“Not Like a Big Gap, Something We Could Handle”: Facilitating Shifts in Paradigm in the Supervision of Mathematics Graduates upon Entry into Mathematics Education

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

Do bold shakeups of the learning-teaching agreement work? A commognitive perspective on a LUMOS low lecture innovation

Mathematics undergraduates, and their lecturers, often describe the transition into university mathematics as a process of enculturation into new mathematical practices and new ways of constructing and conveying mathematical meaning (Nardi, 1996). Whatcharacterises the breadth and intensity of this enculturation varies according to factors such as (Artigue, Kent & Batanero, 2007): student background and preparedness for university level studies of mathematics; the aims and scope of each of the courses that thestudents take in the early days of their arrival at university; how distant the pedagogical approaches taken in these courses are from those taken in the secondary schools that the students come from; the students’ affective dispositions towards the subject and their expectations for what role mathematics is expected to play in their professional life. On their part, lecturers’ views on their pedagogical role may also vary according to factors such as (Nardi, 2008): length of teaching experience; type of courses (pure, applied, optional, compulsory etc.) they teach; perceptions of the goals of university mathematics teaching (such as to facilitate access to the widest possible population of participants in mathematics or select those likely to push the frontiers of the discipline); and, crucially, institutional access to innovative practices, e.g. through funded, encouraged and acknowledged research into such practices.In this paper I draw on my experiences as a member of the International Advisory Board of the LUMOS project (Barton & Paterson, 2013) to comment on aspects of aforementioned student enculturation. Here I see this enculturation as the adaptation of different ways to act and communicate mathematically. I take a perspective on these ways to act and communicate as discourses and I treat the changes to the mathematical and pedagogical perspectives of those who act as discursive shifts. To this purpose, I deploythe approach introduced by Anna Sfard (2008) and known as the commognitive approach

Challenging the mathematician’s ‘ultimate substantiator’ role in a low lecture innovation

In this paper we draw on our experiences as member of the International Advisory Board and principal investigator of a research project on undergraduate mathematics teaching and learning to comment on the study of university mathematics as a process of enculturation into new mathematical practices and new ways of constructing and conveying mathematical meaning. We see this enculturation as the adaptation of different ways to act and communicate mathematically. We take a discursive perspective and we treat the changes to the mathematical and pedagogical perspectives of those who act – students and lecturers – as discursive shifts (Sfard, 2008). Our particular focus is on the shifts concerning the ‘ultimate substantiator’ role typically attributed to the lecturer

Introducing the concept of infinite series: Preliminary analyses of curriculum content and pedagogical practice

Introducing the concept of infinite series: preliminary analyses of curriculum content and pedagogical practice

Balancing classroom management with mathematical learning: Using practice-based task design in mathematics teacher education

In this paper we present the results from a study conducted in a UK institution in which 21mathematics 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

The construction of meanings for trend in active graphing

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 spreadsheets 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. © 2000 Kluwer Academic Publishers

Consistency, specificity, reification of pedagogical and mathematical discourses in student teacher narratives on the challenges of their school placement experience

International audienceIn this poster presentation we discuss how the mathematical and pedagogical content addressed in the taught component of a mathematics teacher education programme interacts with teacher-students' experiences in school placements and their reflection on these experiences. We invited mathematics teacher-students to provide scenarios drawn on their experience in schools soon after their first block of school placement, then these scenarios (12) were discussed by17 teacher-students in groups and in class discussions. Scenarios and discussions were analysed according to four characteristics: consistency between stated beliefs and intended (or reflected upon) practices, specificity of the reflection to the classroom situations under consideration, reification of pedagogical discourse, and reification of mathematical discourse.</p

Routines in the didactical and mathematical discourses of closed-book examination tasks

International audienceIn this paper, we investigate the discourse of the closed-book examinations using a commognitive perspective. We analyse the routines of the discourse aiming to describe lecturers' expectations about students' engagement with mathematical discourse. Our data consists of the examination tasks of a year one course from a mathematics department in the United Kingdom and interviews with the lecturers of the course. In our analysis we distinguish between mathematical and didactical routines in the lecturers' discourse about examinations. Our analysis reveals that the majority of the mathematical routines are substantiation and recall and that the didactical routines focus largely on: directions given on the how of the mathematical routines; the gradual structure of tasks; students' enculturation.</p