useful description of the affective domain can be based on distinctions in three dimensions: 1. rapidly changing affective states vs. relatively stable affective traits; 2. cognitive, motivational and emotional aspects of affect; and 3. the social, the psychological and the physiological nature of affect. Another direction of development has been to explore the structural nature of affect empirically. I will review some instruments that have been developed to measure different dimensions of beliefs, motivation and emotional traits. Moreover, I will look at some empirical results concerning how the different dimensions are related to each other, and how they develop over time.