Whole-class Instruction Research Articles

Teaching Mathematics with a New Curriculum: Changes to Classroom Organization and Interactions

This report describes a high school mathematics teacher's decisions about classroom organization and interactions during his first two years using a new curriculum intended to support teachers' development of student-centered, contributive classroom discourse. In year one, the teacher conducted class and interacted with students primarily in small groups. In year two, he conducted more whole-class instruction. In both years, teacher-student interactions contained univocal and contributive discourse, but in year two the teacher sustained contributive discourse with students for longer periods. The teacher facilitated the most significant changes to classroom discourse in the instructional format with which he had the greatest experience (whole-class instruction). Over the period of this study, two key factors appeared to affect the teacher's decisions about classroom organization and interactions: his perception of students' expectations about mathematics classroom roles and activity, and his own discomfort associated with using a new curriculum. These areas are important candidates for future research about teachers' use of innovative mathematics curricula.

Early childhood intervention and early adolescent social and emotional competence: second-generation evaluation evidence from the Chicago Longitudinal Study

Background: To explore whether social or emotional outcomes for high-risk early adolescent youth that attended an established preventive intervention called the Chicago Child–Parent Center Preschool Program (CPC) are moderated by individual, family and program variations. Purpose: Two questions are addressed: (1) Do the effects of CPC preschool participation on early adolescent social and emotional competency vary by sex of child, family risk status, parent education and family structure? (2) Do estimated effects on early adolescent social and emotional competency vary by program length in the preschool and school-age components of the program? Programme description: Located in or close to elementary schools in the Chicago public school system, the CPC program provides educational and family-support services to children between the ages of 3 and 9 (preschool to 2nd or 3rd grade). Within a structure of comprehensive services similar to Head Start, the intervention emphasises the acquisition of basic skills in language arts and math through relatively structured but diverse learning experiences that include teacher-directed, whole-class instruction, small-group and individualised activities, and frequent field trips. Sample: Data for this investigation were drawn from the Chicago Longitudinal Study (CLS). The CLS follows a cohort of 1539 disadvantaged, minority children (93% African-American, 7% Latino or Other) who were born in 1980 and attended kindergarten programs within the Chicago Public School System in 1985/86. Out of the full sample of 1539, a subset of 989 children (64% of the sample) received preschool services from one of Chicago's 20 Child–Parent Center (CPC) programs. An additional set of 550 children (36% of the sample) did not attend CPC preschool and serve as a non-CPC comparison group. The study sample are 1378 primarily African-American youth who participated in the CLS and had scores for two or more identifiable social and emotional competency indicators by age 15. Design and methods: Follow-up of a non-randomised alternative intervention matched-group cohort at age 15 years. Differential effects were estimated using multiple regression. Program interaction terms (e.g., program × sex or program × parent high school graduate) were added to the basic regression model specification that already included the main effects of each variable included in the interaction. Results: Some 12% (or 11 of 92) of the interaction terms for social and emotional outcomes by age 15 were significant at the 0.01 or 0.05 level. The most frequently detected differential effects were for family risk level (high or low) and sex of child. Conclusions: Most children appear to benefit equally from participation in the CPC program. The prediction from ecological theory that children experiencing a large number of environmental risk factors (e.g., high family risk status and low parental education levels) are more likely to benefit from program participation was supported.

Be an Active Co-teacher

Co-teaching, the pairing of general and special education teachers in a general education classroom, requires a high degree of expertise on the part of both teachers. Done well, it can be compared to a strong marriage— partners sharing and planning, reflecting and changing. Done poorly, it can be described as a blind date— co-teachers just waiting for the year to end. Each day, co-teachers must balance their roles as content and process specialists to deliver the appropriate services to their students. Although co-teachers can employ certain techniques, such as dividing the class into two or more groups and each teacher presenting either the same material (parallel teaching) or different material (station teaching) to a group (Cook & Friend, 1995), many times one co-teacher, usually the general education teacher, is the primary instructor and presenter for the entire class (Magiera & Zigmond, 2005). The other coteacher is then left to take on a seemingly less important supportive role. In fact, one of the downsides of coteaching is that one co-teacher, usually the special education teacher, feels less essential (Austin, 2001). For there to be a high level of efficiency and effectiveness, the co-teacher who is not leading instruction needs to know a variety of activities to employ (Murawski & Dicker, 2004). Although this co-teacher might not be directly presenting material, the role, nonetheless, should be essential and important, and observers should see how unique a co-taught classroom can be (Wilson, 2005). The following 20 ways illustrate meaningful activities for co-teachers to employ while their partners are presenting whole-class instruction.

Fine grain assessment of students’ mathematical understanding: participatory and anticipatory stagesin learning a new mathematical conception

This study addressed a twofold problem – the soundness of a theoretical stage-distinction regarding the process of constructing a new (to the learner) mathematical conception and how such distinction contributes to fine grain assessment of students’ mathematical understandings. As a context for the study served the difficult-to-grasp concept of ‘inverse’ order relationship among unit fractions, that is, the larger the number of parts the smaller the size of each part (e.g., 1/7 > 1/10 although 10 > 7). I conducted this study as a whole-class teaching experiment in a third grade classroom at a public school in Israel. The qualitative analysis of tasks presented to students and students’ responses to those tasks, as well as a quantitative measurement of percents of student responses to assessment questions, indicated that the distinction between a participatory and an anticipatory stage is sound and useful in guiding the teacher’s selection of tasks to assess/teach students’ mathematical thinking. In particular, this analysis demonstrates that in a classroom where the vast majority of students appear to understand a new concept, a substantial portion of the class – those who formed the new conception only at the participatory stage – may be at risk of being left behind. This study also highlights a new way of organizing assessment to minimize such unfortunate situations, including three levels of assessment rigor a teacher can use in regular classroom settings.

The teacher's responsibility in whole‐class debriefing of mathematical activity

Prompted by recent moves in the United Kingdom to guide teachers’ practices in whole-class, direct interactive teaching, in this article, we offer an opportunity for North American mathematics educators to reflect on possibilities for whole-class teaching of mathematics. We focus particularly on the plenary aspect of lessons—what might be considered the debriefing of mathematical activity—and specifically on the teacher’s responsibility during those sessions, both to his or her students and to the authenticity of the discipline of mathematics. Drawing on data from a Grade-3 classroom and invoking complexity science as a theoretical lens to explore the classroom as a complex learning system, we present implications for teaching in whole-class debriefings of mathematical activity.

Teachers' and students' verbal behaviours during cooperative and small‐group learning

Teachers play a critical role in promoting interactions between students and engaging them in the learning process. This study builds on a study by Hertz-Lazarowitz and Shachar (1990) who found that during cooperative learning teachers' verbal behaviours were more helpful to and encouraging of their students' efforts while during whole-class instruction, their verbal behaviours tended to be more authoritarian, rigid, and impersonal. This study seeks to determine if teachers who implement cooperative learning engage in more facilitative learning interactions with their students than teachers who implement group work only. The study also seeks to determine if students in the cooperative groups model their teachers' behaviours and engage in more positive helping interactions with each other than their peers in the group work groups. The study involved 26 teachers and 303 students in Grades 8 to 10 from 4 large high schools in Brisbane, Australia. All teachers agreed to establish cooperative, small-group activities in their classrooms for a unit of work (4 to 6 weeks) once a term for 3 school terms. The teachers were audiotaped twice during these lessons and samples of the students' language, as they worked in their groups, were also collected at the same time. The results show that teachers who implement cooperative learning in their classrooms engage in more mediated-learning interactions and make fewer disciplinary comments than teachers who implement group work only. Furthermore, the students model many of these interactions in their groups. The study shows that when teachers implement cooperative learning, their verbal behaviour is affected by the organizational structure of the classroom.

No Body, Never Mind

No Body, Never Mind

Acting against conflict and bullying. The Brisbane DRACON project 1996–2004—emergent findings and outcomes

In 1996, the authors were invited to join an international research project, DRACON (=DRAma + CONflict), into the use of drama for assisting conflict management in schools, with a particular initial brief to investigate the cultural components. The Brisbane DRACON project has been based at Griffith University in Brisbane, and has incorporated sites throughout New South Wales and Queensland. The aim of the Brisbane project has been to use drama to assist young people in schools towards a cognitive understanding of the nature, causes and dynamics of conflict and bullying, in order to give them the tools to take control of their own conflicts and conflict agendas, personally and in the context of the school community, rather than relying on externally imposed and hierarchical conflict management programs. The project has been embedded throughout within the normal school curriculum, and the eventual goal is to change the ethos of schools by creating new networks of understanding and support. The Brisbane project has so far entailed nine annual cycles of action research centred on secondary school students in Queensland and New South Wales (NSW), and also incorporating primary school students. Fifteen high schools have taken part, with between one and five classes of students involved in each school, and from Cycle 4 onwards, a total of 16 primary schools connected with those high schools have also been included, each with between one and five classes involved. From Cycle 2 onwards, the aim has been pursued using a combination of two equal and integrated strategies: drama and whole-class peer teaching. Cycles 4–6 focussed particularly on cultural aspects of conflict, and Cycles 7–9 on bullying. This paper sets out to tell the story and emerging outcomes of the research.

Mathematics Teaching in Italy: A Cross-Cultural Video Analysis

This study investigates the cultural nature of teaching. It compares a sample of 39 videotaped Italian mathematics lessons to German, Japanese, and U.S. lessons videotaped in TIMSS. This study expands on earlier work that was based on a smaller sample; analysis is also extended to the nature of the mathematical content presented. The results confirm the existence of an Italian cultural pattern for mathematics teaching, whose features we outline here. Italian teachers prefer whole-class instruction to individual seatwork; they engage in teacher talk/demonstration to transmit information; and they often call on students to solve problems at the board before the rest of the class. Italian lessons are characterized by the inclusion of a large number of mathematical principles and properties. These are explained 50% of the time, and simply stated the rest of the time. This study adds yet another perspective from which mathematics teaching can be studied, and, by acknowledging the difficulty to change cultural practices, it offers practical implications for teacher learning.

Questioning Learning

This paper draws on observation data from 54 teaching episodes in Year 2 and Year 6 whole-class teaching. It describes the findings of the analysis and illustrates how ‘interactive’, whole-class teaching is characterised by questions requiring predetermined answers. Speculative questions, which invite opinions, hypotheses and imaginings, or process questions, which invite children to articulate their understanding occupy little of the classroom talk arena. Despite national initiatives to develop greater use of whole-class teaching with higher levels of interactivity, teachers use questioning to maintain control and to support their teaching, rather than pupil learning. The paper raises important issues about the nature of interactivity in whole-class teaching and about the role questions play in supporting and extending pupils’ learning experiences.

Reading Lessons in Guinea, France, and the United States: Local Meanings or Global Culture?

Is classroom practice becoming more homogeneous around the world, or will teachers continue to work very differently across different countries? This article addresses those questions by comparing firstand second-grade reading lessons in France, Guinea, and the United States. It shows that what reading lessons in each country have in common is not, as some have found in the case of middle-school mathematics lessons, whole-class instruction. Rather, what reading lessons in these three countries have in common is a “mixed method” of reading instruction, that is, the practice of combining explicit instruction in decoding and explicit attention to reading for meaning. Within that very general framework, teachers in France, Guinea, and the United States create distinctive lesson structures. Indeed, lesson structures vary so much within and between countries that what the lessons have in common might on the surface appear trivial. And yet, as I argue here, the common mixed method has had a powerful impact on reading instruction, particularly in Guinea. Although global models have little substance until local teachers act to give them meaning and structure, global models nonetheless inhabit and inhibit practice. World culture theorists, otherwise known as neo-institutionalists, argue that schooling takes similar organizational shapes around the world and everywhere features a centralized, compulsory, mass system and a converging official curriculum. Some scholars have extended the argument to encom-

Metaphor and Numerical Diagrams in the Arithmetical Activity of a Fourth-Grade Class

Fourth-grade students who participated in a yearlong, whole-class teaching experiment not only reconceptualized natural numbers but also generated flexible solution strategies to perform numerical computations mentally and in writing. Students' reconceptualization of number was mediated by their perceived resemblance between the physical action of splitting an object into parts and the mental action of splitting a number into units. Such a resemblance, evoked by the word split as used by the students, can be considered to be a metaphor in the Peircean theory of signs. This spontaneous metaphor mediated students' constructions of numerical strategies. Students communicated such strategies through different signs like numerical diagrams, verbal numerical arguments, and other idiosyncratic arithmetical notations. Students presented the same solution strategy using signs in different semiotic systems and translated signs in one system into signs of another system. Students' arithmetical activity indicated a shift from an instrumental understanding of basic arithmetic to a relational understanding mediated by their symbolic initiative. The article contains an analysis of the collective construction of this metaphor and its role in mediating the semiotic and arithmetical activity of the students. This article presents an analysis of the arithmetical and semiotic activity of a class of fourth-grade students who participated in a yearlong, whole-class teaching experiment. The analysis indicates that a metaphor, collectively conceptualized by the students, mediated their reconceptualizations of natural number in terms of units and the emergence of numerical strategies to operate with them. Numerical diagrams, verbal numerical arguments, and other idiosyncratic notation were signs used by the students to present solution strategies to the class.

Principled Understanding? Teaching the Active and Passive Voice

This paper describes some of the misconceptions and confusions in metalinguistic understanding which are established by the teacher during whole-class teaching of the active and passive voice. It draws on findings from a larger study investigating how teachers use talk in whole-class settings to scaffold children's learning. Through a detailed analysis of the teacher's interactions with her class, the paper illuminates the significance of clarity in explanations and choice of examples and the importance of secure subject knowledge. It demonstrates how the teaching of metalinguistic knowledge requires more than an ability to identify and define terminology, and how an overemphasis upon content can lead to a failure to acknowledge the cognitive and conceptual implications of pedagogical decisions.

New Economy, New Pedagogy?

In England, the government wishes to integrate education into the economy. In this endeavour it has continued the previous Conservative government's stance on retaining direct, whole-class teaching in primary schools. It has retained the Office for Standards in Education (Ofsted). Standards of achievement in numeracy and literacy have increased. The country's international competitiveness is assumed to have been enhanced. But questions are being raised about this approach, mainly in government departments other than the Department for Education and Skills, notably in the Department for Media, Culture and Sport and in the Department for Industry. Their concerns can be put plainly: the Ofsted-endorsed traditional pedagogy will not well serve an emerging knowledge-based economy wherein creativity is at a premium. For its part, the government is ambivalent, seemingly reluctant to loosen its pedagogical grip on primary education, yet beginning to realise that pedagogical change is needed. Its reluctance seems not to turn on the lack of an academic basis for a new pedagogy, but on the financial implications of introducing a more progressive pedagogy which would require higher teacher-pupil ratios, and on the political risks of endorsing a more 'radical' pedagogy. The analysis is set within the context of economic globalisation and postmodern culture.

Teachers' Interpretations of Effective Whole-class Interactive Teaching in Secondary Mathematics Classrooms

Prompted by ongoing concerns over standards of numeracy, eight mathematics teachers from four secondary schools in south Wales formed a teacher inquiry group to research the impact of introducing whole-class interactive teaching strategies into their own practice. Possible teaching approaches and activities were developed and agreed during group meetings. These were trialled by the teachers during their normal mathematics lessons. Lesson observations, interviews with teachers and discussions at the group meetings, however, indicated that the implementation of the approaches varied significantly across teachers. This paper analyses the variation in interpretations and teaching styles, and discusses their impact on the quality of the classroom discourse. The determining features discerned within the classroom dialogue included the extent to which pupils were encouraged to reflect on their mathematical knowledge, and the ways in which teachers were able to scaffold pupils' learning.

Small-group composition and peer effects

This paper reviews research on grouping of students within classes and its effects on learning. Primary consideration is given to grouping and mixing students by ability, though consideration is also given to grouping and mixing students by ethnicity and gender as well as to research on the effects of group size. Results of meta-analyses of grouping show a small but meaningful advantage of forming students into groups for instruction as compared to using whole-class instruction. In teacher-led, homogeneous ability groups, peer effects result from the normative environment to the extent that peers contribute to norms for behavior, constructed through cycles of reciprocal teacher–student interaction. In peer-led, heterogeneous ability groups, peer effects stem directly from group interactions and discourse among students that lead to cognitive restructuring, cognitive rehearsal, problem solving, and other forms of higher-level thinking. Similarly, in groups of different ethnic and gender composition, peer effects stem from interactions among students according to their perceived status and relative influence within the groups. We argue that these peer influences interact with instructional processes to mediate the effects of group composition on students’ learning.

Relationships between instructional language and primary students' learning.

Causal modeling was used to examine how primary students’ language ability interacted with pace and redundancy of instructional language during an expository science lesson to explain students’ attention and learning. Language ability and pace of the instructional language, mediated by students’ attention to the lesson, accounted for significant variance in learning outcomes. Higher language ability related to greater learning. Overall, slow-paced instructional language was positively related to learning, but students attended less to it than to fast-paced talk. Students with special needs attended significantly less and learned less, whereas students not so identified attended slightly less but learned more. Teachers’ talk matters, but because instructional language impacts differentially on students, heuristics for modifying it are not straightforward. In communicative settings involving large groups, most individuals do more listening than talking. This is particularly so for students in many elementary classrooms, where the teacher does up to 80% of the talking, and the remaining 20% of the talking time is shared by all of the students (Cazden, 1988). Despite recent changes in educational practices (Lapadat 2000a, 2000b; Pappas, Kiefer, & Levstik, 1999), this nonreciprocity of talking time persists across educational levels. In such classrooms, students’ receptive language knowledge and the listening strategies they use have a close relationship with their academic learning outcomes. However, even in classrooms where talk is distributed more equitably than in typical whole-class expository teaching, such as in constructivist, small group, and cooperative learning models (Lauritzen & Jaeger, 1997), students’ ability to engage, listen, and respond are still important determinants of both communicative and academic success. Roth and Spekman (1989) called for more research focusing on students’ knowledge of and ability to understand and use language, pointing out that this is crucial in coming to understand how students understand, participate in, and learn from the interactions that make up instruction. Even during expository instruction, talk is constructed interactively (O’Connor & Michaels, 1996; Pappas et al., 1999). Just as young primary school students have the task of attending to and understanding the teacher’s talk (and peers’ talk) in order to learn in school, so too does the teacher need to talk in ways that students understand in order to teach effectively (Derwing, 1991). If students have insufficient linguistic knowledge or do not engage, or if teachers fail to adjust their instructional language, academic learning will be affected. As expository instruction is so frequently used in schools, it is all the more important to do it well. In classrooms in which talk is distributed differently than in wholeclass expository teaching, teachers’ effective use of instructional language in small groups or with individuals, as well as in segments of whole-class instruction, remains a critical component of effective teaching (Lindsay, 1996; Merritt, 1982; O’Connor & Michaels, 1996). This is a challenging task, as students bring diverse understandings to learning, based on their prior knowledge, language skills, cognitive processing abilities, cultural perspectives, motivations, and interests.

Achievement effects of multigrade and monograde primary schools in the Turks and Caicos Islands

This article reports on a study that compares the reading progress of students in multigrade schools with the reading progress of students in monograde schools. The research was conducted in a small island state in the Caribbean. The results of the study indicate that multigrade schools are particularly effective at promoting the reading progress of low-achieving students. It is hypothesised that this is partly because of differences in the approach to instruction in multigrade and monograde classrooms. Whereas monograde classrooms tend to be characterised by undifferentiated whole-class teaching, in multigrade classes students have more opportunity to engage in small-group work. The implications of the findings are explored for policy, practice and research.

The metamorphosis of the ‘virtuoso’: pedagogic patterns in Hong Kong primary mathematics classrooms

Classrooms in the East Asian region are primarily portrayed as teacher-centred, with a tense atmosphere stressing mechanical or rote learning. Using data derived from a project that evaluated the impact of a major curriculum reform in Hong Kong, this paper argues that these descriptions fail to capture many salient features of pedagogy. A total of 122 Primary One mathematics lessons were observed in twelve schools over a three-year period from 1995 to 1998. Analysis indicated that although whole-class instruction was still the dominant mode of pedagogy, the role of the teacher as a virtuoso performing to a whole class was being modified.

Using Guided Notes to Improve the Academic Achievement of Incarcerated Adolescents with Learning and Behavior Problems

This investigation examined the effects of guided notes on the academic performance of seven students with learning and behavior problems, who were in a medium-security juvenile detention center. The findings of this study indicate that using guided notes could be an effective strategy for improving the academic performance of incarcerated youths with learning and behavior problems. The results of this study replicate earlier studies in which guided notes were used during whole-class instruction (i.e., Courson, 1989; Lazarus 1991, 1993; Pados, 1989).