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.     

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.     

教师课堂教学行为对学生学业成绩的影响:一个跨文化研究

教师一向被认为是影响学生学业成绩的重要因素。本研究采用第三次国际数学和科学研究TIMSS2003中的数据,以学生数学成绩为因变量,教师课堂教学行为为自变量,使用多层线性回归的方法,比较了美国、瑞典、日本和香港这四个国家(地区)教师课堂教学行为对学生学业成绩的影响。研究结果发现,教师特定的行为因素,教学的准备、对作业的重视、对考试的重视、对推理和问题解决的重视、电脑的使用确实能有效影响美国和瑞典的学生成绩,但对两个亚洲国家(地区)没有影响;教师的性别、教龄、教育水平、所学专业和教师资格再次被证实对学生成绩没有显著影响;学生的家庭和自身的因素(如学生年龄、性别、完成作业的时间,对数学的自信和对数学的评价)能够对学生成绩产生重要影响。     

Classroom Interactions: Gender of Teacher,Gender of Student,and Classroom Subject

An observational study investigated the effects of gender of teacher, gender of student, and classroom subject (mathematics vs. English literature/language) on teacher–student interactions. A total of 597 high school students (294 males and 303 females) and 36 teachers (28 males and 8 females) were observed in either 18 mathematics classes or 18 literature/language classes. Students and teachers were predominately Caucasian, with the majority of students from a lower- or middle-class background. Observations were coded using the interactions for sex equity in classroom teaching (INTERSECT) observational instrument. It was found that female mathematics teachers, male literature/language teachers, and female literature/language teachers tended to interact somewhat more with male students than with female students. This tendency was not the result of male students having initiated more direct verbal interactions with teachers.     

Improving Classroom Quality with The RULER Approach to Social and Emotional Learning: Proximal and Distal Outcomes

The RULER Approach to Social and Emotional Learning (“RULER”) is designed to improve the quality of classroom interactions through professional development and classroom curricula that infuse emotional literacy instruction into teaching–learning interactions. Its theory of change specifies that RULER first shifts the emotional qualities of classrooms, which are then followed, over time, by improvements in classroom organization and instructional support. A 2-year, cluster randomized controlled trial was conducted to test hypotheses derived from this theory. Sixty-two urban schools either integrated RULER into fifth- and sixth-grade English language arts (ELA) classrooms or served as comparison schools, using their standard ELA curriculum only. Results from multilevel modeling with baseline adjustments and structural equation modeling support RULER’s theory of change. Compared to classrooms in comparison schools, classrooms in RULER schools exhibited greater emotional support, better classroom organization, and more instructional support at the end of the second year of program delivery. Improvements in classroom organization and instructional support at the end of Year 2 were partially explained by RULER’s impacts on classroom emotional support at the end of Year 1. These findings highlight the important contribution of emotional literacy training and development in creating engaging, empowering, and productive learning environments.     

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.     

School Counselor Inclusion: A Collaborative Model to Provide Academic and Social‐Emotional Support in the Classroom Setting

The increasingly diverse student demographics reflect a myriad of needs in the interrelated arenas of educational achievement, social‐behavioral adjustment, and career development, while federal legislation, the ethical standards of the American School Counselor Association (ASCA; 2004a), and the ASCA (2005a) National Model have emphasized academic achievement and success for all students. This article describes a new model of school counselor “inclusion” that involves collaboration with classroom teachers and changes the setting of school counselor interventions to the classroom for small‐group and individual work.     

Creativity and Cooperation in the Elementary Music Classroom*

The author examines attitudes towards, and the effects of focus on, creativity and cooperation in the elementary music classroom. First, elementary music teachers were interviewed regarding their values towards creativity and cooperation. Then, a curriculum was field tested that utilized cooperative learning and emphasized activities designed to encourage creative thinking and problem solving. A pretreatment-posttreatment study, with experimental and control group, was conducted to measure actual changes in student levels of creativity and attitudes towards cooperation. A follow-up of creativity measures was conducted four years later. Results indicate that elementary music teachers can adapt cooperative learning models to their teaching and can, short-term, influence students' levels of creativity and attitudes towards cooperation. Implications and opportunities for social-psychological creativity research and classroom educators are discussed. In 1983, Goodlad observed that, in general, there was a “gap between the rhetoric of individual flexibility, originality, and creativity … and the cultivation of these [things] in our schools” (p. 241) and that schools provided students with little opportunity to develop “satisfying relations with others based on respect, trust, cooperation, and caring” (p. 240). Goodlad encouraged teachers in the arts to provide opportunities for creative problem solving and to “boldly demonstrate the potentiality for doing through the arts what cannot be done readily through the other fields” (p. 238). His appeal to arts teachers is reminiscent of Maslow (1968):     

Classroom discourse and the distribution of student engagement

Research in the social psychology of achievement motivation stresses the contribution of the classroom motivational context to problems of student engagement among low achieving students. This analysis contributes to that literature through a focused analysis of English and language arts instruction during the middle school years. Using data from the Partnership for Literacy Study the author investigates the relationship between classroom evaluation during question and answer sessions and two forms of student engagement, participation in classroom discourse, and student effort on classroom and homework assignments. When teachers focus on provoking student thought and analysis, and postpone evaluation during question and answer sessions by engaging in dialogic instruction, levels of student effort are more evenly distributed among students. Moreover, the relationship between levels of initial achievement and student effort is weaker in classrooms where teachers incorporate elements of dialogic instruction into question and answer sessions. However, dialogic instruction had no effect on the distribution of participation in classroom discourse itself.     

Embodied learning: Teaching sexuality and religion to a changing student body

Sexuality, more so than other subject areas, magnifies the embodied nature of teaching and learning as well as conspicuously silences open dialogue given its taboo status in many religious and theological contexts. Yet, student learning about sexuality that incorporates knowledge of and about religion, in particular, may greatly improve the public discourse about sexuality through our students as responsible citizens and as leaders in their chosen professions. To bridge this gap, through a year‐long collaboration, a group of professors and instructors with expertise and experience teaching sexuality and religion in a variety of disciplines and diverse institutional and religious contexts developed, tested, and refined classroom teaching strategies to shift from a content‐based “subject matter” to an embodied learning experience, resulting in perspective transformation as a primary student‐learning outcome. Findings in the form of “guiding questions,” encourage instructors to attend to contextual, experiential, and performative aspects of the classroom environment.     

Technology and At-Risk Young Readers and their Classrooms

This study examined the ways in which 18 first-grade teachers and their students in 11 high-risk urban schools began to use literacy-focused technology. The goal of the study was to observe the technology in use by the students, to observe the classroom dynamics and teachers’ instructional choices centered around technology use, to look at student learning, and to investigate student and teacher perceptions and beliefs as they began to use technology for literacy. Analyses of classroom and pupil observational data and of student performance data indicated positive effects of the literacy technology on classroom instruction and student literacy achievement. Further, interviews of students and teachers confirmed that the literacy technology was perceived as engaging and effective by both groups of stakeholders. The study also generated implications for further research and practice in schools struggling to make change.     

Instructional development for teachers in higher education: Effects on students’ perceptions of the teaching–learning environment

Background. Although instructional development for teachers has become an important topic in higher education, little is known about its actual impact. In particular, evidence regarding the impact of teachers’ instructional development on students’ perceptions of the teaching–learning environment is scarce. Aims. The impact of an instructional development programme for beginning university teachers on students’ perceptions of the teaching and learning environment was investigated. We also explored whether this impact is dependent on class size and student level (first years vs. non‐first years). Sample. Quantitative data were gathered from more than 1,000 students at pre‐ and post‐tests, using a quasi‐experimental design. Method. A multi‐level analysis was conducted in which five models were estimated. Results. A basic model made clear that teachers did differ from each other with respect to the dependent variables concerned; however, differences in scale scores also resulted to a large extent from differences between students. A second model, in which the moderating impact by way of teacher characteristics, context, and student characteristics was not taken into account, reported no significant effect of training. A third model, examining the net impact of instructional development revealed some impact, which was, remarkably, negative. A first interaction model proved a differential impact of instructional development for teachers teaching first years and those teaching non‐first years. A second one showed that the impact of training depended on the number of students one teaches. Conclusions. Instructional development for teachers in higher education does not easily result in effects on students’ perceptions of the teaching and learning environment. Perspectives for further research into instructional development are discussed.     

Mathematics instruction in Head Start: Nature,extent, and contributions to children's learning

This study employed the most recent (2006) cohort of the nationally representative Family and Child Experiences Survey (FACES) to explore the nature of mathematics instruction in Head Start and the child, family, and teacher factors that contribute to children's mathematics learning over the preschool year. In total, 2501 preschoolers and their families, as well as their teachers (n = 335), participated in the study from fall 2006 to spring 2007. Results showed that teachers reported frequent mathematics instruction, although direct observations did not entirely confirm this frequency. A variety of factors predicted children's mathematics knowledge at Head Start entry, and several – including instructional quality – were linked to learning over time. No thresholds in instructional quality emerged. Overall, this study provides new information about classroom mathematics instruction and child learning among the nation's most vulnerable early learners.     

An ethnographic inquiry of cooperative learning implementation

Qualitative research methods were employed to explore variations in teacher implementation of a research-based model of cooperative learning. Participants included five middle school math and science teachers who were trained in the Johnson, D.W. and Johnson, R.T. [Johnson, D. W., & Johnson, R. T. (1983). The socialization and achievement crisis: Are cooperative learning experiences the answer? Applied Social Psychology, 4, 199-124.] model of cooperative learning. Implementation was examined via interview and observation. Principles from cognitive psychology defined constructs for study, which included teacher concepts, plans, and enactment of cooperative learning in the classroom. Study design included features characteristic of ethnographic inquiry: prolonged engagement, purposeful sampling, persistent observation, multiple source data collection, and recursive interpretation. Triangulation of data sources revealed that relationships between concepts, plans and enactment were mediated by teaching style, teaching context, and degree of teaching expertise. Findings suggest that when attempting to implement cooperative learning lessons, teacher may benefit from attention to teacher and student roles, curricular requirements, instructional time, and classroom management skills. Findings further demonstrate the important contributions of qualitative research to the cooperative learning literature.     

Linking Teacher Instruction and Student Achievement in Mathematics: The Role of Teacher Language

Although high-quality early educational environments are thought to be related to the growth of children’s skills in mathematics, relatively little is known about specific aspects of classroom instruction that may promote these abilities. Data from a longitudinal investigation were used to investigate associations between teachers’ language while teaching mathematics and their students’ growth in mathematical skill during the 2nd grade. Specifically, the extent to which mathematics lessons included cognitive-processing language (CPL)—instruction that is rich in references to cognitive processes, metacognition, and requests for remembering—was related to changes in students’ math achievement. Demonstrating the role of the language of instruction, the findings indicated that children whose 2nd-grade teachers included greater amounts of CPL during instruction evidenced greater growth in math fluency and calculation than did their peers whose teachers employed lower levels of CPL.     

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.     

Mathematics beliefs and instructional strategies in achievement of elementary-school students in Japan: results from the TIMSS 2003 assessment

Recent findings concerning mathematics assessment indicate that students in Japan consistently score above international averages. Researchers have examined specific mathematics beliefs and instructional strategies associated with mathematics achievement for students in Japan. This study examined relationships among self-beliefs, classroom instructional strategies, and mathematics achievement for a large national sample of students (N=4,207) from the TIMSS 2003 international sample of fourth graders in Japan. Several significant relationships between mathematics beliefs and test scores were found; a number of classroom teaching strategies were also significantly associated with test scores. However, multiple regression using the complete set of five mathematics beliefs and five instructional strategies explained only 25.1% of the variance in mathematics achievement test scores.     

A Developing Approach to Studying Students’ Learning through Their Mathematical Activity

We discuss an emerging program of research on a particular aspect of mathematics learning, students’ learning through their own mathematical activity as they engage in particular mathematical tasks. Prior research in mathematics education has characterized learning trajectories of students by specifying a series of conceptual steps through which students pass in the context of particular instructional approaches or learning environments. Generally missing from the literature is research that examines the process by which students progress from one of these conceptual steps to a subsequent one. We provide a conceptualization of a program of research designed to elucidate students’ learning processes and describe an emerging methodology for this work. We present data and analysis from an initial teaching experiment that illustrates the methodology and demonstrates the learning that can be fostered using the approach, the data that can be generated, and the analyses that can be done. The approach involves the use of a carefully designed sequence of mathematical tasks intended to promote particular activity that is expected to result in a new concept. Through analysis of students’ activity in the context of the task sequence, accounts of students’ learning processes are developed. Ultimately a large set of such accounts would allow for a cross-account analysis aimed at articulating mechanisms of learning.     

Promoting Freedom,Responsibility, and Learning in the Classroom: The Learning Covenant a Decade Later

Abstract. This essay discusses an approach to teaching religious studies in a general education or core curriculum that I have experimented with for the last decade, which I call the “Learning Covenant.” The Learning Covenant brings together various pedagogical theories, including transformational, experiential, contract, and cooperative learning, in an attempt to address diverse learning styles, multiple intelligences, and student learning assessment. It has advantages over more traditional teacher‐directed approaches to teaching, including meeting student resistance to “required” courses head‐on by inviting them to identify learning needs regardless of chosen vocation and meeting them in the context of a religious studies course, recognizing the multiple ways in which students learn and providing a variety of opportunities for students to express their learning, and allowing students opportunity to take increased responsibility for their own learning. The essay will focus on the Learning Covenant's development, components, strengths, and drawbacks.     

Developing a Learning Progression for Curriculum,Instruction, and Student Learning: An Example from Mathematics Education

Learning progressions have been demarcated by some for science education, or only concerned with levels of sophistication in student thinking as determined by logical analyses of the discipline. We take the stance that learning progressions can be leveraged in mathematics education as a form of curriculum research that advances a linked understanding of students learning over time through careful articulation of a curricular framework and progression, instructional sequence, assessments, and levels of sophistication in student learning. Under this broadened conceptualization, we advance a methodology for developing and validating learning progressions, and advance several design considerations that can guide research concerned with engendering forms of mathematics learning, and curricular and instructional support for that learning. We advance a two-phase methodology of (a) research and development, and (b) testing and revision. Each phase involves iterative cycles of design and experimentation with the aim of developing a validated learning progression. In particular, we gathered empirical data to revise our hypothesized curricular framework and progression and to measure change in students. thinking over time as a means to validate both the effectiveness of our instructional sequence and of the assessments designed to capture learning. We use the context of early algebra to exemplify our approach to learning progressions in mathematics education with a focus on the concept of mathematical equivalence across Grades 3-5. The domain of work on research on learning over time is evolving; our work contributes a broadened role for learning progressions work in mathematics education research and practice.