Search

Collaboration between Mathematicians and Mathematics Educators is crucial in advancing knowledge on the teaching and learning of Mathematics, particularly in advanced Mathematics pedagogy. However, there is a need for the type of collaborations where Mathematicians and Mathematics Educators can find common ground, and the synergy of their expertise results in new, hybrid meanings and understandings that can benefit practice. This paper aims to help researchers from these communities come together by presenting a novel methodology for collaborative inquiry and qualitative data analysis--"dialogical inquiry"--based on Mikhail Bakhtin's theory of dialogism. In this framework, "truth" is conceived as never finalised but always coevolving through dialogue that involves participants with different "voices" and "languages". We describe the three principles that underpin "dialogical inquiry": motivation, power balance and a process for solving disagreements. These three principles interact together to create a space where critically productive dialogue allows for meanings to coevolve and new, hybrid understandings to emerge. We illustrate our operationalisation of these principles (i.e., the methods of "dialogical inquiry") in two areas: understanding solutions to linear ordinary differential equations and making meaning of the Bakhtinian concept of superaddressee. We reflect on our use of this methodology in Mathematics Education research and invite the readers to create their own dialogic spaces of collaboration.

University students' expectations of digital technologies in their studies are greatly influenced by their previous exposure both within the secondary school classroom and in their private lives. These expectations often play a powerful role in their approaches and learning strategies in their first-year university classes. In this work, we investigated students' expectations and utilisation of digital technologies in their transition from high school to tertiary studies. A survey encompassing the Expectancy-Disconfirmation Paradigm was conducted amongst second year students across the university. The results showed students expected to use advanced IT technologies and equipment at university. The high expectations were similar regardless of demographic parameters, such as gender, school type or field of studies. The findings also indicated that most students perceived little disconnection between the technology they used in high school and that of university. The majority of students seemed satisfied and even positively surprised by the use of technology in their university courses.

A novel approach to integrating Cluster Analysis (CA) within qualitative inquiry is presented, grounded in a large, unstructured dataset from open and rather unstructured interviews. This dataset was previously subjected to typical (theory sensitive) thematic analyses. Transformed into quantitative binary matrix structures, the CA offers robustness and transparency as it systematically exhausts the whole dataset in a replicable procedure. However, then the transformation becomes bi-directional, as resulting clusters provoke new qualitative interpretations and even further quantitative analyses. This approach led to theoretically interpretable results that significantly extended previous understandings of relations between 'values' and 'learning approach' relating to mathematics learner identity. This integrated methodology is evaluated for its significance to the substantive field, but is discussed more widely for social science research drawing on such interview datasets in general.

Using Cultural-Historical Activity Theory, we analyze lecturers' views on the aims and teaching practices of mathematical modelling (MM) education in Norway and England. We aim to expose the tensions that exist within the activity of teaching MM at university, such as those between multiple, sometimes competing, aims for teaching MM, or between the lecturers' professional identities and the structure of university degrees. Our conceptualization of these tensions might help lecturers consider how to overcome obstacles in their own contexts.

In this article, we argue that although mathematics educators are concerned about social issues, minimal attention has been paid to student-student interactions outside the classroom. We discuss social network analysis as a methodology for studying such interactions in the context of an undergraduate course. We present results on the questions: Who studies with whom? What are students' study habits, and are these systematically related to the habits of those with whom they interact? Do individual and collaborative study habits predict attainment? We discuss the implications of these findings for research on undergraduate learning and on social issues in mathematics education, suggesting that social network analysis may provide a bridge between mathematics education researchers who focus on cognitive and on social issues.

This paper explores the messages that first-year mathematics students receive in the context of their academic studies during their transition from school to university mathematics. Through observations of lectures and discussions with first-year mathematics undergraduates in an English university, we identified and analysed the messages that two of their lecturers transmitted to them during this transitional phase. The results suggest that strongly framed messages are more easily perceived by students and affect them during their transition. Additionally, messages that have been received in the school context continue to have control over students' thinking and on many occasions can impede adjustment to the new setting.

In this paper we explore how students can experience the relevance of mathematical modelling activities. In the literature we found that relevance is a connection among several issues (relevance of what? to whom? according to whom? and to what end?). We framed this concept in terms of Cultural-Historical Activity Theory (CHAT), a theory for analysing how individuals engage in activities within social environments. We designed modelling activities within a mathematics course for engineering students: there were ample mathematical modelling tasks, a guest lecture by an employee from an engine company who used mathematical modelling in his job, and a group work modelling assessment with a presentation to the whole group. After the course, we interviewed ten students with a wide range of final grades in the course. We analysed the interview data in light of the theoretical framing of the concept of relevance. Our analysis showed that, generally, students experienced the modelling activities as relevant, and that they imagined themselves working in professional practices for which mathematics is relevant. However, doing mathematics was also judged as being relevant only to obtain grades, leave school and enter professions for which mathematics might not be needed. We offer recommendations for making mathematics education more relevant to more students.

A wide body of literature has highlighted how high achievement in mathematics in secondary school does not necessarily motivate students to both choose and succeed on mathematically demanding programmes at post-compulsory level. The recent Enterprising Science project [Archer et al. (2015, "J. Res. Sci. Teach.," 52, 922-948)] and before that, the ASPIRES project [Archer et al. (2013, London: Kings College)], have both highlighted that access to science capital is perhaps more important than prior achievement in shaping students' aspirations and their future trajectories in Science, Technology, Engineering and Mathematics. In this article, we critically analyse the notion of science capital and its role in mediating students' choice of and experience of studying mathematically demanding degree programmes at university. Drawing on data from the TransMaths project, we present two cases--Stacey and Elton--who are both enrolled on the same "Mathematics for Physics" course at university. We show that although both discuss access to science capital in narrating their choice of degree, they do so in different ways and this invariably interplays with different forms of identification with "Mathematics for Physics". We conclude that there is a need to re-conceptualize science capital so that the dialectic relationship between its exchange and use value is theorized more fully. Whilst some students may access science capital as a means to accumulate capital (e.g. qualifications) for its own sake (exchange value), others appear to recognize the "use value" of science learning and knowledge and this produces different forms of engagement with science (and mathematics). We therefore argue that authoring oneself in the name of a STEM identity is crucial in mediating how one perceives science capital. Finally, we argue that mathematics should be a central part of this framework since it significantly contributes to the exchange value of science as a form of capital (especially Physics), but it also offers use value in scientific labour (e.g. in modelling scientific problems).

Mathematics has long been known to be problematic for university engineering students and their teachers, for example, Scanlan. This paper presents recent data gathered from interviews with engineering students who experienced problems with mathematics and their lecturers during their transition through the first year in different programme contexts. Our interviews with the students reveal how they understand the relation between engineering and mathematics and we draw on the concept of "use- and exchange-value" to explore this relationship more fully. This paper challenges both the pedagogical practice of teaching non-contextualized mathematics and the lack of transparency regarding the significance of mathematics to engineering. We conclude that the value of mathematics in engineering remains a central problem, and argue that mathematics should be a fundamental concern in the design and practice of first-year engineering. [This article was written with the TransMaths Team.]

Computer-aided assessment (CAA) has been used at a university with one of the largest mathematics and engineering undergraduate cohorts in the UK for more than ten years. Lecturers teaching mathematics to first year students were asked about their current use of CAA in a questionnaire and in interviews. This article presents the issues that these lecturers faced as they made use of this assessment tool. Lecturers explained how they attempted to overcome these issues. The findings show that while the lecturers were happy to use the CAA system because it is efficient and timesaving, there were concerns that it might not always be beneficial for students. The bases for lecturers' concerns were that some students developed tendencies to depend on the feedback to complete assessments and to develop procedural, context-dependent strategies for solving problems.

This paper examines "resilience" of mathematics students in transition from a sociocultural perspective, in which resilience is viewed as relational and in particular as a function of the social and cultural capital students may bring to the new field. We draw on two students' stories of transition, in which we recognise elements traditionally viewed as "risks" for mathematics students in transition into institutions where new demands are made. However, in each case it seems that some of their apparent background "risk factors"--coming from poorer socioeconomic backgrounds and disadvantaged schools--have come to serve to constitute capital, buttressing their particular resilience, as they provide a crucial kind of autonomy that is particularly valued in the new institution. We identify the learners' reflexivity as having been crucial to this accumulation of capital and we discuss some educational implications. (Contains 3 notes.)

We address the current concerns about teaching-to-the-test and its association with declining dispositions towards further study of mathematics and the consequences for choice of STEM subjects at university. In particular, through a mixed study including a large survey sample of over 1000 students and their teachers, and focussed qualitative case studies, we explored the impact of "transmissionist" pedagogic practices on learning outcomes. We report on the construction and validation of a scale to measure teachers' self-reported pedagogy. We then use this measure in combination with the students' survey data and through regression modelling we illustrate significant associations between the pedagogic measure and students' mathematics dispositions. Finally, we discuss the potential implications of these results for mathematics education and the STEM agenda. (Contains 7 notes, 4 figures and 7 tables.)

The construct of identity has been used widely in mathematics education in order to understand how students (and teachers) relate to and engage with the subject (Kaasila, 2007; Sfard & Prusak, 2005; Boaler, 2002). Drawing on cultural historical activity theory (CHAT), this paper adopts Leont'ev's notion of "leading activity" in order to explore the key "significant" activities that are implicated in the development of students' reflexive understanding of self and how this may offer differing relations with mathematics. According to Leont'ev (1981), leading activities are those which are significant to the development of the individual's psyche through the emergence of new motives for engagement. We suggest that alongside new motives for engagement comes a new understanding of self--a "leading identity"--which reflects a hierarchy of our motives. Narrative analysis of interviews with two students (aged 16-17 years old) in post-compulsory education, Mary and Lee, are presented. Mary holds a stable "vocational" leading identity throughout her narrative and, thus, her motive for studying mathematics is defined by its "use value" in terms of pursuing this vocation. In contrast, Lee develops a leading identity which is focused on the activity of studying and becoming a university student. As such, his motive for study is framed in terms of the exchange value of the qualifications he hopes to obtain. We argue that this empirical grounding of leading activity and leading identity offers new insights into students' identity development.

This paper reports how students talk about their aspirations in regard to higher education (HE) and their mathematics, what "repertoires" they use to mediate this discourse, and how students' predominant "repertoire style" relates to their cultural background. Our analyses draw on an interview sample (n=40) of students selected because they are "on the cusp" of participation or non-participation in mathematically demanding programmes in further and higher education. The interviews explored the students' aspirations for their future in general and HE in particular, influences on these choices, and the place of mathematics in these. Thematic analysis revealed four interpretative repertoires commonly in use, which we call "becoming successful", "personal satisfaction", "vocational", and "idealist" repertoires. Most of the sample was found to use a single, predominant repertoire, which we call their repertoire "style": what is more, this style is found to be strongly related to background factors independently obtained. The implications for policy and practice are discussed. (Contains 2 tables.)

The aim of this project was to examine the effectiveness of feedback offered by computer-aided assessment (CAA). CAA provides practice tests for undergraduates, and feedback to help them improve their scores and mathematical understanding. However, there is a lack of evidence-based literature on the effect of formative feedback in mathematics learning (Crockett et al. 2009), and so a desire for research to examine the effectiveness of the feedback that CAA provides (Sangwin 2007). The authors refer to Ramaprasad (1983), Taras (2002) and Yorke (2003) when defining formative feedback to comprise: (1) a judgement made against a given standard; (2) advice for the student to close the gap between current performance and this standard; and (3) evidence to demonstrate an improvement has been made. Mathematics undergraduates working with CAA at Loughborough University may access practice tests multiple times for a limited period usually a week prior to a summative testing period. The questions in the practice tests are similar to those in the following summative test. The CAA system marks each attempt, and returns a score with feedback for each question. Feedback usually comprises full worked solutions. Research questions include: (1) Are students able to identify learning gaps by using CAA?; (2) Are students given the advice they require to reduce these learning gaps?; and (3) Can students demonstrate an improvement with respect to these learning gaps? Focus groups enabled the authors to seek the opinions of students directly, and to pursue the points they raised in more detail. This permitted the authors to capture the issues for a few cases, and the authors sought to investigate the generalisability of their conclusions with questionnaires. The sample was taken from a class of 237 registered students. The students in this group believed CAA helped them to identify learning gaps.

In this paper we describe the validation of two scales constructed to measure pre-university students' changing disposition (i) to enter Higher Education (HE) and (ii) to further study mathematically-demanding subjects. Items were selected drawing on interview data, and on a model of disposition as socially- as well as self-attributed. Rasch analyses showed that the two scales each produce robust one-dimensional measures on what we call a 'strength of commitment to enter HE' and 'disposition to study mathematically-demanding subjects further' respectively. However, the former scale was initially found to suffer psychometrically from a ceiling effect, which we 'corrected' by adding some harder items at a later data point, and revised the scale according to our interpretation of subsequent results. We finally discuss the potential significance of the constructed measures of learning outcomes, as variables in monitoring or even explaining students' progress into different subjects in HE. [ABSTRACT FROM AUTHOR]