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We present the analysis of an episode of mathematical problem solving in a group, where data came from multiple advanced recorders, including multiple video cameras, Smartpen recorders, and mobile eye tracking glasses. Analysis focused on a particular group that was ineffective in their problem-solving process. Relying on the commognitive theory of learning on the one hand, and on quantitative descriptors of eye-tracking data on the other hand, we ask how do the interpretations of the discourse analysis and gaze data complement each other in understanding the obstacles to problem-solving in this episode. The setting included four Finnish 9th grade students solving a geometrical problem in the students' authentic mathematics classroom. The commognitive analysis revealed intensive social communication (subjectifying) along with the mathematical one (mathematizing), which seemed to interfere with the problem-solving process. Specifically, it masked the differences in students' interpretation of the tasks, and did not allow explication of meta-rules according to which students endorsed mathematical claims. Diagrams of quantified gaze data enabled a more macro-level picture of the full 15 min interaction, revealing differential loci of attention of the group members and thus triangulating the micro-analysis.

Mobile eye-tracking research has provided evidence both on teachers' visual attention in relation to their intentions and on teachers' student-centred gaze patterns. However, the importance of a teacher's eye-movements when giving instructions is unexplored. In this study we used mobile eye-tracking to investigate six teachers' gaze patterns when they are giving task instructions for a geometry problem in four different phases of a mathematical problem-solving lesson. We analysed the teachers' eye-tracking data, their verbal data, and classroom video recordings. Our paper brings forth a novel interpretative lens for teacher's pedagogical intentions communicated by gaze during teacher-led moments such as when introducing new tasks, reorganizing the social structures of students for collaboration, and lesson wrap-ups. A change in the students' task changes teachers' gaze patterns, which may indicate a change in teacher's pedagogical intention. We found that teachers gazed at students throughout the lesson, whereas teachers' focus was at task-related targets during collaborative instruction-giving more than during the introductory and reflective task instructions. Hence, we suggest two previously not detected gaze types: contextualizing gaze for task readiness and collaborative gaze for task focus to contribute to the present discussion on teacher gaze.

This article explores five educators' conceptions of the characteristics of mathematically gifted students and a social learning environment that supports their development in a school for mathematically gifted adolescents in Finland. We conducted this qualitative study through semi-structured interviews and participant observations in a Finnish upper secondary school with a special mathematics program. The research shows that gifted students and their educators form a tight community, the social learning environment of which supports shared motivation, healthy perfectionism, and practicing social skills. The results deepen the understanding of gifted education in the Finnish context and the significance of educators' shared understanding of social activities as a basis for successful gifted education.

Teacher's gaze communicates consciously and unconsciously her pedagogical priorities to the students. By creating and responding to eye contact initiatives, people can communicate both status and affection. This research explores the frequency of teacher-student eye contacts and their connection to teachers' scaffolding intentions. The data consisted of mobile gaze tracking recordings of two teachers and stationary classroom videos during three collaborative mathematical problem-solving lessons. The quantitative analysis showed that most of the teacher gazes on student faces did not lead to dyadic eye contacts and those gazes that did, occurred often during affective and cognitive scaffolding. These results offer us novel and important insight in the nonverbal part of scaffolding interaction.

This study focuses on a comparison of personal meanings that students from Finland (FIN) and Germany (GER) assign to (learning) mathematics. Participants are 256 Finnish and 276 German ninth graders. The survey consists of 18 scales that are based on the theory of personal meaning. The original German version was translated into Finnish. Using item response theory (IRT) partial credit models, the psychometric properties of the scales were found to be good. As statistical procedure, Differential Item Functioning (DIF) analysis and mean comparisons were conducted to compare the two groups' (FIN and GER) responses. Indicators of educational system and curriculum could be found in students' responses to explain similarities and differences between the two samples. In both countries, social inclusion is meaningful for most of the students ("Support by teacher," "Experience of relatedness," and "Emotional-affective relation to teacher"). In addition, it is personally meaningful for Finnish students to do well in mathematics. This shows a link to identity-related questions such as confirming important aspects of the self. Hence, personal meanings related to mathematics are more common in Finland than in Germany ("Active practice of mathematics," "Cognitive challenge," and "Self-perfection").

In this reflective methodological paper we focus on affordances and challenges of video data. We compare and analyze two research settings that use the latest video technology to capture classroom interactions in mathematics education, namely, The Social Unit of Learning (SUL) project of the University of Melbourne and the MathTrack project of the University of Helsinki. While using these two settings as examples, we have structured our reflections around themes pertinent to video research in general, namely, research methods, data management, and research ethics. SUL and MathTrack share an understanding of mathematics learning as social multimodal practice, and provide possibilities for zooming into the situational micro interactions that construct collaborative problem-solving learning. Both settings provide rich data for in-depth analyses of peer interactions and learning processes. The settings share special needs for technical support and data management, as well as attention to ethical aspects from the perspective of the participants' security and discretion. SUL data are especially suitable for investigating interactions on a broad scope, addressing how multiple interactional processes intertwine. MathTrack, on the other hand, enables exploration of participants' visual attention in detail and its role in learning. Both settings could provide tools for teachers' professional development by showing them aspects of classroom interactions that would otherwise remain hidden.

Given the recent development of mobile gaze-tracking devices it has become possible to view and interpret what the student sees and unravel the associated problem-solving processes further. It has also become possible to pinpoint joint attention occurrences that are fundamental for learning. In this study, we examined joint attention in collaborative mathematical problem solving. We studied the thought processes of four 15-16-year-old students in their regular classroom, using mobile gaze tracking, video and audio recordings, and smartpens. The four students worked as a group to find the shortest path to connect the vertices of a square. Combining information on the student gaze targets with a qualitative interpretation of the context, we identified the occurrences of joint attention, out of which 49 were joint visual attention occurrences and 28 were attention to different representations of the same mathematical idea. We call this joint representational attention. We discovered that 'verifying' (43%) and 'watching and listening' (35%) were the most common phases during joint attention. The most frequently occurring problem solving phases right after joint attention were also 'verifying' (47%) and 'watching and listening' (34%). We detected phase cycles commonly found in individual problem-solving processes ('planning and exploring', 'implementing', and 'verifying') outside of joint attention. We also detected phase shifts between 'verifying', 'watching and listening', and 'understanding' a problem, often occurring during joint attention. Therefore, these phases can be seen as a signal of successful interaction and the promotion of collaboration.

Reciprocal eye contact is a significant part of human interaction, but its role in classroom interaction has remained unexplored, mostly due to methodological issues. A novel approach in educational science, multiple-person mobile gaze-tracking, allows us to gather data on these momentary processes of nonverbal interaction. The current mixed-method case study investigates the role of teacher-student eye contact in interpersonal classroom interaction using this methodological approach from three mathematics lessons. We combined gaze-tracking data with classroom videos, which we analyzed with continuous coding of teachers' interpersonal behavior. Our results show that teacher communion and agency affect the frequency and durations of teachers and students' gazes at each other. Students tend to gaze their teachers more during high teacher communion and low agency, but qualitative and quantitative differences between the teachers and their classes emerged as well. To conclude, the formation of eye contacts is situational and affected by momentary interpersonal changes as well as the qualities of teacher-student interactions.

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.

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.

This paper presents a systematic review of university students' emotions in connection with virtual learning based on 91 articles published between 2002 and 2017 in four international journals that focus on virtual learning and educational technology or on learning in higher education. These journals were considered potential channels for research on emotions in virtual learning and higher education. The objective was to analyse the articles for concepts and theoretical background related to virtual learning and emotions, contextual focus, methodological choice, and/or results. The review showed that the most common emotion-related concept was "satisfaction." The most common context for the articles was a complete non-physical learning environment (e.g. Second Life). Approximately 60% of the articles used quantitative methods. The most common design for studying emotions was an explanatory design. Students' emotions were mainly studied through concepts related to emotion (e.g. "satisfaction"). Yet only a few of the studies focused on the fluctuation of emotions in the course of events, relying instead on post hoc data that treat students' emotions as traits rather than states.

New school buildings are often designed for flexible innovative learning environments (ILEs) to support learning future skills better than before. However, little is known about the relationship between environment and pedagogy. This article examines the relationship between the environment and pedagogy from the perspective of primary school teachers in the context of teaching mathematics. We interviewed 26 teachers from 10 Finnish ILEs and did a thematic analysis. The relationship between the environment and pedagogy forms a complex network of entangled tensions between teacher's inner space, community's social space and physical space. When the tensions between these spaces were resolved in a positive way, ILEs enabled pedagogy that diversified mathematics education, improved student cohesion and teachers' well‐being at work. However, the ILEs' transformation process often appears to be left unfinished, leading to unsuccessful resolution of tensions. Further, our findings highlight the importance of four‐dimensional environmental competence in exploiting the affordances enabled by ILE. [ABSTRACT FROM AUTHOR]

Parental involvement is considered essential for children’s educational outcomes. Previous research has connected parental involvement to children’s mathematical achievement. However, it remains unclear how parental values and communication regarding education and academic achievement relate to children’s mathematical achievement and attitudes. The current study aims to fill this gap by building on an earlier project with quantitative data conducted twice, consisting of mathematical tests for children and surveys for children, parents, and teachers. Based on exploratory factor analyses and a theoretically constructed model, we conducted confirmatory factor analyses to establish a structural equation model. The results showed that children’s mathematical achievement and attitudes correlated with the parent’s educational values. In addition, the analyses revealed that the children’s mathematical outcomes were more strongly related to the parents’ values than to the parents’ communication with the children. Limitations of the study and implications for the importance of parents’ values and communication were discussed. [ABSTRACT FROM AUTHOR]

The aim of this article was to find the connections between teachers' actions (N = 7) and their 3rd graders' performances (N = 86) when solving an open problem. A lot of information about the teaching sessions was gathered by video recordings and collecting pupils' solutions. Teachers' actions were analysed carefully through the phases of a problem-solving lesson (launch phase, explore phase, and discuss and summarise phase). Pupils' solution levels were categorised and their performances were compared in different teaching groups. Based on our data, teachers' way of teaching varied greatly in every phase. In the launch phase, the way in which the teachers presented the problem and especially how they illustrated the central concepts affected pupils' performances. The teacher's way of guiding and the choice of the equipment was central in the explore phase. However, even though some teachers revealed the central ideas of the solution during the launch and explore phases, this had no effect on the pupils' solutions.

This study investigates behavioral executive functions (EFs) in the mathematics classroom context among adolescents with different mathematics performance levels. The EF problems were assessed by teachers using a behavioral rating inventory. Using cutoff scores on a standardized mathematics assessment, groups with mathematics difficulties (MD; n = 124), low mathematics performance (LA; n = 140), and average or higher scores (AC; n = 355) were identified. Results showed that the MD group had more problems with distractibility, directing attention, shifting attention, initiative, execution of action, planning, and evaluation than the LA group, whereas the differences in hyperactivity, impulsivity, and sustaining attention were not significant. Compared to the AC group, the MD group showed more problems with all behavioral EFs except hyperactivity and impulsivity, while the LA group showed more problems only with shifting attention. Male adolescents showed more behavioral EF problems than female adolescents, but this gender difference was negligible within the MD group. The practical implications of the results are discussed.

In large scale international assessment studies, questionnaires are typical used to query students' home possessions. Composite scores are computed from responses to the home resource questionnaires and are used as a measure of family socioeconomic background in achievement comparison or for statistical control. This paper deals with profiling the socio-economic status (SES) of Ghanaian students' in the context of the TIMSS 2011 study. Latent class analysis was used to profile students into respective SES classes based on the students' responses to 11 questions concerning their home resources. The results showed three clearly distinct socio-economic profiles: high-, middle- and low-SES. Moreover, a discriminate analysis was conducted to explore the degree to which the groups are accurately classified. The discriminant analysis was able to correctly classify 92.20% of the individual students into their appropriate SES group. A gender comparison of these classes suggested stable measurement invariance for the latent class indicators. This article contributes to addressing the composition of SES by providing statistical criteria to evaluate SES using empirical data.

Research during COVID-19 has shown that rapid transition to distance learning environment has influenced student's emotions. Yet, there is a lack of studies about how this transition might have changed achievement emotions in mathematics. We investigated six mathematics-related achievement emotions (enjoyment, pride, anger, anxiety, shame, and boredom) among Finnish high school students (N = 1348) in contact learning and distance learning. We analysed the relationship between gender, achievement emotions, and the learning environment using latent growth curve structural models. Our results revealed that students reported higher levels of boredom and lower levels of pride, enjoyment, shame, and anxiety in distance learning than in contact learning. The distance learning effect was stronger for females than for males, particularly for students following the advanced syllabus. Female students reported a larger decrease in pride and enjoyment and a larger increase in boredom than male students when moving from contact learning to distance learning. The theoretical and practical implications of the results are discussed. [ABSTRACT FROM AUTHOR]

Mathematics-related affect is established regarding both individual and interindividual levels. However, the interaction between the levels has not been elaborated. Furthermore, it is known that people may draw either from intrinsic or extrinsic experiences to construct their identities depending on their cultural environment. Thus, affective individual and interindividual levels seem to interact with culture. In this study we focus on the significance of and the interaction between the individual and the interindividual levels of affect. This is done with respect to 2 different types of countries (Finland and Chile) to include cultural effect. We use questionnaire-based data and pupils' drawings of their mathematics class to find out about their individual and interindividual experiences. By using mixed data, we are not only getting a wider picture of pupils' affect but we can also avoid the most typical errors made in the cross-cultural comparisons as the pupils' own voice is strengthened. The main finding in the study is that the 2 affective levels are not congruent and that the incongruence appears differently in different types of cultures.

Large-scale studies measure mathematics-related affect using questionnaires developed by researchers in primarily English-based countries and according to Western-based theories. Influential comparative conclusions about different cultures and countries are drawn based on such measurements. However, there are certain premises involved in these kinds of "imposed-etic approaches," such as (1) universalism within the examined components, (2) universalism within the components' significances, (3) the congruence between languages and conceptions, and (4) the components' coverage of the phenomena. Therefore, researchers have criticized these premises citing a large number of reasons. In this study, the validity of conclusions based on results relying on the imposed-etic approach is questioned by examining to what extent the premises behind this approach can be justified. We investigate the premise of universality within the examined components by scrutinizing the limitations of a typical questionnaire. To what extent can such a questionnaire reveal affective domain structures for pupils in two countries as dissimilar as Finland and Chile? We found that there can be no meaningful precision. Universalism across components within the mathematics-related affect structure is not guaranteed in the two cultures, and the use of such questionnaires is simply unjustifiable. We also thoroughly examined the three other premises underpinning the Western-based imposed-etic perspective.

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.

This case study explored how children's moral expressions like love and violence differ according to the mode of narrative, comic strips or written narratives. Sixteen third-grade children from a primary school in Finland took part in the study. Children's moral expressions were divided into justice and care. Reading frequency of fairy tales and linguistic and artistic abilities were also assessed in order to make a more in-depth interpretation of elements that underlie these different moral voices. The data for four of the children are presented in detail as the basis for the discussion. Children expressed their morality more strongly in comic strips--potentially offering a more sophisticated method for examining how children express their morality.

Important questions regarding mathematical giftedness are how and when it is possible to identify. To be identified as gifted, the student must have natural potential but also an appropriate mix of motivation, support, and challenges. This study is based on longitudinal data following students from 3rd grade in primary school to the end of upper secondary school between 2005 and 2015. We focus on top achievers (<2% of age cohort) of the national mathematics final exam at the end of upper secondary school. We investigate how accurately top achievers at the end of secondary school can be identified in 3rd, 6th, and 9th grades using national tests. We identify mathematical tasks that predict future top achievement and analyze how attitudes, gender, and parental background factors relate to high proficiency. Most top achievers had already been identified by 3rd grade and almost all of them by 9th grade. However, recognizing future top achievers was not very accurate, as they were indistinguishable from many students whose performance did not reach the same level over time. The best predictor for future top achievement was a student's ability to solve non-routine and atypical tasks in early school years. [ABSTRACT FROM AUTHOR]

In this study, we consider 5 preservice teachers who had negative views of mathematics at the beginning of elementary teacher education. We focus on methodological challenges: how to analyze their mathematical identity talk which to some readers can sound incoherent. Teacher change studies have often ignored the methodological challenges on which we focus on in this article. We compare preservice teachers' talk at the beginning and at the end of a mathematics education course. When analyzing the data, we combined discursive, rhetorical, and narrative approaches. We identified 6 central interpretative repertoires that were manifested in preservice teachers' identity talk: Victim, Ego-defensive, Fatalist, Gaining an Insight, Self-development, and Responding to the Expectations of the Change. The Ego-defensive and Fatalist repertoires were activated especially when students talked about mathematical tests. The most central rhetorical devices were category entitlement, categorization, active voicing, use of disclaimer, and use of metaphors or extreme utterances. At the end of the course, the talk of the more confident preservice teachers was more coherent than the others' talk. Our study shows that combining different approaches can bring useful views for understanding preservice teachers' multiple identities.

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.

The research focuses on Estonian university students' emerging teacher identity and their interest in becoming teachers. Five hundred and sixty-five first, third and fifth year students participated in the survey. The results suggest that pedagogical reasons for entering teacher education and clear motives for studying are significant indicators of teacher potential. Pedagogical reasons for entering teacher education or the teaching profession and the wish to function as a change agent in the society were related to academic self-efficacy beliefs and the belief that the teacher expertise is mainly pedagogical in nature. However, at the point in their studies at which the students are able to choose their masters programme and entry into teacher education, their likelihood of choosing teacher education remains low, indicating that there is a need to develop pedagogical content, study counselling and career guidance services to encourage students' continued interest in and entry to teacher education and the teaching profession. (Contains 4 tables and 4 figures.)

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.

Understanding and reporting students' affective experiences with mathematics is difficult if those experiences do not resonate with personal experiences. Utilising fiction-writing in narrative reporting can be a technique that helps both the researcher and the reader of the research report to immerse themselves in the student's experiential world. In this article, the author explores some methodological justifications for such writing, giving an example of the use of fiction-writing techniques in a narrative account of a student who experiences anxiety in an interaction with her mathematics teacher.