Young learners' mathematics-related affect : A commentary on concepts, methods, and developmental trends

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.Peer reviewe

Explorations on visual attention during collaborative problem solving

In this plenary, I reflect on the MathTrack reseach project that examines the role of visual attention in the multimodal social interaction in the classroom contexts of collaborative non-routine problem solving. The project is using multiple mobile eye-tracking devices to record teacher and student visual attention when students work in groups solving a non-routine geometry problem. Project outcomes include methodological innovations for working with eye movement data, findings about joint representational attention, and the importance of eye contact in teacher-student interaction. Our experience suggests that eye movement research in classrooms should focus on analysing visual processes and making within-person analyses

Third Graders' Perceptions on Moral Behaviour on Bullying If They Had the Infinite Powers of Superhero Defenders

Bullying is a serious moral concern affecting the victim's welfare and achievement in school. Lately, research on bullying phenomenon has led to successful procedures in which passive bystanders are asked to become defenders of the victims of bullying. This case study explores children's perceptions on moral behaviour on bullying and, moreover, what type of moral voice they would express if they had the infinite powers and means of superhero defenders. Children created masks, posters, and flags for ideal superheroes and described their personalities. In addition, they drew comic strips about the skills they wish to teach new hero students in superhero school. The results indicate that children's moral voices can be divided primarily into justice and care. In addition, some expressed also the dark voice of the vigilante. Findings suggest that superheroes offer one tool for educators and children to ponder about the role of defenders for the victims of bullying. The topic focuses on the core of school life, relationships between pupils, and their moral development. Sixteen third grade children (aged 9-10) from a primary school in Finland took part in the study. The results for two of the children are presented in detail as the basis for discussion.Peer reviewe

Finnish mathematics teachers’ beliefs about their profession expressed through metaphors

The purpose of this study was to investigate Finnish mathematics teachers’ beliefs about teaching and teachers as expressed through metaphors. Because teachers’ beliefs play a significant role in their teaching, it is important to recognize those beliefs. Metaphors provide insights into beliefs that are not explicit or consciously held. In this study we investigated what kind of metaphors Finnish mathematics teachers in different schools and in different stages of their careers use. This study focused on Finnish 7-9 grade mathematics teachers’ (n=70) metaphors about teacher. The metaphors were classified into five categories: teacher as a subject specialist, teacher as a pedagogue, teacher as a didactics expert, self-referential and contextual metaphors. Teacher as a didactic expert was the most frequently used metaphor (49%). The information gained from this metaphor analysis show teachers’ beliefs about themselves. Changing teachers’ beliefs can help to change teachers’ behaviours and in such way improve teaching and learning process.Peer reviewe

Making and observing visual representations during problem solving : An eye tracking study

This paper presents a case study of following visual attention during collaborative geometry problem solving. We first analyse the emergence and spread of the incorrect idea of curved lines as the optimal shortest solution. Then, we examine the different visual representations made for solution ideas and how these are observed by the collaborating peers.Peer reviewe

TIMSS data in an African comparative perspective : Investigating the factors influencing achievement in mathematics and their psychometric properties

Relationships among motivational constructs from the 2011 Trends in International Mathematics and Science Study (TIMSS 2011) were investigated for eight-graders in all the five participating African countries, representing 38,806 (49 % girls). First, we investigated the psychometric properties (factor structure, reliabilities, method effect, and measurement invariance---country and gender) of the mathematics motivational constructs across the five educational systems. There was empirical support for the multidimensionality of the construct and the TIMSS 2011 motivational construct was largely invariant across cultures. Furthermore, a series of confirmatory factor analyses revealed that there is a need to control method effects associated with negatively worded items in the measurement model. There was support suggesting that in many cultures responses to negatively worded items are systematically different. The factor structures and reliabilities (i.e., confidence and the like mathematics scales) were affected by negatively worded items. Second, the relationships between the constructs, achievements and background variables such as parental education, gender and students' educational aspirations were investigated. We identified several significant relationships between self-belief and mathematics achievement. Differences in the latent mean achievement and the motivational construct were similar to those that have been described in the literature as "paradoxical" and "perplexing". Nations with high mathematics achievement seem to have students with more negative mathematics self-belief. Some results extend, whereas others refute the findings of previous research. For instance, the relationship between students' mathematics confidence and mathematics achievement was lower than the relationship between the value of mathematics and achievement in some countries and it was the reverse in others. However, consistent with cultural stereotypes, boys rated their mathematics competence higher than girls. The findings are discussed with reference to implications for cross-cultural research and practice.Peer reviewe

"My personal relationship towards mathematics has necessarily not changed but..." : analyzing preservice teachers' mathematical identity talk

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Students' views on mathematics in single-sex and coed classrooms in Ghana

In this study, we investigated students’ views on themselves as learners of mathematics as a function of school-by-sex (N = 2034, MAge = 18.49, SDAge = 1.25; 12th-grade; 58.2% girls). Using latent variable Structural Equation Modeling (SEM), the measurement and structural equivalence as well as the equality of latent means of scores across single-sex and coed schools were tested. Findings regarding the latent mean differences revealed that girls in single-sex schools had significantly higher mathematics self-confidence than did students’ in coed schools. Girls in coed schools had significantly lower mathematics self-concepts than did boys in single-sex, girls in single-sex and boys in coed schools. Girls in single-sex schools had significantly higher family encouragement than students’ in all other school types. Moreover, a more complex dynamics were found on the teacher quality variate. This paper argues for a deeper understanding of sex-school interaction and of possible causes of students’ views on mathematics.Peer reviewe

Home Resources as a Measure of Socio-economic Status in Ghana

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