Constructions of mathematicians in popular culture and learners’ narratives: a study of mathematical and non‐mathematical subjectivities

In this paper, based on a project funded by the UK Economic and Social Research Council considering how people position themselves in relation to popular representations of mathematics and mathematicians, we explore constructions of mathematicians in popular culture and the ways learners make meanings from these. Drawing on an analysis of popular cultural texts, we argue that popular discourses overwhelmingly construct mathematicians as white, heterosexual, middle‐class men, yet also construct them as ‘other’ through systems of binary oppositions between those doing and those not doing mathematics. Turning to the analysis of a corpus of 27 focus groups with school and university students in England and Wales, we explore how such images are deployed by learners. We argue that while learners’ views of mathematicians parallel in key ways popular discourses, they are not passively absorbing these as they are simultaneously aware of the clichéd nature of popular cultural images.     

Everyday pedagogical practices in mathematical play situations in German “Kindergarten”

This study describes situations in German daycare facilities (Kindergarten) in which the development of mathematical thinking in children is specifically encouraged through examination of common play objects. Using micro-sociological methods of analysis, the mathematical potential of such interactions between teacher and child is elaborated within the framework of everyday pedagogical practices (Bruner, 1996) and instructional models (Rogoff; Mind, Cult Activ 1(4): 209–229, 1994). It is also considered which concepts of mathematics may be important in these interactions.     

‘I’m not a “maths‐person”!’ Reconstituting mathematical subjectivities in aesthetic teaching practices

In this study I have investigated how alternative ways of teaching mathematics influence and affect Early Childhood Education (ECE) students’ attitudes towards maths and how they understand their own subjectivities as more or less mathematical during a 10‐week alternative maths course. The investigated course adopts a feminist post‐structural approach based on critical pedagogy and deconstructive theory and includes an interdisciplinary approach to investigative mathematics. The data used include the memory/narrative writings and process‐writings of 75 female teacher‐education students, collected from three different cohorts, in which the students describe their learning processes throughout the maths course. The study shows that, in the main, the students became much more positively inclined to the subject of mathematics after the maths course and agreed that this course had changed their understanding of their own mathematical subjectivity, albeit in different and varying ways.     

Working like real mathematicians: developing prospective teachers’ awareness of mathematical creativity through generating new concepts

This paper describes the experience of a group of 17 prospective mathematics teachers who were engaged in a series of activities aimed at developing their awareness of creativity in mathematics. This experience was initiated on the basis of ideas proposed by the participants regarding ways creativity of school students might be developed. Over a period of 6 weeks, they were engaged in inventing geometrical concepts and in the examination of their properties. The prospective teachers’ reflections upon the process they underwent indicate that they developed awareness of various aspects of creativity while deepening their mathematical and didactical knowledge.     

Supporting children’s mathematical understanding: professional development focused on out-of-school practices

This study describes the Reflection Connection Cycle professional development designed to support teachers’ use and appreciation of students’ out-of-school practices related to school mathematics. The year-long program incorporated group lesson design, readings, and video analysis for 14 elementary school (ages 5–12) teachers. Analysis of lesson development, written reflections, and analysis of teacher talk revealed important patterns related to the difficulty in writing lessons that built on students’ informal understandings. While initial lessons focused solely on the context of practices like gardening and sports, subsequent lessons show a greater concern for the mathematics in which children were engaged within a practice. A Multi-approach Engagement Framework is presented both as a tool to support further professional development efforts and as a means to describe stability and change in teachers’ efforts to connect in-school and out-of-school mathematical understandings.     

Interesting and difficult mathematical problems: changing teachers’ views by employing multiple-solution tasks

The study considers mathematical problem solving to be at the heart of mathematics teaching and learning, while mathematical challenge is a core element of any educational process. The study design addresses the complexity of teachers’ knowledge. It is aimed at exploring the development of teachers’ mathematical and pedagogical conceptions associated with systematic employment of multiple-solution tasks (MSTs) in a “problem-solving” course for prospective mathematics teachers (PMTs). Our attention to teachers’ mathematical conceptions focused on the development of PMTs’ problem-solving competences. Our attention to teachers’ meta-mathematical and pedagogical conceptions focused on changes in teachers’ views concerning the level of interest and level of difficulty of the mathematical tasks. We differentiated between the systematic and craft modes of professional development integrated in the course. Systematic mode involved problem-solving sessions and reflective discussions on collective solution spaces. Craft mode involved interviewing school students. The study demonstrates the effectiveness of MSTs for PMTs’ professional development.     

Unpacking foreshadowing in mathematics teachers’ planned practices

This paper provides an empirical exploration of mathematics teachers’ planned practices. Specifically, it explores the practice of foreshadowing, which was one of Wasserman’s (2015) four mathematical teaching practices. The study analyzed n?=?16 lessons that were planned by pairs of highly qualified and experienced secondary mathematics teachers, as well as the dialogue that transpired, to identify the considerations the teachers made during this planning process. The paper provides empirical evidence that teachers engage in foreshadowing as they plan lessons, and it exemplifies four ways teachers engaged in this practice: foreshadowing concepts, foreshadowing techniques, foregrounding concepts, and foregrounding techniques. Implications for mathematics teacher education are discussed.

     

Chinese students’ groupwork practices and experiences in China

Chinese students constitute the most rapidly growing international cohort of students enrolled in many Western tertiary settings, and it is important to understand more about their preparation for engaging with commonly used teaching approaches such as groupwork. This study investigated their attitudes and experience of groupwork while enrolled at a large Chinese university. Semi-structured and video-stimulated recall interview data were collected from 16 third-year Finance students over a 5-week field study. Results showed that this group of Chinese students experienced more out-of-class than in-class groupwork activities. These out-of-class groupwork sessions fell into three categories: (1) student initiated, (2) student league initiated and (3) teacher initiated. Students identified both individual and collective benefits from groupwork, highlighting that Chinese students value groupwork and actively seek to engage with it in the Chinese tertiary context. This study contributes to the understanding of Chinese students’ group practices in Chinese tertiary settings.     

What’s the problem? Meaning making and learning to do mathematical word problems in the context of digital tools

The general background of this study is an interest in how digital tools contribute to structuring learning activities. The specific interest is to explore how such tools co-determine students’ reasoning when solving word problems in mathematics, and what kind of learning that follows. Theoretically the research takes its point of departure in a sociocultural perspective on the role of cultural tools in thinking, and in a complementary interest in the role of the communicative framing of cognitive activities. Data have been collected through video documentation of classroom activities in secondary schools where multimedia tools are integrated into mathematics teaching. The focus of the analysis is on cases where the students encounter some kind of difficulty. The results show how the tool to a significant degree co-determines the meaning making practices of students. Thus, it is not a passive element in the situation; rather it invites certain types of activities, for instance iterative computations that do not necessarily rely on an analysis of the problems to be solved. For long periods of time the students’ activities are framed within the context of the tool, and they do not engage in discussing mathematics at all when solving the problems. It is argued that both from a practical and theoretical point of view it is important to scrutinize what competences students develop when using tools of this kind.

Minding mathematicians’ discourses in investigations of their feedback on students’ proofs: a case study

Educational Studies in Mathematics - This article presents a research apparatus for investigating and making sense of stories that emerge from feedback that mathematicians provide on...     

Drawing space: mathematicians’ kinetic conceptions of eigenvectors

This paper explores how mathematicians build meaning through communicative activity involving talk, gesture and diagram. In the course of describing mathematical concepts, mathematicians use these semiotic resources in ways that blur the distinction between the mathematical and physical world. We shall argue that mathematical meaning of eigenvectors depends strongly on both time and motion—hence, on physical interpretations of mathematical abstractions—which are dimensions of thinking that are typically deliberately absent from formal, written definition of the concept. We shall also show how gesture and talk contribute differently and uniquely to mathematical conceptualisation and further elaborate the claim that diagrams provide an essential mediating role between the two.     

Using ‘Fictional’ Story in Teacher Research

A deputy headteacher in a mixed comprehensive school of some 1200 students, aged 12-18 years describes her responsibilities, which include ‘continuing professional development’. She began an action research project in 1991 on how to develop not only her role in becoming more reflective in her day to day practice, but also how to develop opportunities for teachers to take time out of everyday ‘busyness’ in order to reflect on and improve pedagogical practices. She set up an action research group for teachers in school and many of the projects undertaken were validated by Kingston University, thus enabling teachers to gain a postgraduate Diploma in Action Research as part of an in-house course, in which teachers chose their own focus for development, and learnt to support and critique each other's work. As part of the methodology they used ‘story’ to help come to a focus, to put their thoughts in order, to clarify what they were thinking and to move forward their professional development. What follows is one account of how story was used to begin to develop thinking.     

College Students’ Participation in Fundamental Scientific Research

Russian university students need to be involved in research as part of their educational experience. An example of how this may be done, and the issues that need to be addressed in such an approach, are provided by the program at Perm State University of Pedagogical Humanities.     

Under-threes’ mathematical learning – teachers’ perspectives

This project highlights preschool teachers’ views of toddlers’ learning in mathematics. The Swedish national curriculum covers even the youngest children who are 1–3?years old. Interesting questions are thus: what should mathematics be for this age group and how should preschool teachers work with maths to achieve the curriculum objectives? Data were collected through interviews with six preschool teachers working in four different preschools. The data show that the teachers emphasize the body as very important for the learning process, which means that for these children, it is not a matter of simply talking about mathematical concepts, but experiencing them bodily. The teachers also report that they now pay more attention than previously to what material the children use and how they interact with it. They are more aware of how they organize and offer the various materials in the preschool and how this influences the way children use them and, consequently, their learning processes.     

Applying artificial intelligence insights in a CAI program for “open sentence” mathematical problems in primary schools

Elementary school children are often unclear which operations to use when tackling mathematical problems of the open sentence kind (e.g. 3+*=7). We give details of (a) some of their impasse-repair and other problem-solving strategies; (b) computer models of knowledge and misconceptions underlying those strategies; and (c) a CAI program which can identify strategies and remedy gaps in knowledge and misconceptions. Tests of that program with second graders in five schools over six weeks indicate that one third profited significantly. The results are further discussed.1. Jacobijn A. C. Sandberg, is now at the Department of Social Science Informatics, University of Amsterdam, The Netherlands.Note