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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.

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.

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.

This study examines how authentic assessment could nurture students’ epistemic agency: their sense of agency in using, evaluating and producing knowledge. Authentic assessment commonly emphasises ‘realism’ and ‘employability skills’. As important as these ideas are, this approach to authentic assessment neglects the key academic value of knowledge, a gap we address by adding epistemology into the conversation. Our qualitative case study explores an archaeology course whose authentic assessment design relied heavily on digital technologies. We empirically analyse students’ sense of epistemic agency after articulating the affordances of the course’s authentic assessment design. Our findings show that digitally-mediated authentic assessment promoted students’ relationship with knowledge in three ways. Students understood themselves as (i) active learners, (ii) active users of knowledge and (iii) epistemic agents who contributed to public archaeological knowledge. We reframe authentic assessment as a catalyst for students’ epistemic agency, enabling students to contribute to social good. [ABSTRACT FROM AUTHOR]

With the myriad theories generated through research over the years, a continuing challenge for researchers is to navigate the multitude of theories in order to communicate their research, integrate empirical results, and make progress as a field by building upon empirical research. The Social Unit of Learning project was purposefully designed so that researchers from multiple disciplines with different theoretical perspectives could work together to examine the complexity of the mathematics classroom. In this paper, we reflect on the multiple analytical accounts generated from the project, drawing from the notions of complementarity and commensurability. Two parallel analyses, applying the commognitive framework and the theory of representations respectively, are used as illustrative examples for discussion regarding complementarity and commensurability. The paper addresses two focal questions, as follows: in what ways do divergence or contradiction in incommensurable analytical accounts reflect methodological discrepancies or fundamental differences in the underpinning theories? Furthermore, in what ways do the accounts generated by the parallel analyses predicated on different theories lead to differences in instructional advocacy? The answers to these questions provide empirically-grounded insights into the consideration of incommensurability in educational research, and suggest ways in which researchers and practitioners might apply the notion of complementarity to reconcile or exploit incommensurable analytical accounts that have resulted in different instructional advocacies. [ABSTRACT FROM AUTHOR]

This study addressed the need to explore the reliability and validity of the recently renewed aptitude test based on the multiple mini-interview (MMI) format in Finnish teacher education programmes. Utilising a nationwide dataset (N = 3306), we explored the reliability of the format using intraclass correlations and multilevel modelling. Furthermore, we validated the intended structure of the MMI with confirmatory factor analysis and contrasted the scores of the MMI with other admission scores, i.e. cognitive measures. The results showed mostly small effects of clustering of the applicants according to the different interviewers and circuits. The largest variance component for the MMI total score was the applicant (73.3%), followed by measurement error (15.09%). The intended structure was validated, and the MMI seemed to measure different attributes from other admission measures. Thus, the study demonstrated satisfactory reliability and validity of MMI in admission to teacher education, yet the stations need further development. [ABSTRACT FROM AUTHOR]