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Engaging with others’ mathematical ideas: Interrelationships among student participation, teachers’ instructional practices, and learning

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Abstract

This paper explores the relationships between student participation in classroom conversations, teacher practices, and student learning in elementary school mathematics classrooms. Six teachers and 111 children aged 8–10 participated in the study. Students and teachers were videotaped as they discussed how to solve mathematical problems during whole-class and small-group discussions. The results show that the level of student engagement with each other's ideas and the incidence of students providing detailed explanations of their problem-solving strategies were positively related to student achievement. While teachers used a variety of instructional practices to encourage students to attend to and engage with each other's thinking, how teachers followed up on their initial moves was important for whether students engaged with others’ ideas at a high level.

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... According to sociocultural and situated learning theories, learning and cognition are situated in meaningful talk, tasks and activities through social interaction Collins et al., 1989;Greeno, 2003;Vygotsky, 1987). In the classroom, the use of productive talk that encourages students to express and develop their ideas, give reasons for those ideas and engage with others benefits student learning Webb et al., 2014). Nevertheless, teachers often find it difficult to engage students in effective discussions that involve deep reasoning and argumentation (Alexander, 2017;Clarke et al., 2013;Howe & Abedin, 2013;Resnick et al., 2018). ...
... Research shows that effective classroom talk that positions students as active participants benefits both their learning and skill development (Gillies, 2016;Howe & Abedin, 2013;Littleton & Mercer, 2013;Michaels et al., 2008;Resnick et al., 2015). While students benefit from monitoring their thinking when expressing and developing their ideas, they also benefit from listening to others and having their views challenged-practices that can contribute to learning and retention (Mercer, 1996;Webb et al., 2014). Moreover, effective classroom talk encourages lesson enjoyment, lowers anxiety (Chen, Zhang, et al., 2020), and increases interest and motivation (Kiemer, 2017;Kiemer et al., 2015), which can be transferred from one domain to another (e.g., Chapin et al., 2009;Topping & Trickey, 2007). ...
... We know that a central principle of dialogic instruction is that teachers should guide students to express, share and co-construct knowledge not only for themselves but also by thinking and interacting with other students Webb et al., 2014). Ms. Hu did this by involving several students in the discussion, encouraging them to verbalize their opinions and reasons, and guiding them to reason with other students. ...
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Although classroom discourse that positions students as active participants benefits both their learning and cognitive development, teachers often find it challenging to implement dialogic instructions in the classroom. This study reports on a video-based teacher professional development (PD) program that leverages visualizations and analytics in supporting teacher change in whole-class dialogue in mathematics classrooms. Both experimental and comparison teachers (n = 24 and 22, respectively) were provided with information on dialogic instructions, and experimental teachers used the Classroom Discourse Analyzer to reflect on videos of their lessons and their peers' lessons in a year-long PD program. The intervention teachers significantly moved toward less dominant classroom talk—they reduced the number of words spoken per lesson, and their students significantly increased the number of words per turn in whole-class discussions, relative to the comparison teachers. Furthermore, analysis of the classroom discourse shows qualitative changes in the intervention teachers' discourse. PD workshop and teacher self-reflection data are analyzed to examine how visualizations and analytics in the PD program may serve as a cross-boundary object to support peer collaboration in reflective practice, and to increase teachers' awareness of their teaching development.
... Much work has been done to understand how different factors influence the effectiveness of collaborative learning. These factors include students' participation and social behavior when they learn together (e.g., Abdu et al., 2019;Barron, 2003;Dillenbourg, 1999;Kontorovich et al., 2012;Webb et al., 2014), effects of teacher support (Dekker & Elshout-Mohr, 2004;van Leeuwen & Janssen, 2019;Webb, 2009), and, specifically for the current article, the effects of different group formations on the effectiveness of learning (e.g., Lou et al., 1996;Pearlstein, 2021). Educators can use learning analytics systems to support collaborative learning (Wise & Schwarz, 2017): For example, by presenting data about the indicators of collaborative learning situations (D'Angelo et al., 2015;Schwarz et al., 2018;Wise & Schwarz, 2017), supporting teachers' decision-making in regard to collaborative learning (Martinez-Maldonado, 2019;van Leeuwen, 2015), supporting co-reflection on the collaborative learning process (Schwarz et al., 2015) and, specifically to this current article, group formation (see Borges et al., 2018;Maqtary et al., 2019). ...
... Research on collaborative learning consistently shows the importance of mutuality and mutual dependence in the success of collaborative learning (e.g., Cohen, 1994;Pearlstein, 2021;Schwartz, 1999;Webb et al., 2014). Some researchers foster mutuality by eliciting and/or grouping students to make sure voices differ at the onset of the interaction (Asterhan & Schwarz, 2007;Glachan & Light, 1982;Gutierrez-Santos et al., 2016;Schwarz et al., 2000;Schwarz & Asterhan, 2011). ...
... Nevertheless, the effectiveness of a collaborative learning situation also depends upon other factors, such as the support given to learners (e.g., Dekker & Elshout-Mohr, 2004) and how students interact when they learn together. Collaborative learning is effective when the learners are all engaged, ask questions, listen to each other, and think either together or alone (e.g., Barron, 2003;Schwarz et al., 2000;Webb et al., 2014). These are all confounding factors that may or may not have appeared when students learned in groups in the current study and may sway this study's results one way or another. ...
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This article queries how learning analytics systems can support content-specific group formation to develop students’ thinking about a specific mathematical concept. Automated group formation requires identifying personal characteristics, designing tasks to probe students’ perceptions, and grouping them to increase individual learning chances. Designers of automated group formation recommendation modules (GFRMs) rarely consider content-specific objectives. We draw on theories on conceptual learning in mathematics and dialogic thinking to emphasize the role of a dialogic gap between students’ voices to enhance individual learning. In an experiment, fifty 8th and 9th grade students solved three mathematical tasks in a pre-intervention-post-set-up: individually, then in dyads, and then individually again. We used a learning analytics system to collect fine-grained content-specific data on students’ responses based on four pre-defined aspects of the parabola concept. We compared students’ answers with those of their peers in order to identify interpersonal relations. The experiment results indicate that students’ thinking about the parabola concept was the most successfully developed when every group member had a different perception of this concept. We illustrate the learning trajectories of four students and elaborate on the learning sequence of one of these students in particular. This article suggests that the centrality of a dialogic gap in developing personal learning is probably content independent. We thus call for software engineers to think about GFRMs that can support content-specific learning and instruction.
... Williams et al.'s use of Flow Theory (Csikszentmihalyi, 1997, 1990 was unique, but our conceptualization of engagement relates more to studies in which the object of engagement was mathematical ideas. Webb et al. (2014) and Franke et al. (2015) both explicitly examined students' engagement with mathematical ideas. Webb et al. examined upper elementary school students' engagement by classifying their interactions with other students' ideas into three levels: high level engagement involves students adding to their peer's suggested strategy, adding further detail to the approach, or suggesting an alternative approach that explicitly referenced the idea already posed; medium level engagement involves students explicitly referencing the details of their peer's idea without additional detail; low level engagement involves students referencing or acknowledging another student's idea in a general way. ...
... Rasmussen et al. (2020) built on these studies of engagement with students' mathematical ideas and focused on students' engagement with others' mathematical reasoning in the context of a master's level mathematics course. They did not focus on the level of engagement (as did Webb et al., 2014 andFranke et al., 2015) but instead focused on different ways of engaging with another's reasoning. In particular, they identified five ways of engaging with others' reasoning: interpreting, evaluating, making connections, entertaining, or empathizing. ...
... We conceptualize engagement as participating in an activity "with some cognitive or affective investment" (Middleton et al., 2017, p. 668) directed toward an object, which, for us, is other students' mathematical reasoning via collective argumentation. We build on Webb et al. (2014) and Franke et al. (2015) in characterizing students' engagement with mathematical ideas, going beyond levels of engagement to characterizing ways of engaging similarly to Rasmussen et al. (2020). ...
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One goal of inquiry-oriented instruction is student engagement with others’ mathematical ideas. This paper analyzes a relatively short episode in which students engaged with others’ ideas; the instructor facilitated engagement in order to support students in making mathematical progress. Students expressed some bafflement pertaining to the apparently paradoxical zero area and infinite perimeter of the Sierpiński triangle. The instructor strategically facilitated collective argumentation centered on their reasoning, resulting in several ideas that functioned-as-if-shared in the classroom community. In this report we capitalize on this classroom discussion to contribute to theory and methods for investigating the complex intersection of engagement and argumentation.
... While theory and research support dialogic instructional approaches, some have noted that the complexities of dialogic teaching make it difficult for teachers to implement (Buchs et al., 2017;Hoffman & Mercer, 2016;Hunter, 2008). Dialogic teaching requires educators to make in-the-moment decisions regarding how to support groups of learners based on their mathematical strategies (Franke et al., 2007;Webb et al., 2014). Instead of following a The framework describes noticing practices integral to dialogic instruction and promotes inquiry for future research related to teaching moves in dialogic classrooms. ...
... Group coordination refers to the extent to which learners actively engage with others' ideas (Barron, 2000(Barron, , 2003Webb et al., 2014). Coordination includes actively listening to others' ideas, building on others' proposals and engaging in turn-taking behaviours (Barron, 2000(Barron, , 2003Webb et al., 2014). ...
... Group coordination refers to the extent to which learners actively engage with others' ideas (Barron, 2000(Barron, , 2003Webb et al., 2014). Coordination includes actively listening to others' ideas, building on others' proposals and engaging in turn-taking behaviours (Barron, 2000(Barron, , 2003Webb et al., 2014). Groups who are highly coordinated listen to and discuss a variety of solution proposals from all group members and only reject proposals when valid reasons are given. ...
Article
Over the past three decades, research and policy in many geographic regions has promoted a shift from direct, lecture‐oriented mathematics instruction to inquiry‐based, dialogic forms of instruction. While theory and research support dialogic instructional approaches, some have noted that the complexities of dialogic teaching make it difficult for teachers to implement. One mechanism by which teachers can improve their decision‐making practices in dialogic classrooms is learning to notice (i.e. becoming aware of learners’ processes). While research has contributed frameworks for understanding how teachers notice individual learners’ mathematical thinking, there is little conceptualization regarding how teachers notice group processes in mathematics classrooms, which is integral to dialogic instruction. We offer a noticing framework termed professional noticing of coordinated mathematical thinking that describes how teachers notice group activity in mathematics classrooms. Professional noticing of coordinated mathematical thinking is conceptualized as a bi‐dimensional process: noticing groups’ mathematical activity and noticing groups’ coordinated activity. Teachers must become aware of how groups approach the mathematical and collaborative nature of a task, since both of these aspects inform whether learners develop opportunities to learn in groups. The framework describes noticing practices integral to dialogic instruction and promotes inquiry for future research related to teaching moves in dialogic classrooms.
... Classroom examples include explaining another student's strategy for comparing fractions or making a suggestion to another student about what evidence might support a peer's prediction about what will happen next in a book the class is reading together. Franke et al., 2015;Webb et al., 2014 Episode ...
... Engaging with Others' Ideas and Mathematics. Engaging with others' ideas has been most persistently investigated by a team of math education researchers from UCLA conducting research in third and fourth-grade classrooms at a diverse elementary school near their university (e.g., Franke et al., 2015;Ing et al., 2014;Webb et al., 2014). The team worked in six classrooms over the course of a school year and recorded both small-and large-group conversations. ...
... Engaging with Others' Ideas and Mathematics. Engaging with others' ideas has been most persistently investigated by a team of math education researchers from UCLA conducting research in third and fourth-grade classrooms at a diverse elementary school near their university (e.g., Franke et al., 2015;Ing et al., 2014;Webb et al., 2014). The team worked in six classrooms over the course of a school year and recorded both small-and large-group conversations. ...
Thesis
Research in U.S. elementary school classrooms suggests that discussion with peers is associated with positive student outcomes in multiple content areas, while scholars of democratic education claim that engaging in discourse where differing points of view are presented can help students develop as citizens. However, scholarly literature has not yet connected these two disparate areas of scholarship in empirical research on classroom discourse. In this case study, I examine how fifth-grade students engage with one another’s ideas across the school day over the course of a month in a classroom where the teacher provides frequent opportunities for discussion. Specifically, I ask how the students in this classroom engaged with one another’s ideas in literacy, math, and social studies; the power and authority differences apparent in these interactions; how students do this differently in different subject areas; and how the classroom teacher supports students in doing this work. Data for this study includes field notes of classroom instruction and talk, audio recordings of small and whole group conversations, student work, classroom artifacts, and interviews. Findings indicate that students in the classroom engaged with others’ ideas by responding directly to others’ ideas or indirectly referring to others’ ideas in a variety of ways in both literacy and mathematics, though the way students engaged with others’ ideas differed by subject matter. These differences included what students engaged with others’ ideas about, the extent to which students discussed single ideas or many ideas, and the ways in which students engaged with others’ ideas. Students’ engagement with others’ ideas also provided students with further opportunities to learn by bringing significant subject-matter content into the discussions. Importantly, however, evidence suggests that students’ classroom status and authority may have affected how they engaged with others’ ideas. Finally, the classroom teacher supported students’ engagement with others’ ideas by creating an environment conducive to making sense of academic content, tending to how students related to one another, holding particular understandings and beliefs about the content she taught, and making specific moves during classroom discussions. This study contributes to the development of theory about how students interact with one another’s ideas in multiple school subjects and how one teacher supports such work.
... Engaging without probing, such as acknowledging their ideas or making a brief suggestion, was rarely linked to correct and complete responses between the students. Similarly, Webb et al. (2014) found that, when sharing solutions after small-group or individual work, students engaged with one another's ideas the most when teachers posed specific questions to help a student elaborate upon their solution in relation to another student's. This also led to higher student achievement. ...
... In our review of literature, we identified many instances of questioning categories that aligned with NCTM's (2014) definition of gathering information (i.e., recall of facts or rote knowledge) and probing thinking (i.e., engaging students in making their thinking more clear and complete). In fact, probing questions seem to be one of the most consistently defined categories of teacher questioning, as well as the best supported in terms of facilitating students' construction of correct explanations and conceptual learning Kazemi & Stipek, 2001;McCarthy et al., 2016;Piccolo, Harbaugh, Carter, Capraro, & Capraro, 2008;Webb et al., 2009Webb et al., , 2014. It is clear that probing questions targeting specific aspects of students' work can support students to develop correct and complete explanations and engage with one another's thinking, which may ultimately lead to higher achievement. ...
... In other cases, there were implicit examples of how making mathematics visible might overlap with other categories of questioning, such as when a teacher poses conceptual questions (e.g., Kazemi & Stipek, 2001) or uses technology to focus on mathematics (e.g., Akkoç, 2015). Similarly, questions related to encouraging justification and reflection (i.e., questions pushing students to argue for the validity of their work) are treated less explicitly in much of the empirical research on teacher questioning, though there are some exceptions (Cengiz, Kline, & Grant, 2011;Drageset, 2014Drageset, , 2015Webb et al., 2014). From the examples that do exist, it is clear that these two categories of questioning-making mathematics visible and encouraging justification-are often more difficult for teachers to enact and place substantial demand on students in classroom discussions. ...
Article
We conducted a review of literature to answer the following research questions: (1) What types of questions do teachers pose in mathematical discussions? (2) What evidence exists of the effects of different types of questioning on students’ learning and participation? (3) What are the implications of existing research for teacher preparation? Existing literature can broadly be categorized according to studies that distinguish between higher order and lower order questioning, studies that characterize and distinguish probing questions, and studies that address teacher questioning in technology-rich environments. The demands of different types of questions need to be considered in light of the broader contributions that such questions make to students’ mathematical learning.
... Two processes of idea building/intellectual collaboration have been found to be related to students' learning: provision of detailed explanations, and engagement with others' ideas (Webb et al., 2014;Ing et al., 2015). Vygotsky's (1934) theory emphasizes the importance of group members being willing to listen to each other's ideas and respecting it, in order to support idea building. ...
... These trends could be one of the main factors that explain the difference in both the groups of students' social reasoning at posttest. These findings also support previous research that has shown how engaging with others' ideas, providing explanations, considering multiple representations are essential for students' learning (Warner, 2008;Webb et al., 2014;Ing et al., 2015). ...
Article
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This comparative case study features two small groups of students engaging in collaborative dialog about social issues. Based on social constructivist theories, the two groups were compared across three major components of the small groups system: social dynamics, intellectual collaboration, and teacher scaffolding. Our goal was to holistically analyze these small group processes to understand why some small groups were highly successful while others were not, even within the same intervention and with the same teacher. Successful groups were those in which all students were able to access the conversational floor, many ideas were considered, students were able to share ideas and discuss collaboratively, and students were able to raise multiple forms of social reasoning to support and explain ideas. Change in social reasoning essay scores prior to and after the intervention were also considered as evidence of group success. Results show that teacher scaffolding and existing student processes served to amplify one another reciprocally. The teacher heightened productive social norms when they were present, which then served to encourage productive intellectual collaboration. However, when productive group norms were not present, the teacher took increasing control over
... Other studies have indicated a positive relationship between participation in classroom talk and learning for individual students. This association implies that the more an individual student verbally participates in classroom discussion and the higher the quality of that student's contribution, the better learning outcomes are achieved by that student (Ing et al., 2015;Larrain et al., 2019;Sedova et al., 2019;Webb et al., 2014). The effects of classroom talk would, therefore, vary for individual students in the class depending on the nature of their participation. ...
... Previous studies have shown that student engagement in communication has a positive impact on learning. A link has been identified between the frequency and quality of verbal participation of a particular student in the classroom and that student's results (Ing et al., 2015;Sedova et al., 2019;Webb et al., 2014). The data for the silent students in this study indicate that these students take a reserved attitude to the potential benefits of classroom talk. ...
Article
Background This study is concerned with the ways that patterns of student participation in classroom talk are constructed, focusing on silent students who participate in whole-class conversation to a limited extent. Methods We conducted an ethnographic survey in two ninth-grade classes. We made video recordings of the lessons and interviewed the students and teachers. We observed eight focal silent students—four high-achieving and four low-achieving. Findings Participation patterns of high-achieving and low-achieving silent students diverge. High-achieving silent students are often called on by the teacher, and they give extended answers to difficult questions. Low-achieving silent students are called on rarely. High-achieving silent students use silence to consolidate their position as exceptionally capable students; low-achieving silent students use it to consolidate their position as less capable. However, it is possible to engage low-achieving silent students if the teacher notices their momentary spontaneous urge to participate and creates space for their voice in the classroom. Contribution The paper focuses on the silent students who are often overlooked in studies on classroom talk. It calls for specific attention paid to low-achieving silent students who are limited in their learning opportunities and thus facing educational disadvantage.
... Learning opportunities provided by dialogic classroom discourse are expected to foster students' epistemological understanding of how knowledge is constructed, positive view of their competence, transferable high-order cognitive skills, and deepened understanding of disciplinary knowledge (Rezniskaya & Gregory, 2013). Accumulated evidence links dialogic classroom discourse to the important learning outcomes (e.g., Howe, Hennessy, Mercer, Vrikki, & Wheatley, 2019;Kiemer, Gröschner, Pehmer, & Seidel, 2015;Webb et al., 2014). ...
... With these skills, teachers can select strategies that are more likely to create a classroom environment that promotes students' reasoned participation and contribution . For example, the talk moves facilitate students to think by themselves and to engage with others' ideas Webb et al., 2014). Another example would be the evidence-supported Fig. 1. ...
Article
The present study investigated the efficacy of an intervention program to assist teachers in the development of conceptual and practical tools for engaging students in dialogic classroom discourse. Sixteen fourth-grade mathematics teachers received 28 h of the intervention over a semester of 4 ½ months. Compared to the nonintervention group, the intervention teachers showed a reduced tendency to evaluate student responses and were more likely to promote students to engage with others’ ideas. Students of the intervention group responded to the teachers’ changes by demonstrating increased amount of contributions in classroom discussion. The results indicate that increasing awareness on dialogic classroom discourse provides an encouraging platform for teacher professional development to improve the quality of disciplinary teaching and learning.
... Two processes of idea building/intellectual collaboration have been found to be related to students' learning: provision of detailed explanations, and engagement with others' ideas (Webb et al., 2014;Ing et al., 2015). Vygotsky's (1934) theory emphasizes the importance of group members being willing to listen to each other's ideas and respecting it, in order to support idea building. ...
... These trends could be one of the main factors that explain the difference in both the groups of students' social reasoning at posttest. These findings also support previous research that has shown how engaging with others' ideas, providing explanations, considering multiple representations are essential for students' learning (Warner, 2008;Webb et al., 2014;Ing et al., 2015). ...
Article
Full-text available
This comparative case study features two small groups of students engaging in collaborative dialog about social issues. Based on social constructivist theories, the two groups were compared across three major components of the small groups system: social dynamics, intellectual collaboration, and teacher scaffolding. Our goal was to holistically analyze these small group processes to understand why some small groups were highly successful while others were not, even within the same intervention and with the same teacher. Successful groups were those in which all students were able to access the conversational floor, many ideas were considered, students were able to share ideas and discuss collaboratively, and students were able to raise multiple forms of social reasoning to support and explain ideas. Change in social reasoning essay scores prior to and after the intervention were also considered as evidence of group success. Results show that teacher scaffolding and existing student processes served to amplify one another reciprocally. The teacher heightened productive social norms when they were present, which then served to encourage productive intellectual collaboration. However, when productive group norms were not present, the teacher took increasing control over the group, which further hampered productive social and intellectual interactions.
... First, dialogicity is present in students' actual arguments in the form of student moves, such as elaborating, which indicate engagement with other students' ideas. Webb et al. (2014) provided evidence that students' engagement with their peers' ideas predicted student achievement more than explaining one's own ideas. Thus, this kind of engagement with others' ideas is a feature of productive discussion. ...
... Besides enabling students' dialogic moves, dialogic/interactive approach enabled student moves that were both dialogic and justifying. These instances can be seen as the heart of dialogic argumentation in the analysed data as the students were engaging with other students' ideas (Webb et al., 2014), and at the same time produced evidence. These instances existed in the steps 1 and 4 that included situations where a student responded the teacher's open question by proposing something original and the teacher received this neutrally. ...
... Departing a little from potential confrontation in small-group work, Noreen Webb and others analysed cooperative behaviour, that is, when students give or receive help from others (N. Webb, 1982;N. Webb et al., 2008N. Webb et al., , 2014. Empirically, they examined the exchange of explanations about the content (N. Webb, 1982). They argued that, when students give explanations, they can clarify their views through justifications and develop understanding to solve gaps or inconsistencies. When receiving explanations, students can correct mistakes, connect new information ...
... Nevertheless, building on each other's ideas at a high level in an agreeable way-such as adding details to one's contributions-also positively correlates with achievement (N. Webb et al., 2014). ...
Thesis
This thesis studies the adherence of a talk-intensive approach to teaching and ‎learning in the Brazilian context. While classroom talk is often classified as monologic ‎due to being narrow and controlled by teachers, educational research has identified a ‎kind of collaborative and cognitively productive talk that positively affects learning ‎outcomes. This dialogic talk is rare in most classrooms. Many teacher professional ‎development programmes have been designed to bridge this gap. This project builds ‎on this vast literature to explore three key aspects in the development of a more ‎dialogic classroom talk: small-group work, conceptual learning, and whole-class ‎teaching.‎ To produce such a dialogic case, an intensive, small-scale, researcher-led ‎intervention was implemented in one primary school. The programme lasted for three ‎months and consisted of three modules, each focusing in one of the aspects ‎highlighted above. Data consisted of pre-post knowledge tests, audio recording of ‎small-group work, video recording of whole-class teaching, and interviews. Classroom ‎talk was analysed through both quantitative and qualitative methods. Within the ‎Brazilian research field, this study is arguably the first with such aims and scope.‎ In small-group talk, students spent only half of the time talking about the task’s ‎content, when they used one third of dialogic utterances. Group talk features varied ‎reasonably across tasks and no positive variation was found regarding dialogicity. It is ‎argued that the students did not appropriate the use of ground rules for talk ‎effectively. Although statistically significant, only small effects were found on students’ ‎learning (knowledge tests). This result was discussed in relation to the role of different ‎teaching modalities, talk formats, and classroom climate in promoting the co-‎construction of knowledge. The investigation showed how talk served as a means for ‎learning. More specifically, five types of explanatory sequences were identified when ‎teachers and students collectively built scientific explanations. In whole-class ‎teaching, episodes of teachers’ dialogic practices were analysed and revealed which ‎conditions favoured such emergence.‎ Overall, this research sheds light on the potentialities and challenges of dialogic ‎practices in a Brazilian primary school. The study contributes with new empirical data ‎by systematically mapping groups’ and teachers’ discursive practices over seven ‎tasks and nine lessons. Pre-designed classroom materials were very productive in ‎fostering dialogic talk and teachers made many different decisions to render their own ‎lessons more dialogic. Finally, the broad scope of this thesis—connecting ‎professional development, use of classroom materials, student learning, and ‎classroom talk— allowed putting forward recommendations for future intervention ‎such as duration, pace, content, data-based reflective inquiry, and dialogic culture.
... In the latter case the interanimation of students' ideas is higher (Scott et al., 2006) and thus can be considered more dialogic. Similarly, Webb et al. (2014) consider two aspects of productive dialogue: students voicing their own ideas and engaging with other students' ideas. According to Webb et al., engagement may be high (adding details to a peer's idea), medium (referencing details of a peer's idea), or low (acknowledging a peer's idea). ...
... Even students' comments about less important features of their colleagues' ideas show some engagement with others' ideas. When compared to the levels of engagement in Webb et al. (2014), our highest level of dialogic interactions is somewhat similar to adding details to or referencing details of a peer's idea, and our second level resembles acknowledging a peer's idea. In addition, we have used the levels in characterising different kinds of dialogic argumentation. ...
Article
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In this study, we focus on dialogic argumentation among students in a whole class setting in mathematics and physics in lower secondary school. By drawing on previous studies on the structure of argumentation and dialogic interactions, we suggest that transparency of student reasoning and students' engagement with each other's ideas are two key aspects in dialogic argumentation. We examine what levels might exist in these key aspects and how they can exist simultaneously. We collected data by video recording mathematics and physics lessons in lower secondary school, and created a coding scheme for students' dialogic and justifying moves. By using the coding scheme, we recognized different kinds of argumentation with respect to how dialogic student–student interaction is and how transparently student reasoning is expressed. Furthermore, we found different ways how students can provide justifications as a dialogic reaction to others' ideas.
... To, že participace ovlivňuje vzdělávací výsledky žáků, dokládá řada výzkumů zahraniční, ale i české provenience (např. Applebee et al., 2003;Šeďová et al., 2019;Webb et al., 2014). Vedle četnosti žákovské participace je stejně zásadní způsob, kterým se žáci na výuce komunikačně podílejí. ...
... It can be seen that the rhythm of teacher-student interaction is fast. In addition, this type of interaction pattern forms a question chain that is the teacher asking immediately after the student answers the previous question, which can deepen student's own thinking and sharing with others [20]. In summary, according to the classroom atmosphere and rhythm, the first type of interaction pattern is defined as the immediate interaction pattern. ...
Article
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Recently, the development of technology has enriched the form of classroom interaction. Exploring the characteristics of current classroom teaching interaction forms can clarify the deficiencies of teaching interactions, thereby improving teaching. Based on the existing classroom teaching interactive coding system, this paper adopted ITIAS coding system, and took classroom with interactive whiteboard, interactive television or mobile terminals as research scene, selected 20 classroom videos of teaching cases in this environment as research objects. Computer vision, one of the artificial intelligent technologies was applied for video analysis from four aspects: the classroom teaching atmosphere, the teacher-student interaction, the student-student interaction, the interaction between human and technology. Through cluster analysis, three clusters of sample’s behavioral sequences were found. According to the analysis on the behavioral sequences and the behavioral transition diagram of each cluster, three classroom teaching interaction patterns were identified, including immediate interaction pattern, waiting interaction pattern and shallow interaction pattern.
... A way to involve students in mathematical thinking and reasoning is through solving tasks in smallgroup work (Dekker, Elshout-Mohr & Wood, 2004;Webb, Franke, Wong, Fernandez, Shin, & Turrou, 2014). Solving problems together can foster students' explanations and justifications, because students become motivated to warrant their own ideas and to challenge each other's thoughts and request students to present and discuss arguments can promote rich mathematical discourse, students' use of varied reasoning and clear up some (mis)understandings (Mueller & Yankelewitz, 2014). ...
... The teacher's orchestration of classroom discourse crucially influences student understanding and skill development Resnick et al., 2015). When students have opportunities to elaborate on their own thinking and negotiate ideas with their classmates, they often re-examine prior knowledge, test the completeness/incompleteness of their mental models, and evaluate each other's hypotheses (Webb et al., 2014). After reviewing studies related to these theories and frameworks, Resnick et al. (2018) identified four kinds of effects on student learning from productive classroom discourse: increased learning of the subject matter under study (better initial learning), learning gains that endured longer (learning retention), better learning in other subject matter that had not been taught through discussion (far transfer), and better performance on tests of reasoning skills (general intelligence). ...
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How to help teachers learn and foster productive classroom talk? In what ways can video be used to support teacher learning? This article presents a randomized controlled trial examining the efficacy of using visualizations to enhance video use in a teacher professional development program. Free online copy is available at: https://tinyurl.com/yymhvksp
... Some studies (e.g., Herrenkohl, Tasker & White, 2011) detected a direct and positive relation between the COM questions and students' scientific discourse and the learning that occurred. In the mathematics classroom, Webb et al. (2014) found out that when the teachers used the COM questions by an intentional and pressing manner, the cognitive productivity 56 was increased since the students tried to deeply illustrate their underlying reasoning by being semantically comprehensible to the peer community. ...
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In this study, the influence of diversifying typologies and proportional occurrences of teacher educators’ questioning on the prospective teachers’ cognitive contributions was explored deeply. Four teacher educators participated in the study and their in-class implementations were recorded and discursively analysed through systematic observation approach as a branch of sociocultural discourse analysis. The teacher educators enacted eight types of questioning: observe-compare-predict, communicating, monitoring, evaluating-judging-critiquing, challenging, evidencing, concluding, labelling. Four questioning typologies; communicating, monitoring, evaluating-judging-critiquing, challenging, were pervasively staged among others. The communicating questions and monitoring questions were found as specific types of utterances of the teacher educators in opening up and enriching further and more sophisticated cognitive productivity of the prospective teachers. The communicating and monitoring questions seemed to be functionalised by the teacher educators as discursive pre-organiser or pre-conditioner talk moves in fostering more complex cognitive contributions of the prospective teachers. The evaluatingjudging- critiquing and challenging questions appeared having explicit and tangible influences on the cognitive productivity of the prospective teachers and these types of questions’ joint effects on the rather sophisticated cognitive generations were also confirmed. Recommendations were offered for teacher educators’ in-class discursive practices.
... Thus, the facilitator could have applied his expertise in leading the learning process while students went through various activities and these could have transformed their interpersonal activities into inter-psychological activities gradually (Shi, 2017). Moreover, the role of students who are committed to contributing ideas to learn and the facilitator who provides encouragement and support to engage interaction between peers during group work (Webb et al., 2014) were evident in this study. Therefore, these may be the reason for the GOIS group to outperform students in the NGNI group in the overall argumentative essay writing performance. ...
... Teaching and learning to communicate must be an essential requirement at all educational levels. Oral communicative competence is currently recognised as one of the most influential transversal competencies on any type of learning, and various studies have demonstrated that students' oral participation in the classroom is fundamental to the development of skills for understanding (Webb et al., 2014). Vygotsky is the most recognised pioneer in current studies on the role of oral language in learning and, above all, in the construction of thought (Vygotsky, 2012). ...
Article
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This paper shows an example in which Service-Learning (SL) methodology allows to satisfy a demand made by the community that coincides with a requirement of student learning; a teaching model is shown in contexts that encourage meaningful social and real interaction for oral communication. This study presents a SL experience among 19 university students and 163 high school students. Through peer learning strategies higher education students help high school students of vulnerable contexts succeed. Through the Communication Project, university volunteers prepare training workshops to improve the oral communicative competence in English and Catalan of high school students to help them in their final work defenses. The goal is to measure the impact that SL benefits have on all students' evaluations and perceptions of their respective learning processes. The aim of this paper is to discuss the value of service learning to students because there currently exists a gap in this understanding. The mixed-methods research using a sample of higher education students to develop this discussion is applied. The data obtained through a questionnaire before and after the intervention showed a statistically significant improvement of self-perceived oral communication in both languages. Also, after the workshop , SL students reported significant changes connected to a concept of learning that included self-confidence, leadership ability, and responsibility.
... However, active student participation must be supported by the teachers and does not evolve automatically (Ing et al., 2015;Webb et al., 2014). Before students can engage in dialogic discourse, they first need to be encouraged to exchange ideas and share their thinking (Clarke et al., 2016). ...
Article
Dialogic practices encourage students to actively participate in productive classroom discourse. In this paper, we investigate whether changes in teachers' dialogic discourse practice are related to students' perceived activation, motivation and cognitive engagement on a sample of 450 high-school students. Nineteen teachers participated in a 1-year professional development program that was designed to help teachers adopt a more dialogic discourse practice. The extent to which teachers changed their discourse practice varied between teachers and some teachers did not change their practice. Results suggest that students whose teachers changed their discourse practice reported higher levels of perceived activation at the end of the program. Moreover, longitudinal multilevel modeling revealed that students perceived stronger increases in their autonomy support, competence support and cognitive engagement when teachers changed their discourse practice. The paper highlights the important role of dialogic discourse from a motivational perspective.
... This may be due to teachers focusing more on the teaching time available or the central examinations or being inadequate in terms of conducting group work. It has been considered that small group work in the area of mathematics is recommended as an instructional way to develop students' higher-order thinking skills and problem-solving abilities (Kutnick et al., 2017;Noddings, 1989;Webb et al., 2014). Effective group work requires more than simply seating children around a table and giving them opportunities to develop cognitive-based explanations and justifications when they share ideas (e.g., Emmer & Gerwels, 2002). ...
Article
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This study investigates how a sample of middle school mathematics teachers interpret and use compulsory textbooks in the Turkish classroom context based on their: (i) purposes of using textbooks; (ii) frequency and duration of using textbooks; (iii) approaches to using textbooks; and (iv) preferences concerning an ideal mathematics textbook. The research was carried out using the case study model. Data were collected from 17 middle school teachers in six public schools via semi-structured interviews and classroom observations. A content analysis approach was applied to analyse the data collected from the questionnaire completed by the participants. The results indicated that the teachers used textbooks for both pedagogic purposes and giving student assignments. The teachers revealed varied approaches to using textbooks, including adherence, elaboration, and creation with most of them using an elaboration approach. The teachers commonly used textbooks in whole-class activities rather than individual and group work. The findings also indicated that teachers criticized compulsory textbooks from various aspects when describing an ideal mathematics textbook. This study shows the necessity for further studies that focus on teachers' textbook design capacity to explore the relationships between teachers and textbooks and that examine the role of using different textbooks in the learning process.
... Mathematics education research also suggests a set of practices that teachers who effectively use a student-centered, discussion-based approach engage in when they plan for and enact high-quality lessons (Stein et al., 2008). These include anticipating possible student thinking pathways , designing finely tuned goals regarding what students will know and understand (Hiebert et al., 2018), setting up challenging tasks (Jackson et al., 2013), encouraging students to use multiple perspectives/strategies and explain their responses or solution strategies (Tarr et al., 2008), and promoting student engagement with each other's ideas during whole class discussions (Franke et al., 2015;Webb et al., 2014). Similar practices were found to be conducive to effective student-centered instruction in cognitive science research, for example, using complex mathematical problems and asking students to generate multiple solutions (Kapur, 2012(Kapur, , 2014 and connecting student thinking to canonical solutions (Schwartz & Martin, 2004). ...
Article
Rigorous college-and-career readiness standards require significant shifts in typical mathematics instruction. Many schools and districts employ coaches to support instructional changes. Although there is evidence that coaching programs can support teaching improvement, research has yet to identify high-leverage coaching practices. In collaboration with a network of state leaders and coaches, our research team refined a model for math coaching and documented the practices coaches employed in one-on-one work with teachers. Analysis of videotaped coaching conversations and teaching events suggests that model-trained coaches improved their capacity to use a high-leverage coaching practice—deep and specific prelesson planning conversations—and that growth in this practice predicted teaching improvement, specifically increased opportunities for students to engage in conceptual thinking.
... At the heart of accountable talk theory is the notion that teachers should organize discussions that promote students' equitable participation in a rigorous learning environment. The use of talk moves is an "important and universally recognized dimension of teaching" (Correnti et al. 2015), and prior research has established strong linkages between productive classroom discourse and student achievement e.g., (Boston 2012;Munter 2014;Resnick, Michaels, and O'Connor 2010;Walshaw and Anthony 2008;Webb et al. 2014). ...
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TalkMoves is an innovative application designed to support K-12 mathematics teachers to reflect on, and continuously improve their instructional practices. This application combines state-of-the-art natural language processing capabilities with automated speech recognition to automatically analyze classroom recordings and provide teachers with personalized feedback on their use of specific types of discourse aimed at broadening and deepening classroom conversations about mathematics. These specific discourse strategies are referred to as "talk moves" within the mathematics education community and prior research has documented the ways in which systematic use of these discourse strategies can positively impact student engagement and learning. In this article, we describe the TalkMoves application's cloud-based infrastructure for managing and processing classroom recordings, and its interface for providing teachers with feedback on their use of talk moves during individual teaching episodes. We present the series of model architectures we developed, and the studies we conducted, to develop our best-performing, transformer-based model (F1 = 79.3%). We also discuss several technical challenges that need to be addressed when working with real-world speech and language data from noisy K-12 classrooms.
... For example, there have been several studies in the past two decades that have investigated the effects of cooperative learning on science outcomes [21][22][23][24]. Other studies have investigated effects in mathematics [25][26][27]. Far fewer studies have investigated effects in literacy (see study Marcos and colleagues [8] for a recent exception) and social studies [28]. Even though, the studies of cooperative learning in science and mathematics consistently report positive benefits for students, the recent intervention study of Wanzek and colleagues [28] in social studies is less convincing. ...
Article
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Literature shows cooperative learning has positive benefits for students’ learning and social outcomes. Even though cooperative learning studies have been conducted in all areas of the curriculum, few studies have investigated whether there are similar effects for students across several curriculum areas or age groups. Moreover, less attention has been given to how professional learning and development (PLD) opportunities can contribute to changes in instructional practice. We illustrate how research on cooperative learning can be translated into practice, through a one-year University-School partnership. The current study is focused on our PLD work in one large private school based in New Zealand. Analysis of school data (quantitative student data and qualitative teacher data) indicated that, by the end of the school year, students reported experiencing more cooperative learning opportunities in their classes. Teachers believed that the PLD supported change in their practice and noted positive changes in student engagement. Analysis of student data also revealed differential outcomes by subject and age group. Overall, our study showed that PLD opportunities can contribute to the successful implementation of cooperative learning.
... This correlates with both Piaget (1932) and Erickson's (1996) views and was referred to by Webb (1991) as the cognitive elaboration approach, describing the cognitive processes learners use such as explanations, representations and argumentation, and the elaborated speech which can arise from them. Studies (Webb et al., 2014;Howe, 2010) have shown that elaborated forms of speech can have positive modifying effects on cognitive structures when peers work together, though Mercer and Littleton (2007) point out that instances of productive peer to peer elaborated dialogue are rare. According to Barnes and Todd (1977) small groups are rarely inherently productive without specific framing of tasks and teacher intervention. ...
Thesis
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Depictions of classroom teaching and learning in politics, policy and media tend to be over simplified and mechanistic. Insights from research on classroom learning draw largely on the ‘what works’ paradigm, which presents learning as directly caused by teaching. ‘What works’ approaches dominate education discourse, despite their failure to capture the complex, interactive dynamics and ‘messy’ topography of classrooms. This study sought to generate novel insights about small group and classroom learning by acknowledging, rather than ignoring, their complexity. Using complexity thinking (a heuristic drawn from complexity theory) as a conceptual frame, this thesis presents findings from original classroom-based research exploring the emergence of learning in small group activity. Mixed method data, including social network analysis, pupil self-reporting, interviews and observation, were collected during one week in a year four classroom of a UK primary school. Data integration revealed interesting and otherwise tacit insights about antecedents of group and individual learning. Findings suggest that learning has emergent qualities and that individuals exert influence on collective learning due to emergent system dynamics, including social status, personality and knowledge states. Contributions to knowledge include insights about the interplay of top-down and bottom-up organising principles in small group and classroom systems. The thesis also evaluated the usefulness of complexity thinking as an analytical frame for understanding group learning, with mixed conclusions. The study has the potential to offer novel contemporary interpretations of classroom teaching and learning from a systems perspective.
... Each turn was coded from two dimensions: whether the turn contained a new idea and the productive talk moves in it, if any. This study considered three types of productive talk moves in peer talk: reasoning, evaluation, and invitation, which were summarized based on existing discursive productive talk moves identified in various contexts (e.g., King, 2002;Lazonder et al., 2003;Teo and Daniel, 2007;Michaels et al., 2010;Webb et al., 2014;Hennessy et al., 2016;Gillies, 2017). The reasoning type included intrathinking talk moves, such as "elaborate, " "justify, " "speculate, " and "reflect" on one's own contributions, and collective reasoning talk moves, such as "add on, " "co-justify, " "co-speculate, " and "co-reflect" on others' or collective contributions. ...
Article
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According to the complex dynamic systems (CDS) perspective, learning emerges at various system levels. This study built a coherent theoretical framework based on CDS and Bakhtinian dialogic theory and further employed the concept of attractor (i.e., certain stable states that recur over time) in CDS theory to investigate the trajectories of idea emergence and how they diversified group outcomes in dialogic collaborative problem solving (D-CPS). Two contrasting groups were compared using visual and qualitative analysis approaches. The analysis based on idea tree diagrams showed that new ideas emergent in group discussion tended to attract local utterances and performed features of attractors in CDS in both high-performing and low-performing groups. The analysis based on idea hierarchy diagrams revealed how ideas emerged at various system levels. It was also found that status problems were likely to affect the functioning of regulative feedback loops, which might give rise to different structures of idea evolution. This study proposed CDS theory as an alternative perspective, augmented by the ethical considerations of Bakhtinian dialogism, for examining the dynamics of D-CPS.
... Such 'talk moves' are designed to help teachers to interact with students and are also used to prompt and encourage peer-to-peer interaction. Different focuses of research into talk moves include: initial moves to engage discussion, moves to follow up ideas, moves to encourage students to interact with each other's ideas and moves to make student thinking visible (Ritchhart et al., 2011;Webb et al., 2014). Encouraging students to relate their thinking to a previous expression is an example of talk move that helps to build connections between ideas and prompt interaction. ...
... A pre-post-test comparison revealed a correlation between more strongly discussion-oriented instruction and better student performances. Webb et al. (2014) found in their study that elementary school students who engaged with others' contributions, i.e., supported, developed or criticized other contributions, achieved a higher mathematics performance than those who did not engage in the discussion in this way. Analyzing naturally occurring teacher-student-interaction (two lessons in 72 classrooms) Howe et al. (2019) confirm a positive correlation between student learning and teacher-student-interaction involving querying and elaboration, two (of twelve) operationalized indicators of dialogic teaching. ...
Article
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Research studies have long shown that dialogic classroom interactions can have a positive impact on student learning. Despite this, in practice, monologic classroom discussions still predominate. This comparative scarcity of dialogic classroom discussions is linked to the considerable challenges inherent in cultivating them, both for teachers and their students. The aim of this paper is to demonstrate the extent to which, during a one-year teacher professional development program, students' vocal participation in whole-class discussions can be successfully fostered. As data material, we used videotaped classroom discussions of six classes (three mathematics and three history classes) from pre-, post-, and delayed post-test intervention lessons, as well as from three practice phases of the training. The discussions were evaluated using quantitative analyses and content analysis. In all six classes, the pre-post-test comparison revealed an increase in students' talk share. In four of the six classes, more students participated after the intervention than before. The type of student contributions changed in all classes: The students more often justified their contributions and referred to other students' contributions. The insights gained regarding the mostly non-linear progression of individual developments, and regarding subject-based differences , yield useful hints for the design of professional development formats.
... As mentioned above, dialogicity is a central notion in education. The improvement of dialogic interactions in classroom and among students has been the focus of many studies in the last decade, aiming at promoting dialogic learning (see for example, Dawson and Venville, 2010;Erduran et al., 2004;Webb et al., 2014). From an educational perspective, dialogicity is a specific communicative attitude, corresponding to being open to different points of view (Scott et al., 2006, p. 610) and engaging with them (Howe et al., 2019). ...
Article
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Empathy, broadly defined as the ability to experience another's emotions and perceptions, is one of the major attitudes and actions underpinning an individual's participation in dialogue across diversity. The goal of this methodological paper is to operationalize empathy as a discursive construct, manifested in children and adolescent dialogic interactions. A coding scheme is developed based on three distinct steps. First, a review of the operational definitions of empathy is carried out, to capture how its related values, skills, and dispositions have been detected thus far. Second, the definitional elements resulting from this overview are represented in the dialogical notion of other-orientedness, which can be manifested, actually and potentially, in discourse. Moves are distinguished in 8 categories based on their disposition to be potentially other-oriented (dialogicity), which becomes actually manifested depending on their relevance to the discourse they are used in. Dialogicity and relevance are captured by the coding scheme proposed in this paper, which is validated and used to illustrate how it can reveal dialogical empathy and the development of common ground in interactions.
... Such 'talk moves' are designed to help teachers to interact with students and are also used to prompt and encourage peer-to-peer interaction. Different focuses of research into talk moves include: initial moves to engage discussion, moves to follow up ideas, moves to encourage students to interact with each other's ideas and moves to make student thinking visible (Ritchhart et al., 2011;Webb et al., 2014). Encouraging students to relate their thinking to a previous expression is an example of talk move that helps to build connections between ideas and prompt interaction. ...
Book
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Leong, Y. H., Kaur, B., Choy, B. H., Yeo, J. B. W., & Chin, S. L. (Eds.). (2021). Proceedings of the 43rd Annual Conference of the Mathematics Education Research Group of Australasia (MERGA): Excellence in Mathematics Education: Foundations and Pathways. Singapore: MERGA. Available online at https://www.merga.net.au/Public/Publications/Annual_Conference_Proceedings/2021-MERGA-conference-proceedings.aspx
... First, the extent to which teachers in our study considered individual children's thinking in their number selections is unclear. Research has shown that the more teachers attend to individual children's thinking during instruction, the more children learn (Fennema et al., 1996;Ing et al., 2015;Webb et al., 2014). Although some teachers singled out individual children or specific groups of children when justifying their number selections, many did not, and our interview protocol did not press teachers on this issue. ...
Article
This study explored the complexity of teachers’ considerations during number selection, which is a core element of problem planning. We examined teachers’ purposeful number selection for Equal Sharing problems, a type of fraction story problem. Participants included 47 elementary-school teachers engaged in a multiyear professional development focused on enhancing responsiveness to children’s fraction thinking. Our research extends Land’s (2017) work on teachers’ number selection, by focusing on a single content domain (fractions) and by using children’s mathematical thinking as a unifying analytical lens. Findings include descriptive patterns in teachers’ specific number selections and the introduction and illustration of a framework for teachers’ purposeful number selection for fraction story problems. The framework details three categories of considerations: (a) accessibility with respect to children’s existing understandings, (b) the range of strategies children are likely to use to solve the problem, and (c) the mathematics that could be leveraged by discussing children’s strategies.
... From this it is possible to say that a high frequency of coupling is closely aligned to understanding and is linked to better student results. The findings from this study are in line with findings previously outlined by the studies of Webb et al. (2014) and Ing et al. (2015), illustrating that speaker listener coupling affects different students in similar ways, depending on the complexity of the network they are able to form during internalization (Process 2) see Figure 3. This may result from structural and functional aspects of the human brain which are specifically used to address socialization within the human experience. ...
Article
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Verbal communication to relay information between students and the teacher, i.e., talk, lies at the heart of all science classrooms. This study investigated and began to characterize the neurological basis for the talk between science teachers and students in terms of speaker-listener coupling in a naturalistic setting. Speaker-listener coupling is the time-locked moment in which speaker vocalizations result in activity in the listeners brain. This activity is highly predictive and tightly ties to listener understanding. The design for this study was an observational stimulus-response study using neuroimaging data obtained from talk sessions between a teacher and a student. Results were obtained using a functional near-infrared spectrometer and an artificial neural network model. Examination of the data suggested that speaker-listener coupling occurs between a student and a teacher during successfully understood verbal communications. This study promotes further research into the exploration of how individual interactions between persons (speakers and listeners) via talk are perceived and influence individual cognition. Study outcomes suggest coupled brains create new knowledge, integrate practices and content, and verbal and nonverbal communication systems which are constrained at two levels the environmental level and the speaker listener level. The simplicity of brain-to-brain coupling as a reference system may simplify the understanding of behaviors seen during the learning of science in the classroom.
... Dyadic coding could build upon this foundational research by expanding to multiple grade levels, content areas, and school settings, as well as classifying students in multiple ways to determine the extent to which diminished opportunity patterns occur or are disrupted, in what context, when, for whom, and how the implications of these patterns may differ as a function of the outcome measure. A third reason for capturing dyadic interactions is because individual students' participation, such as opportunities to answer questions, to make counter-arguments, can enhance their achievement (Ing et al. 2015;Sedova et al., 2019;Webb et al. 2014). Sedova et al. (2019) directly studied if students who talk more in whole class lessons learn more in ninth-grade language arts lessons. ...
Article
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Because of poverty, many children do not receive adequate prenatal care, nutrition, or early childhood education. These inequities combine to ensure that many students enter school with considerably less academic content knowledge and skills for learning than their peers. Teachers and schools did not create these gaps, but they must address them. The impact of schools in reducing gaps has been explored for decades only to yield inconsistent findings. One possible reason for these contradictory results is because these studies ignore classroom process. We argue for the inclusion of process in research on opportunity and achievement gaps to better articulate if schools provide inequitable learning opportunities. Further, we argue for dyadic (teacher to individual student) measurement of classroom process because commonly-used observation instruments only measure teachers' interactions with the whole class. These instruments obscure differential teacher treatment that may exist in some classrooms. To improve policy and practice, we call for supplementing extant measures of teachers' whole-class interactions (process) and student outcome (product) measures
... The principal facets of argumentative activity-justifying claims, generating conjectures and their justifications, and evaluating arguments-are all essential components of doing and communicating mathematics. In addition, accumulative research suggests that participation in argumentative activities-which encourage students to explore, confront, and evaluate alternative positions, voice support or objections, and justify different ideas and hypotheses-promotes meaningful understanding and deep thinking (Mueller et al., 2014;Staples & Newton, 2016;Webb et al., 2014;Weber et al., 2008). Furthermore, students' engagement with mathematical argumentation has been positively linked to the development of students' mathematical autonomy (Yackel & Cobb, 1996), mathematical dispositions (Whitenack & Yackel, 2002), and communicative skills (Andriessen, 2006). ...
Article
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Argu mentative problem solving in mathematics classrooms is a crucial practice that supports important student learning goals via collaborative deliberation and consensus building, but also places substantial cognitive and affective demands on both students and teacher. In this in-depth qualitative study, we considered how students’ emotions during argumentative discourse relate to their learning of real-life functional situations, an area of mathematics highlighted in the literature as foundational yet difficult. Observations, written reflections, and interviews of six Year 9 (14–15-year-old) students’ experience of argument construction, critique, and consensus building were analyzed for insights into emotions experienced during small-group argumentative problem solving, and how various emotions might support or hinder students’ mathematics learning. The emotion of frustration was experienced frequently and was found to facilitate persistence and the correction of misconceptions, but also to hinder the learning in contributing to ongoing tension and eventual resignation. Peer critique was found to stimulate negative emotions but positive learning processes, such as seeking other ways to explain one’s reasoning, and re-evaluating one’s own incorrect solutions.
... Correlational evidence also suggests a positive link between explaining and engaging with others' ideas and learning outcomes. Positive relationships with mathematics and science learning outcomes have been shown for providing explanations as part of arguments or justifications, and supporting, rebutting, and building on others' suggestions (Chi & Menekse, 2015;Chinn et al., 2000;Howe et al., 2007;Roscoe & Chi, 2008;Veenman et al., 2005;Webb, 1989Webb, , 1991Webb et al., 2009Webb et al., , 2008Webb et al., , 2014Webb & Palincsar, 1996). Furthermore, explaining and engaging with others' ideas (e.g., restating or paraphrasing another student's strategy and applying it) have been found to correlate with mathematics achievement among students who explicitly need help (Webb & Mastergeorge, 2003). ...
Article
Educators, researchers, and policy makers recognize that student participation in classroom mathematics conversations, especially explaining one’s own thinking and engaging with others’ ideas, can promote students’ mathematics learning. However, precisely how participating in these ways supports learning has not often been examined in detail. Using in-depth analyses of videotaped whole-class discussions, small-group collaborative work, and private partner conversations in two third-grade mathematics classrooms on six occasions over a five- month period, we show advances that students made in their mathematical thinking or mathematical work in the context of explaining their thinking and/or engaging with others’ ideas. The detailed analyses focus on students who had previously scored low on standardized tests of mathematics proficiency. The results show how students not considered to have extensive mathematics knowledge can forge new connections between mathematical ideas and representations, and extend their problem-solving strategies in ways that are directly related to their participation.
... While the ACT framework provides a schema for understanding how teachers support mathematical thinking in dialogic instruction (sociomathematical norms), teachers must also consider how to promote group coordination (general social norms). Group coordination refers to the extent to which learners actively engage with their peers' ideas to develop common ground or mutual understanding (Barron, 2000(Barron, , 2003Webb et al., 2014). Barron (2000) summarizes group coordination as follows: ...
Article
The purpose of this study was to identify and categorize in-the-moment teaching moves which support productive general social norms and sociomathematical norms during dialogic instruction by drawing on transcripts of classroom episodes. To understand how teachers construct in-the-moment teaching moves, this paper is grounded in a revised version of the Advancing Children’s Thinking framework. In particular, the framework reveals three interconnected dimensions of teaching moves: (1) eliciting group strategies, (2) supporting conceptual understanding and group coordination, and (3) extending group mathematical thinking and coordination. Drawing on this framework, we use a novel self-study methodology to construct a sequence of in-the-moment teaching moves that support the development of productive social and sociomathematical norms in dialogic classrooms. These teaching moves include (1) inviting strategies and encouraging all members to actively listen; (2) exploring, clarifying, and questioning the mathematical details of all strategies as a group; (3) promoting understanding of differing strategies; (4) comparing and evaluating differing strategies as a group; and (5) connecting the group’s thinking for making progress on the task/advancing current strategy to become viable. Implications for research and practice are offered.
Article
Productive learning of algebra is supported when students reflect on multiple strategies, compare them and discuss the rationale behind and relative merits of particular strategies. Comparison and Discussion of Multiple Strategies (CDMS) is an instructional approach designed to support these processes in math classrooms. In the current study, 16 Algebra I teachers received professional development and supplemental materials to support CDMS when teaching a unit on linear equation solving and 475 of their students completed assessments of their linear equation solving knowledge before and after the unit. Thirteen Algebra I teachers and their 359 students were the business-as-usual control group. CDMS increased how often teachers engaged their students in comparison of multiple strategies, sustained small group work, and sustained mathematical discussions. Students in CDMS classrooms also had higher knowledge of linear equations on the posttest, particularly procedural flexibility, even after controlling for pretest knowledge and school demographic differences. Thus, encouraging teachers to regularly compare and discuss multiple strategies increases students’ algebra learning. Findings highlight the need to expand theories of algebra learning to include attention to procedural flexibility, illustrate an instructional theory and method to promote broader learning about algebra, and provide evidence for effective instructional practices.
Article
Hand-raising is an everyday student behavior during classroom discourse. The present study investigates hand-raising as an observable indicator of behavioral engagement and its relation to student achievement. We examine students’ hand-raising behavior during a videotaped lesson in high school classrooms (N = 266 students). Results from multilevel regression modeling linked the frequency of students’ engagement in hand-raising to academic achievement. Further, structural equation modeling was applied to investigate the interrelations between hand-raising, cognitive engagement, and teacher emotional support. Results indicate that hand-raising is associated with cognitive engagement and perceptions of teacher support and suggest that hand-raising may mediate the relation between teacher emotional support and academic achievement. The discussion highlights the utility of student hand-raising as a proxy for students’ active participation and engagement. We emphasize the study’s contribution to the engagement literature.
Article
Students with learning disabilities are often excluded from conversations about high-quality mathematics instruction as well as conversations about equitable mathematics instruction. As such, they may not be provided many opportunities to engage in mathematics with teachers who implement practices that the field of mathematics education would consider “high-quality” or “equitable”. In this paper, we examine how three students with learning differences participate in instruction that demonstrates aspects of high quality and equitable mathematics instruction. Our findings outline practices that appeared to support increased opportunities for students to demonstrate their own reasoning and sense making in mathematics. Contributions of this work include illuminations of specific pedagogical moves that may support students identified as having learning disabilities to engage in more student-centered, conceptually-oriented mathematics.
Article
Informed by attachment theory and self-determination theory, the goal of this study was to test the hypothesis that behavioral engagement mediates the longitudinal associations between teacher–child relationship quality and academic achievement. In addition, in an exploratory manner, we expected to identify some additional transactional relations among these variables. Participants were 301 children (Mage = 65.72 months, SD = 4.18 months; 49% boys) and their teachers. In each spring semester from kindergarten to second grade, teachers reported on the closeness and conflict in the teacher–child relationship and on children's academic skills. Each year, trained observers rated children's behavioral engagement in the classroom, and a different group of research assistants assessed children's academic skills using subscales from the Woodcock–Johnson III Tests of Achievement. Cross–lagged panel models indicated that teacher–child conflict in kindergarten was indirectly related to teacher–reported academic skills in second grade through behavioral engagement in first grade. There was also evidence of transactional, negative relations between teacher–child conflict and behavioral engagement from kindergarten to first grade. These findings highlight behavioral engagement as a mechanism linking early teacher–child conflict and children's later academic skills.
Article
This study examined 69 Chinese preschool teachers’ use of feedback strategies in their math lessons. Guided by the Initiation-Response-Follow-up (IRF) framework, math lessons were coded using quality feedback strategies in CLASS (CLASS-PreK; Pianta et al., 2008). Specifically, the frequency of teachers’ feedback strategies as well as their effectiveness of engaging children in higher-order thinking were examined. Results showed that teachers were quite familiar with the use of feedback strategies such as recognition, back-and-forth exchanges, and teacher persistence. Moreover, in terms of promoting children’s critical thinking, teachers were ineffective when scaffolding and querying children’s responses and actions.
Article
Peer talk shapes the trajectory of group thinking. Studies have explored productive peer talk moves that can facilitate high-order group thinking, yet few have focused on the extent to which students consecutively take up these talk moves to sustain group thinking. There is no consensus on how to understand or measure the sustainability of productive peer talk. This study establishes a construct to help characterize a group's capacity to consecutively engage in high-order collective thinking and to investigate the impact of such sustainability on group outcomes. The proposed construct, group thinking sustainability (GTS), was conceptualized as a three-level nested hierarchy (comprised of reciprocity, productivity, and constructiveness) and further operationalized as the average length of a corresponding overt turn-taking sequence in group discussions. This study applied this construct to a sample of 168 primary school students who were divided into groups of four and asked to collaboratively solve three mathematical problems within 30 minutes. The results revealed that GTS can help characterize and differentiate a group's capacity to sustain productive peer talk. GTS can also help predict group outcomes and explain why some groups were more successful than others. This study provides novel insights into understanding and measuring GTS across groups. It also suggests a three-level scaffolding (i.e., turn-taking, productive talk, and knowledge construction) that teachers can use to support sustainable group thinking in collaborative peer talk.
Chapter
In this chapter, we elaborate on components of dialogic teaching. We present repertoires of teaching talk, and indicators and principles as elements that together bring dialogic teaching to life. Further, we describe some initiatives aimed at getting dialogic teaching into the classroom through professional development programs for teachers. We evaluate the success of individual studies and consider what caused the very diverse outcomes of these studies. The diverse outcomes provide evidence that it is not easy to train teachers to implement dialogic teaching in their classrooms. With this notion in mind, in the last part of this chapter we analyze what obstacles teachers face when trying to teach dialogically.
Chapter
This chapter is an introduction to this book. First, we reveal our motivation for writing it—to contribute to understanding how teachers can improve classroom dialogue and thereby boost student learning. Second, we present the organization of the book and the content of individual chapters. Third, we define dialogic teaching. Fourth, we outline the essential concepts and theoretical inspirations that were the basis for this study.
Chapter
This chapter concludes the story of our TPD and research project. First, we will summarize the main results reported in the individual chapters to briefly review what we have found. Second, we open a discussion about what led to any changes. We consider how the participating teachers surpassed various obstacles associated with dialogic teaching that are usually seen as critical. We also describe the general processes that we see as responsible for the success of participating teachers in transforming their teaching practices—appropriation of teaching tools and reflection. Finally, we share some concluding remarks, including our thoughts on possible directions for future research.
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Packed with valuable strategies for teachers and fun activities for children, this book is a must for any school wishing to make group work a more effective and successful way of learning. Teachers who have become more confident with the approaches developed for this book find that their classes are better behaved, children spend more time on task and they become less dependent on the teacher. The book shows teachers how to create an inclusive and supportive classroom by developing the social, communicative and group working skills of all pupils. Tried-and-tested, step-by-step approaches encourage both children and their teachers to develop supportive relationships that have been found to facilitate academic performance, positive social behaviour and motivation. Strategies for setting up and running effective group work are a key feature of the book. © 2009 Ed Baines, Peter Blatchford and Peter Kutnick. All rights reserved.
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Cognitively Guided Instruction (CGI) researchers have found that while teachers readily ask initial questions to elicit students’ mathematical thinking, they struggle with how to follow up on student ideas. This study examines the classrooms of three teachers who had engaged in algebraic reasoning CGI professional development. We detail teachers’ questions and how they relate to students’ making explicit their complete and correct explanations. We found that after the initial “How did you get that?” question, a great deal of variability existed among teachers’ questions and students’ responses.
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The purpose of this classroom-based experiment was to explore methods for helping students generate conceptual mathematical explanations during peer-mediated learning activities. Participants were 40 general education classrooms in grades 2, 3, and 4, which were assigned randomly to 3 treatments: peer-mediated instruction (PMI) with training in how to offer and receive elaborated help (PMI-Elaborated); PMI with training in elaborated help and in methods for providing conceptual mathematical explanations (PMI-Elaborated+Conceptual); and contrast (i.e., no PMI). Teachers implemented PMI treatments for 18 weeks with their naturally constituted mathematics classes. From each of the 40 classes, we pre- and posttested the mathematics achievement of 4 students who represented 4 points on the achievement continuum. We also coded student interactions from tutoring generalization sessions videotaped 10 weeks after all training had been completed. Analyses revealed that PMI-Elaborated+Conceptual tutors asked more participatory, procedural questions and provided more conceptual explanations. Moreover, the achievement of PMI-Elaborated+Conceptual students was higher than that of PMI-Elaborated students, which in turn surpassed that of the contrast group. Findings are discussed in terms of teachers' use of collaborative learning methods.
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In this study I investigated how collaborative interactions influence problem-solving outcomes. Conversations of twelve 6th-grade triads were analyzed utilizing quantitative and qualitative methods. Neither prior achievement of group members nor the generation of correct ideas for solution could account for between-triad differences in problem-solving outcomes. Instead, both characteristics of proposals and partner responsiveness were important correlates of the uptake and documentation of correct ideas by the group. Less successful groups ignored or rejected correct proposals, whereas more successful groups discussed or accepted them. Conversations in less successful groups were relatively incoherent as measured by the extent that proposals for solutions in these groups were connected with preceding discussions. Performance differences observed in triads extended to subsequent problem-solving sessions during which all students solved the same kinds of problems independently. These findings suggest that the quality of interaction had implications for teaming. Case study descriptions illustrate the interweaving of social and cognitive factors involved in establishing a joint problem-solving space. A dual-space model of what collaboration requires of participants is described to clarify how the content of the problem and the relational context are interdependent aspects of the collaborative situation. How participants manage these interacting spaces is critical to the outcome of their work and helps account for variability in collaborative outcomes. Directions for future research that may help teachers, students, and designers of educational environments learn to see and foster productive interactional practices are proposed. The properties of groups of minds in interaction with each other, or the properties of the interaction between individual minds and artifacts in the world, are frequently at the heart of intelligent human performance (Hutchins, 1993, p. 62).
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This article presents a model of the generative processes of reading comprehension. The article begins with a discussion of the four parts of the model: generation, motivation, attention, and memory. The discussion then reviews laboratory and classroom research relevant to the model. A series of experiments by the author and his colleagues are presented to support the instructional utility of the model. The article concludes with a discussion of the model and its relation to the teaching of reading comprehension in schools.
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This article reviews research on the effects of between- and within-class ability grouping on the achievement of elementary school students. The review technique—best-evidence synthesis—combines features of meta-analytic and narrative reviews. Overall, evidence does not support assignment of students to self-contained classes according to ability (median effect size [ES] = .00), but grouping plans involving cross-grade assignment for selected subjects can increase student achievement. Research particularly supports the Joplin Plan, cross-grade ability grouping for reading only (median ES = +.45). Within-class ability grouping in mathematics is also found to be instructionally effective (median ES = +.34). Analysis of effects of alternative grouping methods suggests that ability grouping is maximally effective when done for only one or two subjects, with students remaining in heterogeneous classes most of the day; when it greatly reduces student heterogeneity in a specific skill; when group assignments are frequently reassessed; and when teachers vary the level and pace of instruction according to students’ needs.
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Research suggests potential problems when group work is used in school science to support the integrated acquisition of conceptual understanding and testing procedures. Yet integrated acquisition is promoted by current policy, and is a popular classroom strategy. Work by Howe et al. (Learning and Instruction 10 (2000) 361) indicates that the problems may be overcome if pupils: (a) discuss conceptual material in small groups and reach consensus; (b) subject consensual positions to guided empirical appraisal. The present paper reports a study with 9–12-year old pupils, which tests the proposal of Howe et al. using heat transfer as its topic, in contrast to the shadow size of Howe et al. In broad terms, the results are consistent with what Howe et al. report, although there are subtle differences in both outcome and process. Nevertheless, the similarities are such as to indicate a robust technique, with clear relevance to classroom practice. To facilitate application, the paper outlines what the technique requires in terms of group organisation and teacher support, and suggests that in both cases there is consistency with current practice.
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Prior research on collaborative learning identifies student behaviors that significantly predict student achievement, such as giving explanations of one’s thinking. Less often studied is the role of teachers’ instructional practices in collaboration among students. This article investigates the extent to which teachers engage in practices that support students’ explanations of their thinking, and how these teacher practices might be related to the nature of explanations that students give when asked by the teacher to collaborate with each other. The teachers observed here, all of whom received specific instruction in eliciting the details of student thinking, varied significantly in the extent to which they asked students to elaborate on their suggestions. This variation corresponded to variation across classrooms in the nature and extent of student explanations during collaborative conversations and to differences in student achievement.