Strategic Facilitation of Problem-Based Discussion for Teacher Professional Development

Engaging teachers in discussing and analyzing problems of practice has great potential for teacher professional development, yet little is known about how to facilitate such discussion. This study examined the strategies that experienced facilitators used to promote productive discussion among science teachers. Participants were 6 facilitators and 35 in-service teachers who participated in a professional development program that adopted a problem-based learning approach for teacher learning. Data analysis showed that experienced facilitators used a variety of strategies in their facilitation, including questioning, revoicing, making connections, clarifying, reframing, summarizing, role playing, meta-talk, and modeling. In particular, questioning and revoicing were the most important strategies in all sessions studied, accounting for about half of the facilitators' talk. Analysis further revealed both productive and disruptive characteristics of questioning and revoicing. In addition, analysis found that teachers were able to make progress in participating in the problem-based learning discourse in different ways. This study has implications for research on teacher professional development, problem-based learning, and learner-centered instruction.     

Same school,separate worlds: A sociocultural study of identity,resistance, and negotiation in a rural,lower track science classroom

This ethnographic study examined how rural, lower track, underrepresented students made sense of their place in school and what role school science played in their cultural reproduction. The objectives of the study were to identify key components of science classroom discourse, analyze means of negotiating these components, and explicate participants' beliefs and roles in defining microcultural identities specific to rural, underrepresented school contexts. Eight students and their teacher participated in this study, which drew heavily upon teacher and student revoicing of common events. Results showed that the quality of science instruction was subverted through a process of negotiation between students and teachers in the context of low expectations and the school culture. Implications for research and practice are discussed. © 2001 John Wiley & Sons, Inc. J Res Sci Teach 38: 574–598, 2001     

USING LISTENING JOURNALS IN MATH METHODS

The purpose of this teacher action research was twofold: to learn more about preservice teachers' preconceived notions related to listening and to investigate how a listening journal assignment impacted preservice teachers' views of listening as an important aspect of discourse. The participants were enrolled in a mathematics methods course for PreK–3 (early childhood) majors during their last semester of coursework prior to student teaching. Data in the form of final reflections from participants' listening journals and researchers' field notes were analyzed. Findings suggest that the preservice teachers entered the course without truly considering listening as an important component of teaching methods related to facilitating classroom discourse. The listening journal assignment helped them begin to think more deeply about listening and the different definitions and modes of listening; however, at the end of the semester, many still wrote about their own personal journeys with listening and not about the role of listening as a key element in promoting classroom discourse and learning.     

Using an Undergraduate Geometry Course to Challenge Pre-service Teachers' Notions of Discourse

This investigation uses classroom discoursein an undergraduate mathematics course tochallenge pre-service secondary mathematicsteachers' notions about mathematical discourse,what it might resemble in the classroom, andhow its various forms can be cultivated byclassroom teachers. The research setting was arequired geometry course taught by the author.Eleven pre-service mathematics teachers intheir junior or senior year of an undergraduate program participated. Results indicated participants made a transition toward an image of discourse as an active process by which students use the collective knowledge of their peers to build mathematical understanding and developed in their ability to participate in such discourse.This awareness, along with participants'analyses of their own habits of discourse asclassroom teachers, prompted shifts in theirprojected image of the role of discourse intheir future practices of teaching. Resultssuggested further that the undergraduatemathematics classroom (as opposed to themethods classroom) offers a powerful and uniqueforum in which pre-service secondary teacherscan practice, articulate, and collectivelyreflect on reform-minded ways of teaching.     

“To make the tacit explicit”: Teacher education, emerging discourse, and conceptions of teaching

The influence of teacher education on teaching is a problematic area, both in practice and in research. Often, because much research adopts a “first-order” perspective which focuses on teachers' behaviors, influences of teacher education are seen as temporary, negligible, or difficult to determine. The study reported here grew out of a general concern to document, via a “second-order” perspective which examines their thinking and perceptions, how teachers modify or improve what they do through formal teacher education. It addresses three important areas which have received little attention in recent research: foreign language teaching, in-service graduate education, and the role of a shared, professional discourse in developing teachers' conceptions of teaching. The paper presents a summary of the findings of an 18-month longitudinal study which examined how foreign language teachers' conceptions of their classroom practice developed as they took part in an in-service teacher education program. The paper discusses how the program's shared professional discourse contributes to increasing the complexity of the teachers' thinking about their teaching and suggests that as they learn to articulate their de facto ways of thinking in the shared discourse, the teachers gain greater control over their classroom practice and are thus more able to shape it to their own ends.     

The link between student-perceived teacher talk and student enjoyment,anxiety and discursive engagement in the classroom

This study seeks to understand the emotional connection of teachers' academically productive talk (APT) with student learning from the students' perspective. Using a sample of 2,225 students (N_{7th grade} = 1,146 and N_{8th grade} = 1,079) from 16 middle schools in a city of China, we investigate the relationship between students' perceptions of their teachers’ APT, student emotions (enjoyment and anxiety) and their discursive engagement with others in the mathematics classroom. Results from structural equation modelling and mediation analysis show that after controlling for gender, family resources and mathematics achievement, student-perceived teacher APT was positively associated with their discursive engagement with classmates. Furthermore, student enjoyment and anxiety in class mediated the relationship between student-perceived teacher APT and student discursive engagement with classmates. Multi-group analysis revealed that the model was invariant across genders and grades, indicating that the associations were applicable to male and female students as well as to seventh and eighth graders. These findings shed light on the emotional relationship of teacher APT with the discursive engagement of their students. Although prior research observes a positive relationship between teacher productive classroom talk and student discursive engagement primarily through classroom observations and teacher reflections, this study provides evidence from the students’ perspective and highlights the mediating role of student emotions in the relationship.     

Challenges of critical colleagueship: examining and reflecting on mathematics teacher study group interactions

This article examines mathematics teacher collegiality by focusing on both the ways in which teachers interacted as critical colleagues in a long-term professional development project and the evolving role of the teacher–educator–researcher as the facilitator of this project. The professional development collaboration comprised two phases: one focused on reading classroom discourse literature and one focused on supporting each other through cycles of action research related to mathematics classroom discourse. Lord’s (1994) critical colleagueship framework is used to examine how a study group of middle-grades (ages 11–16) mathematics teacher–researchers took (or did not take) a more critical stance toward their own teaching practice and that of their colleagues. We found that challenging interactions were related to instances in which the teachers interacted as critical colleagues and were marked by particular features including the use of particular words and the use of personal experience as a form of evidence. We present the ways in which we came to understand what it might look like to scrutinize one’s practice and findings related to the development of this type of collegiality across the two different phases of this project. We end with a section in which the teacher–educator–researcher who facilitated the professional development project reflects on the ways in which the analysis caused her to reconsider both the nature of argumentation in mathematics study group settings and what implications this has with respect to her own practice as a facilitator.     

Reflection on the teaching-learning process in the initial training of teachers. Characterization of the issues on which pre-service mathematics teachers reflect

Our aim was to highlight the issues of the reflections of pre-service mathematics teachers in their learning portfolio about the teaching-learning process taking place in a university teacher-training classroom. Category systems were designed which, together with the analysis system used, could provide a method helpful to teacher educators, teachers and to future research. The pre-service teachers showed difficulty in considering themselves as ‘authentic’ mathematics teachers. The study revealed that the preparation of a portfolio can help pre-service teachers learn more about themselves and provide educators insight into how to help pre-service mathematics teachers engage in the teaching-learning process.     

Renaming experience/reconstructing practice: Developing new understanding of teaching

Although teacher-thinking research is now well established, the specific mechanisms through which teachers construct new understandings of their teaching have not been closely examined. This paper presents four interrelated concepts—teachers' conceptions of practice, tensions in their practice, articulation, and local and professional language—which emerged as grounded categories from a longitudinal study of change in teachers' practice. The study focused on how a group of foreign language teachers integrated new ideas, encountered in an inservice masters' degree program, in their thinking about and activity in the classroom. The analysis traced the ways in which the teachers reconstructed their classroom practice, using professional discourse to rename their experience and thus to assign new or different meanings to their actions. The concepts, presented with illustrations from the study and accompanying analysis, have implications for research on teaching and teacher education as well as the design and execution of teacher education programs.     

小学高年级数学应用题有效教学策略探究

教师作为引导学生主动探究学习的“指路人”,应当把实现数学课堂有效教学、培养学生综合学习能力作为一项基本的教学目标。尤其是小学高年级学生,他们已经具备基础的数学运算能力,因此教师要进一步提高他们的数学学习能力,为后续的数学学习道路夯实基础。本文将浅谈如何更好地进行小学高年级数学应用题有效教学。     

Work in Mathematics Classes: The Context of Students' Thinking During Instruction

The research program described in this article has focused on the work students do in classrooms and how that work influences students' thinking about content. The research is based on the premise that the tasks teachers assign determines how students come to understand a curriculum domain. Tasks serve, in other words, as a context for students' thinking during and after instruction. The first section of this article contains an overview of the task model that guided research. The second section provides a summary of findings concerning the properties of students' work in classrooms, with special attention to work in mathematics classes. I conclude with a brief discussion of implications of this research for understanding classroom processes and their effects.     

The multiple voices of a mathematics classroom community

Several mathematics educators have expressed their concern about conflicting visions of educational reform among parents and teachers, which could result in the emergence of multiple voices in discussions of achievement and instruction. The aim of this article is to examine the multiple voices of educational reform in the discourse of a third grade classroom community. In order to achieve our aim, we integrated the social and the individual as well as the past, present, and future in our analysis of the discourse in this classroom community using theoretical frameworks and methods from cultural psychology. Although our analyses focused on the classroom teacher, we employed units of analysis capable of bridging the individual and her social context. We began our analysis by focusing on a sample of whole-class discussions of students’ strategies for solving multi-digit word problems. This analysis isolated two distinct voices: one that occurred during discussions of students’ invented strategies and the other that emerged during talk about standard algorithms. We extended our analysis to include information about the historical, social, and institutional context of the classroom community in order to understand the origins and functions of these two voices. This additional information helped us appreciate the interconnections between the teacher’s personal feelings, beliefs, recollections, and expectations; and her interpersonal transactions with her students, their parents, and other educators. We concluded with a discussion of the implications of the study for understanding one of the dilemmas of educational reform and for advancing research in classroom discourse. This revised version was published online in July 2006 with corrections to the Cover Date.     

Introducing a symbolic interactionist approach on teaching mathematics: the case of revoicing as an interactional strategy in the teaching of probability

This study examines an interactional view on teaching mathematics, whereby meaning is co-produced with the students through a process of negotiation. Further, teaching is viewed from a symbolic interactionism perspective, allowing the analysis to focus on the teacher’s role in the negotiation of meaning. Using methods inspired by grounded theory, patterns of teachers’ interaction are categorized. The results show how teachers’ actions, interpretations and intentions form interactional strategies that guide the negotiation of meaning in the classroom. The theoretical case of revoicing as a teacher action, together with interpretations of mathematical objects from probability theory, is used to exemplify conclusions from the proposed perspective. Data are generated from a lesson sequence with two teachers working with known and unknown constant sample spaces with their classes. In the lessons presented in this article, the focus is on negotiations of the meaning of chance. The analysis revealed how the teachers indicate their interpretations of mathematical objects and intentions to the students to different degrees and, by doing so, create opportunities for the students to ascribe meaning to these objects. The discussion contrasts the findings with possible interpretations from other perspectives on teaching.     

Troubling teacher identity: preparing mathematics teachers to teach for diversity

This paper reports on an action research project designed to explore the complexities of pre‐service mathematics teacher resistance to social justice issues. Research on equity and mathematics education has indicated that such resistance seems particularly strong for mathematics teachers. Twelve pre‐service mathematics teachers participated in a course‐based research project to explore this issue. Participants completed a classroom discourse analysis and a self‐study narrative as part of their secondary mathematics methods course. The findings suggest that attention to issues of identity construction within school mathematics can be successfully embedded in methods courses in order to better prepare mathematics teachers to teach for diversity.     

Values in the mathematics classroom

Abstract

Values, moral values and democratic values are attracting the attention of education researchers in general and mathematics education researchers in particular. Little research has studied pre-service teachers’ perceptions of values in the classroom, their perceptions of the relationship between the different variables of values in the classroom, as well as their relationship with the democratic society. The present research attempts to do so. Twenty-two graduate pre-service teachers who participated in ‘New trends in mathematics education’ course discussed how to cultivated values in the mathematics classroom. Moreover, they answered survey questions related to the cultivation of values in this classroom. We used a combination of deductive and inductive content analysis to characterize the pre-service teachers’ texts. The research results indicate that the pre-service teachers perceived values as encouraging students’ activity in the mathematics classroom. In addition, the pre-service teachers perceived values as encouraging specific categories of values needed as skills for the citizen in a democratic society, as creativity, critical thinking and metacognition.     

I BOOK REVIEWS

This study examines the influence of graphing calculators on a teacher's assessment practices in a college algebra course. The researcher focused on three techniques of alternative assessment: oral discourse, teacher observations, and problem‐solving investigations. The teacher's assessment practices were revealed during 6 weeks of classroom observations. The researcher examined the teacher's assessment practices before and after the teacher used graphing calculators as tools for teaching and learning mathematics. The use of the graphing calculators enhanced the teacher's assessment practices as related to oral discourse, classroom observations, and problem‐solving investigations. The results of the study indicate the potential for technological tools to influence teachers’ practices of alternative assessment in the mathematics classroom.