STUDY ON LATVIAN MATHEMATICS TEACHERS’ ESPOUSED BELIEFS ABOUT TEACHING AND LEARNING AND REPORTED PRACTICES

The aim of the research was to compare espoused beliefs about teaching and learning and reported practices for the teachers of mathematics in Latvia. The sample consisted of 390 teachers of mathematics from different regions of Latvia. The present research is a part of an international comparative research within the NorBa project (Nordic–Baltic Comparative Research in Mathematics Education) that makes use of a quantitative questionnaire for mathematics teachers. The results show that the espoused beliefs of Latvian teachers of mathematics on efficient teaching tend more to a constructivist approach, whilst reported practices are more oriented to a traditional approach; yet, there exist statistically significant differences for teachers of different social and demographical groups. The research outcomes may be used for the improvement of teacher further education programmes.     

From authoritative discourse to internally persuasive discourse: discursive evolution in teaching and learning the language of science

Learning science interpreted in existing theoretical frameworks often means that students are assimilated, accommodated or enculturated from the entity of the vernacular world to the entity of the scientific world. However, there are some unsolved questions as to how students can best learn purely a new language or new knowledge of science. The purpose of this study is to conduct microanalysis of moment-to-moment interactions in order to understand how science language is taught and learned in details. Informed by Bakhtin’s dialogism, the analysis indicates that learning science is a process of appropriating authoritative discourse into internally persuasive discourse. Based on our analysis and findings, we propose the framework of discursive evolution to describe the process of teaching and learning the language of science. Four different stages of discursive evolution are identified to demonstrate the discursive changes during the course of science teaching and learning discourse: (a) using deictic references to connect scientific terminologies, (b) understanding science terminologies through its derivatives, (c) communicating science practices conventionally through science terminologies, and (d) communicating science practices innovatively through mutated science terminologies. The findings suggest that science teaching and learning comprise a heterogeneous process which draws on both science and non-science language and is a constantly evolving process. Understanding teaching and learning as a heterogeneous and constantly evolving process allows us to reunite the roles of teachers and students as mutually responsible collaborators rather than science knowledge givers and consumers.     

Technology use and mathematics teaching: teacher change as discursive identity work

Teacher change towards developing competences for technology use in mathematics teaching has been the focus of current educational reforms worldwide. However, a considerable amount of research denotes the extent to which teachers resist a full integration of technology in mathematics classrooms. The present paper is based on an ethnographic study and focuses on how mathematics teachers – as they participate in an intensive training course – perform identity work whilst collectively articulating meanings concerning the potential of technology-based mathematics learning. By means of discourse theory, we analyse how they try to fix meaning as they engage and interact with varied discourses of ‘change’. Our findings indicate that mathematics teachers' attempts to articulate meaning are organised around discourses that concern directly societal and learning issues of technology use in mathematics teaching.     

The use of language in understanding subject matter

Empirical results show that frequently the meaning of expressions used by students in expressing their understanding of subject matter does not correspond to the meaning of those expressions in the subject matter theory that the students are expected to learn. There is also often a lack of identity of meaning between the same students’ use of the same expression from one use of the expression to another, in very similar contexts. The context gives a specific meaning to any expression. This variation in context and meaning is very central to the phenomena of teaching and learning. In educational research there is a need to differentiate between specific meanings expressed in conceptualizing subject matter, on the one hand, and concepts and meanings seen as parts of cognitive systems and social languages, on the other. The contextual character of the use of language is crucial to the understanding of teaching and learning and needs to be more carefully considered. The article is a discussion of the problem of varying meanings of language expressions in relation to major traditions of research, focusing on meanings and concepts within the field of learning and teaching.     

Truth and the renewal of knowledge: the case of mathematics education

Mathematics education research must enable adjustment to new conditions. Yet such research is often conducted within familiar conceptualisations of teaching, of learning and of mathematics. It may be necessary to express ourselves in new ways if we are to change our practices successfully, and potential changes can be understood in many alternative, sometimes conflicting, ways. The paper argues that our entrapment in specific pedagogic forms of mathematical knowledge and the styles of teaching that go with them can constrain students’ engagement with processes of cultural renewal and changes in the ways in which mathematics may be framed for new purposes, but there are some mathematical truths that survive the changing circumstances that require us to update our understandings of teaching and learning the subject. In meeting this challenge, Radford encountered a difficulty in framing notions of mathematical objectivity and truth commensurate with a cultural–historical perspective. Following Badiou, this paper distinguishes between objectivity, which is seen necessarily as a product of culturally generated knowledge, and truth, as glimpsed beyond the on-going attempt to fit a new language that never finally settles. Through this route, it is shown how Badiou’s differentiation of knowledge and truth enables us to conjure more futuristic conceptions of mathematics education.     

Exploiting the potential of bilingualism: Irish-medium primary mathematics teachers’ self-reported practices in relation to utilising language-as-resource

The specific role of language in the teaching and learning of mathematics in bilingual contexts has been well documented. Previous research has tended to focus on the negative impact of language on learning, but there is a move towards a non-deficit view of bilingualism and utilising language-as-resource in the mathematics classroom. This paper builds on the concept of language-as-resource by considering the specific linguistic characteristics of a language in supporting mathematics learning, in order to reap the benefits of bilingualism. A detailed questionnaire was utilised in order to examine Irish-medium primary teachers’ practices in relation to teaching mathematics through the medium of Irish. Teachers (n?=?315) from 77 Irish-medium primary schools (77% of the targeted sample) have responded to the survey. Their self-reported practices reveal a lack of utilisation of a language-as-resource orientation and the incorporation of specific features of the Irish language and culture, when teaching mathematics. In order for teachers to exploit the benefits of bilingualism and classroom opportunities for learning, resources and professional development programmes need to be established that incorporate the development of pedagogical approaches that support a language-as-resource orientation.     

STEM learning research through a funds of knowledge lens

This article examines STEM learning as a cultural process with a focus on non-dominant communities. Building on my work in funds of knowledge and mathematics education, I present three vignettes to raise some questions around connections between in-school and out-of-school mathematics. How do we define competence? How do task and environment affect engagement? What is the role of affect, language, and cognition in different settings? These vignettes serve to highlight the complexity of moving across different domains of STEM practice—everyday life, school, and STEM disciplines. Based on findings from occupational interviews I discuss characteristics of learning and engaging in everyday practices and propose several areas for further research, including the nature of everyday STEM practices, valorization of knowledge, language choice, and different forms of engagement.     

Valuing difference in teachers and learners: building on Kolb's learning styles to develop a language of teaching and learning

Abstract

The first part of this paper provides a brief historical account of the development of mathematics teaching and learning through the medium of Welsh. It provides a review of developments which have seen the teaching and learning of mathematics through a native but minority language become an accepted part of the curriculum for a great number of pupils. It goes on to examine the nature of bilingual education currently to be found in Wales by considering two main types of bilingual schools which currently serve Welsh pupils and which have contributed towards a modest but notable minority language revival. It is in this context that current practice relating to Welsh‐medium mathematics is explored and a number of questions concerning current mathematics teaching, learning and assessment practices are raised. While celebrating the success and expansion of bilingual education in Wales, attention is drawn to the need to subject current practice to closer scrutiny. Although the paper focuses on the particular situation to be found in Wales, the issues and questions raised are clearly of interest to those involved with other bilingual educational programmes.     

Researching research: mathematics education in the Political

We discuss contemporary theories in mathematics education in order to do research on research. Our strategy consists of analysing discursively and ideologically recent key publications addressing the role of theory in mathematics education research. We examine how the field fabricates its object of research by deploying Foucault’s notion of bio-politics—mainly to address the object “learning”—and ?i?ek’s ideology critique—to address the object “mathematics”. These theories, which have already been used in the field to research teaching and learning, have a great potential to contribute to a reflexivity of research on its discourses and effects. Furthermore, they enable us to present a clear distinction between what has been called the sociopolitical turn in mathematics education research and what we call a positioning of mathematics education (research) practices in the Political.     

Understanding leading as travelling practices

In this paper, we propose the concept of leading as travelling practices in order to understand how enhanced pedagogical practices ‘catch on’ in educational sites. Drawing on parallel case studies in Australia, Sweden and Norway, we analyse how leading practices moved within and between settings, transforming the discursive, material and social conditions for teaching and learning. We examine the composition and ecological connections of these leading practices with professional learning and pedagogical practices in schools and pre-schools. We conclude that practice-informed lens can shed new light on the spread of practices, which foster the conditions necessary for transformed pedagogy.     

Redefining professional identity: the voice of a language teacher in a context of collaborative learning

Following a narrative and biographic approach, in this study, we present the case of an in-service language teacher and her professional learning trajectory in the context of the project ‘Languages and education: constructing and sharing training’. This project aimed at the construction of a collaborative teacher education context for learning and transformation of experiences, views and practices in language education, and involved teachers, teacher educators and researchers. Based on a single case study, the analysis tries to disclose the teacher’s discursive displacements as hints of professional transformation while she reinterprets the learning taking place in the collaborative education process. The signs of change are visible in the way she constructs meanings regarding her professional identity, re-identifies her mission as a language teacher and reconsiders her professional identity. Finally, we reflect upon how collaborative teacher education scenarios may foster teachers’ personal professional learning and renewed self-images.     

Teaching Mathematics in Multilingual Classrooms

In this paper we present the way in which language issues have become a relevant factor in research which aims to study the socio-cultural aspects of mathematics education in classrooms with a high percentage of immigrant students. Our research on language issues focuses on two aspects, namely the language as a social tool within the mathematics classroom and the language as a vehicle in the construction of mathematical knowledge. We introduce our problem within this area and provide a rationale for our research methodology, not avoiding its drawbacks,but rather giving examples of the kinds of difficulties we encountered. The paper highlights the integrated nature of the social, cultural and linguistic aspects of mathematics teaching and learning, and illustrates the fact that, even if the mathematical language can be considered universal, the language of ‘doing mathematics within the classroom’ is far from being universal. This revised version was published online in July 2006 with corrections to the Cover Date.     

Student teachers and cultural diversity in an Australian regional university

This article examines student teachers' discursive constructions of difference, cultural diversity and race as they write and talk about their cultures and identities in relation to teaching and learning in the first year of a Primary Teaching Degree in a regional Australian university.
The qualitative case study which informs this paper considered the discursive resources that students bring to teacher education from their past experiences and contact with cultural differences in communities, families and schools. It examined various discourses around cultural diversity that are available to them in the teacher education course and how their discursive practices are mediated and reconstructed in the particular university context. A major goal was to explore how universities in largely homogeneous settings might firstly work with the resources that students bring to teacher education and, secondly, assist students to consider the implications of cultural and linguistic diversity for teaching language and literacy.     

Multimodal Interaction Analysis: a Powerful Tool for Examining Plurilingual Students’ Engagement in Science Practices

Research in Science Education - Science teaching and learning are discursive practices, yet analysis of these practices has frequently been grounded in theorizations that place language at the...     

Who is not multilingual now?

What is the relationship between research into multilingualism and research concerned more generally with language and communication in mathematics education? Diversity in linguistic practices is universal in modern society and poses problems for teaching and learning even in apparently monolingual contexts. Research in multilingualism and mathematics education offers constructs and insights that can inform research and pedagogy more widely.     

The role of gestures in the mathematical practices of those who do not see with their eyes

In this paper, we aim to contribute to the discussion of the role of the human body and of the concrete artefacts and signs created by humankind in the constitution of meanings for mathematical practices. We argue that cognition is both embodied and situated in the activities through which it occurs and that mathematics learning involves the appropriation of practices associated with the sets of artefacts that have historically come to represent the body of knowledge we call mathematics. This process of appropriation involves a coordination of a variety of the semiotic resources??spoken and written languages, mathematical representation systems, drawings, gestures and the like??through which mathematical objects and relationships might be experienced and expressed. To highlight the connections between perceptual activities and cultural concepts in the meanings associated with this process, we concentrate on learners who do not have access to the visual field. More specifically, we present three examples of gesture use in the practices of blind mathematics students??all involving the exploration of geometrical objects and relationships. On the basis of our analysis of these examples, we argue that gestures are illustrative of imagined reenactions of previously experienced activities and that they emerge in instructional situations as embodied abstractions, serving a central role in the sense-making practices associated with the appropriation of mathematical meanings.     

One speaker,two languages: Learning opportunities in the mathematics classroom

The data reported in this article come from a large project whose goal was to explore how Latin American students in Catalonia, Spain use their two languages—Spanish and Catalan—to support their learning of mathematics in small groups with other students who are Spanish- or Catalan-dominant. For 5 years, lessons from bilingual mathematics classrooms in three public secondary schools were video-recorded and transcribed. In the presentation of findings, I discuss three language practices that emerged from the analyses of several classroom instances as follows: (1) caution with mathematical vocabulary, (2) invention of terms, and (3) word-for-word translation. One example is chosen to represent each practice and some of its situated effects. The first two examples support the view that the experience of language difficulties, either real or presumed, contributes to generating opportunities that may be beneficial to mathematics learning. The third example, where the focus on the mathematics is hindered, points to a contrasting finding. Unlike other studies in the field, which have reported the difficulties and obstacles that arise in learning and teaching due to bilingualism in the classroom, I propose a change of focus through the conceptualization of language as a potential for thinking and doing, and particularly for learning and teaching mathematics.     

Quality Mathematics Instructional Practices Contributing to Student Achievements in Five High-Achieving Asian Education Systems: An Analysis Using TIMSS 2011 Data

Although teaching quality is seen as crucial in affecting students’ performance, what types of instructional practices constitute quality teaching remains a question. With the theoretical assumptions of conceptual and procedural mathematics teaching as a guide, this study examined the types of quality mathematics instructional practices that affect students’ mathematics learning across five high-performing Asian education systems using the Trends in International Mathematics and Science Study (TIMSS) 2011 dataset. It found that no combinations of the components of conceptual and procedural mathematics teaching practices exist consistently across the five education systems. Results from the study provide important implications for practitioners and policy makers regarding how to improve mathematics teaching and learning in these Asian education systems as well as elsewhere.     

THE INTERACTIONAL ACCOMPLISHMENT OF NOT KNOWING IN ELEMENTARY SCHOOL SCIENCE AND MATHEMATICS: IMPLICATIONS FOR CLASSROOM PERFORMANCE ASSESSMENT PRACTICES

The day-to-day business of being a science or mathematics teacher involves the continuous assessment of students. This, in turn, is an inherently discursive process. The aim of the present study is to examine some of the specific discursive practices through which science and mathematics knowing is jointly produced through classroom interaction. In particular, we examine the coproduced nature of two students’ not knowing—one in an outdoor elementary school science lesson and the other in an elementary school mathematics lesson. Our analysis is based on ideas in discursive psychology and challenges conventional interpretations of students’ academic performance in school science and mathematics.