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In this paper we present the results from a study in which 21 mathematics trainee teachers engage with two practice-based tasks in which classroom management interferes with mathematical learning. We investigate the trainees' considerations when they make decisions in classroom situations and how these tasks can trigger their reflections on the teaching and learning of mathematics. In our analysis we used the constructs of "Social" and "Sociomathematical norms" (Cobb & Yackel, 1996) and "Teaching Triad" (Jaworski, 1994). Results indicate commendable norms trainees aspire to establish in their classroom, such as peer respect, value of discussion and investigative mathematical learning. However, they often miss the opportunity to engage students with metacognitive discussions and mathematical challenge as they focus on behavioural issues or endorse dichotomous and simplistic views of mathematical learning. We credit these tasks with allowing insight into trainees' considerations and we propose their further implementation in teacher education programmes.

Non-mathematics specialists' competence and confidence in mathematics in their disciplines have been highlighted as in need of improvement. We report from a collaborative, developmental research project which explores the conjecture that greater integration of mathematics and biology in biology study programs, for example through engaging students with Mathematical Modeling (MM) activities, is one way to achieve this improvement. We examine the evolution of 12 first-semester biology students' mathematical discourse as they engage with such activities in four sessions which ran concurrently with their mandatory mathematics course and were taught by a mathematician with extensive experience with MM. The sessions involved brief introductions to different aspects of MM, followed by small-group work on tasks set in biological contexts. Our analyses use the "theory of commognition" to investigate the tensions between "ritualized and exploratory participation" in the students' MM activity. We focus particularly on a quintessential "routine" in MM, "assumption building": we trace attempts which start from ritualized engagement in the shape of "guesswork" and evolve into more productively exploratory formulations. We also identify signs of persistent "commognitive conflict" in the students' activity, both "intra-mathematical" (concerning what is meant by a "math task") and "extra-mathematical" (concerning what constitutes a plausible solution to the tasks in a biological sense). Our analyses show evidence of the fluid interplay between ritualized and exploratory engagement in the students' discursive activity and contribute towards what we see as a much needed distancing from operationalization of the commognitive constructs of ritual and exploration as an unhelpfully dichotomous binary.

Mathematics is the discipline that a significant majority of most incoming researchers in mathematics education have prior qualifications and experience in. Upon entry into the field of mathematics education research, these newcomers--often students on a postgraduate programme in mathematics education--need a broadened understanding on how to read, converse, write and conduct research in the largely unfamiliar territory of mathematics education. The intervention into the practices of post-graduate teaching and supervision in the field of mathematics education that I describe here aims at fostering this broadened understanding and thus facilitating newcomers' participation in the practices of the mathematics education research community. Here I outline the theoretical underpinnings of the intervention and exemplify one of its parts (an Activity Set designed to facilitate incoming students' "engagement with the mathematics education research literature"). I supplement the discussion of the intervention with comments sampled from student interview and student written evaluation data as well as observations of the activities' implementation. The main themes touched upon include: "learning how to identify appropriate mathematics education literature"; "reading increasingly more complex writings in mathematics education"; "coping with the complexity of literate mathematics education discourse"; "working towards a contextualised understanding of literate mathematics education discourse." I conclude with indicating the directions that the intervention, and its evaluation, is currently taking and a brief discussion of broader implications, theoretical as well as concerning the supervision and teaching of post-graduate students in mathematics education.

In this paper we outline the main tenets of the commognitive approach and we exemplify its application in studies that investigate the learning and teaching of mathematics at university level. Following an overview of such applications, we focus on three studies that explore fundamental discursive shifts often occurring in the early stages of studying Calculus. These shifts concern the lecturers' and students' communicative practices, routines of constructing mathematical objects and ways of resolving commognitive conflicts. We then propose that commognitive constructs such as subjectification can be deployed towards "scaling-up" the hitherto fine-grained focus of commognitive analyses. Finally, we conclude with observing how the commognitive approach relates to constructs from other sociocultural approaches to research in university mathematics education, such as "legitimate peripheral participation" from the theory of Communities of Practice and "didactic contract" from the Theory of Didactic Situations.

Explores how students can be re-engaged with their mathematics so that they feel more positive about their school mathematics experiences. Describes three main components that emerged from interviews with the students: (1) the nature of 'fun' in the mathematics classroom; (2) preferred ways of working; and (3) the structures that organize students' mathematics learning. (KHR)

Looks back over a number of exploratory studies that have researched young children's construction of meaning for graphs produced from data entered into spreadsheets. Discusses children's use of normalizing, an activity in which children 'correct' data towards some perceived norm. (Author/MM)

Identifies and explores the difficulties in the novice mathematician's encounter with mathematical abstraction. Observes 20 first-year mathematics undergraduates and extracts sets of episodes from the transcripts of the tutorials and interviews within five topics in pure mathematics. Discusses issues related to the learning of one mathematical topic, Group Theory. (Contains 26 references.) (Author/ASK)

Non-mathematics specialists' competence and confidence in mathematics in their disciplines have been highlighted as in need of improvement. We report from a collaborative, developmental research project which explores the conjecture that greater integration of mathematics and biology in biology study programs, for example through engaging students with Mathematical Modeling (MM) activities, is one way to achieve this improvement. We examine the evolution of 12 first-semester biology students' mathematical discourse as they engage with such activities in four sessions which ran concurrently with their mandatory mathematics course and were taught by a mathematician with extensive experience with MM. The sessions involved brief introductions to different aspects of MM, followed by small-group work on tasks set in biological contexts. Our analyses use the theory of commognition to investigate the tensions between ritualized and exploratory participation in the students' MM activity. We focus particularly on a quintessential routine in MM, assumption building: we trace attempts which start from ritualized engagement in the shape of "guesswork" and evolve into more productively exploratory formulations. We also identify signs of persistent commognitive conflict in the students' activity, both intra-mathematical (concerning what is meant by a "math task") and extra-mathematical (concerning what constitutes a plausible solution to the tasks in a biological sense). Our analyses show evidence of the fluid interplay between ritualized and exploratory engagement in the students' discursive activity and contribute towards what we see as a much needed distancing from operationalization of the commognitive constructs of ritual and exploration as an unhelpfully dichotomous binary. [ABSTRACT FROM AUTHOR]

We examine teachers’ use of resources as they prepare to teach the topic of numerical series of real numbers, in order to identify how their personal relationship with mathematical content—and its teaching—interacts with their use of a commonly used textbook. We describe this interplay between textbook and personal relationship, a term coined in the Anthropological Theory of the Didactic (ATD, Chevallard, 2003), in terms of documentation work (resources, aims, rules of action, operational invariants), a key construct from the documentational approach (DA, Gueudet & Trouche, in Educational Studies in Mathematics, 71, 199-218, 2009). We do so in the case of five post-secondary teachers who use the same textbook as a main resource for teaching the topic. Documentational analysis of interviews with the teachers led to the identification of their aims and rules of action (the what and how of their resource use as they organise their teaching of the topic) as well as the operational invariants (the why for this organisation of their teaching). We describe the teachers’ documentation work in two sets of aims/rules of action: scaffolding mathematical content (series as a stepping stone to learning about Taylor polynomials and Maclaurin series), and organising student learning about series through drill exercises, visualisation, examples, and applications. Our bridging (networking) of theoretical constructs originating in one theoretical framework (personal relationship, ATD) with the constructs of a different, yet compatible, framework (documentation work, DA) aims to enrich the latter (teachers’ documentation work) with the individual agency (teachers’ personal relationships with the topic) provided by the former. [ABSTRACT FROM AUTHOR]

In this paper we present the results from a study conducted in a UK institution in which 21 mathematics pre-service teachers engage with two practice-based tasks featuring incidents where classroom management interferes with mathematical learning. We investigate their considerations when they make decisions in classroom situations and how these tasks can trigger their reflections on the teaching and learning of mathematics. In our analysis we used the constructs of social and sociomathematical norms (Cobb & Yackel, 1996) and Teaching Triad (Jaworski, 1994). Results indicate commendable norms pre-service teachers aspire to establish in their classroom, such as peer respect, value of discussion and investigative mathematical learning. However, they often miss the opportunity to engage students with metacognitive discussions and mathematical challenge as they focus on behavioural issues or endorse dichotomous and simplistic views of mathematical learning. We credit these tasks with allowing insight into pre-service teachers' considerations and we propose their further implementation in teacher education programs. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we draw on a 16-month study funded by the Learning and Teaching Support Network in the UK and entitled Mathematicians as Educational Co-Researchers. The study''s aims were two-fold. Primarily we intended to explore mathematicians’ reflections on issues identified in the literature as highly topical in the area of teaching and learning of undergraduate mathematics. We also wished to explore the conditions under which mutually effective collaboration between mathematicians and researchers in mathematics education might be achieved. Participants were 20 mathematicians from 6 mathematics departments and the study involved a series of Focus Group Interviews where pre-distributed samples of mathematical problems, typical written student responses, observation protocols, interview transcripts and outlines of relevant bibliography were used to trigger an exploration of pedagogical issues. Here we elaborate the theme ‘On the Pedagogical Insights of Mathematicians’ as it emerged from the data analysis. We do so in two parts: in the first part we present the participants’ reflections on issues of interaction and communication within the context of teaching and learning in higher education. The data suggest that the lecturers believe that mathematical learning is achieved more effectively as an interactive process and recognise that lecturing is not a method generally conducive to interaction. However, they discuss ways in which interaction can be achieved and refer to seminars, tutorials and feedback to students’ writing as other opportunities for interaction that must not be missed. In the second part, we focus on the lecturers’ pedagogical reflections regarding the abstract nature of university mathematics and, in particular, the ways in which teaching can facilitate the transition from the concrete to the abstract. We conclude with a brief evaluation of the project by the mathematicians themselves. [Copyright &y& Elsevier]

The development of increased and accessible computing power has been a major agent in the current emphasis placed upon the presentation of data in graphical form as a means of informing or persuading. However research in Science and Mathematics Education has shown that skills in the interpretation and production of graphs are relatively difficult for Secondary school pupils. Exploratory studies have suggested that the use of spreadsheets might have the potential to change fundamentally how children learn graphing skills. We describe research using a pedagogic strategy developed during this exploratory work, which we call Active Graphing, in which access to spread sheets allows graphs to be used as analytic tools within practical experiments. Through a study of pairs of 8 and 9 year old pupils working on such tasks, we have been able to identify aspects of their interaction with the experiment itself, the data collected and the graphs, and so trace the emergence of meanings for trend. [ABSTRACT FROM AUTHOR]

The article reflects on the successful completion of three years of journal's growth as well as introduction of new editorial arrangements. It discusses the appointment of Lara Alcock and Alf Coles as the editor of the Current Reports section and editor of Book Reviews section, respectively. It offers information on the introduction of Masters and doctoral level mathematics education research and long-term support for new mathematics education researchers and lecturers in different countries.

Information about several papers discussed at the Seventh Congress of the European Society for Research in Mathematics Education (CERME 7) held February 9-13, 2011 in Poland is presented. Topics include the epistemology of mathematics in science departments, an approach to trace university mathematicians' discourse, and the shifting profile of students in an Irish institution who take service mathematics courses. The individual character of pre-service secondary mathematics teachers is tackled.

The article focuses on a study being conducted in Great Britain and Canada, to analyze the teaching and learning of infinite series concept in mathematics education. It reports the analysis of pedagogical practices and curriculum content done by the study, and mentions its review of the texts and interviewing of mathematics teachers. It discusses study's findings on coverage of the concept, its historical references, and lack of figural representations in the texts. The study also found the need for using examples, visual representations, and applications for better understanding of the concept.

The author reflects on the current educational system with regards to the mathematics subject. He takes pride with the introduction of the first issue of "Research in Mathematics Education" (RME) and considers such journal as a new departure in mathematics education publishing system, with the aim to become informative and relevant to researchers worldwide. He also stresses that RME gives way to an exciting new venture with the Taylor & Francis Group PLC under the Routledge imprint.