Representations of teaching and standards-based reform: are we closing the debate about teacher education?

Since the mid-eighties, national organizations have been working together in an effort to reform schools and, more specifically, to reform teaching. Paralleling the movement toward developing curriculum standards for students, professional standards for teachers have also been developed for the purpose of teacher education program accreditation. The objective of this national coalition is to strengthen the teaching profession and raise its standards—eventually enhancing the quality of student learning—by redesigning teacher licensing and accountability requirements for teacher education programs, and engaging teachers in on-going professional development. In this study we address three specific questions: (1) what representations of teaching and teachers are portrayed in the professional teaching standards, their related policies and assessment? (2) how are standards-based reform policies affecting teacher education programs? (3) what representations or conceptions of teaching and teachers are currently reflected in teacher education programs in the context of this reform? To address these questions two states were selected as test cases. Reform documents, policies and practices, as well as interviews with key participants in the reform (e.g., teacher educators, state-level administrators) are described and analyzed, and constitute the evidential basis for this study. The patterns emerging from the data indicate that teacher educators’ degrees of resistance or cooperation with externally imposed frameworks is influenced by their conception of teaching, education and its purpose. Further, as teacher educators uncritically participate in the standards-based movement it becomes impossible for them to entertain alternative perspectives on teaching and education outside of the framework provided to them by the standards.     

Effective Professional Development in Science and Mathematics Education: Teachers' and Facilitators' Views

This study compares the views of teachers and professional development facilitators about effective professional development (PD). We analyzed interviews with 72 teacher participants and 23 PD facilitators involved in nine science and mathematics PD projects. The teachers' themes for characterizing effective PD included classroom application, teacher as learner, and teacher networking. Similarly, the PD facilitators discussed effective PD as having classroom application and experiences for teachers as learners. In addition, PD facilitators shared the need to develop collegial relationships with teachers and improve teacher knowledge. These views correspond to some of the standards and recommendations described in policy and research documents on effective PD. Criteria of effective PD in these documents that the participants did not mention included: (1) challenging teachers' content and pedagogical content knowledge with transformative learning experiences, (2) encouraging teacher leadership for sustained support, and (3) focusing on student learning by instructing teachers on how to use student data to inform their teaching practice. Our findings have implications for designing PD that reflects the criteria of standards-based reform.     

从技能训练走向全人发展——美国绩效标准本位教师教育课程改革分析

在教师教育标准作为教师教育改革和保障教师教育质量的一个基本前提下,受到认知主义、建构主义学习理论和课堂评价的影响,美国推进了绩效标准本位教师教育课程的改革,改变过去过于注重技能训练的标准,从教师观、教学观、教学知识基础观和评价观上提出了新的标准,以期把教师培养成为一位专业的智力工作者,形成基于情境以学生为中心的教学观,让教师掌握多向度的、综合性的教学知识,注重教学整体质量的评价,促使高素质教师发展。这一改革构建了教学专业化的复杂性的理念,教师教育课程改革呈现出从技能训练走向综合发展、对个体和个体知识关怀的实践取向的全人发展观趋势,为优化我国教师教育课程改革提供了启示。     

Convergence of observer ratings and student perceptions of reform practices in sixth-grade mathematics classrooms

As part of a research project examining relationships between instructional practices and student cognitive and social outcomes in middle-school mathematics classes, external observers and students reported perceptions of teachers’ instructional practices. The extent to which students in classrooms identified by external raters as reform-oriented actually perceive instruction in ways aligned with reform principles has not been established. A 25-item observation protocol aligned with the reform practices called for in the Standards of the National Council of Teachers of Mathematics (NCTM) was used to develop a quantitative profile of instructional practices across two lessons in each of 28 classes of 15 participating teachers. Students in each of the observed classes completed a 49-item survey of their perceptions of instructional practices. As items for both the observation protocol and Student Survey were designed to measure alignment with the same dimensions of reform practice, the convergence of these two data sets was examined as a means to confirm the observation ratings. The findings show moderately strong correlations between ratings of external observers and perceptions of sixth-grade students across three dimensions (pedagogy, tasks and mathematical interactions) of reform-oriented teacher practice in mathematics classrooms. Implications of these findings for future research are discussed. The research in this article was supported by the National Science Foundation (NSF) under grant REC 0125868. The opinions expressed here are those of the authors and do not necessarily reflect the view of NSF. The research was also supported by the Roysters’ Fellowship to Mark Ellis from the Graduate School at the University of North Carolina at Chapel Hill.     

Designing Curriculum-Based Mathematics Professional Development for Kindergarten Teachers

This study examines the influence of a year-long mathematics professional development program on Kindergarten teachers’ beliefs, content knowledge, instructional practices, and their students’ achievement. The professional development program is grounded in the theoretical construct of learner-centered professional development and focuses on supporting teachers’ integration of standards-based pedagogies aligned with the Common Core State Standards in Mathematics. Data analysis included examining 15 Kindergarten teachers’ mathematics content knowledge, their beliefs about mathematics, their enactment of student-centered pedagogies, and student achievement on curriculum-based assessments. Findings indicated that teachers adopted more student-centered pedagogies and embraced more student-centered beliefs about mathematics teaching during their time in the project. Further, Kindergarten teachers also demonstrated gains in their mathematical content knowledge, and those content knowledge gains were linked to gains in student achievement.     

Teaching Engineering Practices

Engineering is featured prominently in the Next Generation Science Standards (NGSS) and related reform documents, but how its nature and methods are described is problematic. This paper is a systematic review and critique of that representation, and proposes that the disciplinary core ideas of engineering (as described in the NGSS) can be disregarded safely if the practices of engineering are better articulated and modeled through student engagement in engineering projects. A clearer distinction between science and engineering practices is outlined, and prior research is described that suggests that precollege engineering design can strengthen children’s understandings about scientific concepts. However, a piecemeal approach to teaching engineering practices is unlikely to result in students understanding engineering as a discipline. The implications for science teacher education are supplemented with lessons learned from a number of engineering education professional development projects.     

The Influence of Teachers’ Efficacy and Beliefs Regarding Mathematics Instruction in the Early Childhood Classroom

This was a correlational study conducted with a population of prekindergarten educators from a large, metropolitan school district. The purpose was to examine if there were relationships between and among early childhood teachers’ sense of self-efficacy, their beliefs about the importance of mathematics, and their mathematics instructional practices. Examining teachers’ efficacy and beliefs can inform educational practice and help to differentiate between more and less successful instructional practices when teaching mathematics in the early childhood classroom. Data were collected on teacher efficacy and teacher beliefs about the importance of mathematics with two self-report questionnaires. The hypothesis that the teachers higher in efficacy will rate the importance of mathematics higher on the teacher-belief scale than the teachers with lower efficacy was found to be true with this sample, but the correlation was weak. The level of efficacy of the early childhood teachers in this sample confirmed that in assessing their capabilities, they rate themselves high in instructional strategies, classroom management, and student engagement. The early childhood teachers did not rate their belief in mathematics as high as their efficacy. Observations of mathematics instructional practices were conducted with twenty teachers. It was hypothesized that the combination of high teacher efficacy and high teacher mathematics beliefs would show alignment with the presence of standards-based mathematics instructional practices. The results were not statistically significant. No correlation signals a need for more research to explore what other personal or external factors relate to mathematics instructional practices in the early childhood classroom. The research may inform pre kindergarten teachers and teacher educators about effective instructional strategies and knowledge needed to launch early childhood students on a developmentally appropriate pathway to mathematical literacy.     

Political rationales and ideological stances of the standards-based reform of teacher education in the US

Movements to reform teacher education are underway in many parts of the world, including Europe, Australia, New Zealand, and the US. These attempts at reform are motivated by various forces, but appear to reflect an international convergence toward uniformity, conformity, and compliance. Our purpose here is to analyze the forces and contradictions that currently shape the education of teachers and the nature of their work in the US. Given the scarcity of debate and research in the face of the sweeping implementation of reform mandates, we raise here critical questions about their political, philosophical, and intellectual integrity and their intended and unintended consequences for teaching and for teachers’ autonomy. In this article we analyze teacher education reforms in the US in three steps. First, we examine the policies that have shaped the implementation of standards-based reform in teacher education, the assumptions that underlie them, and the means by which they are promoted (e.g., standards, assessment, increased regulations). Second, we analyze these reform policies and practices in the context of globalization and the global economy, forces that seem to define the ideological stances of the reform. Finally, we conclude by considering the implications for teaching, teacher knowledge, and teacher education.     

Chinese teachers’ perceptions of academically oriented teacher preparation

Academically oriented teacher preparation, which prioritises subject matter knowledge for teaching, is still widely practised in Confucian societies. Few studies, however, have investigated the impact of this academic model on teaching practices in Confucian contexts. Drawing on interviews and classroom observations of six Chinese mathematics teachers, this study identifies the affordances and limitations of a typical academically oriented teacher preparation in today’s China. Although this helped the sampled teachers establish their initial self-efficacy for teaching it limited the teachers’ awareness of and their capacity for engaging all students to learn. The paper argues that academically oriented teacher preparation programmes in Confucian societies may need to reform their curricula so as to help their graduates advance both excellence and equity in education through their teaching.     

Aligning Mathematics Teacher Work Sample Content with Selected NCTM Standards: Implications for Preservice Teacher Education

Teacher Work Sample Methodology has been described as an alternative means/set of procedures for assessing teacher effectiveness in producing student learning that are more authentic than traditional means of teacher certification. To investigate the degree to which the methodology aligns with state/national standards, 50 work samples produced by student teachers at Western Oregon University between fall 1991 and spring 1999 were analyzed to determine: (1) the efficiency of Teacher Work Sample Methodology in moving state and national standards, for example, the NCTM standards, into the classroom; and (2) the extent to which Teacher Work Sample Methodology promotes alignment of standards, content, instruction and assessments of instruction. The research found that a majority of the student teacher work samples demonstrated weak alignment or no alignment between stated instructional objectives and selected NCTM Curriculum and Evaluation Standards (Problem Solving, Communication, Reasoning, and Connections). However, in most of the work samples, more than half of the pre/post-assessment methods (performance, knowledge) were aligned with the instructional objectives.     

How are Developmentally Appropriate or Traditional Teaching Practices Related to the Mathematics Achievement of General and Special Education Students?

Recently, developmentally appropriate practices have been distinguished from traditional practices and have been advocated as one way to reform primary general education classrooms. Relatively little research has examined the efficacy of developmentally appropriate versus traditional practices. In particular, concerns have been raised about the effectiveness of this approach for students with disabilities. This study examined the relationship between primary teachers' implementation of developmentally appropriate and traditional teaching methods and the mathematics achievement of general and special education students. Observations, interviews and questionnaires were used to measure the mathematics teaching practices used with general and special education students. Because developmentally appropriate and traditional teaching practices are often characterized in terms of a continuum, principal components methods were used to generate continuous composite variables that described teacher presentation, materials, grouping, and curriculum. The outcome measure was a curriculum- based measure of mathematics achievement. Principal components results showed that the composite variables most clearly associated with the developmentally appropriate v. traditional continuum were not related to mathematics achievement. Instead, consistent with previous research, achievement was associated with a reported measure of instruction that emphasized mathematical processing and strategy instruction. Further, a reported "laissez faire" method that emphasized individual student choice and treated special education students like general education students was negatively related to achievement, as was placement in special education class.     

多媒体技术在数学课堂教学中的应用

讨论了在数学教学过程中应用多媒体技术的意义和范围。指出,多媒体技术为数学教学提供了强有力的技术支撑,数学教师必须从素质教育的立场出发,改变教育观念,改革教学方法,面向全体学生,把以教师为中心的教学方式转变为以学生为中心的教学方式。遵循人的认知规律,强调学生的认知过程,改变重视结论、忽视认知过程的传统教学习惯。     

Cognitive Scientists Prefer Theories and Testable Principles With Teeth

The visions of mathematics classrooms called for by current educational reform efforts pose great challenges for kindergarten through Grade 12 schools and teacher education programs. Although a number of colleges and universities throughout the country are making changes in their teacher education programs to reflect these reform recommendations, we have little systematic information on the nature of these programs or their impact on prospective teachers. These issues are of central concern in the study-Learning to Teach Secondary Mathematics in Two Reform-Based Teacher Education Programs-that we draw on in this article. The article focuses on 1 preservice teacher's (Ms. Savant) knowledge, beliefs, and practices related to proof, tasks, and discourse. A situative perspective on cognition and components of teachers' professional knowledge frame our research. We examined data on Ms. Savant's experiences in her teacher education program to understand the influences of teacher education on her development as a mathematics teacher. This research indicates that Ms. Savant's teacher education experiences did make a difference in her development as a teacher. Her mathematics methods course provided a large collection of tasks, engaged her and her preservice colleagues in discourse, and provided her with both formal and informal experiences with proof-all of these experiences reflecting reform-based visions of mathematics classrooms. The situative perspective on cognition directed our attention to issues of compatibility of goals and visions across the various university and kindergarten through Grade 12 classroom settings, and it helped us to understand why some aspects of reform-based pedagogy are more easily learned than others: Why some ideas and practices learned as a student in the university setting are more easily transported to the novice teacher's kindergarten through Grade 12 field setting. We conclude that compatibility of these settings on several key dimensions is essential for the settings to reinforce each other's messages, and thus work in conjunction, rather than in opposition, to prepare reform-minded teachers.     

PROFESSIONAL NOTICING PRACTICES OF NOVICE MATHEMATICS TEACHER EDUCATORS

The focus on professional noticing in mathematics education has recently gained increased interest as researchers work to understand how and what is noticed and how this translates into practice. Much of this work has focused on the professional noticing practices of inservice teachers and preservice teachers, with less attention focused on those educating teachers. This research explores how novice mathematics teacher educators professionally notice as they engage in teaching experiments and create models of student’s mathematical thinking. Findings indicate the novice teacher educators are including some evaluative comments in their professional noticing practices but lack in-depth interpretive analysis about student thinking and rarely make connections between student’s thinking and the broader principles of teaching and learning. These findings provide evidence for the importance of supporting teacher educators with developing their abilities to professionally notice.     

MATHEMATICS TEACHER EDUCATION AND QUALITY

‘Quality’ in mathematics teaching does not relate solely to pupil achievement, to teaching approaches or to deeply held beliefs about the nature of mathematics and its teaching and learning, but to all of these. A model of a teacher's mathematics‐related belief‐system is presented, and the issue of the contrast between espoused and enacted beliefs is discussed. ‘Quality’ in mathematics teacher education raises all of these issues, as well as the aims, goals and means of the teacher preparation process itself. The paper concludes by arguing against the ‘apprenticeship’ model of mathematics teacher education, for depriving student teachers of theory and of practical research experience. A well known dictum paraphrased states that theory without practice is empty, but that practice without theory is blind. ‘Quality’ in mathematics teaching and teacher education depends on both theory and practice in systematic cooperation.     

On the alignment of teachers’ mathematical content knowledge assessments with the common core state standards

Instruments designed to measure teachers’ knowledge for teaching mathematics have been widely used to evaluate the impact of professional development and to investigate the role of teachers’ knowledge in teaching and student learning. These instruments assess a mixture of content knowledge and pedagogical content knowledge. However, little attention has been given to the content alignment between such instruments and curricular standards, particularly in regard to how content knowledge and pedagogical content knowledge items are distributed across mathematical topics. This article provides content maps for two widely used teacher assessment instruments in the USA relative to the widely adopted Common Core State Standards. This common reference enables comparisons of content alignment both between the instruments and between parallel forms within each instrument. The findings indicate that only a small number of items on both instruments are designed to capture teachers’ pedagogical content knowledge and that the majority of these items are focused on curricular topics in the later grades rather than in the early grades. Furthermore, some forms designed for use as pre- and post-assessment of professional development or teacher education are not parallel in terms of curricular topics, so estimates of teachers’ knowledge growth based on these forms may not mean what users assume. The implications of these findings for teacher educators and researchers who use teacher knowledge instruments are discussed.

     

How are Developmentally Appropriate or Traditional Teaching Practices Related to the Mathematics Achievement of General and Special Education Students?

Recently, developmentally appropriate practices have been distinguished from traditional practices and have been advocated as one way to reform primary general education classrooms. Relatively little research has examined the efficacy of developmentally appropriate versus traditional practices. In particular, concerns have been raised about the effectiveness of this approach for students with disabilities. This study examined the relationship between primary teachers' implementation of developmentally appropriate and traditional teaching methods and the mathematics achievement of general and special education students. Observations, interviews and questionnaires were used to measure the mathematics teaching practices used with general and special education students. Because developmentally appropriate and traditional teaching practices are often characterized in terms of a continuum, principal components methods were used to generate continuous composite variables that described teacher presentation, materials, grouping, and curriculum. The outcome measure was a curriculum- based measure of mathematics achievement. Principal components results showed that the composite variables most clearly associated with the developmentally appropriate v. traditional continuum were not related to mathematics achievement. Instead, consistent with previous research, achievement was associated with a reported measure of instruction that emphasized mathematical processing and strategy instruction. Further, a reported “laissez faire” method that emphasized individual student choice and treated special education students like general education students was negatively related to achievement, as was placement in special education class.