Changing pre-service mathematics teachers’ beliefs about using computers for teaching and learning mathematics: the effect of three different models

This study examines the effect of three different computer integration models on pre-service mathematics teachers’ beliefs about using computers in mathematics education. Participants included 104 pre-service mathematics teachers (36 second-year students in the Computer Oriented Model group, 35 fourth-year students in the Integrated Model (IM) group and 33 fifth-year students in the Exploring Mathematical Relationships with Mathematical Software (EMReMaS) group. The results indicated a remarkable change in beliefs within the EMReMaS and IM groups concerning computer use in teaching and learning mathematics. The present study offers empirical evidence that the pre-service mathematics teachers’ experiences in computer-based mathematics courses played a significant role in this change. Teacher education programmes should consider this learning method for pre-service teachers.     

Troubling “understanding mathematics in-depth”: Its role in the identity work of student-teachers in England

In this paper, we focus on an initiative in England devised to prepare non-mathematics graduates to train as secondary mathematics teachers through a 6-month Mathematics Enhancement Course (MEC) to boost their subject knowledge. The course documentation focuses on the need to develop “understanding mathematics in-depth” in students in order for them to become successful mathematics teachers. We take a poststructural approach, so we are not interested in asking what such an understanding is, about the value of this approach or about the effectiveness of the MECs in developing this understanding in their participants. Instead we explore what positions this discourse of “understanding mathematics in-depth” makes available to MEC students. We do this by looking in detail at the “identity work” of two students, analysing how they use and are used by this discourse to position themselves as future mathematics teachers. In doing so, we show how even benign-looking social practices such as “understanding mathematics in-depth” are implicated in practices of inclusion and exclusion. We show this through detailed readings of interviews with two participants, one of whom fits with the dominant discourses in the MEC and the other who, despite passing the MEC, experiences tensions between her national identity work and MEC discourses. We argue that it is vital to explore “identity work” within teacher education contexts to ensure that becoming a successful mathematics teacher is equally available to all.     

Students’ use of personal technologies in the university classroom: analysing the perceptions of the digital generation

Faculty frequently express concerns about students’ personal use of information and communication technologies in today’s university classrooms. As a requirement of a graduate research methodology course in a university in Ontario, Canada, the authors conducted qualitative research to gain an in-depth understanding of students’ perceptions of this issue. Their findings reveal students’ complex considerations about the acceptability of technology use. Their analysis of the broader contexts of students’ use reveals that despite a technological revolution, university teaching practices have remained largely the same, resulting in ‘cultural lag’ within the classroom. While faculty are technically ‘in charge’, students wield power through course evaluations, surveillance technologies and Internet postings. Neoliberalism and the corporatisation of the university have engendered an ‘entrepreneurial student’ customer who sees education as a means to a career. Understanding students’ perceptions and their technological, social and political contexts offers insights into the tensions within today’s classrooms.     

A categorization of the “whys” and “hows” of using history in mathematics education

This is a theoretical article proposing a way of organizing and structuring the discussion of why and how to use the history of mathematics in the teaching and learning of mathematics, as well as the interrelations between the arguments for using history and the approaches to doing so. The way of going about this is to propose two sets of categories in which to place the arguments for using history (the “whys”) and the different approaches to doing this (the “hows”). The arguments for using history are divided into two categories; history as a tool and history as a goal. The ways of using history are placed into three categories of approaches: the illumination, the modules, and the history-based approaches. This categorization, along with a discussion of the motivation for using history being one concerned with either the inner issues (in-issues) or the metaperspective issues (meta-issues) of mathematics, provides a means of ordering the discussion of “whys” and “hows.”

Language of learning and teaching in schools: an issue for research in mathematics teacher education?

Most countries in Africa have introduced the use of local languages as the language of learning and teaching for the first few years of schooling. Meaning that for the first few years of learning, learners learn mathematics in their local languages. In response to this, most research has focused on the challenges of using local languages in multilingual mathematics classrooms in schools. Not much research focuses on how the teacher educators prepare the prospective teachers to teach mathematics in multilingual classrooms. To further knowledge in the area of multilingualism in mathematics education, I, in this paper, present an analysis of the literature on multilingual teacher education in Africa. Specifically, I look at what it is that governments in interested countries are doing in teacher education programs in response to the introduction of local languages in schools. From the literature examined, I found that although there is awareness in a number of countries of the need for multilingual teacher education, not much has been done in order to train mathematics teachers on how to use local languages in the classroom. I therefore recommend that, for those countries that have implemented or planning to introduce the use of local languages in schools, some reforms should also take place in teacher education programs in terms of training the prospective teachers how to teach in local languages.     

Learning to write in higher education: students’ perceptions of an intervention in developing understanding of assessment criteria

This paper reports on the second phase of a project designed to improve students’ understanding of assessment demands. In Stage 1, Level 1 students were involved in a range of activities culminating in peer marking. This peer assessment was, itself, marked by the tutors to encourage students to engage positively with the process. Stage 2 of the project investigated whether these various intervention activities had any long-term impact on sports studies students’ approach to writing assignments. Interviews were conducted with six students who participated in Stage 1. For comparison purposes, a matched group of students from another vocationally-related course were also interviewed. The findings suggest that the peer assessment did encourage students to pay attention to assessment information. However, the students placed greater stress on the role of informal support, particularly verbal clarification of written guidance and feedback. The article concludes with a discussion of the implications for practice.     

A primary teacher’s mathematics teaching: the development of beliefs and practice in different “supportive” contexts

This article refers to a longitudinal case study of a primary school teacher over a period of 4 years. The focus is on the development of the teacher’s beliefs regarding mathematics teaching and learning from the last year of her university studies up to the third year of teaching mathematics in school. This development has been investigated within three different contexts, which have been distinguished in terms of the kind of support provided to this teacher. Two dominant beliefs emerged which have been traced through the period of the study from both the teacher’s reflections and actions. The first belief drew on the idea that what was considered an easy mathematical task by an adult could also be easily understood by children, while the second was that children learn mathematics through their actual involvement in a variety of teaching activities. The results indicate the way that teacher’s experiences from her university studies, actual classroom practice and inservice education interact and influence her beliefs and professional development.     

Developing a deeper understanding of <Emphasis Type="Italic">mathematics teaching expertise</Emphasis>: an examination of three Chinese mathematics teachers’ resource systems as windows into their work and expertise

In order to develop a deeper understanding of mathematics teaching expertise, in this study we use the Documentational Approach to Didactics to explore the resource systems of three Chinese mathematics “expert” teachers. Exploiting the Western and Eastern literature we examine the notion of “mathematics teaching expertise”, as it is perceived in the East and the West. The data consist of two rounds of in-depth interviews, observations and teachers’ representations of their resource systems, where teachers describe their resources connected to their practice, their perceptions of mathematics teaching expertise, and how to develop it. Subsequently, the data are analyzed with respect to the different facets of the notion of teaching expertise and related to the teachers’ views and practices, in order to deepen our understandings of what proficiency in mathematics teaching might mean and how to develop it, seen through the lens of ‘resources’. The significance of the study relates to the enhancement of mathematics teachers’ expertise and capacity building when working in collectives (e.g., in teacher professional development), in order to develop a strong workforce for supporting and helping to improve pupil learning.     

“Eyes in the Back of Your Head”: moral themes in African American narratives of racial conflict

Abstract

This paper examines seven narratives of racial conflict elicited from African American adults and young people. Analysis focusses on the relational nature of the racial conflicts. Issues of power and authority inherent in the sociopolitical context in which racial knowledge develops and moral judgements regarding racial differences are determined are found to be likewise embedded in interracial interpersonal relationships. Adopting Brown & Gilligan's (1990) methodological approach to reading narratives of conflict and choice, the two moral themes of justice and care are explored in the constitution and resolution of the conflicts shared. Concerns specific to the psychological development of African Americans and to the transmission of race‐related morals and values in black cultures are addressed.     

Book Review: A review of the book by Liping Ma (2020) Knowing and teaching elementary mathematics: teachers’ understanding of fundamental mathematics in China and the United States (3rd ed.)

Educational Studies in Mathematics -     

Exploring the characteristics of an optimal design of non-programming plugged learning for developing primary school students’ computational thinking in mathematics

Existing computational thinking (CT) research focuses on programming in K-12 education; however, there are challenges in introducing it into the formal disciplines. Therefore, we propose the introduction of non-programming plugged learning in mathematics to develop students’ CT. The research and teaching teams collaborated to develop an instructional design for primary school students. The participants were 112 third- and fourth-grade students (aged 9–10) who took part in three rounds of experiments. In this paper, we present an iterative problem-solving process in design-based implementation research, focusing on the implementation issues that lead to the design principles in the mathematics classroom. The computational tasks, environment, tools, and practices were iteratively improved over three rounds to incorporate CT effectively into mathematics. Results from the CT questionnaire demonstrated that the new program could significantly improve students’ CT abilities and compound thinking. The results of the post-test revealed that CT, including the sub-dimensions of decomposition, algorithmic thinking, and problem-solving improved threefold compared to the pre-test between the three rounds, indicating that strengthened CT design enhanced CT perceptions. Similarly, the students’ and teacher’ interviews confirmed their positive experiences with CT. Based on empirical research, we summarize design characteristics from computational tasks, computational environment and tools, and computational practices and propose design principles. We demonstrate the potential of non-programming plugged learning for developing primary school students’ CT in mathematics.

     

High-tech,hard work: an investigation of teachers’ work in the digital age

This paper explores the ways in which digital technologies are now implicated in the work – and specifically the labour – of school teachers. Drawing upon qualitative studies in two Australian high schools, the paper examines the variety of ways in which teachers’ work is now enacted and experienced along digital lines. In particular, the paper highlights the association of digital technologies with the standardization, evidencing, intensification and altered affect of teachers’ work. The paper questions the extent to which these trends might be seen as constituting ‘new’ forms of labour, with the research data pointing to continuities and disjunctures in terms of teachers’ autonomy and professionalization. The paper also considers how these conditions are experienced in different ways across the teaching workforce. The paper concludes by reflecting on how fairer and/or empowering working conditions might be achievable through alternate uses of digital technology.     

Developing mathematics teacher knowledge: the paradidactic infrastructure of “open lesson” in Japan

In this paper, we first present a theoretical approach to study mathematics teacher knowledge and the conditions for developing it, which is firmly rooted in a systemic approach to didactic phenomena at large, namely the anthropological theory of the didactic. Then, a case of open lesson is presented and analysed, using this theoretical approach, to show how the format of open lesson contributes to the construction and diffusion of didactic knowledge in the community of mathematics teachers in Japan. The basic idea of this format is that teachers from other schools are invited to observe a class taught by a teacher then participate in a discussion session with him on the details of the lesson. For the case study, we analyse the lesson plan prepared for an open lesson, the observed lesson and the teachers’ discussion. As a result, an open lesson session has been described as a specific form of post-didactic practice related directly to an actual observed lesson, and aiming specifically at elaborating the theoretical aspects of teacher’s didactic practice in the lesson and beyond it.     

��Good�� mathematics teaching for students of color and those in poverty: the importance of relational interactions within instruction

In considering ??good teaching?? in mathematics, scholars usually refer to teacher knowledge and instructional practices that promote understanding. However, researchers have found that these two elements of instruction are often not as prevalent in urban contexts, a space where high percentages of students of color and the poor are educated. Additionally, recent work calls for understanding other classroom mechanisms that impact the mathematics learning of students of color. Using video, field notes, and an interview, this research examines a case study of one urban classroom of Latino and African American students. Their teacher engages them in substantive mathematics and reform-minded pedagogical strategies, but a number of relational interactions raise issues of how these micro-interactions can mediate access to mathematics. The study found four dimensions in which relational interactions mediated access to mathematics: addressing behavior, framing mathematics ability, acknowledging student contributions, and attending to culture and language. The paper ends with raising questions for future research and calling for a broader framing of instruction that incorporates relational dimensions of the classroom.     

Mobile game-based learning in the era of “shifting to digital”

Educational technology research and development -     

Technological,pedagogical and content knowledge in one-to-one classroom: teachers developing “digital wisdom”

One-to-one (1X1) laptop initiatives become prevalent in schools aiming to enhance active learning and assist students in developing twenty-first-century skills. This paper reports a qualitative investigation of all 7th graders and their 15 teachers in a junior high-school in Northern Israel gradually implementing 1X1 model. The research was conducted during a second year of 1X1 implementation at the school level, which was a first year of teaching and learning with laptops for all study participants. The study triangulates non-participant lessons’ observations and semi-structured interviews with 15 teachers. The data were collected twice: at the beginning and toward the end of the 2011–2012 academic year – in total, 30 observations and 30 interviews were conducted. The results were examined through phenomenological research techniques and discussed in terms of the technological, pedagogical and content knowledge (TPACK) and “digital wisdom” approaches. The teachers showed significant increase of technological knowledge. However, only moderate connections between technology and pedagogy as well as between technology and content were found. Some of the teachers functioned as moderators, scaffolding students and supporting their individual or collaborative learning. However, many teachers struggled with effective management of 1X1 classroom. Neither conjunction of teacher TPACK nor facilitation of student digital skills was observed. The paper suggests an overlap of the TPACK framework and the digital wisdom approach and provides implications for curriculum developers and educational policy-makers.     

Leading learning and teaching: an exploration of ‘local’ leadership in academic departments in the UK

This paper reports on a small-scale longitudinal study of ‘local’ leadership roles at two UK universities. The research explored perceptions of the leadership provided by a specific group of staff who held roles for enhancing learning and teaching. Based on ethnographic design principles, the study was based at one UK higher education institution with another as a comparator. Data were collected through semi-structured interviews and focus groups with ‘local’ leadership role-holders and their colleagues. Semi-structured interviews were conducted with academic managers. Analysis of the data was based on grounded theory and thematic analysis. The discussion and conclusion suggests that, to maximize the impact of these roles, the leadership aspects of them should be made explicit, recognized by colleagues at all levels and supported by leadership development. Further investigation into local leaders’ career progression may provide valuable insights for the relatively limited body of knowledge and practice of leadership within professional teams.     

Leading learning and teaching: an exploration of ‘local’ leadership in academic departments in the UK

Tertiary Education and Management - This paper reports on a small-scale longitudinal study of ‘local’ leadership roles at two UK universities. The research explored perceptions of the...     

Research and teaching in the universities of Denmark: Does such an interplay really exist?

The unity of research and teaching is an ingrained principle in university policy in Denmark, but this principle has also been subjected to increasing criticism. This article presents an investigation, consisting of about 50 interviews with teachers from higher educational institutions in Denmark, aiming at the illumination of this issue. According to the conclusions of this investigation it is the basic experience of the teachers that an important interplay exists between research and teaching of the individual teacher, and that almost none would prefer to work in a pure research institution. At the same time the teachers have some crucial reservations. Firstly it can be difficult to administer this twofold task. Secondly the interrelationships are dependent on several factors, the most important of which is the level of teaching and the disciplinary context. This latter factor is explained by differences pertaining to the very nature of varying disciplines - demonstrated and analyzed with reference to Thomas Kuhn and Basil Bernstein. Finally, the importance of the interrelationships between research and teaching for higher educational and research policies in broader perspective is discussed.