Explanations in Mathematics Classrooms: A Discourse Analysis

Abstract

This article focuses on student explanations as a discourse practice central to mathematics teaching and learning. I discuss classrooms as hybrid discourse spaces and focus on how talk is used to accomplish social action. In doing so, I contrast several different social and sociomathematical norms for explanation and suggest that students’ choices of discourse practices position them within the classroom. Further, I caution educators against assuming that complete and detailed explanations are always best to support student learning. I discuss how explanations that are coconstructed by several students can actually support joint engagement in mathematical work and help peers stay “on the same page” while avoiding hierarchical positioning.     

Recurrent routines: Analyzing and supporting orchestration in technology-enhanced primary classrooms

The increasing presence of multiple Information and Communication Technologies (ICT) in the classroom does not guarantee an improvement of the learning experiences of students, unless it is also accompanied by pedagogically effective orchestration of those technologies. In order to help teachers in this endeavour, it can be useful to understand how this orchestration takes place in real-world classrooms, and to provide teachers with professional development opportunities that can be easily applied to their everyday classroom practice. This paper describes a qualitative field study conducted in five primary school classrooms where a new collaborative software was introduced alongside existing classroom technology. For six months, teachers designed and orchestrated classroom activities in these authentic, technologically-rich settings. The analysis of the resulting activity designs and enactments uncovered a limited set of recurrent elements of teacher practice, or routines. These routines and their graphical representation are posited as a useful analysis tool for researchers in understanding complex teacher practices with ICT. Moreover, the authors propose that these routines offer new opportunities for professional development of teachers in effectively using ICT in their classrooms. Initial uses of these routines in teacher workshops, with encouraging results, are also presented.     

Making rounds: The routine work of the teacher during collaborative learning with computers

This paper provides a detailed analysis of the work of the teacher during collaborative-learning activities. Whilst the importance of the teacher for the success of collaborative learning has frequently been recognized in the CSCL literature, there is nevertheless a curious absence of detailed studies that describe how the teacher intervenes in pupils’ collaborative-learning activities, which may be a reflection of the ambivalent status of teachers within a field that has tried to transfer authority from teachers to pupils. Through a close analysis of different types of teacher interventions into pupils working in pairs with a storyboarding tool, this paper argues, firstly, that concerns of classroom management and pedagogy are typically intertwined and, secondly, that although there may be tensions between the perspectives of teachers and pupils these do not take the form of antagonistic struggles. The paper concludes that it may be time to renew our interest in the work of teachers in the analysis of collaborative-learning activities.     

Enacting a technology-based science curriculum across a grade level: The journey of teachers' appropriation

Studying teacher enactment of an innovation helps us understand the process of effective spread of a curricular innovation to teachers who have differing levels of content readiness, pedagogical orientations, teaching competency, different student profiles, and professional development experiences. Towards this, we explore how different teachers in the same grade level appropriated a common science curriculum enabled by mobile technologies in their classrooms. The innovative science curriculum: Mobilized 5E (Engage–Explore–Explain–Elaborate–Evaluate) Science Curriculum was developed through an iterative cycle of design-based research. As curriculum designs were not self-sufficient by themselves, the enactments of the teachers differed in how they leveraged on students' artifacts, how they integrated the technology into the class, the ways in which they interacted with the students, and how they scaffolded students' activities in a mobile learning setting. In this study, the teachers' enactments of mobilized 5E lessons were observed, analyzed and compared, with the aim of exploring the differences of lesson enactment amongst them. The results showed that teachers' different pedagogical orientations affected their instructions, especially their ways of technology integration in the class, and their patterns of interactions with the students. Based on the exploration of the teacher enactment of the mobilized 5E curriculum, implications are drawn concerning the implementation of innovative curricula implementation and the supports for teacher professional development of such innovation with the ultimate purpose of sustaining and scaling.     

Automatic classification of activities in classroom discourse

Classroom discourse is the primary medium through which teaching and learning occur. Managed skillfully, it can provide an opportunity for students to develop their understanding and to profit from the ideas of their peers and the teacher. Yet it is difficult for teachers to be mindful of the nature and distribution of classroom discourse at the same time as they juggle other instructional concerns. It is possible to record, transcribe, and analyze classroom discourse, but it is not possible to do this quickly enough to give a teacher timely feedback. We report on the development and validation of an automated system for recording and analyzing aspects of classroom discourse that can result in timely feedback. Based on the LENA system, it aims to identify three common discourse activities: teacher lecturing, whole class discussion and student group work. The system consists of a speech processing module (diarisation performed by the LENA system) and an activity detection module that detects the discourse activities by using classification analysis. Results showed that our automatic detection of discourse activities converged well with those of human coders. The system enables timely and relatively inexpensive generation of a classroom discourse profile, which helps teachers to visualize and potentially improve their classroom discourse management skills.     

Teaching in flipped classrooms: Exploring pre-service teachers' concerns

To effectively promote the student-centered movement, it is important to understand pre-service teacher concerns about teaching in technology-integrated flipped classrooms. This study surveyed more than 470 pre-service teachers' concerns on teaching with flipped learning instruction. To understand the role of individual differences, personal characteristics such as self-efficacy for teaching, teacher knowledge, and other demographics were investigated. The results indicated the pre-service teachers had mostly self-concerns. Self-efficacy and non-technological teacher knowledge were associated with most stages of concern. Females had more awareness and management concerns; non-science pre-service teachers had more information, personal, and collaboration concerns; seniors had the highest awareness for flipped classrooms, and the effects of other personal characteristics on stages of concern were identified. The significant findings draw implications for teacher educators and teacher education programs in updating curriculum and instruction so as to equip pre-service teachers with the essential knowledge and skills for teaching effectively in 21st century classrooms.     

Korean science teachers’ perceptions of the introduction of socio‐scientific issues into the science curriculum

Abstract:

This study examined Korean secondary science teachers’ perceptions of the introduction of socio‐scientific issues (SSI) into the science curriculum. The guiding research questions were (a) What are teachers’ perceptions of SSI and the place of these issues in the science curriculum? and (b) What are some factors that impede or facilitate addressing SSI in Korean secondary classrooms? The factors that were explored included teachers’ perceptions of the necessity of addressing SSI, teachers’ personal science‐teaching efficacy (PSTE) beliefs regarding SSI, and other relevant situational factors. The 86 participants (65% female) completed a questionnaire comprising Likert‐type and open‐ended questions. Next, follow‐up, semi‐structured interviews were conducted with a random sample of 12 participants. Results indicated that participants perceived a need to address SSI positively. However, only a minority dealt with such issues in their classrooms and then only sporadically. Participants had low PSTE beliefs related to teaching about SSI. They perceived the lack of instructional time and the unavailability of relevant materials as the primary obstacles that hindered the teaching of SSI. It is argued that the culture of pre‐college science education in Korea, which is still largely dominated by a preoccupation with preparing students for admission to institutions of higher education, subsumes those obstacles identified and experienced by the participant teachers.     

Barriers to online critical discourse

This qualitative case study illustrates barriers to informal argumentation and reasoned debate, i.e., critical discourse, in online forums. The case is the computer conference of a 15-week, graduate-level humanities course offered entirely at a distance. Twelve students, all with families and careers, were enrolled in the course. We read all messages as they were posted and interviewed five of the students several times during the course. The students provided three insights into our interpretation that the forums contained little critical discourse: (1) The students did not orient to the conference as a forum for critical discourse, and worse, they had competing orientations; (2) they perceived critiques as personal attacks; and (3) they realized early on that critical discourse was a bothersome means to obtain their participation marks. Certain practices may ease some of these difficulties, including (1) well-structured learning activities with clearly defined roles for teachers and students, and (2) a method of assessing students’ participation that reflects the time and effort required to engage in critical discourse.     

Information technology: building structures in initial teacher training to develop effective practitioners

Abstract It was reported at a recent conference, that staff of teacher training institutions are less willing than teachers to collaborate in the use of information technology in the curriculum. Teacher trainers will discuss, promote and research innovation in this area but this activity seems unable to influence how teacher training programmes are themselves delivered. This paper examines how one teacher training institution is trying to embed information technology in the pedagogy of its courses in ways that enable student teachers to re-construct similar learning experiences in the classroom on teaching practice.     

Teacher-created video instruction in the elementary classroom—Its impact on students and teachers

Despite the proliferation of multimedia devices in elementary classrooms, there is limited research examining teacher-created video instruction, particularly regarding its effect on academic growth and engagement. This study investigated the effect of teacher-created computer-based video instruction (CBVI) using iPads on students' academic, behavioural and affective learning in elementary classrooms. The study used a repeated-measures design with counterbalancing to measure the effects of CBVI during mathematics lessons on student achievement scores, time on-task and attitudes towards learning. Three year three classes (n = 49) completed three lessons, each using a different mode of instruction: CBVI created by the class teacher, CBVI created by a stranger, and a traditional live lesson delivered by the class teacher. Results were analysed using a Linear Mixed Model. No significant growth in performance was detected during video instruction, however a significant growth result was achieved for the traditional live teaching mode (p < 0.001), possibly attributable to the longer duration of experimental session. Behavioural engagement was considerably higher during CBVI lessons than live lessons and students preferred their teacher's voice during CBVI. Three teachers were interviewed to examine how CBVI affected teaching and learning, with two main themes emerging: (1) positive impacts of CBVI upon students; and (2) positive impacts on teacher wellbeing. This research indicates benefits for students and teachers when using teacher-created CBVI. Further research is needed to better understand the factors that influence cognitive development of students using CBVI and to also further explore the effect of CBVI on teacher wellbeing.     

Microcomputers: An educational challenge

Findings from a series of studies indicated that educators perceived that computers will have a strong impact on curriculum and classroom instruction. Unfortunately, educators also expressed reluctance to incorporate educational change in their classrooms. Two major issues for teacher educators and teacher education programs are: (1) how best to prepare teachers to teach and use appropriate computer technology that requires new and different skills and (2) to develop quality teacher preparation programs.     

Educating online student teachers to master professional digital competence: The TPACK-framework goes online

In this article we study how online teacher education programmes may enhance innovative ways of teaching and learning with Information and Communication Technology (ICT). We explore how online teachers are practising professional digital competence, in general and within subject areas, and to what extent they encourage student teachers to develop their own professional digital competence. Based on online teacher education programmes at two distinct higher education institutions (HEIs), we applied mixed method design including quantitative and qualitative approaches to illuminate the aims and the scope. Our study revealed that even if online teacher education programmes represent good avenues for stimulating teachers and student teachers to develop digital competence for pedagogical purposes, this aspect is poorly integrated within the actual programmes, although some interesting examples were demonstrated. By looking at the origins of the discourses on online education and on digital competence, we found that they derive from different stakeholders: while the discourse on online education originated from the management side at both HEIs, the discourse on digital competence derived from certain teaching staff at the two HEIs. Our study indicated that there is still some way to go to innovative solutions and to develop the potential of professional digital competence in online teacher education programmes.     

Cross-community knowledge building with idea thread mapper

Research on computer-supported collaborative learning faces the challenge of extending student collaboration to higher social levels and enabling cross-boundary interaction. This study investigated collaborative knowledge building among four Grade 5 classroom communities that studied human body systems with the support of Idea Thread Mapper (ITM). While students in each classroom collaborated in their local (home) discourse space to investigate various human body functions, they generated reflective syntheses— “super notes”—to share knowledge progress and challenges in a cross-community meta-space. As a cross-community collaboration, students from the four classrooms further used the Super Talk feature of ITM to investigate a common problem: how do people grow? Data sources included classroom observations and videos, online discourse within each community, students’ super notes and records of Super Talk discussion shared across the classrooms, and student interviews. The results showed that the fifth-graders were able to generate high quality super notes to reflect on their inquiry progress for cross-classroom sharing. Detailed analysis of the cross-classroom Super Talk documented students’ multifaceted understanding constructed to understand how people grow, which built on the diverse ideas from each classroom and further contributed to enriching student discourse within each individual classroom. The findings are discussed focusing on how to approach cross-community collaboration as an expansive and dynamic context for high-level inquiry and continual knowledge building with technology support.

     

Reconsidering off‐task: a comparative study of PDA‐mediated activities in four classrooms

Mobile technology is ubiquitous and diverse and permeates many aspects of daily life at home, during leisure activities, and in public spaces. The study presented here is of two sixth grade classes in Michigan, USA and two seventh grade classes in Norway. The students and the teachers in these four classrooms were equipped with mobile technologies (PDAs). We found that the students' PDA‐mediated actions in the classroom were not exclusively used for the tasks and activities set by the teacher, but that the students also used the PDAs on their own initiative – so‐called ‘off‐task’ activities. We analyze the findings by reconsidering off‐task activities from a sociocultural perspective.     

Complexity, class dynamics, and distance learning

Classroom participants learn early on that each classroom has its own dynamic comprised of personalities, motivation levels, skills, and other variables. This paper explores features of complexity theory—nonlinearity and emergent self-organization—relevant to dynamics in physical or virtual classrooms. These central notions of complexity theory and their importance in composition classrooms help explain why students in virtual classrooms are often less successful than their physical classroom counterparts in negotiating the eddies of virtual interactions. The paper closes with a brief consideration of how teachers can interrogate all the elements of teaching and classroom context (whether physical or virtual) to influence the emergent dynamic of our classrooms.     

Bridging the app gap: An examination of a professional development initiative on mobile learning in urban schools

In this study we present a professional development initiative aimed at helping urban teachers in low-income underserved schools in the U.S. learn how to utilize iPads (a representative mobile device) and educational apps (software programs that run on mobile devices) to support teaching and learning. Subsequently, we examine the ways in which four case study teachers utilized iPads and educational apps in their classrooms to support their students' learning experiences. Data included observations of professional development activities, classroom observations, teacher interviews, and student focus groups. Findings revealed that students used iPads and educational apps to (a) access online content, (b) create learning artifacts, and (c) reinforce content learning through personalized instruction. Findings also indicated that use of iPads and educational apps supported student academic growth and empowerment. Results have implications for mobile learning researchers, practitioners, and policy makers, particularly those charged with the design and implementation of professional development programs.     

Casting shadows in the science classroom

Abstract

Research in mathematics and science education frequently directs one's attention to the limited content knowledge of elementary pre‐service teachers. It is believed, however, that research of this nature leads to a deficit approach to understanding more about the teaching and learning of these subjects. In addition to focusing on the knowers of school mathematics and science, there is a call to acknowledge the problematic nature of knowing (in) mathematics and science. In this paper, the metaphor of shadows is used in a critical exploration of what it means to know and how the cultures of classrooms have shaped these images of knowing. Through the voices of pre‐service teachers, this paper directs one's attention to objects that cast shadows on the learning and knowing of mathematics and science. Three such shadow‐casting objects discussed in this paper are textbooks, teachers, and gendered ideology. The paper seeks to critically illuminate the problematic nature of what it means to know (in) mathematics and science by examining the shadowy texture of unquestioned ideologies.     

Co-located single display collaborative learning for early childhood education

The benefits of collaborative learning are well documented. However, most of the research has been done with children beyond the ages of early childhood. This could be due to the common and erroneous belief that young children have not developed the capacity to work collaboratively toward a given aim. In this paper we show how small group co-located collaborative learning on a single display computer improves oral language, logical-mathematical and social skills in pre-school children. Considering that early childhood teachers have a responsibility to provide a supportive environment, teacher mediation is essential in order to achieve collaborative learning. Thus, teachers were trained in the use of the technology and strategies for effective collaborative learning. The study was implemented in 10 kindergarten classrooms with 268 children between the ages of 5 and 6 years old. A group of 5 kindergarten classrooms with equivalent characteristics participated as a comparison group. During the four-month intervention, children worked on collaborative activities at least twice a week. A quasi-experimental approach was used to assess the implementation, including pre- and post-testing. The data showed differences in the learning of oral language, logical-mathematical and social skills, with the experimental group demonstrating significantly greater achievement.