The emergent perspective in rich learning environments: Some roles of tools and activities in the construction of sociomathematical norms

The emergent perspective (Yackel and Cobb, 1996) is a powerful theory for describing cognitive development within classrooms. Yackel and Cobb have shown that the formation of social and sociomathematical norms, and opportunities for learning are intertwined. The present study is an attempt to extend the range of application of the emergent perspective to middle high school classrooms. The learning environments we consider are rich in the sense that (i) the tasks in which students are engaged are open-ended problem-situations (ii) the activities around the tasks are multiphased, consisting of small group collaboration on problem solving, reporting and reflection in a classroom forum with the teacher (iii) the tools used are multi-representational software. We identify here some practices rooted in such rich environments from which several sociomathematical norms stemmed. The present study shows that socio-mathematical norms do not rise from verbal interactions only, but also from computer manipulations as communicative non-verbal actions. This revised version was published online in July 2006 with corrections to the Cover Date.     

The durability of professional and sociomathematical norms intentionally fostered in an early pedagogy course

This study investigated the extent to which three sociomathematical and four professional norms intentionally fostered in an early mathematics pedagogy course through the use of a video-case curriculum re-emerged in a similar context with two groups: (1) teacher candidates in the final mathematics pedagogy course of the same teacher education program and (2) program graduates in their beginning years of teaching. All seven norms were found to be durable over time, with the sociomathematical norm of providing a mathematical argument being the most widely and consistently exhibited among the participants. Comparisons of the behaviors exhibited by the two groups revealed that five of the norms were consistently durable over time with both groups and suggested that participants’ engagement with two of the norms was positively affected by additional classroom experience. Details of differences among the groups and ways in which the norms appeared to support continued teacher learning are examined. The results point to the long-term benefits of developing productive norms early in a teacher education program.     

Social representations as mediators of mathematics learning in multiethnic classrooms

Drawing on socio-cultural theory, we understand the norms regulating the practices within the mathematics classroom as resulting from the social representations of the socially dominant groups and of the school culture related to what constitutes learning mathematics. Immigrant studients, having their own personal histories as members of particular social groups, and having been in school traditions other than the one predominant in the host society, have their own images of what mathematics in school is about. Individuals interacting in the classroom are all re-interpreting the different episodes from the perspective of the social representations of the larger groups with which they identify themselves. In multiethnic classrooms different re-interpretations of the same norms clash. The lack of negotiation gives rise to obstacles to immigrant students’ participation in the mathematical conversations and, therefore, interferes with the students’ learning process.     

Tutoring through the internet: how students and teachers interact to construct meaning

Two episodes of tutoring through the internet have been analysed in terms of situational, interactive and content perspectives. The episodes involved secondary students who submitted queries about chemistry issues to an online service provided by teachers. Studies of the asking of questions and of the dynamics of classroom interactions are employed to discuss the interactive and content factors of this approach to teaching–learning. The functions conveyed by students’ and teachers’ utterances are used to identify the structural patterns of the interactions. The occurrence of classical and inverted I–R–F exchanges, the questioner’s role, the continuity of the dialogues, and other structural patterns, are used to classify the episodes as being Debate and Triadic Dialogue. The notions of mastering cultural tools and scaffolding are used to account for how meaning is constructed through the interactions.     

Investigating classroom community in higher education

The purpose of this research was to demonstrate an empirical relationship between classroom community and students' achievement goals in higher education, and to offer a possible explanation for differences in this relationship for cooperative and non-cooperative classrooms. Structural equation modeling techniques revealed that students' perceptions of interactive learning significantly mediated the relationship between students' goals and their sense of classroom community, but only for classrooms that used cooperative learning techniques. In the traditional lecture-style course surveyed, students' feelings of classroom community and interactive learning were significantly lower than in cooperative learning classrooms. Finally, while mastery goals were significantly higher for cooperative learning students, performance-approach goals were significantly higher for traditional lecture students.     

A critical analysis of the role of wait time in classroom interactions and the effects on student and teacher interactional behaviours

Extending the pauses between teachers’ and students’ turns (wait time) has been recommended as a way of improving classroom learning. Drawing on the Conversation Analysis literature on classroom interactions alongside extracts of classroom interactions, the relationship between these pauses and the interactional behaviour of teachers and students is examined. Extended wait time is built in to classroom interactions because of the IRF (Initiation–Response–Feedback/Follow-up) framework that dominates these interactions. Extending wait time can lead to a variety of changes in the norms of classroom interaction. The structures of interactions in formal classrooms are used to explain the previous findings relating to the extension of wait time. It is also shown that different uses of extended wait time lead to different interactional norms and maintaining extended wait times may not be desirable. Consequently, the article argues for a more nuanced understanding of wait time, desired student behaviours and the interaction of the two.     

Notes on contributors

Authority, a fundamental part of the teaching–studying–learning process, is a problematic and poorly understood component of classroom life. It can be said, in practical terms, that pedagogical authority is constructed in classrooms, in teacher–student interaction and in the spirit of their physical presence, confidence, appreciation, responsibility and respect, and in the way they both relate to the content and norms. Based on the German Didaktik tradition and classroom interaction, an approach for the analysis of pedagogical authority is proposed providing an analytical tool for examining and understanding its constitutive elements and explaining its construction. It posits the existence of three types of interaction or relation from which pedagogical authority emanates: pedagogical interaction, deontic interaction and didactic interaction. Depending on how these relations are enacted in the classroom, they, in turn, may evolve into pedagogical authority. Data collected from four teachers’ interviews in Finnish comprehensive schools are analysed and some empirical evidence is provided to show the characteristics of these relations and how they construct this positive view of authority. More research on pedagogical authority resulting from these relations in classroom settings is needed to account for this critical educational phenomenon.     

Inverting the Transition-to-Proof Classroom

Abstract

In this paper, we examine the benefits of employing an inverted or “flipped” class design in a Transition-to-Proof course for second-year mathematics majors. The issues concomitant with such courses, particularly student acquisition of “sociomathematical norms” and self-regulated learning strategies, are discussed along with ways that the inverted classroom can address these issues. Finally, results from the redesign of a Transition-to-Poof class at the author’s university are given and discussed.     

The role of persuasive research in educational progress

This article describes how scaffolded instruction during whole-class mathematics lessons can provide the knowledge, skills, and supportive context for developing students' self-regulatory processes. In examining classroom interactions through discourse analysis, these qualitative methods reflect a theoretical change from viewing self-regulation as an individual process to that of a social process. This article illustrates how studying instructional scaffolding through the analyses of instructional discourse helps further the understanding of how self-regulated learning develops and is realized in mathematics classrooms. Qualitative methods, such as discourse analyses, and their underlying theoretical frameworks have great potential to help "unlock" theories of learning, motivation, and self-regulation through exploring the reciprocity of teaching and learning in classrooms.     

‘Always allowing the voice’: expectations of student participation and the disciplining of teachers' practice

Student participation in higher education classrooms is considered important for learning and achievement, but what is meant by participation is rarely made clear. In the literature, it often refers to various forms of verbal participation, which are celebrated and also critiqued. In particular, Western pedagogical assumptions and expectations of classroom participation can marginalise students from non-Western cultures. This article discusses the findings from a study of university teaching staff in New Zealand who spoke about their experiences of teaching a diverse range of students. Analysis of narrative data investigates what participation means for these teachers and how they enact it in their classrooms. It reveals the norms and assumptions that underlie their narratives and considers how these norms discipline teachers' practice.     

数学课堂规范的讨论和分析

数学课堂规范包括支配课堂的一般社会规范和围绕特定数学交互的数学规范.数学课堂规范的特征有:数学课堂规范是"预成性"和"生成性"统一的结果;学生数学观念影响数学课堂规范的发展;社会规范和数学课堂规范之间有差异;创生数学课堂规范就是创造一种信任和尊重的学习气氛.做数学的新规范和标准也需面对传统教学方式的桎梏,学生数学观的局限性,以及数学参与公正性等的挑战性和复杂性。     

The diffusion and appropriation of ideas in the science classroom: Developing a taxonomy of events occurring between groups of learners

Abstract: While research on group learning has focused almost exclusively on interactions among individuals within groups, there has been little research on phenomena occurring between groups of learners in classrooms. This exploratory study identifies, describes, and categorizes events occurring between members of different learning groups in three ninth‐grade physical science classrooms. Analysis of interaction data from a collaborative activity involving the construction of complex electrical circuits was used to create a working taxonomy of inter‐group events. This taxonomy was then tested for generalizability with four other collaborative student projects and was found to account for all inter‐group events during these activities. Evidence gathered from videotape, interview, and observational data further indicated that many types of inter‐group interactions are qualitatively different from intra‐group interactions, and that inter‐group interactions contribute significantly to learning within a design‐based classroom context. Students in these classrooms effectively used the special expertise of others outside of their assigned groups and exploited features of the material environment in specific ways with others outside of their assigned groups to create complex products. Examples are included of how concepts, ideas, tools, tool‐related practices, and materials diffused throughout the classroom environment and were appropriated by learners in various ways to contribute to the construction of the design artifacts. © 2000 John Wiley & Sons, Inc. J Res Sci Teach 38: 17–42, 2001     

Teachers’ Organization of Participation Structures for Teaching Science with Computer Technology

This paper describes a qualitative study that investigated the nature of the participation structures and how the participation structures were organized by four science teachers when they constructed and communicated science content in their classrooms with computer technology. Participation structures focus on the activity structures and processes in social settings like classrooms thereby providing glimpses into the complex dynamics of teacher–students interactions, configurations, and conventions during collective meaning making and knowledge creation. Data included observations, interviews, and focus group interviews. Analysis revealed that the dominant participation structure evident within participants’ instruction with computer technology was (Teacher) initiation–(Student and Teacher) response sequences–(Teacher) evaluate participation structure. Three key events characterized the how participants organized this participation structure in their classrooms: setting the stage for interactive instruction, the joint activity, and maintaining accountability. Implications include the following: (1) teacher educators need to tap into the knowledge base that underscores science teachers’ learning to teach philosophies when computer technology is used in instruction. (2) Teacher educators need to emphasize the essential idea that learning and cognition is not situated within the computer technology but within the pedagogical practices, specifically the participation structures. (3) The pedagogical practices developed with the integration or with the use of computer technology underscored by the teachers’ own knowledge of classroom contexts and curriculum needs to be the focus for how students learn science content with computer technology instead of just focusing on how computer technology solely supports students learning of science content.     

A case study on the formation and sharing process of science classroom norms

The teaching and learning of science in school are influenced by various factors, including both individual factors, such as member beliefs, and social factors, such as the power structure of the class. To understand this complex context affected by various factors in schools, we investigated the formation and sharing process of science classroom norms in connection with these factors. By examining the developmental process of science classroom norms, we identified how the norms were realized, shared, and internalized among the members. We collected data through classroom observations and interviews focusing on two elementary science classrooms in Korea. From these data, factors influencing norm formation were extracted and developed as stories about norm establishment. The results indicate that every science classroom norm was established, shared, and internalized differently according to the values ingrained in the norms, the agent of norm formation, and the members’ understanding about the norm itself. The desirable norms originating from values in science education, such as having an inquiring mind, were not established spontaneously by students, but were instead established through well-organized norm networks to encourage concrete practice. Educational implications were discussed in terms of the practice of school science inquiry, cultural studies, and value-oriented education.     

Cognitive regulations in ICT-supported flipped classroom interactions: An activity theory perspective

In recent years, most studies on flipped classrooms or flipped learning have focused on learners’ motivation, academic achievement and teachers’ and students’ perceptions of the flipped classroom. Little research has involved interactions in the flipped classroom. This study aims to show that in-class collaborative learning in the flipped classroom can not only be conceived as a collective activity consisting of discrete actions, but also as a systematic activity. From the activity-theoretical perspective, contradictions were found between components of an activity such as subject, tools, rules, community, division of labor, object and outcome. This study conducted a pre-experiment, selecting one lesson of the seventh-grade Information Technology Course as the learning content, conducted in a flipped classroom. Three triads with different compositions were specifically observed by recording their interactions. More second-level contradictions existed between subject and tools, and division of labor within the low-level triad than within the other two triads, and more first-level contradictions also occurred within the low-level triad than within the other two triads. Most second-level contradictions within the high-level triad were resolved by self-regulation of cognition. Instead, most second-level contradictions within the mixed-level triad were overcome by co-regulation or shared regulation of cognition. This study sheds light on how to effectively design and implement flipped learning, and provides a new approach for analyzing interactions in the classroom.     

Looking through ethnographic eyes at classrooms acting as cultures

In this article we used an orienting framework of interactional ethnography to make visible classrooms acting as cultures. We examined the interactional patterns from two different classrooms as participants jointly negotiated and constructed meaning. We first demonstrated how participants began to construct a classroom culture in the first weeks of school. Next, we examined how taking up an ethnographic perspective assisted a teacher candidate to successfully enter an ongoing classroom culture. In the last analytic sequence, we followed the discursive practices surrounding a fifth grade student who re-entered an ongoing classroom culture after an absence of four months. The results showed that using ethnographic skills of observation and interpretation assisted both the teacher candidate and the returning student to become communicatively and culturally competent members, by recognising the social and academic patterned practices that were already taking shape through the classroom interactions.     

Finnish students’ reasons for their achievement in classroom activities: focus on features that support self-regulated learning

The aim of this study was to investigate how finnish students explain factors that contribute to their achievement in classroom learning activities and whether these factors are related to support of self-regulated learning (SRL) in classroom. Over seven weeks, 24 primary school students were videotaped during their typical classroom activities in 28 lessons to capture moments when they succeeded in learning tasks. From the video observations, 62 episodes were edited and used in stimulated recall interviews in which students were asked to report the reasons they related to their achievement in learning situations. Data-driven content analysis was used to analyse the open-ended interview data. The video observation data were analysed and sorted into theory-driven categories in order to find out how SRL was supported in classrooms. The results showed that students describe achievement through the actions that they took in the learning situations, such as being able accomplish the task. The reasons given for their achievement dealt with ability to accomplish the tasks or doing academic activities in order to achieve in the task. Furthermore, the students recognised classroom activities that support SRL, acknowledging their contribution to their achievement, mostly through the support that they received from their teachers and peers.     

Antiracism defined as equitable sociocultural interactions in prekindergarten: Classroom racial composition makes a difference

This study used secondary data from the My Teaching Partner-Math/Science 2013–2016 randomized control trial to explore whether equitable sociocultural classroom interactions (see Curenton et al., 2019) were associated with the skills of 105 four- and five-year-olds (52% boys; drawn from 20 unique video recordings of preschool teachers/classrooms; 43% were Black, Latine, Asian, or other racially marginalized learners). Equitable interactions predicted children's skills with effect sizes ranging from small (0.01–0.44) to large (1.00). Moderation analyses revealed that when classrooms had more racially marginalized learners, teachers’ use of equitable disciplinary and personalized learning practices were associated with higher executive functioning gains across prekindergarten. Findings illustrate how classroom composition can be a key indicator between equitable classroom interactions and young children's early skills.     

Assessment and the co-regulation of learning in the classroom

ABSTRACT

This paper examines the processes of regulation of student learning that are associated with formative assessment in the classroom. It discusses the concept of co-regulation and presents a model of co-regulation developed in a situated perspective on classroom learning. This model conceptualises co-regulated learning as resulting from the joint influence of student self-regulation and of sources of regulation in the learning environment: namely, the structure of the teaching/learning situation, the teacher’s interventions and interactions with students, the interactions between students, and the tools used for instruction and for assessment. Examples of research showing how co-regulation functions are discussed, in particular students’ use of tools for self-assessment and peer assessment, and the role of teacher–student interactions that encourage active student participation in formative assessment.     

The Use of Collaboration,Authentic Learning,Linking Material to Personal Knowledge,and Technology in the Constructivist Classroom: Interviews with Community College Faculty Members

ABSTRACT

This study explored how faculty members implemented constructivist teaching methods after training. The student-centered teaching methods were interactions and collaborations, authentic learning and real-world experiences, linking material to previously learned information, and using technology in the classroom. Seven faculty members trained in student-centered teaching methods by the professional development department at a community college were interviewed. Interviews were supplemented with teacher-generated documents and classroom observations. All reported implementing the recommended practices in the classrooms, both online and in traditional face-to-face classrooms.