Teacher knowledge,curriculum materials,and quality of instruction: Lessons learned and open issues

This paper draws on four case studies to perform a cross-case analysis investigating the unique and joint contribution of mathematical knowledge for teaching (MKT) and curriculum materials to instructional quality. As expected, it was found that both MKT and curriculum materials matter for instruction. The contribution of MKT was more prevalent in the richness of the mathematical language employed during instruction, the explanations offered, the avoidance of errors, and teachers' capacity to highlight key mathematical ideas and use them to weave the lesson activities. By virtue of being ambitious, the curriculum materials set the stage for engaging students in mathematical thinking and reasoning; at the same time, they amplified the demands for enactment, especially for the low-MKT teachers. The analysis also helped develop three tentative hypotheses regarding the joint contribution of MKT and the curriculum materials: when supportive and when followed closely, curriculum materials can lead to high-quality instruction, even for low-MKT teachers; in contrast, when unsupportive, they can lead to problematic instruction, particularly for low-MKT teachers; high-MKT teachers, on the other hand, might be able to compensate for some of the limitations of the curriculum materials and offer high-quality instruction. This paper discusses the policy implications of these findings and points to open issues warranting further investigation.     

Two negatives don't always make a positive: Exploring how limitations in teacher knowledge and the curriculum contribute to instructional quality

This paper examines the contribution of mathematical knowledge for teaching (MKT) and curriculum materials to the implementation of lessons on integer subtraction. In particular, it investigates the instruction of three teachers with differing MKT levels using two editions of the same set of curriculum materials that provided different levels of support. This variation in MKT level and curriculum support facilitated exploring the distinct and joint contribution of MKT and the curriculum materials to instructional quality. The analyses suggest that MKT relates positively to teachers' use of representations, provision of explanations, precision in language and notation, and ability to capitalize on student contributions and move the mathematics along in a goal-directed manner. Curriculum materials set the stage for attending to the meaning of integer subtraction and appeared to support teachers' use of representations, provision of explanations, and precision in language and notation. More critically, the findings suggest that less educative curriculum materials, coupled with low levels of MKT, can lead to problematic instruction. In contrast, educative materials can help low-MKT teachers provide adequate instruction, while higher MKT levels seem to enable teachers to compensate for curriculum limitations.     

Towards a new cartography of curriculum reform: Reflections on educational decentralization in Argentina

Curriculum reforms have led to discursive and organizational changes in Argentina. These reforms have reshaped school knowledge and institutional patterns of school administration. We analyse the process of this 'curriculum reterritorialization', the contradictions and displacements it produces, and the hybrid products that result from it. Reterritorialization is traced through four interrelated movements: the hybridization of discourses; the design of new maps of relations between the centre and the periphery of the educational system; the new 'regime of truth' that emerges out of these changes; and the role of the intellectual in educational reform. Although they are different in scope and magnitude, these movements provide the tools required to analyse the many ways in which curriculum reform is transforming Argentina's educational experiences.     

Teacher knowledge: a complex tapestry

Teachers need to know a great deal, in many areas and in multiple ways. Teacher knowledge is a complex tapestry, and teachers must successfully weave the multiple threads. In this article, I present a conceptualisation of teacher knowledge that provides a framework for describing the complexity of teacher knowledge. The framework describes three ways of knowing: “knowing how,” “knowing why,” and “knowing what” and then applies these three knowledge discourses across six domains of teacher knowledge. The framework was developed from a study of 14 teachers in their first year of teaching, and in this article the framework is applied to their experiences to illustrate specific gaps in their teacher knowledge. It is proposed that this conceptualisation of teacher knowledge allows those involved in teacher education and induction to more clearly identify professional learning needs and develop their programmes with specificity.     

Teacher educators mediating curricular reform: anticipating the Australian curriculum

Many education systems are experiencing a re-scaling and consolidation of governance through rolling national agendas of standardisation and centralisation. The present article considers the case of Australia as it moves towards implementing its first national curriculum, to explore how teacher educators plan to retain pedagogical space for debate, diversity and contestation of such systemic curricular reform. The present article reports on an interview study conducted with nine teacher educators across the four curriculum areas included in the first wave of the Australian curriculum: English, science, mathematics and history. The analysis reveals how teacher educators reported professional dilemmas around curricular design, and planned to resolve such dilemmas between the anticipated changes and their preferences for what might have been. While different curricular areas displayed different patterns of professional dilemma, the teacher educators are shown to construe their role as one of active curriculum mediators, who, in recontextualising curricular reforms, will use the opportunity to reinsert both residualised and emergent alternatives in their students’ professional value sets. The study also identifies a new set of dilemmas emerging around the politicisation and standardisation of curriculum, and its impact on the teaching profession and teacher educators.     

Reading between the lines: Teaching linear algebra

This paper compares lessons on linear equations from the same curriculum materials taught by two teachers of different levels of mathematical knowledge for teaching (MKT). The analysis indicates that the mathematical quality of instruction in these two classrooms appears to be a function of differences in MKT. Although the two teachers were teaching from the same curriculum materials, the teacher with higher MKT had more complete and concise ways to describe key concepts, had multiple ways to represent ideas about linear equations, could move nimbly among different mathematical expressions of linear relationships, and gave students a larger role in articulating the mathematical ideas of the lesson. However, curriculum materials seem to have moderated what would otherwise have been larger disparities in the quality of instruction between the two teachers. The lower-MKT teacher made minor mathematical errors, stayed on topic, and defined concepts in reasonably accurate ways when he followed the curriculum materials closely.     

Teacher knowledge about oral English instruction and teacher profiles: an EFL perspective

Teacher knowledge, as an important cognitive basis of teaching, has attracted tremendous attention in educational research in the last few decades. This study examines whether teachers’ self-perceived knowledge about oral English teaching differs with regard to their professional profiles in the English as a Foreign Language (EFL) context in China. A sample of 527 teachers from 56 universities in 29 cities across the country responded to a self-report questionnaire. Thirty teachers were interviewed. Teachers’ self-perceived knowledge was assessed by two factors: pedagogical content knowledge about oral English teaching (PCK) and knowledge of students’ oral English characteristics (KOS). The reliability and validity of the instrument are tested and presented. Results showed that EFL teachers generally reported having insufficient PCK and KOS. ANOVA and t-tests revealed no significant knowledge difference among teachers with different teaching experiences, training and overseas exposure. However, teachers’ learning experiences, self-perceived speaking ability and familiarity with teaching methodologies were found to influence teacher knowledge in a significant way. The findings highlight the need for the development of teacher knowledge about oral English teaching in the EFL contexts. Suggestions for further research are provided.     

关于数学教师课程知识来源

数学课程知识包括教材知识和资源知识,数学教师获得课程知识存在7种方法与途径,分别是:作为学生时代的经验;职前培训;在职培训;有组织的教研活动;同事之间的交流;阅读参考文献;自身的教学经验积累与反思.     

Science teachers' pedagogical content knowledge development during enactment of socioscientific curriculum materials

The purpose of this study is to provide insight into short-term professionalization of teachers regarding teaching socioscientific issues (SSI). The study aimed to capture the development of science teachers' pedagogical content knowledge (PCK) for SSI teaching by enacting specially designed SSI curriculum materials. The study also explores indicators of stronger and weaker development of PCK for SSI teaching. Thirty teachers from four countries (Cyprus, Israel, Norway, and Spain) used one module (30–60 min lesson) of SSI materials. The data were collected through: (a) lesson preparation form (PCK-before), (b) lesson reflection form (PCK-after), (c) lesson observation table (PCK-in-action). The data analysis was based on the PCK model of Magnusson, Krajcik, and Borko (1999). Strong development of PCK for SSI teaching includes “Strong interconnections between the PCK components,” “Understanding of students' difficulties in SSI learning,” “Suggesting appropriate instructional strategies,” and “Focusing equally on science content and SSI skills.” Our findings point to the importance of these aspects of PCK development for SSI teaching. We argue that when professional development programs and curriculum materials focus on developing these aspects, they will contribute to strong PCK development for SSI teaching. The findings regarding the development in the components of PCK for SSI provide compelling evidence that science teachers can develop aspects of their PCK for SSI with the use of a single module. Most of the teachers developed their knowledge about students' understanding of science and instructional strategies. The recognition of student difficulties made the teacher consider specific teaching strategies which are in line with the learning objectives. There is an evident link between the development of PCK in instructional strategies and students' understanding of science for SSI teaching.     

Teacher experiences of culture in the curriculum

This study examines the experiences of two middle‐school teachers as they attempt to acknowledge the ethnic, linguistic, and religious diversity of their students in their curriculum and teaching practices. It identifies the complications and challenges they encountered in the process. It presents one curriculum event to explore the ways in which diverse beliefs and values intersected as the teachers implemented the event. It employs a narrative inquiry approach with an emphasis on stories to learn about the experiences of the participants.     

Teacher pedagogical content knowledge,practice, and student achievement†

ABSTRACT

In this exploratory study, we attempted to measure potential changes in teacher knowledge and practice as a result of an intervention, as well as trace such changes through a theoretical path of influence that could inform a model of teacher professional knowledge. We created an instrument to measure pedagogical content knowledge (PCK), studied the impact of a two-year professional development intervention, explored the relationships among teacher variables to attempt to validate a model of teacher professional knowledge, and examined the relationship of teacher professional knowledge and classroom practice on student achievement. Teacher professional knowledge and skill was measured in terms of academic content knowledge (ACK), general pedagogical knowledge (GenPK), PCK and teacher practice. Our PCK instrument identified two factors within PCK: PCK-content knowledge and PCK-pedagogical knowledge. Teacher gains existed for all variables. Only GenPK had a significant relationship to teacher practice. ACK was the only variable that explained a substantial portion of student achievement. Our findings provide empirical evidence that we interpret through the lens of the model of teacher professional knowledge and skill, including PCK [Gess-Newsome, J. (2015). A model of teacher professional knowledge and skill including PCK: Results of the thinking from the PCK summit. In A. Berry, P. Friedrichsen, & J. Loughran (Eds.), Re-examining pedagogical content knowledge in science education (pp. 28–42). London: Routledge Press], highlighting the complexity of measuring teacher professional knowledge and skill.     

课程知识的合法性问题--对《基础教育课程改革纲要(试行)》的社会学分析

本文通过对《基础教育课程改革纲要》中课程知识合法性的追问发现,国家、专家等角色在本次基础教育课程改革中发生了变化。“国家”角色开始隐退,“专家”由“象征性参与者”向“事实性参与者”过渡,使课程知识合法性的主体发生了变化:课程将不纯粹是“传递统治阶级意识形态,进行阶级关系再生产的工具”;“专家”与“国家”在角色、地位上既有磨合又有争夺,从而也改变了课程知识合法性的过程:课程由社会单方“控制”的中介变为多方“认同”、“妥协”的产物。     

The poverty of curriculum theory: a critique of Wraga and Hlebowitsh

This paper offers a critique of a paper by Wraga and Hlebowitsh in the Journal of Curriculum Studies (2003) for narrowness of vision, repetition of already‐familiar material, irrelevance, a retreat into the academy, reductionism, and ultimate sterility as an approach to moving forward the fields of curriculum theory and development. Curriculum discourse should be marked by richness, diversity, discordant voices, fecundity, multiple rationalities, and theories, and should be touched by humanity and practicality in a hundred thousand contexts. To replace outworn but convenient labels and to advance the field, curriculum theory must catch the untidy but authentic lived experiences of curricularists of every hue, draw on emergent disciplines outside education, and touch major issues in everyday life.     

More than canons: teacher knowledge and the literary domain of the secondary English curriculum

Background:?The matter of teacher knowledge in the curriculum subject of English is not simple. Certainly it is not easy to delineate what its ‘content knowledge’ should be and how this relates to other aspects of teacher knowledge. In the context of education policy in England, at a time of change when the nature of the subject and its pedagogy are under scrutiny, the issue acquires heightened relevance from an initial teacher preparation perspective.

Purpose:?This paper sets out to consider the following questions: how do teachers of English acquire their teacher knowledge? What is known about the nuanced process of teacher knowledge development in English? Curriculum content is one element of teacher knowledge, but in the literary domain of English it does not suffice to specify what and how much should be read. The questions are discussed from the perspective of the knowledge development of postgraduate English teachers during initial teacher preparation.

Sources of evidence:?Literature concerning the development of teacher knowledge and expertise both generally and in the curriculum subject of English is critically discussed. Within the literature, the notion of the mentor–novice dialogue is identified as an important way of developing teacher knowledge. Alongside the literature, three illustrative mentor accounts are presented, drawn from the experience of postgraduate students learning to teach English to secondary school pupils.

Main argument:?The mentor accounts suggest that the boundaries of English are not easily demarcated. They indicate that the knowledge developed is other than the ‘content’ knowledge that might be acquired through initial degree studies. It is argued that teacher education demands a conception of teaching that takes full account of this knowledge development. At the same time, specific dispositions that do not automatically follow from prior academic attainment appear to be relevant. It is suggested that how these are cultivated, and how they are distinctive to the subject discipline are important questions for initial teacher preparation.

Conclusions:?Whatever the new contexts for initial teacher preparation, understanding how teachers acquire and apply ‘teacherly’ knowledge deserves as much attention as the content of a subject or the prior attainment of entrants to the profession. Initial teacher preparation arrangements need to acknowledge the complexity of learning to teach English as a curriculum subject. Learning to teach is a nuanced process, requiring engagement with a dedicated pedagogical content knowledge. In literary English teaching, this comprises attention to micro and macro aspects concurrently, for example through attention to individual texts concurrent with consideration of conceptions of readers and reading.     

Teacher educators as curriculum developers: exploration of a professional role

Teacher educators arguably fulfil several roles in their professional context: they can be seen as role models or teachers of teachers, and have additionally been characterised as researchers, mentors, gatekeepers, brokers, and curriculum developers. To address a perceived gap in the literature on the latter role, a quantitative and qualitative exploratory study into educators’ own perceptions of their role as curriculum developers was conducted at a large teacher education department in the Netherlands. Seventy-five educators completed a digital questionnaire. Their responses reveal that the participants generally consider themselves to be curriculum developers, are aware of the responsibilities this professional role entails, and can pinpoint concrete practices in which the role becomes visible. The findings furthermore suggest that educators have been prepared for and develop professionally in this role in a variety of ways, mostly through informal learning with their colleagues at the workplace. Based on these findings, recommendations are made to inform educational practice, policy, and research.     

Learning to Learn to Teach: An ``Experiment' Model for Teaching and Teacher Preparation in Mathematics

This paper describes a model for generating andaccumulating knowledge for both teaching andteacher education. The model is applied firstto prepare prospective teachers to learn toteach mathematics when they enter theclassroom. The concept of treating lessons asexperiments is used to explicate theintentional, rigorous, and systematic processof learning to teach through studying one's ownpractice. The concept of planning teachingexperiences so that others can learn fromone's experience is used to put into practicethe notion of contributing to a sharedprofessional knowledge base for teachingmathematics. The same model is then applied tothe work of improving teacher preparationprograms in mathematics. Parallels are drawnbetween the concepts emphasized for prospectiveteachers and those that are employed byinstructors who study and improve teacherpreparation experiences. In this way, parallelsalso are seen in the processes used to generatean accumulating knowledge base for teaching andfor teacher education.     

Teacher and school characteristics and their influence on curriculum implementation

Reform‐based curriculum materials have been suggested as a mechanism to make inquiry‐based instruction more prevalent in secondary science classrooms, specifically when accompanied by comprehensive professional development (Loucks‐Horsley, Hewson, Love, & Stiles, 1998 ; Powell & Anderson, 2002 ). This research examines the implementation of a reform‐based high school chemistry curriculum in a large, urban school district. We explicitly consider the role of the teachers' knowledge and beliefs in their implementation of the reform‐based chemistry curriculum, as well as school level factors. Qualitative and quantitative data were collected in the form of beliefs interviews and classroom observations from 27 high school chemistry teachers. Analysis of the data revealed that implementation of the curriculum was strongly influenced by the teachers' beliefs about teaching and learning, and the presence of a supportive network at their school sites. © 2007 Wiley Periodicals, Inc. J Res Sci Teach 44: 883–907, 2007     

Computer,craft, complexity,change: explorations into science teacher knowledge

In this article we review the notion of teacher knowledge from four metaphorical standpoints – teacher knowledge as computer, as craft, as complexity and as change. We employ each of these metaphors to examine and analyse the work of one teacher of science. We draw implications from our analysis for teacher education, teacher development and the study of teaching.     

Fidelity of implementation: bringing written curriculum materials into the equation

Fidelity of curriculum implementation (FOI) is an important area of research because of the critical role it plays in understanding how and why curriculum materials work and how they can be improved. This analysis explores written features within the Math Trailblazers curriculum that may influence the ways teachers implement mathematics curriculum materials. In particular, we examine FOI data from prior research in order to identify features within the materials themselves that may influence why teachers adhere to the intended curriculum to varying degrees. This paper reports on our analysis of examining five whole number lessons previously analysed for level of FOI alongside an analysis scale of written curriculum features. Our purpose in this analysis is to examine features of the written curriculum that potentially mediate teachers’ implementation of the materials in line with the intended curriculum. In doing so, our analysis further emphasises the critical role teachers play in curriculum implementation, and thus may provide some insight for curriculum developers as they consider ways in which to design the written curriculum that increase the likelihood that teachers will adhere to the intended curriculum.