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This article is a commentary for the special issue on affect and mathematics in young children, written from the perspective of research on affect in mathematics education. The studies in this special issue focus on the individual learners' affective traits and use primarily surveys as the method. The most common type of affect is emotions, but some studies do examine student beliefs and motivation. The analysis of concept definitions and operationalizations identified some inconsistencies between the different articles, especially with how they operationalize anxiety either as sadness, worry, or fear. The results of the studies provide evidence that young learners' affect can be reliably measured and that there is a correlation between affect and achievement. This correlation is weaker than for older students and longitudinal data suggests that the causal direction is more likely from achievement to affect.

In this article we consider how elementary education students' views of mathematics changed during their mathematics methods course. We focus on four female students: two started the course with mainly positive views of mathematics and a task orientation, two with negative views of the subject and an ego-defensive orientation. The biggest change observed was that the trainees' views of teaching and learning mathematics became more positive. Moreover, what had been an ego-defensive orientation changed towards a social-dependence orientation. The crucial facilitators of change seemed to be (1) handling of and reflection on one's experiences of learning and teaching mathematics, (2) exploring content with concrete materials, and (3) collaboration with a partner or working as a tutor of mathematics.

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.

As a unifying feature of this Special Issue, we have asked proponents of each framework to analyse an empirical classroom account of one student's process of solving a mathematical problem. Here, for the case study of "Frank", we give the main data that were available to all authors.