Differential Participation During Science Conversations: The Interaction of Focal Artifacts,Social Configurations,and Physical Arrangements

Recent conceptualizations of knowing and learning focus on the degree of participation in the practices of communities. Discursive practices are the most important and characteristic practices in many communities. This study was designed to investigate how the content and form of classroom discourse was influenced by different combinations of artifacts (e.g., overhead transparencies, physical models), social configurations, and physical arrangements. Over a 4-month period, we collected data (video-taped activities, interviews, ethnographic observations, artifacts, and photographs) in a Grade 6-7 science class studying a unit on simple machines. Four different activity structures differed in terms of the social configuration (whole class, small group) and the origin of the central, activity-organizing artifact (teacher designed, student designed). This study describes how different artifacts, social configurations, and physical arrangements led to different interactional spaces, participant roles, and levels of participation in classroom conversations and, concomitantly, to different discursive forms and content. The artifacts had important functions in maintaining and sequencing conversations. Depending on the situation and the role of participants, artifacts served as resources for students' sense making. Each of the different activity structures supported different dimensions of participating in conversations and, for this reason, we conclude that science educators teaching large classes should employ a mixture of these activity structures. Overall, students developed considerable competencies in discursive and materials practices related to simple machines.     

Developing interactive mathematical talk: investigating student perceptions and accounts of mathematical reasoning in a changing classroom context

In recent years there has been an increased focus on the need for teachers to develop learning communities where all students have opportunities to engage in interactive discourse. However, there are few studies that focus on student perceptions and accounts of mathematical reasoning in classrooms with interactive mathematical talk as a focus of reform. A framework of teacher actions to develop classroom and mathematical practices was developed from classroom observations. Photo-elicitation interviews were used to investigate student perception and accounts of mathematical explanations and reasoning. The professional development programme, shifts in the teacher actions, and subsequent shifts in student perception and their recall of their own and peers’ mathematical reasoning over a school year are highlighted. Developing interactive dialogue in the classroom took considerable time and attention. Facilitating change to the way students both participated and understood their obligations required constant, ongoing attention to both the classroom and mathematical practices.     

Representational Tools and Mathematical Understanding

Understanding how cultural mediators and social interaction promote meaningful learning requires that each student's perspective, reasoning, and construction processes be taken into account. In my analysis of the classroom episodes, I consider individual students' progress as they use tools, discuss data distributions, and interact with their teachers and their peers. I argue that data display tools provide a partial context for discussions but do not constrain the students' interpretations or the way they reason about the data. Students' approaches to the mathematical relations discussed in the classroom result rather from the meaning they attribute to the different features of the displays, the teachers' questions, and the evolving interaction with their peers.     

Constructivism in Mathematics Classrooms: Listening to Ghanaian Teachers’ and Students’ Views

One of the challenges of implementing a new curriculum is how to bridge the gap between the underlining principles of the curriculum and the cultural and social orientations of the society which includes teachers and students. This article reports on a study that explored how the cultural and social orientations of teachers and students can influence the implementation of a constructivist curriculum in mathematics classrooms. The data for the study came from 250 students and 41 mathematics teachers, using questionnaires, observations, and interviews. The results showed that inasmuch as mathematics teachers and their students acknowledge the importance of student’s active participation and teamwork, these practices have not been fully conceptualised into the Ghanaian mathematics classroom due to some cultural factors. Two main cultural factors were discovered from the analyses of the results. Firstly, the culture of acknowledging only correct answers in class has a negative impact on individual students’ confidence and participation during mathematics lessons. Also, the culture of teamwork is not fully accepted within Ghanaian classrooms as most students find it difficult working in groups and accepting and appreciating each other’s view. It was evident in all lessons that students were ridiculed by their peers when they provide a wrong answer to a question and this affected individual students’ participation in the classroom. Therefore, we suggested that teachers should be pro-active in promoting a classroom environment which is free from fear and intimidation to motivate students to be actively involved in the classroom discourse.     

Discourses of time and maturity structuring participation in mathematics and further mathematics

Abstract

This paper examines how young people account for choosing mathematical subjects, and how these processes sustain, or not, their continued participation. It draws on a 2-year qualitative study of 24 young people’s accounts of following advanced mathematical pathways within a widening participation programme. Working within a post-structural framework, I combine two arguments: firstly, that local discourses of time, age and maturity position contemporary adolescence as a time of ‘becoming’ that aligns personal aspirations with mathematical progress, and secondly that students’ accounts of choice and aspiration require multiple imaginings of present and future selves. I identify distinct discourses –moving/improving and getting ahead - that structure the intelligibility of participation in mathematics and further mathematics respectively. I argue that tracing the alignments between students’ accounts of themselves and/ in mathematics offers potential to understand emergent practices in mathematics participation but also how exclusions are re-inscribed along classed and gendered lines.     

“Noticing” as an Alternative Transfer of Learning Process

As transfer researchers have begun to investigate a broader range of phenomena, they have correspondingly put forward new processes to provide explanatory accounts for the occurrence of transfer. This move coincides with a call to acknowledge the contribution of social interactions, language, cultural artifacts, and normed practices to the generalization of learning. In this article, we posit “noticing” as a plausible transfer process and investigate both individual noticing and the social organization of noticing via the focusing framework. Specifically, we relate the nature of students' reasoning on transfer tasks with what students notice mathematically in classrooms when many sources of information compete for their attention, and then we account for noticing as socially situated in classroom discourse practices, features of mathematical tasks, and the nature of mathematical activity.     

The Interplay of Teacher and Student Actions in the Teaching and Learning of Geometric Proof

Proof and reasoning are fundamental aspects of mathematics. Yet, how to help students develop the skills they need to engage in this type of higher-order thinking remains elusive. In order to contribute to the dialogue on this subject, we share results from a classroom-based interpretive study of teaching and learning proof in geometry. The goal of this research was to identify factors that may be related to the development of proof understanding. In this paper, we identify and interpret students' actions, teacher's actions, and social aspects that are evident in a classroom in which students discuss mathematical conjectures, justification processes and student-generated proofs. We conclude that pedagogical choices made by the teacher, as manifested in the teacher's actions, are key to the type of classroom environment that is established and, hence, to students' opportunities to hone their proof and reasoning skills. More specifically, the teacher's choice to pose open-ended tasks (tasks which are not limited to one specific solution or solution strategy), engage in dialogue that places responsibility for reasoning on the students, analyze student arguments, and coach students as they reason, creates an environment in which participating students make conjectures, provide justifications, and build chains of reasoning. In this environment, students who actively participate in the classroom discourse are supported as they engage in proof development activities. By examining connections between teacher and student actions within a social context, we offer a first step in linking teachers' practice to students' understanding of proof.     

Learning in collaborative settings: students building on each other’s ideas to promote their mathematical understanding

The purpose of this study is to contribute insights into how collaborative activity can help promote students’ mathematical understanding. A group of six high school students (15- to 16-year olds) worked together on a challenging probability task as part of a larger, after-school, longitudinal study on students’ development of mathematical ideas in problem-solving settings. The students solved the problem and produced a valid justification of their solution. This study shows that collaborative activity can help promote students’ mathematical understanding by providing opportunities for students to critically reexamine how they make claims from facts and also enable them to build on one another’s ideas to construct more sophisticated ways of reasoning. Implications for classroom teaching and ideas for future research are also discussed. The study helps address a documented need for a better understanding of how mathematical learning evolves in social settings.     

Participating in Classroom Mathematical Practices

In this article, we describe a methodology for analyzing the collective learning of the classroom community in terms of the evolution of classroom mathematical practices. To develop the rationale for this approach, we first ground the discussion in our work as mathematics educators who conduct classroom-based design research. We then present a sample analysis taken from a 1st-grade classroom teaching experiment that focused on linear measurement to illustrate how we coordinate a social perspective on communal practices with a psychological perspective on individual students' diverse ways of reasoning as they participate in those practices. In the concluding sections of the article, we frame the sample analysis as a paradigm case in which to clarify aspects of the methodology and consider its usefulness for design research.     

Teachers' framing of argumentation goals: Working together to develop individual versus communal understanding

For students to meaningfully engage in science practices, substantive changes need to occur to deeply entrenched instructional approaches, particularly those related to classroom discourse. Because teachers are critical in establishing how students are permitted to interact in the classroom, it is imperative to examine their role in fostering learning environments in which students carry out science practices. This study explores how teachers describe, or frame, expectations for classroom discussions pertaining to the science practice of argumentation. Specifically, we use the theoretical lens of a participation framework to examine how teachers emphasize particular actions and goals for their students' argumentation. Multiple-case study methodology was used to explore the relationship between two middle school teachers' framing for argumentation, and their students' engagement in an argumentation discussion. Findings revealed that, through talk moves and physical actions, both teachers emphasized the importance of students driving the argumentation and interacting with peers, resulting in students engaging in various types of dialogic interactions. However, variation in the two teachers' language highlighted different purposes for students to do so. One teacher explained that through these interactions, students could learn from peers, which could result in each individual student revising their original argument. The other teacher articulated that by working with peers and sharing ideas, classroom members would develop a communal understanding. These distinct goals aligned with different patterns in students' argumentation discussion, particularly in relation to students building on each other's ideas, which occurred more frequently in the classroom focused on communal understanding. The findings suggest the need to continue supporting teachers in developing and using rich instructional strategies to help students with dialogic interactions related to argumentation. This work also sheds light on the importance of how teachers frame the goals for student engagement in this science practice.     

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.     

Keeping them in line: choreographing classroom spaces

This paper provides teachers with an opportunity for thinking about the kinds of ‘people’ constructed in their classes, the kinds of ‘dances’ choreographed and the ways space is organised for learning. We argue that this is essential for teachers to think about if they are to enact socially just professional practices. In this study, we explore the ways in which students learn to be particular kinds of people. We understand this as happening through their participation in communities of practice. Becoming a member of a community of practice, of a classroom and of a school is a process of developing a particular identity, modes of behaviour and ways of knowing. It is through these ‘normalising’ practices that power is constituted, boundaries constructed and certain ‘kinds of people’ are recognised, represented and constituted, whilst others are not. All individuals are implicated in these processes and active in the construction of their own as well as others’ identities. This paper locates this discussion using social relations of gender and ethnicity, and considers how diversity and difference are actively constituted and play out in one primary school classroom. How students participate in the spatial practices and the construction of pedagogical spaces, what identities are available to them in these spaces and which they take up, is explored. The metaphor of dance is used to analyse these spaces, a metaphor which helps us to understand the complexity of classroom relationships and the way macro‐social practices are both reflected and reconstituted in classroom practices. We argue that the ways teachers think about how they place students, space students and construct students are crucial for student and teacher learning.     

Writing in Mathematics: An Alternative Form of Communication for Academically Low‐Achieving Students

Abstract. Classroom communication figures prominently in current math reform efforts. In this study, we analyze how one teacher used writing to support communication in a seventh‐grade, low‐track mathematics class. For one school year, we studied four low‐achieving students in the class. Students wrote in journals on a weekly basis. Using classroom observations and interviews with the teacher, we developed profiles of the four students, capturing their participation in class discussions. The profiles highlighted an important similarity among the four students: marginal participation in both small‐group and whole‐class discussions. However, our analysis of the students' journals identified multiple instances where the students were able to explain their mathematical reasoning, revealing their conceptual understanding, ability to explain, and skill at representing a problem. In this respect, journals potentially facilitate another important form of classroom communication. The promise of writing is that it offers an alternative to the visions of classroom communication that are strictly oral in nature.     

Elementary students' views of explanation,argumentation, and evidence,and their abilities to construct arguments over the school year

Science includes more than just concepts and facts, but also encompasses scientific ways of thinking and reasoning. Students' cultural and linguistic backgrounds influence the knowledge they bring to the classroom, which impacts their degree of comfort with scientific practices. Consequently, the goal of this study was to investigate 5th grade students' views of explanation, argument, and evidence across three contexts—what scientists do, what happens in science classrooms, and what happens in everyday life. The study also focused on how students' abilities to engage in one practice, argumentation, changed over the school year. Multiple data sources were analyzed: pre‐ and post‐student interviews, videotapes of classroom instruction, and student writing. The results from the beginning of the school year suggest that students' views of explanation, argument, and evidence, varied across the three contexts with students most likely to respond “I don't know” when talking about their science classroom. Students had resources to draw from both in their everyday knowledge and knowledge of scientists, but were unclear how to use those resources in their science classroom. Students' understandings of explanation, argument, and evidence for scientists and for science class changed over the course of the school year, while their everyday meanings remained more constant. This suggests that instruction can support students in developing stronger understanding of these scientific practices, while still maintaining distinct understandings for their everyday lives. Finally, the students wrote stronger scientific arguments by the end of the school year in terms of the structure of an argument, though the accuracy, appropriateness, and sufficiency of the arguments varied depending on the specific learning or assessment task. This indicates that elementary students are able to write scientific arguments, yet they need support to apply this practice to new and more complex contexts and content areas. © 2011 Wiley Periodicals, Inc. J Res Sci Teach 48: 793–823, 2011     

Extending science beyond the classroom door: Learning from students' experiences with the Choice,Control and Change (C3) curriculum

This article describes the experiences of seventh‐grade students living in high poverty areas of New York City who participated in the Choice, Control and Change (C3) science curriculum. Data were collected from eight case study students in the form of individual interviews, classroom observations, and student artifacts. Analysis of these data revealed that students were able to extend their C3 science understandings beyond the classroom door by developing and expressing science agency in the following ways: (1) critically analyze the conditions of their food environment, (2) purposefully make healthier choices, and (3) expand the food and activity options available to themselves and others. Through participation in the C3 curriculum, and the science content and practices addressed therein, students began to view their worlds with a more critical mindset and to devise ways to transform themselves and the conditions of their own and others' lives. Based on the findings, we propose taking a closer look at how we might create meaningful and relevant learning opportunities for students through connecting school science with issues of personal and social significance in students' lives outside of school. © 2011 Wiley Periodicals, Inc. J Res Sci Teach 49: 244–269, 2012     

Mind,Language and Artworks as Real Constraints on Students' Critical Reasoning about Meaning in Art

To engage in discussions of artwork meaning is to engage in critical reasoning, a factor that is central to the interpretation of artworks in the art classroom. While this may appear as a common‐sense claim that reflects the tacit assumptions most art educators have about students' critical dispositions in art, it is also evident that little is known about the deeper structures underlying students’ critical reasoning and how such structures shape students’ interpretations of artworks. Drawing on my research on students’ theories of critical meaning in art, this article explores the nature of practical and theoretical constraints on students’ critical reasoning about the meaning of artworks. I account for how intentional beliefs, language and representational artefacts function as a nexus of real constraints that condition students’ advance into interpretations of the social meaning of art. After briefly outlining the design and methodology of my study, I examine students’ critical reasoning performances during the formative period of development between middle to late childhood. The findings reveal that with increasing age students gradually learn to exercise their own critical intentions and represent inferences that acknowledge the significance of constitutive rules and force of a collective intentionality in the artworld on their interpretations of artworks as artefacts. I then make some conclusions about the relationship of domain‐specific shifts in art understanding, the role of intentionality, representational understanding, beliefs about art and reasoning skills to the linguistic, theoretical and artefactual constraints conditioning students’ intuitive advance into real understandings of art.     

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.     

“But at school … I became a bit shy”: Korean immigrant adolescents’ discursive participation in science classrooms

In reform-based science curricula, students’ discursive participation is highly encouraged as a means of science learning as well as a goal of science education. However, Asian immigrant students are perceived to be quiet and passive in classroom discursive situations, and this reticence implies that they may face challenges in discourse-rich science classroom learning environments. Given this potentially conflicting situation, the present study aims to understand how and why Asian immigrant students participate in science classroom discourse. Findings from interviews with seven Korean immigrant adolescents illustrate that they are indeed hesitant to speak up in classrooms. Drawing upon cultural historical perspectives on identity and agency, this study shows how immigrant experiences shaped the participants’ othered identity and influenced their science classroom participation, as well as how they negotiated their identities and situations to participate in science classroom and peer communities. I will discuss implications of this study for science education research and science teacher education to support classroom participation of immigrant students.