Do organizational conditions influence teacher implementation of effective classroom management practices: Findings from a randomized trial

Although there is a growing evidence base about effective classroom management practices, teacher implementation of these practices varies due to a number of factors. A school's organizational health is one aspect of the broader social environment that has been hypothesized to influence implementation of interventions. Yet, empirical evidence is limited on whether organizational contexts can influence teacher implementation of effective interventions and subsequently, classroom environments and student outcomes. In the present study, teachers in an urban school district were randomly assigned to receive training in the Incredible Years Teacher Classroom Management program (IY TCM), a classroom management intervention. We examined how teacher perceptions of their school environment moderated intervention effects for previously established treatment outcomes – implementation of effective classroom methods, students' social behaviors, emotional regulation, and social competence. Results showed that treatment effects on teacher implementation and student outcomes were moderated by teachers' sense of affiliation to their school. Specifically, main effects on implementation of effective classroom management strategies were only observed among teachers whose perceptions of initial teacher affiliation was low or average; whereas main effects on student outcomes were only found for teachers with initial high levels of affiliation.     

A Study of Whole Classroom Mathematical Discourse and Teacher Change

This article presents a comparison of the first 2 years of an experienced middle school mathematics teacher's efforts to change her classroom practice as a result of an intervening professional development program. The teacher's intention was for her teaching to better reflect her vision of reform-based mathematics instruction. We compared events from the 1st and 2nd year's whole class discussions within a multilevel framework that considered the flow of information and the nature of peer- and teacher-directed scaffolding. Discourse analyses of classroom videos served both as an analytic tool for our study of whole classroom interactions, as well as a resource for promoting discussion and reflection during professional development meetings. The results show that there was little change in the teacher's specific goals and beliefs in light of a self-evaluation of her Year 1 practices, but substantial changes in how she set out to enact those goals. In Year 2, the teacher maintained a central, social scaffolding role, but removed herself as the analytic center to invite greater student participation. Consequently, student-led discussion increased manifold, but lacked the mathematical precision offered previously by the teacher. The analyses lead to insights about how classroom interactions can be shaped by a teacher's beliefs and interpretations of educational reform recommendations.     

教师变量对小学生数学学习观影响的多层线性分析

32名小学数学教师与这些教师所教班级的1691名学生参与了本研究.两个测量工具评价了教师的数学学科知识与学科教学知识,对教师的55节数学课进行了录像;并按照学习任务的认知水平与课堂对话的特点进行了编码,采用问卷法测查了学生对数学学习的看法与态度.多水平分析表明:教师的学科教学知识、课堂学习任务的认知水平、课堂师生对话的权威来源与教师运用学生想法的程度对学生数学学习观具有显著预测作用;教师的学科知识对学生数学学习观的预测未达到显著性水平.     

Investigating Links from Teacher Knowledge,to Classroom Practice,to Student Learning in the Instructional System of the Middle-School Mathematics Classroom

Using data collected in 125 seventh-grade and 56 eighth-grade Texas classrooms in the context of the “Scaling Up SimCalc” research project in 2005–07, we examined relationships between teachers’ mathematics knowledge, teachers’ classroom decision making, and student achievement outcomes on topics of rate, proportionality, and linear function—three important and cognitively demanding prealgebra topics. We found that teachers’ mathematical knowledge was correlated with student achievement in only one study out of three. We also found a lack of correlations between teachers’ mathematical knowledge and critical aspects of instructional decision making. Curriculum and other learning resources (e.g., technology, student–student interactions) are clearly important factors for student learning in addition to, and in interaction with, teachers’ mathematical knowledge. Our results suggest that mathematics knowledge for teaching may have a nonlinear relationship with student learning, that those effects may be heavily mediated by other instructional factors, and that short-term content knowledge gains in teacher workshops may not persist in classroom instruction. We discuss a need in the field for richer models of how “mathematical knowledge for teaching” works in the context of complete instructional systems.     

An Investigation of Teachers' Beliefs of Students' Algebra Development

Elementary, middle, and high school mathematics teachers (N = 105) ranked a set of mathematics problems based on expectations of their relative problem-solving difficulty. Teachers also rated their levels of agreement to a variety of reform-based statements on teaching and learning mathematics. Analyses suggest that teachers hold a symbol-precedence view of student mathematical development, wherein arithmetic reasoning strictly precedes algebraic reasoning, and symbolic problem-solving develops prior to verbal reasoning. High school teachers were most likely to hold the symbol-precedence view and made the poorest predictions of students' performances, whereas middle school teachers' predictions were most accurate. The discord between teachers' reform-based beliefs and their instructional decisions appears to be influenced by textbook organization, which institutionalizes the symbol-precedence view. Because of their extensive content training, high school teachers may be particularly susceptible to an expert blindspot, whereby they overestimate the accessibility of symbol-based representations and procedures for students' learning introductory algebra.     

Seeing the Complexity of Standing to the Side: Instructional Dialogues

In this article, we analyze the complexity of using instructional dialogues in the teaching of mathematics. We trace a 10-lesson unit on functions and their graphs taught by Magdalene Lampert to a 5th-grade classroom. We use this trace to help analyze and systematize the complexity of the classroom discourse. Analysis shows that Lampert's instructional dialogues served 2 purposes: They developed coconstructed instructional explanations of the key mathematical concepts, and they allowed the class to navigate a meaningful path through the relevant mathematics. In creating an instructional explanation, the class as a group flagged the central questions, coordinated and differentiated between the central ideas, and anticipated and made public potential errors. Although misconceptions were often raised as part of the public knowledge space, students individually and collectively resolved these misconceptions publicly through the dialogues. The path through the mathematics was supported through the careful use of agendas, sets of conditions under which an aside was taken from the agendas, and the careful problematizing of the mathematics. Routines, metatalk, and the crafting and maintenance of the intellectual climate played important roles in supporting the instructional dialogues. In the cases of routines and metatalk, we make comparisons to other instances of expert teaching. We also show evidence of student engagement and significant student learning that transcended individual participation patterns. We explore implications for teacher education.     

Teacher practices associated with students' sense of the classroom as a community

Data from observations of 232 elementary classrooms and from student questionnaires were used to test a model linking teacher classroom practices to students' sense of the classroom as a community (assessed by questionnaire) through intermediate effects on students' classroom behavior. The model was generally confirmed and showed that teacher practices (emphasis on prosocial values, elicitation of student thinking and expression of ideas, encouragement of cooperation, warmth and supportiveness, andreduced use of extrinsic control) were related to student classroom behaviors (engagement, influence, andpositive behavior), which, in turn, were related to students'sense of community. Teachers' encouragement of cooperative activities appeared to be particularly important in this sequence. The appropriateness of the model was tested for schools serving populations that were both high and low in level of poverty, and all estimates of path coefficients were found to be invariant across these groups.     

Developmental dynamics between mathematical performance,task motivation,and teachers' goals during the transition to primary school

Background. It has been suggested that children's learning motivation and interest in a particular subject play an important role in their school performance, particularly in mathematics. However, few cross‐lagged longitudinal studies have been carried out to investigate the prospective relationships between academic achievement and task motivation. Moreover, the role that the classroom context plays in this development is largely unknown. Aims. The aim of the study was to investigate the developmental dynamics of maths‐related motivation and mathematical performance during children's transition to primary school. The role of teachers' pedagogical goals and classroom characteristics on this development was also investigated. Sample. A total of 196 Finnish children were examined four times: (0) in October during their preschool year; (1) in October and (2) April during their first grade of primary school; and (3) in October during their second grade. Method. Children's mathematical performance was tested at each measurement point. Task motivation was examined at measurement points 2, 3, and 4 using the Task‐value scale for children. First‐grade teachers were interviewed in November about their pedagogical goals and classroom characteristics. Results and conclusions. The results showed that children's mathematical performance and related task motivation formed a cumulative developmental cycle: a high level of maths performance at the beginning of the first grade increased subsequent task motivation towards mathematics, which further predicted a high level of maths performance at the beginning of the second grade. The level of maths‐related task motivation increased in those classrooms where the teachers emphasized motivation or self‐concept development as their most important pedagogical goal.     

The relations between students' sense of school belonging,perceptions of school kindness and character strength of kindness

This study explored the associations between secondary school students' sense of school belonging, their perceptions of school kindness, and character strength of kindness, and examined possible differences in these constructs across gender groups. The study, which included 1973 Hong Kong secondary school students, revealed that students' sense of school belonging was positively correlated with their perceptions of school kindness at the school and student levels (0.021 and 0.185, respectively). Furthermore, students' sense of school belonging was positively linked to character strength of kindness at the student level, although this relationship was found to be non-significant at the school level. At both levels of analysis, the positive relationships between students' perceptions of school kindness and character strength of kindness were significant. In addition, girls reported higher levels of character strength of kindness than boys. The findings of this study provide a better understanding of the relationships between sense of school belonging, school kindness, and character strength of kindness. Implications for research are also discussed.     

Spirituality as Struggle: Poetics,experience and the place of the spiritual in educational encounter

This paper begins to explore and interpret the unsatisfactory conditions surrounding the term spirituality. It finds in this unsatisfactoriness a set of contradictions producing a sense of struggle. Using poetry, narrative and experience, it locates spirituality in contexts of struggle. It argues that if spirituality can be interpreted in certain senses as struggle, spiritual education (or development) becomes education in and for struggle. This in turn suggests lessons for our future treatment of, and practical approach to, world religions and other forms of experience in the classroom.     

Avoiding misinterpretations of Piaget and Vygotsky: Mathematical teaching without learning,learning without teaching,or helpful learning-path teaching?

This article provides an overview of some perspectives about special issues in classroom mathematical teaching and learning that have stemmed from the huge explosion of research in children's mathematical thinking stimulated by Piaget. It concentrates on issues that are particularly important for less-advanced learners and for those who might be having special difficulties in learning mathematics. A major goal of the article is to develop a framework for understanding what effective mathematics teaching and learning is, because doing so is so important for struggling students and for research about them. Piaget's research had a fundamental influence on the on-going tension between understanding and fluency in the classroom, supporting efforts toward increasing understanding. But in some countries, misinterpretations of Piaget led to practices that are counterproductive for children, especially struggling learners. Such misinterpretations are identified and a more balanced approach that also draws on Vygotsky is described—a learning-path developmentally-appropriate learning/teaching approach.     

How Much Does Creative Teaching Enhance Elementary School Students' Achievement?

This study examined the relationship between creative teaching and elementary students' achievement gains. Forty‐eight upper elementary school teachers' classroom instruction was observed and evaluated over the course of 8 different lessons throughout the year. For each teacher, during each lesson, both a creative teaching frequency score and a quality score were derived. These scores were then used as predictor variables in a structural equation model to determine the magnitude of the relationship between creative teaching and classroom achievement gains in reading, language, and mathematics. Our results demonstrated that (a) the majority of teachers do not implement any teaching strategies that foster student creativity; (b) teachers who elicit student creativity turn out students that make substantial achievement gains; and (c) classrooms with high proportions of minority and low‐performing students receive significantly less creative teaching.     

Regulation of Teacher Elicitations in the Mathematics Classroom

Using the perspective of instructional conversation, we investigated how one teacher regulated student participation and conceptual reasoning in the middle-school mathematics classroom. We examined the elicitations—questions and provocative statements—made by the teacher over a four-day algebra lesson. Analyses showed how the teacher systematically regulated the level of cognitive complexity of his elicitations in reaction to students' responses. When students gave inaccurate or incomplete answers, the teacher tended to reduce the level of cognitive complexity needed to respond to a subsequent elicitation, with the apparent impact being that he scaffolded participation and reasoning. When students provided responses that were mathematically accurate, the teacher usually increased the elicitation level, which subsequently engaged students in more sophisticated forms of reasoning.     

The Structure of Frege's Thoughts

Fregean thoughts (i.e. the senses of assertoric sentences) are structured entities because they are composed of simpler senses that are somehow ordered and interconnected. The constituent senses form a unity because some of them are ‘saturated’ and some ‘unsaturated’. This paper shows that Frege's explanation of the structure of thoughts, which is based on the ‘saturated/unsaturated’ distinction, is by no means sufficient because it permits what I call ‘wild analyses’, which have certain unwelcome consequences. Wild analyses are made possible because any ‘unsaturated’ sense that is a mode of presentation of a concept together with any ‘saturated’ sense forms a thought. The reason is that any concept can be applied to any object (which is presented by a ‘saturated’ sense). This stems from the fact that Frege was willing to admit only total functions. It is also briefly suggested what should be done to block wild analyses.     

Access Through Compensation: Emancipatory View of a Mathematics Learning Disability

Abstract

In this article, we provide a novel view of mathematics learning disability (MLD) by studying a student with an MLD (Dylan) who had compensated so effectively that she was able to major in statistics. We push back on the dominant deficit model used in studies of MLD, and consider issues of access and compensation from a Vygotskian theoretical frame. Through 8 videotaped interview sessions, we identified that Dylan’s primary difficulties were with mathematical notation and number sense, which resulted in issues accessing standard mathematical forms. Analysis revealed 8 compensatory strategies that Dylan used to address these issues of access. We frame our approach as emancipatory research. Dylan was involved in all phases of the study’s design, implementation, analysis, and dissemination, and is the second author. This work acknowledges that individuals with disabilities have research agendas of their own and have critical insight to share about the lived experience of their disability.     

Making Numbers Come to Life: Two Scoring Methods for Creativity in Aurora's Cartoon Numbers

Although creativity has long been recognized as an important aspect of mathematical thinking, both for the advancement of the field and in students' developing expertise in mathematics, assessments of student creativity in that domain have been limited in number and focus. This article presents an assessment developed for creativity that provides a score for mathematical creativity (MaC) in addition to a score for general creativity in the numeric domain, or what we might call numerical creativity (NuC). We developed different rating scales for each and then explored how each scoring method accounts for the students' mathematical/numerical and creative skills. The psychometric properties for both scoring approaches were examined. Each method was shown to reflect different relationships with other performance tests. In addition, it is proposed that MaC may provide useful insight into students' levels of adaptive expertise in mathematics, as reflected by their ability to apply mathematical knowledge (i.e., language, operations, concepts) to novel situations, representing an informative supplement to performance indicators of math achievement.     

Learning to Notice Mathematics Instruction: Using Video to Develop Preservice Teachers' Vision of Ambitious Pedagogy

Video is used extensively in teacher preparation, raising questions about what and how preservice teachers learn through video observation and analysis. We investigate the development of candidates' noticing of ambitious mathematics pedagogy in the context of a video-based course designed to cultivate ways of seeing and interpreting classroom interactions. Qualitative analysis of candidates' observations of teaching at the beginning and end of the course generated a framework of practices and associated approaches for noticing instructional interactions. The 3 practices include attending to features of instruction, elaborating on observations, and integrating observations to reason about instruction. Findings reveal that variations in candidates' noticing was tied to their attention to the details of the features of ambitious pedagogy and to the extent to which they integrated observations to examine the relation between student thinking, teaching practice, and mathematical content.