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Research exploring undergraduates' tool preferences in tertiary mathematics is currently limited. In this paper, we explore the tools mathematics and engineering students use when studying mathematics and the ways undergraduates combine these tools. Results from our survey (N = 628) showed that students in our sample use mostly their notes, the university's virtual learning environment (VLE), other students and textbooks. Mathematics students were found using more online encyclopaedias, the university's VLE, instant messaging and other students, whereas engineering students reported using more textbooks. By performing a cluster analysis, undergraduates were assigned to five distinct tool-use profiles: the peer-learning group (above average use of other students, instant messaging apps and social media); the online-learning group (above average use of online videos, online encyclopaedias, Wolfram Alpha and the university's VLE); the blended-learning group (above average use of all the tools at their disposal); the no-users group (below average use of all tools except textbooks); and the selective-learning group (above average use of textbooks, online videos and lecturers). The majority of mathematics students were distributed across the peer-learning, online-learning and blended-learning groups, whereas most of the engineering students were found in the blended-learning, no-users and selective-learning groups.

This paper arises from a study of how concepts related to understanding functions develop for students across the years of secondary/high school, using small samples from two different curricula systems: England and Israel. We used a survey consisting of function tasks developed in collaboration with teachers from both curriculum systems. We report on 120 higher achieving students, 10 from each of English and Israeli, 12-18 years old. Iterative and comparative analysis identified similarities and differences in students' responses and we conjecture links between curriculum, enactment, task design, and students' responses. Towards the end of school, students from both curriculum backgrounds performed similarly on most tasks but approached these by different routes, such as intuitive or formal and with different understandings, including correspondence and covariational approaches to functions.

From a Marxian/Vygotskian perspective, learning is social in origin and it happens in the presence of others that are more knowledgeable. Extending this view to the learning of mathematics, such learning also becomes inseparable from the presence of others (people and artefacts). Researchers over decades have studied different interactions to see how such learning with others occurs, what is the role of the (more knowledgeable) other, and if at all this role alternates between the participants. In this paper, we looked at a 5-year-old's (Lila) interaction with her mother (Mellony) and a television remote control as Lila attempted to count in threes using the three by three physical layout of the numbered buttons 1-9 on the remote control. We specifically looked at the emergence of the Zone of Proximal Development (ZPD) as Lila's attention was caught by the properties of the remote control and by her mother's questions. We also pay attention to how the role of the more knowledgeable other alternates among the participants. Our findings suggest that Lila, at times, used resources provided by the physical properties of the remote control and sometimes, used resources provided by Mellony to think about the task of counting in threes. In Lila's interaction, we interpreted a multi-directional ZPD as the role of the more knowledgeable other alternated between Mellony, Lila and the remote control.

Currently, there is a dearth of studies exploring the kind of tools that undergraduates use when studying mathematics with previous approaches focusing mostly on digital or institutionally provided resources. In this article, we present and discuss the results from our investigations into the different types of tools that a cohort of second year engineering undergraduates uses. Our survey (N = 201) showed that although to some extent students use resources external to their university, their practices are dominated by tools that their institution provides to them. Analysis of six follow-up interviews revealed that when students use the most popular resources they aim mostly for exam-related goals. This suggested that students in our sample choose to use certain tools because these enable them to pursue their exam-driven goals.

Dealing with multiple representations and their connections plays a key role for learners to build up conceptual knowledge in the mathematics classroom. Hence, professional knowledge and views of mathematics teachers regarding the use of multiple representations certainly merit attention. In particular, investigating such views of preservice teachers affords identifying corresponding needs for teacher education. However, specific empirical research is scarce. Taking into account the possible role of culture, this study consequently focuses on views about using multiple representations held by more than 100 English and more than 200 German preservice teachers. The results indicate that there are culture-dependent aspects of preservice teachers' views, but also that there are common needs for professional development.

The influences on governments for policy changes in schools range across many agencies, including the political party in power. When policies change, the sources of these influences are not always clear. The project whose work is presented in this special issue examines what these changes look like in terms of the differences in assessment tasks of school pupils' mathematics, over time. In this article we attempt to develop a graph, which we argue will have general applicability internationally, that can help to reveal the sources and nature of those influences. We construct the graph in interaction with an examination of the most recent changes in two countries. We argue that our analysis is a necessary complement to the project's findings in that it enables us to identify the fields of recontextualisation, their relative strengths in terms of influence and hence conjecture their impact on the mathematics curriculum.

Changes in school mathematics curricula, pedagogy and assessment, and as a consequence the pressure for changes in initial teacher preparation, are consequences both of government policy initiatives and pressure from unofficial agents such as the research community, teachers and others, though with great variation across the world. In the case of England, it has resulted in strong regulation, including inspection, of initial teacher education too. In this article, I draw on sociological theory to help in mapping the relations between official and unofficial agents and in interpreting the effects on mathematics teacher educators, in particular. The article draws in the main on the changing position in England over the last decade or so, and a case study analysis is carried out of a key official document to illustrate the application of theoretical tools provided by sociologists and others for examining the relations between agents and agencies and on their consequences.

This article describes 11 papers in which the authors report their research on technology as enhancement in the teaching and learning of mathematics, in the context of the application of activity theory for design and/or analysis. There is considerable diversity across the papers in how the authors have interpreted their task and in particular how they pick up notions from the activity theory literature, taken in its broadest sense. Stephen Lerman, concludes that inertia, lack of vision by policy makers, lack of financial resources, and the unsolved challenge of giving all mathematics teachers an opportunity to gain expertise in technologies such that they can incorporate them into their thinking about teaching (Morgan, 1994) have all resulted in still researching the orchestration of technology-enhanced mathematics learning rather than the complete transformation of children's learning of mathematics (and other elements of the curriculum). Lerman argues that as a community, educators have not helped themselves by sometimes securing huge research and development grants to develop highly sophisticated software with wonderful results in pupils' experiences but that have scarcely reached beyond the present capabilities of schools. Still, given recently published research papers on the subject, Lerman remains hopeful that creative and well-researched technology use has much to offer, even within the parameters of the current curricula.

This paper is drawn from a doctoral thesis (Rosa, 2008) that examines the relations established between the construction of online identities and the teaching and learning of the definite integral concept in an online learning course. The role-playing game (RPG) is played out through chat and calls for the creation of characters (online identities) by each player. In the research process on online learning in mathematics education, Rosa (2008) discusses the role of the construction of online identities. We characterise how this process, in a general way, draws on qualitative research processes and, in a specific way, is linked to the construction of mathematical knowledge in cyberspace. We discuss who the research subjects are in mathematics education research. The results suggest that: (a) cyberspace is a natural environment in an online RPG context; (b) the playful process in online learning in mathematics education brings important new aspects to our understanding of mathematical knowledge as a social construction; (c) the investigation becomes a game; (d) research subjects are who they want to be while they are in flow, that is, there is intentionality; (e) the challenge of research methodology inside cyberspace must be faced by researchers; and (f) the researcher needs to consider those different identities as integral to the research process.

This article presents the results of an investigation carried out across 20+ country-regions under the auspices of ICMI Study 15 into the structures, approaches and general characteristics of the mathematics preparation and development of teachers. We use a global framework provided by the larger research literature on teacher education to contextualize the findings. The article provides an analytic perspective on (a) teacher education systems' characteristics including institutional arrangements and regulations; (b) teacher's recruitment, selection, and credentials; (c) teacher education programs' structure and approaches; (d) teacher educators' characteristics; and (e) the structure and content of the curriculum. This article highlights the important differences and similarities across systems that provide mathematics education and development to teachers. This article concludes with a discussion on implications for future empirical research on mathematics teacher education.