Engaging with issues of emotionality in mathematics teacher education for social justice

This article focuses on the relationship between social justice, emotionality and mathematics teaching in the context of the education of prospective teachers of mathematics. A relational approach to social justice calls for giving attention to enacting socially just relationships in mathematics classrooms. Emotionality and social justice in teaching mathematics variously intersect, interrelate or interweave. An intervention, using creative action methods, with a cohort of prospective teachers addressing these issues is described to illustrate the connection between emotionality and social justice in the context of mathematics teacher education. Creative action methods involve a variety of dramatic, interactive and experiential tools that can promote personal and group engagement and embodied reflection. The intervention aimed to engage the prospective teachers with some key issues for social justice in mathematics education through dialogue about the emotionality of teaching and learning mathematics. Some of the possibilities and limits of using such methods are considered.     

International graduate students' difficulties: graduate classes as a community of practices

This study explores the factors that cause international graduate students to struggle and these students' ways of dealing with such problems in light of sociocultural theory, which views learning as a social and cultural act. The findings show that graduate classes function as communities of practices in which classmates and professors mutually engage with each other, share a repertoire and engage in joint enterprises. The practices were not always transparent to international students, which became a source of difficulty and often led them to feel excluded. Peripheral participation comprised a significant part of some students' learning process and identity formation, but it allowed them to participate in course-related activities as fully as they felt comfortable doing. This study suggests a need for more sensitive and dialogical efforts by educators in higher education to provide better learning environments for international learners.     

Critical Conversations on Social Justice in Undergraduate Mathematics

Abstract

This article explores how critical conversations engage undergraduate mathematics faculty in a community of practice that enhances their knowledge about teaching and learning mathematics for social justice. More broadly, critical conversations are defined as a cooperative learning strategy that can be used to identify, explore, and respond to various interests and issues situated across differing values and beliefs. We present a case study of a critical conversation that took place at a 2016 Mathematics for Social Justice workshop organized by a group of junior faculty. Participant reflections situate perspectives that can help novice and experienced instructors design conversations about teaching mathematics for social justice. Specifically, individual and group reflections highlight the importance of: (i) framing and reflecting on the conversation; (ii) exploring implications and content connections; and (iii) identifying barriers. Implications for faculty members and mathematics departments are provided.     

重视数学教学效率提高数学教学质量--"数学教学效率论"课题简介

全国教育科学“十五”规划课题——数学教学效率论，于2003年底立项，总课题分为12个子课题．在江西、四川、新疆、陕西、广东、贵州和天津成立了子课题组．2004年11月26～29日在四川省成都市新部一中召开了“数学教学效率论”中期成果研讨会，计划于2005年10月在新疆召开结题会议，该课题研究的意义在于：是解决现实数学教育问题的需要；是比较教育研究的需要；是数学教育发展形势的迫切需要，关于数学教学效率应从两个维度来认识：在学生的时间投入方面，指能够充分利用时间，全身心、积极、主动地参与数学学习；在数学教学结果方面，指多方面的学习效果——认知成绩、理性精神、效率意识、良好认知结构和数学学习能力，因此，在评价方法上采取的是：基于模糊综合评判的层次分析法。     

An Orientation on the Mathematics Classroom that Emphasizes Power and Identity: Reflecting on Equity Research

In this paper, I reflect on equity research in order to describe a perspective on the mathematics classroom as a non-neutral place where issues of power and identity play out in teaching and learning processes. This view of the mathematics classroom takes seriously issues of equity in the form of power and what becomes constituted as legitimate mathematics while attending to the out-of-school practices in which students engage. This orientation and its related issues are significant in that they provide an alternative perspective on investigating equity in mathematics classrooms that is in contrast to efforts that focus specifically on comparing standardized test scores of specific groups based solely upon racial classifications.Lynn Liao Hodge is an assistant professor in mathematics education. Her research interests include issues of equity and identity in mathematics education and how classroom practices create opportunities for students to develop both an appreciation and a deep understanding of mathematics. Additionally, she is interested in investigating experiences that support the increased participation of women and minorities in mathematics, science, and engineering related professions. Address correspondence to Lynn Liao Hodge, Department of Theory and Practice in Teacher Education, The University of Tennessee, Knoxville, TN 37996-3442, USA; e-mail: lhodge4@utk.edu     

To know or not to know – mathematics, that is a question of context

As one of the so-called basic skills, 'mathematics' or 'numeracy' is at the top of the list of subjects in adult education programmes. Together with political investment in general and further education, practitioners and theoreticians focus on 'knowing and learning in different contexts'. Jean Lave's theory about 'situated learning' may be regarded as a confrontation with the idea of learning as acquisition of propositional knowledge. One characteristic of adult education in mathematics is that the participants bring with them adult life experience from their everyday and work. Another characteristic is their perspective in educating themselves. There is an apparent contradiction between many adults being blocked in relation to mathematics in formal settings and being competent in their everyday life. It is possible to make sense of this contradiction by analytically expanding the context for knowing and learning mathematics from the participants' experiences and perspectives to also include the adults' dispositions, cf. Pierre Bourdieu's concept of 'habitus' as a guiding principle for practice. By interpreting the account of her life by a 75 year old woman concerning her attitudes to mathematics, the author illustrates and discusses the two analytical concepts ('situated learning' and 'habitus') and their suitability for analysing adults knowing or not-knowing mathematics in different situation contexts. This revised version was published online in July 2006 with corrections to the Cover Date.     

The Dialectic Relationship between Research and Practice in Mathematics Teacher Education

This paper addresses issues linking research in student teacher learning with reflection on practice in mathematics teacher education. From a situated perspective on learning and practice, we explore our own practice as teacher educators while researching student teacher learning in our classrooms. We describe a study on student teacher learning, considering student teacher learning as a “process of becoming”, and how the results of this research have affected our development as mathematics teacher educators and members of a community of inquiry. Our work shows how in the mathematics teacher education context the relationship between theory and practice becomes an element of both teacher educator and researcher development.     

Authentic,dialogical knowledge construction: a blended and mobile teacher education programme

Background: Knowledge construction and technology have been identified as critical for an understanding of the future of teacher education. Knowledge is discovered, applied and created collaboratively from authentic starting points. Today’s new mobile and blended learning environments create increased opportunities for such processes, including learner-centred approaches, authenticity and dialogical knowledge construction. However, teaching still requires appropriate learning design and structuring. The presented study explored, and was designed and implemented, using the ‘Dialogical Authentic Netlearning Activity’ (DIANA) pedagogical model, which is seen as one of the learning designing models for existing digital, open and mobile learning environments.

Purpose: The purpose of this study was to identify the challenges and opportunities inherent in the adoption of the DIANA model and to examine student-teachers’ reflections concerning authentic and dialogical knowledge construction. The focus is on the learning process.

Sample: Participants were 63 student-teachers who were following the study module ‘Networks in Vocational Education’ at the School of Professional Teacher Education, in Hämeenlinna, Finland.

Design and methods: This qualitative study uses a deductive content analysis to discern relationships between the data and the existing theory. The data for this study were drawn from an online questionnaire and participants’ self-reflective accounts.

Findings: The results indicate that achieving deep-oriented learning through dialogical actions is the most challenging part of using the DIANA model. Some of the students had difficulty understanding the concept of ‘authenticity’.

Conclusions: The findings of this study suggest enhancing learner-centred scaffolding and guidance, particularly at the outset of the learning process. In addition, methods that develop dialogical skills and competences ought to be integrated into teacher education as extensively as possible, in order to make collaborative work and problem-solving genuinely dialogical and equal.     

Analyzing Mathematical Teaching-Learning Situations — the Interplay of Communicational and Epistemological Constraints

This is a commentary paper in the volume on “Teachings situations as object of research: empirical studies within theoretical perspectives”. An essential object of mathematics education research is the analysis of interactive teaching and learning processes in which mathematical knowledge is mediated and communicated. Such a research perspective on processes of mathematical interaction has to take care of the difficult relationship between mathematics education theory and everyday mathematics teaching practice. In this regard, the paper tries to relate the development in mathematics education research within the theory of didactical situations to developments in interaction theory and in the epistemological analysis of mathematical communication.     

Whither social theory?

What is the place of social theory in mathematics education research, and what is it for? This special issue of Educational Studies in Mathematics offers insights on what could be the role of some sociological theories in a field that has historically privileged learning theories coming from psychology and mathematics as the main theoretical frames informing research. Although during the last 10 years the term “socio-cultural” has become part of the accepted and widespread trends of mathematics education research when addressing learning, this issue gathers a collection of papers that depart from a “socio-cultural” approach to learning and rather deploy sociological theories in the analysis of mathematics education practices. In this commentary paper, we will point to what we see to be the contributions of these papers to the field. We will do so by highlighting issues that run through the six papers. We will try to synthetize what we think are the benchmarks of the social approach to mathematics education that they propose. We will also take a critical stance and indicate some possible extensions of the use of social theory that are not addressed in this special issue but nonetheless are worth being explored for a fuller understanding of the “social” in mathematics education.     

A response to strategies and tactics through participatory action research in a developmental mathematics course

This paper explores the value of participatory action research in a community college developmental mathematics course. The authors used the framework of critical mathematics education in order to understand the critical conversations of students about their learning experiences, and also to help the instructor of the course develop the curriculum that attended to student experiences. The authors also draw on Michel de Certeau’s ideas about strategies and tactics to understand how students responded to their past learning experiences. Data results from the study show that students can gain a better understanding of their own learning and subsequently develop deeper content knowledge when they are more involved in the teaching and learning process. Lastly, the authors conclude that as adult learners grow in their understanding of the learning processes and of the content being presented, participatory action research can play an important role in the entire development of thinking and intellectual engagement.     

The impact of action learning on analysis of occupation

Technology and millennials have created a shift in the world and how it operates. This impact has been experienced in the field of occupational therapy education. As a result of this paradigm shift, an analysis of effective teaching methodologies was carried out to assess the most effective way to engage the millennials in an analysis of occupation process, which is a critical foundation for effective critical thinking and clinical practice for occupational therapists. An action learning assignment was utilized to bridge this gap. The action learning assignment immersed the students in a safe learning environment that recreated many types of domains that needed to be analyzed. As a result, the students experienced first-hand the outcomes of effective and ineffective analysis and problem-solving during their action learning project. Therefore, the students were able to reflect and critically think through alternatives and hear about other students' projects. Overall, the action learning project yielded positive learning and engaging outcomes.     

The Dialectic Relationship between Research and Practice in Mathematics Teacher Education

This paper addresses issues linking research in student teacher learning with reflection on practice in mathematics teacher education. From a situated perspective on learning and practice, we explore our own practice as teacher educators while researching student teacher learning in our classrooms. We describe a study on student teacher learning, considering student teacher learning as a “process of becoming”, and how the results of this research have affected our development as mathematics teacher educators and members of a community of inquiry. Our work shows how in the mathematics teacher education context the relationship between theory and practice becomes an element of both teacher educator and researcher development.     

I thought to myself: what a long way I’ve come … : teacher writing for professional learning

As governments the world over continue to advocate the importance of teacher professional learning, researchers and practitioners continue to explore ways to enact that learning in meaningful ways. The value of narrative for teacher education has been widely discussed and several studies show that learning is significant when teacher–writers engage in written dialogue. This article is a critical, narrative-based account of the professional learning of Orly, an Israeli teacher. Written reflection and narrative play a crucial mediating role in her learning. This practitioner inquiry explores narrative writing as a means of learning, empowerment and professional renewal for Israeli educators. The author presents multiple ways in which language from a professional learning context can connect with classroom practice and discusses the dialogical nature of this kind of learning.     

Using what matters to students in bilingual mathematics problems

In this study, the author represented what matters to bilingual students in their everyday lives—namely bilingualism and everyday experiences—in school-based mathematical problems. Solving problems in pairs, students demonstrated different patterns of organizing and coordinating talk across problem contexts and across languages. Because these patterns bear consequences for how bilinguals experience mathematics learning, the author takes these patterns as the basis to argue that mathematics education for bilingual students should capitalize on bilingualism and experiences as cognitive resources.     

The computer as a cultural influence in mathematical learning

My starting point in this paper is that there is a cultural gap between the mathematics that children do as part of their everyday experience and the mathematics that they learn at school; my thesis is that the computer has (perhaps uniquely) the potential to bridge this divide. The paper will examine the cultural impact-both actual and potential-of the computer on children's mathematical education; at the ways in which the introduction of the computer does and will changes the ambient space in which children learn mathematics.I begin with a brief discussion of the cultural context of mathematics learning and the relationship between informal, everyday mathematical activity, and formal, school mathematies. This perspective leads to a closer examination of what it means to do mathematics, and on the relationship of a technology to the mathematics embedded within a given culture. I discuss the issue of injecting meaning into mathematical activity, and then examine some ways in which the computer might offer a solution to this central problem. Next, I give some examples of the influence of the computer on the culture of the mathematics classroom. Finally, I suggest some of the outstanding issues of research and curriculum development which remain.This paper is based on substantially the same data as is discussed in an article inCultural Dynamics.     

Healing Images and Narratives: Undocumented Chicana/Latina Pedagogies of Resistance

This article draws from a longitudinal study of 38 in-depth testimonio interviews with 10 undocumented Chicanas/Latinas from 2008 to 2014, first as college students and then as professionals. A Chicana feminist theoretical perspective in education was utilized to explore how undocumented Chicana/Latina ways of knowing emerged in the ways they worked with and for immigrant communities as professionals. The study found that participants drew from their multiple identities, social locations, and life experiences as undocumented Chicana/Latina women to engage in pedagogies of resistance—everyday forms of teaching and learning that challenge the subjugation of undocumented communities, and are shaped by personal and collective experiences, knowledge, and identities. The study found that participants utilized mestiza consciousness, convivencia, and bodymindspirit to employ these pedagogies of resistance in their professional work with and for immigrant communities.     

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.     

History of mathematics in secondary school teachers’ training: towards a nonviolent mathematics education

In the context of mathematics teachers’ training, the concept of dépaysement épistémologique (epistemological disorientation) emphasizes that the contact with the history of mathematics, particularly with the use of original sources, pushes aside commonplace students’ perspectives about the discipline and offers them a critical look towards mathematics’s historical, social and cultural aspects. Conceptually supported by the theory of objectivation, an emergent sociocultural theory in mathematics education, this study describes the dépaysement épistémologique lived by future mathematics teachers engaged in the reading of historical texts. A phenomenological approach allowed us to clarify various meanings associated with students’ lived experiences and a dialogical perspective provides a way to get these meanings in tension through a polyphonic narration. Our reading of this polyphonic narration suggests that dépaysement épistémologique associated with the reading of historical texts encouraged empathy from students towards the authors and their future learners, opening up the possibility for a nonviolent mathematics education.