Mathematics Classroom Interaction Research Articles

'Patterns in Mathematics Classroom Interaction' Jenni Ingram

Patterns in Mathematics Classroom InteractionJenni Ingram (Oxford University Press, 2021)

The influence of different teaching and learning strategies in mathematics – a case study

This article is a case study that examines how the different teaching and learning strategies influence mathematical knowledge acquisition at university. The research hinged on how mathematics lecturers at universities teach and how students acquire the disseminated knowledge. Research stresses that most lecturers have teacher-centred teaching approaches and mathematics teaching is with minimal student participation. Research further asserts that teaching approaches that emphasise student participation is critical in enhancing effective classroom interaction. This means that, as students’ learning strategy is dominantly a participatory and collaborative one, lecturers are challenged to create a learning-as participation environment for effective mathematics classroom interaction. The article reports a study that was conducted among university students and lecturers in a mathematics course at a South African university. The findings were that most lecturers at the university use traditional non-interactive teaching approaches that create passive environments in contrast with the predominant participative learning strategies of most students.

The linkages between Chinese children's both cognitive engagement and emotional engagement and behavioral engagement: Mediating effect of perceptions of classroom interactions in math

AbstractStudent engagement not only improves student achievement but also affects the dropout rate. Positive classroom interaction between teachers and students enhances student engagement. The interaction between teachers and students is bidirectional, and student engagement can also affect teachers' classroom teaching behavior. Both student engagement and classroom interaction are multidimensional structures, and each dimension is interrelated and mutually influenced. The purpose of this study was to explore the relationship between perceived mathematics classroom interaction and various dimensions of student engagement. In this study, we recruited 1298 students from grades three to five and seven to eight from 36 classes and 15 schools in China participating in a web‐based survey. The results show that cognitive engagement is positively related to behavioral engagement, and emotional support, classroom organization and instructional support play a mediating role between cognitive engagement and behavioral engagement; Emotional engagement is positively related to behavioral engagement, and emotional support and instructional support play a mediating role between emotional engagement and behavioral engagement.

Embracing pivotal teaching moments: elementary teachers’ role in advancing high cognitive levels of mathematics discourse

The study of pivotal teaching moments (PTMs) offers significant insights into mathematics classroom interactions. PTMs are student-generated instances within a lesson that provide opportunities for teachers to modify planned instruction (Stockero & Van Zoest, 2013). Given the importance of interactions and discourse in students’ mathematical growth and understanding, we examine them in the context of PTM episode triples. PTM episode triples consist of three main elements: (1) a PTM, (2) a teacher response to the PTM, and (3) the immediately ensuing student utterance. Analysis of data from nine elementary mathematics lessons shows that teacher responses that explicitly “pursued students’ thinking” elicited significantly higher cognitive levels of student discourse than teachers who "ignored or dismissed" PTMs or simply "acknowledged [PTMs] but continued as planned." While many researchers have focused on PTM episode “doubles” (combinations of student-generated interruptions and the teacher’s response), no studies to our knowledge have addressed PTM episode “triples” as we have. Implications of these findings prove helpful for identifying concrete ways that educators can increase the cognitive level of student discourse within their classrooms. Further, our integration and modification of existing theory and frameworks for analyzing PTM episode triples—incorporating the relationship between PTMs and teachers’ responses to them, on the one hand, and the cognitive level of the ensuing student utterance, on the other hand—are a unique contribution to the field and provide a method by which researchers and educators can study classroom practice.

Towards effective feedback: an investigation of teachers’ and students’ perceptions of oral feedback in classroom practice

ABSTRACT Few studies have examined how teachers’ oral feedback in whole-class interactions is received, perceived and used by students to enhance learning. This paper details an in-depth study of secondary teachers’ and students’ reflective comments on classroom oral feedback. The study examined perceptions of teachers and students in English and mathematics classroom interactions. Key findings showed that much teacher feedback was not recognised by students, and that when feedback was recognised it was often not perceived as the teacher had intended. Further, feedback in mathematics was more often recognised and perceived as intended compared to English. If feedback is not received by students, or not perceived as intended by the provider, it is unlikely that the feedback message will achieve its intended effect of supporting student learning. The study provides evidence that feedback perceptions – and thus feedback effectiveness – are context-dependent, subject-dependent, and individual-dependent.

Epistemic management in mathematics classroom interactions: Student claims of not knowing or not understanding

An important role of classroom interaction is the processes involved in knowing or coming to know. Following a conversation analytical approach, this study investigates how students’ claims of not knowing, not remembering or not understanding are handled by mathematics teachers in whole class interactions. The study draws on video recordings of 42 mathematics lessons from 8 secondary schools in England. It is argued that claims of not knowing and claims of not remembering perform different social actions and are consequently treated differently by teachers. Claims of not knowing can challenge the assumption that knowledge can be taken-as-shared in a way that claims of not remembering do not. This contributes to the research field of mathematics classroom interaction as it nuances the epistemic management within these interactions and how this can contribute to the norms around the negotiation of meaning.

Unequal bodies: corporeality and social inequality in mathematics classrooms

This paper addresses teachers’ corporeality and its influence on the structuring of mathematics classroom interaction. The present contribution explores the way a teacher’s bodily activity is implicated in the (re)production of social inequality, and challenges the assumption that the teaching and learning of mathematics is primarily a linguistic and semiotic accomplishment. I argue that the teacher’s body is an active force in the formation of mathematically ‘able’ and ‘less able’ students. Drawing on the work of Bernstein (Pedagogy, symbolic control, and identity: Theory, research, critique (Revised Edition), Rowman & Littlefield, Lanham, 2000) and his sociological theory of pedagogy, and expanding his tools to address corporeal factors, I show how students are positioned as high-performing within structures of classroom interaction. Video data from classroom interaction is used to track differences in how teachers reveal and conceal structural peculiarities of school mathematics. Comparing the interaction of different teachers illustrates the role that corporeality plays in establishing distinctive orientations to meaning-making in the mathematics classroom.

Repertoires of three second language learners of mathematics: distal and situational sources of meaning

ABSTRACTThis article presents the results of an analysis of ethnographic data collected in three second language mathematics classrooms in Canada. The elementary school classes consisted of a group of indigenous students, a group of new immigrant students and a class in a French immersion programme. The focus of the analysis was on the sources of meaning students use in mathematics classrooms. The notion of sources of meaning is framed by a Bakhtinian perspective on language, in which they are examined in terms of discourses, voices and languages. For one student in each class, I describe a repertoire of sources of meaning and discuss similarities and differences relating to the sociolinguistic context of each class. Students’ repertoires are shown to include both situational and distal sources of meaning. The relationship between distal and situational sources of meaning reflects the stratified nature of mathematics classroom interaction.

Moving forward with ethnomethodological approaches to analysing mathematics classroom interactions

Ethnomethodological approaches to research such as Interactionism, Conversation Analysis and Discursive Psychology have so far played only a small part in mathematics education research. This is in contrast to the wider use of these approaches in language education, medical discourse research, and legal discourse research. This article outlines the key principles an ethnomethodological approach follows, the methods used and the necessary reconceptualisation of some key concepts that are the focus of much mathematics education research. These are illustrated with some key examples from research in mathematics education, before looking at other fields for potential opportunities not yet realised within research in mathematics classrooms. These opportunities include a range of research questions already receiving a great deal of attention within the field but are yet to be examined from an ethnomethodological perspective. They also include new approaches that involve combining different research approaches which have been used to great effect in other fields.

Students’ and teachers’ focus of attention in classroom interaction — subtle sources for the reproduction of social disparities

Mathematics classroom interaction has often been described as an important context for involving all students. However, this article shows that teacher-student-interaction is still not really in the focus of teachers’ attention. Based on classroom video studies, some authors hypothesize that the implicitness of establishing norms and practices is, among others, an obstacle for students with low socio-economic status. The article intends to put this hypothesis into perspective by investigating teachers’ and students’ focus of attention on classroom interaction in video-stimulated group discussions (six discussions with 5–6 students, four discussions with 5–9 teachers). The data analysis used inductive procedures of category development, frequency analysis, and deeper qualitative analysis of the transcripts. For students’ focus of attention, differential patterns could be extrapolated: Whereas students of high socio-economic status seem to be more attentive to teacher’s contextual expectations, the students of low socio-economic status seem to be more focused on general norms without taking into account contextual expectations. For the teachers, the analysis shows that interactive mechanisms of teacher-student exchanges in classrooms are usually not in the teachers’ focus of attention. Additionally, the teachers address, but rarely problematize the implicitness by which norms and practices are established. Together with the differential findings on students’ attention, these findings are discussed with respect to equity concerns and consequences for professional development of teachers.

Examining Mathematics Classroom Interactions: Elevating Student Roles in Teaching and Learning

<p style="text-align:justify">This article introduces a model entitled, “Responsive Teaching through Problem Posing” or RTPP, that addresses a type of reform oriented mathematics teaching based on posing relevant problems, positioning students as experts of mathematics, and facilitating discourse. RTPP incorporates decades of research on students’ thinking in mathematics and more recent research on responsive teaching practices. Two classroom case studies are presented. A high school unit on functions is explored utilizing individual research on the part of the teacher to enact RTPP lessons. A middle school teacher enacts a RTPP lesson on proportions and utilizes this model to bridge students’ incorrect additive reasoning strategies with correct multiplicative reasoning strategies. The results showed that both teachers were able to elevate students’ roles in classroom discussions through implementation of RTPP. Individual research conducted by the high school teacher informed his RTPP approach while participation in professional development sessions with a classroom embedded component influenced the middle school teacher’s enactment of RTPP lessons. Both teachers used specific teacher moves within RTPP to relinquish their role as mathematics experts in order to elevate their students’ roles in classroom discussions. The RTPP cycle is offered as a potential model for studying mathematics teaching and learning across a variety of secondary mathematics classrooms.</p>

Pedagogical Tensions in Teacher’s Questioning Practices in the Mathematics Classroom: A Case in Mainland China

During the last decades, curriculum reform has been implemented in mainland China to emphasize classroom interaction in mathematics teaching and learning. The intention to create more chances for classroom interaction in large-size classrooms has led to the introduction of self-learning guide which allows students to go through the learning contents before the classroom learning. This study investigates the pedagogical tensions emerging in a mainland Chinese mathematics teacher’s practices of using self-learning guide to reform classroom questioning. The analytical entry point is the examination of the IRF (Initiation/Response/Follow-up) structures evident in the reform-based mathematics classroom interactions. The results show that, by using various reform-based questioning strategies, students were given adequate opportunities to present and share their mathematical thinking and ideas. The nature of the pedagogical tensions has shifted from imbalance of time allocation for classroom discussion and lecturing to imbalance of opportunities for guided classroom discussion and elaborated classroom discussion.

Including students’ diverse perspectives on classroom interactions into video-based professional development for teachers

Video is often used in professional development courses to sensitize mathematics teachers to students’ thinking and issues of classroom interaction. This article presents an approach that incorporates students’ perspectives on mathematics classroom interactions into video-based professional development in order to enhance teachers’ reflection on diverse awareness of students concerning demands within mathematics classroom interactions. This approach is theoretically justified by the empirical research on equal participation in classroom interaction and practically elaborated by video material from Grade 5 students. Empirical snapshots from design experiments with teachers demonstrate that teachers’ sensitivity can be enhanced.

<p>Investigating stratification, language diversity and mathematics classroom interaction</p>

Research on the socio-political dimensions of language diversity in mathematics classrooms is under-theorised and largely focuses on language choice. These dimensions are, however, likely to influence mathematics classroom interaction in many other ways than participants’ choice of language. To investigate these influences, I propose that the notions ofheteroglossia, orders of indexicality and scale-jumping, can provide new theoretical tools with which to understand the links between classroom interaction and broader social patterns of marginalisation. To illustrate the utility of these ideas, I include some analysis of an episode observed in a sheltered elementary school second language mathematics classroom in Canada. Investigando la estratificación, la diversidad lingüística y la interacción en el aula de matemáticas La investigación sobre las dimensiones sociopolíticas de la diversidad lingüística en clases de matemáticas está poco teorizada y mayormente se centra en la elección de la lengua. Estas dimensiones, no obstante, probablemente influyen en la interacción en clase en otros modos distintos a la elección de la lengua. Para investigar estas influencias, propongo que las nociones de heteroglosia, órdenes de indexicalidad y salto de escala, pueden aportar nuevos instrumentos teóricos con los cuales comprender conexiones entre interacción del aula y patrones sociales de marginalización. Para mostrar la utilidad de estas ideas, incluyo los análisis de un episodio de una clase de primaria de matemáticas canadiense con instrucción en una segunda lengua.Handle: http://hdl.handle.net/10481/42389WOS-ESCI

Formal and informal mathematical discourses: Bakhtin and Vygotsky, dialogue and dialectic

The importance of the role of language/discourse in the learning and teaching of mathematics is noted in many mathematics curricula and standards documents. In the research literature, this role has been widely theorised from a Vygotskian perspective. This perspective is limited by some of its underlying assumptions, including an instrumental and systemic view of language as tool and its basis in dialectic. In this paper, I propose a Bakhtinian, dialogic perspective as an alternative. I focus my discussion on the long-standing issue of the relationship between formal and informal mathematical language in the learning and teaching of mathematics. I illustrate this discussion with an examination of interaction in an elementary school mathematics classroom in Quebec, Canada. Based on Bakhtin’s ideas, I argue that mathematical meaning emerges through locally produced, situated dialogic relations between multiple discourses, voices and languages in mathematics classroom interaction. From this perspective, students do not follow a linear path from informal to formal mathematical discourse; rather, they work with the teacher to expand the repertoire of possible ways to make meaning in mathematics.

Students constructing meaning for the number line in small-group discussions: negotiation of essential epistemological issues of visual representations

In mathematics classroom interaction, the multiple meanings of mathematical visual diagrams are often ignored; instead, depending on the given situation, they are read in a well-defined and unitary way. Mathematical visual representations are thus used even less in their epistemological function for learning, but more as pre-given subject matter. The purpose of this paper is to elaborate opportunities for negotiating and clarifying differences, dealing with a great variety of ways of interpreting visual diagrams that are brought into focus in interaction. Theory-based qualitative analyses of two exemplifying video episodes of small-group discussions negotiating their ideas on the topic “number line” show differences of meaning and the importance of conventions followed by mathematical deductions. Two mutually exclusive teacher behaviors within the communicative acts, reconstructed as a dominating way of instruction and a moderating way of focusing, are identified.

Interaction between a First-Year Elementary School Teacher and Students in Mathematics Class

Teaching and learning mathematics in a classroom setting is based on the interactions between the teacher and her students. Using classroom observations and interviews of students and the teacher, this research examines a first-year teacher and her students` interactions in the mathematics classroom. In this mathematics classroom, teacher and students interaction had inconsistency between mathematical topics and non-mathematical topics. For non-mathematical topics, their interactions were very active but for mathematical topics their interactions were very limited. This paper ends with raising questions for future research and calling for the opportunities for first-year teachers to reflect on their interactions with their students, in particular about mathematical topics.

A DISCURSIVE PSYCHOLOGY APPROACH TO THE ANALYSIS OF ATTENTION IN MATHEMATICS CLASSROOM INTERACTION

The notion of attention as a discursive practice has emerged as a key element of my approach to the analysis of students' participation in mathematics classroom interaction. The principal purpose of this paper is to describe and illustrate this approach, which draws on ideas from discursive psychology and conversation analysis and sees talk primarily as a form of social action. It is a principle of conversation analysis that what we say indicates something that we are attending to in that moment. Discursive psychology suggests that the way we use words, reflects the social actions in which we are engaged. By looking at what students attend to, and then at how this attention is rhetorically deployed, insights emerge into how students think together.

Patterns of attention in the interaction of a primary school mathematics student with English as an additional language

This paper presents a preliminary analysis from a study designed to investigate the participation of students learning English as an additional language(EAL) in primary school mathematics. A key question for the study concerns how such students make sense of mathematics classroom interaction. Primary data consists of two transcripts in which a 9-year-old EAL student works on a word problem task with a monolingual peer. The discursive analysis explores the two students' use of patterns of attention in their interaction. The analysis describes three patterns of attention: attention to narrative experience, to the genre of word problems and to the mathematical structure of their problems. These patterns of attention are used in the process of the two students' sense-making together in ways which support the participation of the EAL student.

On some psychological aspects of mathematics achievement assessment and classroom interaction

The way students and teachers evaluate mathematics achievement differs in certain respects. To which causal performance is ascribed determines the teacher's strategy to interact with the student on the one hand and influences the student's willingness to invest additional effort on the other. Certain possible causal factors for success and failure in mathematics and their relation to teacher-student-interaction are discussed in the present article. A rather general cognitive scheme, the teachers reference norm, explains differences between the teacher's perception and assessment of student characteristics and subsequent teaching interventions.