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This study explores how students deal with material resources in their peer interaction when working in pairs in an open-ended problem-solving task. The productive use of material resources can be expected to support successful peer work. However, research into social phenomena in peer interaction is needed in order to identify and describe productive and less productive forms of dealing with material resources as students participate in open-ended problem-solving tasks. Consequently, this explorative study responds to this research need. Based on multimodal data, including video recordings, transcribed talk and the written contributions from four pairs of Year 7 students aged 12-13 years, the analysis focuses on different ways in which students deal with material resources while negotiating their participation as they respond to the task. The findings indicate that aspects of participation are a key factor for describing productive and less productive ways of dealing with material resources by the student pairs. Foregrounding aspects of participation for an increased awareness of potential obstacles to student-centred work is among this study's contributions for classroom practice and theory development.

In this paper, we report on the cross-cultural comparative analysis that was undertaken as part of the Social Unit of Learning project investigating student collaborative problem solving in China and Australia. The video-based research examined the 'negotiative foci' of dyadic student interaction during collaborative problem solving within the mathematics classroom setting. In the analysis we take "negotiative focus" as the central construct and compare the student interactions in terms of their focus on either facts and procedures, didactical norms, or social/interpersonal considerations. We report on the analysis based on an open-ended pair task (Household task) that was completed by year 7 students (mostly 12- to 13-year olds) in China and Australia. In the study we analysed the video and written responses of 20 student pairs from three year 7 classes in China (40 students in total) and 25 student pairs from two year 7 classes in Australia (50 students in total). The findings from this comparative study provide empirical evidence regarding how the participating students in each country interpreted and negotiated meaning as they tackled the open-ended task collaboratively.

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. [Written with the Social Unit of Learning project team.]

The important role of student agency in collaborative problem-solving has been acknowledged in previous mathematics education research. However, what remains unknown are the processes of agency in open-ended tasks that draw on real-life contexts and demand argumentation beyond "mathematical". In this study, we analyse a video recording of two student groups (each consisting of four students) taking part in collaborative problem-solving. We draw on the framework for collaborative construction of mathematical arguments and its interplay with student agency by Mueller et al. (2012). This original framework is supplemented by (i) testing and revising it in the context of open-ended real-life tasks, with (ii) student groups rather than pairs working on the tasks, and by (iii) offering a strengthened methodological pathway for analysing student agency in such a context. Based on our findings, we suggest that the framework suits this new context with some extensions. First, we note that differences in student agency were not only identified in terms of the discourse students drew on, but in how students were able to shift between various discourses, such as between "mathematical" and "non-mathematical" discourses. We identify a novel discourse reflecting student agency, invalidation discourse, which refers to denying other students' agency by framing their contribution as invalid. Finally, we discuss the need to reframe "mathematical" arguments--and indeed student agency--while the task at hand is open-ended and concerns real-life contexts.

This study investigated how teachers in China perceived the effects of online instruction on mathematics learning and examined the challenges they encountered when the country shifted to online instruction during the COVID-19 pandemic. We interviewed 152 mathematics teachers from 20 cities (municipalities) or provinces in China and adopted the four-component didactic tetrahedron model (teacher, technology, student, and mathematics) to identify their struggles with technology, teacher-student interactions, and delivery of mathematics instruction. Results showed that the teachers believed that the effectiveness of online teaching largely depends on student self-discipline. Analysis suggested a need to expand technology use during instruction, reshape the way teachers interact with students, and reorganize teaching methods in face-to-face classroom instruction. This research provided insights into integrating technology with instructional practice, the critical role of teachers in online learning, and other factors that may determine the effectiveness of online teaching.

The major premise of this project is that teachers learn from the act of teaching a lesson. Rather than asking "What must a teacher already know in order to practice effectively?", this project asks "What might a teacher learn through their activities in the classroom and how might this learning be optimised?" In this project, controlled conditions are created utilising purposefully designed and trialled lesson plans to investigate the process of teacher knowledge construction, with teacher selective attention proposed as a key mediating variable. In order to investigate teacher learning through classroom practice, the project addresses the following questions: To what classroom objects, actions and events do teachers attend and with what consequence for their learning? Do teachers in different countries attend to different classroom events and consequently derive different learning benefits from teaching a lesson? This international project combines focused case studies with an online survey of mathematics teachers' selective attention and consequent learning in Australia, China and Germany. Data include the teacher's adaptation of a pre-designed lesson, the teacher's actions during the lesson, the teacher's reflective thoughts about the lesson and, most importantly, the consequences for the planning and delivery of a second lesson. The combination of fine-grained, culturally situated case studies and large-scale online survey provides mutually informing benefits from each research approach. The research design, so constituted, offers the means to a new and scalable vision of teacher learning and its promotion.

Interactive problem solving and learning are priorities in contemporary education, but these complex processes have proved difficult to research. This project addresses the question "How do we optimise social interaction for the promotion of learning in a mathematics classroom?" Employing the logic of multi-theoretic research design, this project uses the newly built Science of Learning Research Classroom (ARC-SR120300015) at The University of Melbourne and equivalent facilities in China to investigate classroom learning and social interactions, focusing on collaborative small group problem solving as a way to make the social aspects of learning visible. In Australia and China, intact classes of local year 7 students with their usual teacher will be brought into the research classroom facilities with built-in video cameras and audio recording equipment to participate in purposefully designed activities in mathematics. The students will undertake a sequence of tasks in the social units of individual, pair, small group (typically four students) and whole class. The conditions for student collaborative problem solving and learning will be manipulated so that student and teacher contributions to that learning process can be distinguished. Parallel and comparative analyses will identify culture-specific interactive patterns and provide the basis for hypotheses about the learning characteristics underlying collaborative problem solving performance documented in the research classrooms in each country. The ultimate goals of the project are to generate, develop and test more sophisticated hypotheses for the optimisation of social interaction in the mathematics classroom in the interest of improving learning and, particularly, student collaborative problem solving.

Contemporary curriculum demands the development of both problem solving skills and negotiative skills required for collaborative group work. Tasks are required that create the best possible conditions for students to develop both of these skill sets. Open-ended tasks have been shown to provide these conditions, but they also require the teacher to relinquish some level of control over student activity, since the open-endedness of the tasks provides students with the opportunity to realize their intentions rather than just the teacher's. It is necessary to investigate the nature of the affordances created by the use of open-ended tasks in order to anticipate how they might best be used for both instruction and learning. What is needed is a structured way to identify the affordances offered by open-ended tasks. This paper reports a study conducted in a laboratory classroom equipped to record classroom social interactions in great detail using advanced video technology. The reported analysis addresses the following question: What are the foci of the students' social interactions during collaborative problem solving while attempting open-ended mathematical tasks? Analysis was carried out in relation to each type of data generated: written response, transcripts and videos. Our research has identified structures to represent these affordances so that teachers can both anticipate them and draw on them in monitoring and facilitating student collaborative problem solving. The structured identification of affordances in relation to (a) written product and (b) negotiative focus provides teachers with two frameworks by which to scaffold student collaborative work while attempting open-ended tasks.

The Early Literacy Knowledge and Skills (ELKS) instrument was informed by the work of Ferreiro and Teberosky based on the notion that young children could be differentiated according to levels of sophistication in their understanding of the rules of written language. As an initial step to evaluate the instrument for teaching purposes, the present study examines its psychometric properties in terms of internal consistency reliability, model-data fit, item discrimination, match between item difficulty and ability range in the sample, and item difficulty according to Ferreiro and Teberosky's theory of early literacy development. Overall, the ELKS instrument showed good psychometric properties in these areas, although two items in particular may require further investigation and possible revision according to the model-data fit index. Future directions to investigate the potential classroom application of the instrument are suggested.