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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.

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.

In the field of mathematics-related affect research, not many comparisons have been done with regard to Western-Latin countries. This article reports the state of 9-year old pupils’ self-related affect with respect to mathematics in two countries, i.e. Finland and Chile. Self-efficacy, mastery goal orientation, effort, and enjoyment of mathematics were under consideration. Through quantitative analysis, it was found that all the factors examined are highly positive in both countries. However, a small difference with regard to beliefs of self-efficacy and effort was found between the countries, in favour to Finland. Yet, young pupils’ self-related mathematical beliefs build up an optimistic view with respect to mathematics learning, and efforts should be made to maintain the situation similar during the following school years.

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.

The article presents results from a cross-cultural NorBa-project “Mathematics teachers’ educational beliefs”. We report Estonian, Latvian and Finnish lower secondary mathematics teachers’ beliefs about good teaching. A principal component analyses identified a two-component structure of teachers’ beliefs about good teaching: (1) Reasoning and conceptual understanding and (2) Mastery of skills and facts. Cross-cultural differences were identified in both of these dimensions. Latvian teachers indicated the strongest agreement with reasoning and conceptual understanding, Estonian teachers with mastery of skills and facts, while Finnish teachers scored lowest on both dimensions. Moreover, we analysed the amount of teachers with different profiles with regard to these two dimensions.

This study compares six teachers’ learning goals for two problem solving lessons and their 9 to 11 year-old students’ solutions to two open-ended problems. Some of the learning aims were explicitly given before the lesson and some were revealed during the lessons. The pupils worked on the first open problem in primary three and the second problem in the primary four. The problem solving lessons were video-recorded and transcribed, and pupils´ solutions were collated and examined. An additional data source was the teachers´ lesson plans, and the videos taken in the teachers´ meeting sessions. The classification of teachers´ actions was based on the teaching model developed from Polya’s problem solving model (planning, introduction, guidance, feedback). This paper examines the significance of the teachers´ aims of the lessons and the introduction of the two problems, with the focus on the pupils´ justification of the solution for both tasks

One of the goals of the working group is to enhance discussion in the CERME - conferences and research between the conferences. Working Group 2 “Affect and mathematical thinking - This includes the role of beliefs, emotions, and other affective factors“ at the CERME 4 -conference was succesful in creating an atmosphere of collaboration among its16 participants. In preparation to the conference took place a call for paper and as a consequence of a reviewing process, 11 papers were accepted for presentation at the conference. The conference program scheduled 7 sessions, each 105 minutes, for work in the group. The chair of the organizing team worked out a concept for this 7 sessions. In 6 of these 7 sessions should take place a presentation of the key ideas and results of the accepted papers followed by a general discussion to the papers. Each session was extended by further activities (small group discussions to various themes, role play, analysis of data, problem solving, etc.). The last session was used for a summary of activities during the conference and highlighting important research questions for the following years.