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Effective Training of the Teachers in Teaching of Mathematics: A Reflective Professional Development Model for Teachers-as-Designers
Abstract
This chapter aims to provide an in-service teaching model, which is named as a “reflective teachers-as-designers professional development model” based on the literature, designed to give teachers an understanding of teaching that focuses on developing real-life contexts and developing global competencies. First, the conceptual framework for the learning of teachers and their capacity as designers are discussed. Then, content components and process components of the model are presented by providing the rationale behind each element.
... Matematik koçluğu tipik olarak ders öncesi görüşme-ders-ders sonrası görüşme gibi üç aşamalı temel bir döngüden oluşur (Aygün ve Işıksal-Bostan, 2019). Bu döngüler sürekli yansıtıcı düşünmeyi içerir (Teemant, 2013) ve bu sayede öğretmene öğretim pratiklerini geliştirmek için çeşitli fırsatlar sunar (Toker, 2021b). Şekil 1 matematik koçluğunda temel olarak kullanılan (Loucks-Horsley vd., 2003) ders döngüsü süreci örneklendirmektedir. ...
... Her ne kadar yararları sınırlı da olsa kısa süreli, tek seferlik, bireysel olarak öğretmenin ihtiyacına sadece genel anlamda cevap veren rutin mesleki gelişim seminerleri, Okul Temelli Yansıtıcı Matematik Koçluğu modelindeki süreklilik arz eden, uygulamaya dönük ve koç ile birebir çalışmayı gerektiren uygulamalardan farklıdır. Mesleki gelişime yönelik bu farklılık öğretmenlerin mesleki gelişim algısında değişiklik yapmasını gerektirir (Toker, 2021b;Zanzali, 2003). Ayrıca, modelin okul temelli olması ve öğretmeni desteklemek yoluyla öğrenci başarısına dolaylı bir katkı sunma potansiyeli öğretmenler için destekleyici görünmektedir. ...
Kaliteli eğitimin bir bileşeni olarak etkili öğretim geleneksel eğitim anlayışında öğrencilerin sınav başarısı ile birebir eşlenirken günümüzde etkili öğretim uygulamaları çok daha kapsamlı olarak ele alınmaktadır. Eğitim-öğretim süreçlerindeki bu yenilikçi bakış açısı doğrultusunda öğretmenlerin öğretim pratiklerinde de yenilikler ve gelişimler söz konusudur. Öğretmenlerin mevcut öğretim uygulamalarında değişiklikler ve yeni uygulamalara uyum sağlaması noktasında mesleki gelişime ihtiyaç duydukları açıktır ve bu ihtiyaç pek çok disiplin alanı için geçerli olduğu gibi matematik öğretmenleri için de geçerlidir. Bu çalışmada matematik öğretmenlerinin mesleki gelişimlerine yönelik bir model matematik koçluğu ele alınmıştır. Çalışmada uluslararası alan yazında büyük ölçekte koçluk, özelde ise matematik koçluğu ile ilgili çalışmalardan elde edilen bulgular ile koçluğun ne olduğu ve neden ihtiyaç duyulduğu, koçluk türleri, koçluk sürecindeki temel unsurlar, koçluk süreci ve uygulanma şekli, etkili koçluk süreci için destekleyici mekanizmalar, sürecin zorlukları ele alınmıştır. Bu bilgiler ışığında Türkiye’de matematik koçluğu sürecinde kullanılabilecek okul temelli bir mesleki gelişim modeli olarak yansıtıcı matematik koçluğu modeli önerisi geliştirilmiştir.
... Reflective practice has been reported to help teachers to increase their awareness-raising and problem-solving abilities (Ünver, 2003), understand and reconstruct their teaching knowledge (Godinez Martinez, 2018), strengthen their professional identities (Gutiérrez et al., 2019), and establish a link between teachers' professional and personal development (Ruge & Mackintosh, 2020;Toker, 2021). Ruge and Mackintosh (2020) argue that reflection occurs through both inner dialogues with ourselves and conversations with others. ...
Emergency remote teaching has accelerated the search for alternative professional development practices that could meet the immediate needs of the teachers and be effectively implemented in times of the COVID-19 pandemic. This research aims to present the Remote Collaborative Reflection (RCR) Model a group of teacher educators (TEs) developed in a collaborative reflective endeavor originating from their own professional needs during emergency remote teaching in the fall term of 2020-2021. It also reveals TE's reflections on the RCR Model in developing and implementing the RCR consisting of several iterative steps. Findings revealed that the TEs reflected on their perceived cognitive, interpersonal, and intrapersonal gains from the RCR highlighting the challenges they faced while carrying out the model. Although the RCR was developed during the pandemic when social distancing was the norm, we believe it might also fit the face-to-face mode of professional development depending on the situational circumstances and needs of practitioners.
A b s t r a c t
Design thinking, an innovative methodology, is used to guide the instruction of traditional subjects to cultivate students’ 21 st century skills. However, little research has clearly explained whether incorporating design thinking into the instruction of traditional subjects affects the achievement of curriculum goals. Therefore, this study aimed to explore the effects of design thinking during the instruction, in terms of reaching curriculum goals. We modified the existing design thinking framework and applied it to the information technology course. Through the experimental design and case study, we investigated how design thinking facilitated achieving the different levels of curriculum goals. Two seventh-grade classes with different instructional designs of informational technology curriculum were observed: i) one studied using the design thinking approach, and ii) another using traditional teaching methods. The results suggested that design thinking can promote the achievement of both low-level curriculum goals (i.e. mastery of the basic information knowledge and skills) and high-level curriculum goals (i.e. production of valuable, diverse, and creative digital works).
The twenty-first century has brought lots of challenges for people in all spheres, including education. In the new context, traditional approaches often seem ineffective and therefore new tools and methods have to be applied. An alternative approach that might be useful in the given context is design thinking – the approach that originated in architecture, design and art, and nowadays is applied in many fields. It is a human-centered problem-solving approach that may be used in the teaching/learning process to develop twenty-first century skills and enhance creativity and innovation. This paper introduces readers to the origin of design thinking, its attributes and processes as well as its application in pedagogy.
Roger Martin, dean of the Rotman School of Management, University of Toronto, is interviewed on the subject of "design thinking"—approaching managerial problems as designers approach design problems—and its potential impact on management education. Under a design-thinking paradigm, students would be encouraged to think broadly about problems, develop a deep understanding of users, and recognize the value in the contributions of others. In Martin's view, the concept of design thinking can potentially address many of the criticisms currently being leveled at MBA programs. The interview is followed by a discussion and critique of the themes Martin raises.
While teacher content knowledge is crucially important to the improvement of teaching and learning, attention to its development and study has been uneven. Historically, researchers have focused on many aspects of teaching, but more often than not scant attention has been given to how teachers need to understand the subjects they teach. Further, when researchers, educators and policy makers have turned attention to teacher subject matter knowledge the assumption has often been that advanced study in the subject is what matters. Debates have focused on how much preparation teachers need in the content strands rather than on what type of content they need to learn. In the mid-1980s, a major breakthrough initiated a new wave of interest in the conceptualization of teacher content knowledge. In his 1985 AERA presidential address, Lee Shulman identified a special domain of teacher knowledge, which he referred to as pedagogical content knowledge. He distinguished between content as it is studied and learned in disciplinary settings and the "special amalgam of content and pedagogy" needed for teaching the subject. These ideas had a major impact on the research community, immediately focusing attention on the foundational importance of content knowledge in teaching and on pedagogical content knowledge in particular. This paper provides a brief overview of research on content knowledge and pedagogical content knowledge, describes how we have approached the problem, and reports on our efforts to define the domain of mathematical knowledge for teaching and to refine its sub- domains.
From October to December 2005, six biology associates were employed to progress the connection between curriculum implementation and the continuing professional development of teachers at regional level. The associates worked with one hundred biology teachers in Teacher Design Teams (TDTs) and together they produced eighteen innovative classroom resources, which have now been made available for the teaching of biology nationally. This article considers the merits of the TDT approach as a form of curriculum implementation and continuing professional development with reference to international literature in the area and the reported experiences of biology associates in working with biology teachers in one region. Findings indicate the benefits which accrue, when teachers are actively engaged in the process of curriculum implementation through TDTs, as well as the challenges they face when inadequate curriculum support is provided.
Our overall intent is to clarify relations between the psychological constructivist, sociocultural, and emergent perspectives. We provide a grounding for the comparisons in the first part of the article by outlining an interpretive framework that we developed in the course of a classroom-based research project. At this level of classroom processes, the framework involves an emergent approach in which psychological constructivist analyses of individual activity are coordinated with interactionist analyses of classroom interactions and discourse. In the second part of the article, we describe an elaboration of the framework that locates classroom processes in school and societal contexts. The perspective taken at this level is broadly sociocultural and focuses on the influence of indlividuals' participation in culturally organized practices. In the third part of the article, we use the discussion of the framework as a backdrop against which to compare and contrast the three theoretical perspectives. We discuss how the emergent approach augments the psychological constructivist perspective by making it possible to locate analyses of individual students' constructive activities in social context. In addition, we consider the purposes for which the emergent and sociocultural perspectives might be particularly appropriate and observe that they together offer characterizations of individual students' activities, the classroom community, and broader communities of practice.
Dispositions have become an important part of the conversation about effective teaching. The purpose of this article is to analyze the disposition domains teacher candidates draw from as they think about their early teaching experiences. A framework of three disposition domains—intellectual, cultural, and moral—was used as a heuristic to analyze 35 teacher candidates’ journals. The candidates reflected on a range of topics, yet few possessed the self-knowledge to identify their assumptions and evaluate how these assumptions influenced their teaching decisions. Candidates with the greatest capacity to unpack their assumptions and who therefore possessed the greatest awareness of their dispositions demonstrated (a) a propensity for questioning the how and why of their thinking and actions, (b) a balance between focusing on students and the self, and (c) an adoption of multiple perspectives. These baseline data provide essential information for teacher educators working to develop candidates’ dispositions.
While there has been some research into the use of context in mathematics assessments pre-16, little, if any, work exists on the role of context in post-16 mathematics. For A- and AS-level mathematics courses in the UK, assessment schemes are required to include questions that test candidates' abilities to apply mathematical models to real-life contexts, and to translate real-life contexts into mathematics. This paper explores the ways in which context occurs in ‘pure’ mathematics questions and, through this, suggests a framework for analysis that encompasses issues such as accessibility, realism and authenticity.
Studies of teachers’ use of mathematics curriculum materials are particularly timely given the current availability of reform-inspired curriculum materials and the increasingly widespread practice of mandating the use of a single curriculum to regulate mathematics teaching. A review of the research on mathematics curriculum use over the last 25 years reveals significant variation in findings and in theoretical foundations. The aim of this review is to examine the ways that central constructs of this body of research—such as curriculum use, teaching, and curriculum materials—are conceptualized and to consider the impact of various conceptualizations on knowledge in the field. Drawing on the literature, the author offers a framework for characterizing and studying teachers’ interactions with curriculum materials.
This study uses a national probability sample of 1,027 mathematics and science teachers to provide the first large-scale empirical comparison of effects of different characteristics of professional development on teachers’ learning. Results, based on ordinary least squares regression, indicate three core features of professional development activities that have significant, positive effects on teachers’ self-reported increases in knowledge and skills and changes in classroom practice: (a) focus on content knowledge; (b) opportunities for active learning; and (c) coherence with other learning activities. It is primarily through these core features that the following structural features significantly affect teacher learning: (a) the form of the activity (e.g., workshop vs. study group); (b) collective participation of teachers from the same school, grade, or subject; and (c) the duration of the activity.
Teacher professional development is essential to efforts to improve our schools. This article maps the terrain of research on this important topic. It first provides an overview of what we have learned as a field, about effective professional development programs and their impact on teacher learning. It then suggests some important directions and strategies for extending our knowledge into new territory of questions not yet explored.
This paper seeks to explore values that are explicitly and implicitly documented in the Malaysian school mathematics curriculum and to compare them with mathematics teachers' perceptions of what values are appropriate to be taught through mathematics. The study finds that what is planned only partially matches what is espoused by the teachers in the sample.
The national conversation around undergraduate science instruction is calling for increased interdisciplinarity. As these calls increase, there is a need to consider the learning objectives of interdisciplinary science courses and how to design curricula to support those objectives. We present a framework that can help support interdisciplinary design research. We developed this framework in an introductory physics for life sciences majors (IPLS) course for which we designed a series of interdisciplinary tasks that bridge physics and biology. We illustrate how this framework can be used to describe the variation in the nature and degree of interdisciplinary interaction in tasks, to aid in redesigning tasks to better align with interdisciplinary learning objectives, and finally, to articulate design conjectures that posit how different characteristics of these tasks might support or impede interdisciplinary learning objectives. This framework will be useful for both curriculum designers and education researchers seeking to understand, in more concrete terms, what interdisciplinary learning means and how integrated science curricula can be designed to support interdisciplinary learning objectives.
In TIMSS-95, participating countries could administer the TIMSS Performance Assessment consisting of practical tasks, and considered to match well with the Dutch intended curriculum. But in 1995, Dutch students did not score as expected on this test, revealing a discrepancy between intended and attained curriculum. Therefore, in 2000, the test was replicated. Results show an increased teachers' acceptance of the test, but – still – no significant gain in Dutch students' achievements. Additionally, if reliability is well controlled, the study revealed that there are valid mathematics assessment alternatives, which can supplement paper-and-pencil tests, not only in The Netherlands.
Studies suggest that young children are quite limited in their knowledge about cognitive phenomena—or in their metacognition—and do relatively little monitoring of their own memory, comprehension, and other cognitive enterprises. Metacognitive knowledge is one's stored knowledge or beliefs about oneself and others as cognitive agents, about tasks, about actions or strategies, and about how all these interact to affect the outcomes of any sort of intellectual enterprise. Metacognitive experiences are conscious cognitive or affective experiences that occur during the enterprise and concern any aspect of it—often, how well it is going. Research is needed to describe and explain spontaneous developmental acquisitions in this area and find effective ways of teaching metacognitive knowledge and cognitive monitoring skills. (9 ref) (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Toward the end of his short life, Lev Vygotsky found himself teaching teachers in a remote part of the USSR. Though his influence as a developmental psychologist is well-established, little is known about his approach to teacher development. This article applies the researcher’s core concept, the zone of proximal development to teacher education. The resulting model for educating teaching candidates within zones of proximal teacher development (ZPTD) integrates Vygotskyan theory into Western models of teacher education. Recommendations are offered with regard the four stages of the ZPTD and implications for the content and sequence of the teacher preparation curriculum.Research highlights► Synthesizes findings from Vygotskyan research in teacher education. ► Recognizes and addresses the powerful influence of prior learning experiences and local teaching practices on candidates’ development. ► Presents a Zone of Proximal Teacher Development and implications for the teacher education curriculum.
Design Thinking has been a subject of teaching, research and real-life application in almost every domain and area of education, research and industrial endeavor for the past many years. This paper explains how to recognize the tenets of constructivist learning theory (constructivist principles) within the teaching-learning of the Design Thinking process. The research, established an integrative approach to theory, method, and practice by developing a taxonomy of constructivist principles to map the process and activities of design thinking. The paper further picks up the thread of developing and fine-tuning a Design Thinking course by presenting, what we call
as the “constructivism tenets-design thinking dashboard” which, while being suitable for business schools (Master of Business Administration), is generic enough to be used with minimal modifications for any other domains where customer experience is important, which is the case for all human endeavours.
Within the study reported here, our broad aim was to think deeply about how to support student teachers as they assessed their students’ mathematical understanding. Our experiences, as teacher educators, have been that although student teachers may recognize emerging student mathematical understanding, they are frequently unclear about how to use formative assessment for teaching decisions. Yet, increasingly, standards for teachers require them to focus on assessment. We analyzed data from one secondary mathematics student teacher, Kevin, in the form of video and transcripts of a teaching episode and his reflection which focused on his assessment of student learning. Salient issues emerged. Kevin emphasized classroom management and superficially assessed student understanding without evidence. Although time constraints pervade our profession, watching video with and posing questions that help student teachers identify the evidence of their students’ mathematical understanding is critical. We conclude that teacher educators and university supervisors need to take a dialogical conversation approach to reflection because reflection must happen with others, not in isolation. We consider other implications for our own work with student teachers to help them grapple with the complexities of assessing student learning.
Complementing the aims of problem-based inquiry, a pedagogical approach called design thinking (DT) has students grapple with issues that require a creative redefinition and reimagining of solutions akin to professional skills of designers, who consider conflicting priorities and complex negotiations to arrive at a solution to an ill-defined problem. This article aims to synthesize the limited existing literature on the use of DT in the K–12 classroom, share two exemplars of DT in action in Grades 3–5 so that science, technology, engineering, arts, and mathematics (STEAM) educators, teacher educators, researchers, and other stakeholders can visualize how it can take shape in the elementary classroom, followed by concluding remarks on DT. The DT framework provides an exciting avenue for teaching more than simply the content areas of STEAM, it provides a vehicle through which a true transdisciplinary learning experience can occur—where students are passionately invested in solving problems as they strive to make the world a better place.
How must teaching change to meet demands for the Common Core Standards and a world that is constantly changing in complex and unpredictable ways? Teachers have what seems like an impossible job, yet one we think can be accomplished if they gave access to tools, resources, and 21stcentury pedagogy, such as those building on design thinking. Attention to innovation, creativity, critical thinking, problem solving, communication and collaboration, are essential for preparing students for the future. Design thinking teaches these processes, skills, and dispositions, and we have committed to understanding their feasibility for K-12 integration. To that end, we facilitate camps, professional development workshops, and standards-based curriculum development. We engage teachers in interdisciplinary STEM challenges with design thinking. The teachers experience new ways to teach and learn, and to start making “mindshifts” that might impact them as teachers––being empathy driven, learning that failure is a positive aspect of the learning process, experiencing the positives of collaboration, and determining how design thinking can be generative in any subject or discipline. Two cases exploring design thinking with teachers are described, and we conclude with implications for current teaching practice and research.
This chapter describes a history of design thinking and how design can play into the Next Generation Science Standards from a practical perspective. We discuss participatory learning and design in disruptive classrooms. Technology-engineering is not simply an applied science since often technologists and engineers develop innovations in which the underlying science is not understood (e.g. the keystone in arches was used before forces as vectors were understood), technological design is uniquely different from inquiry, the design-production cycle entails much more than just the science of the idea, and technological/engineering literacy involves fundamental literacy and understanding technological/engineering principles. We conclude with a practical example and model of Serious Educational Game design that has evolved and modified over 10 years.
The research explored the relationship of learning design thinking and assessing that progress. It addressed the questions: How can we understand what is learned in design thinking classes, and how assessments might contribute to that process in authentic ways? The study followed a reciprocal research and design methodology where basic research and the design of assessment solutions were ongoing, reciprocal, and related to each other in organic ways. We learned that the learning of design thinking dispositions and mindsets is an emergent journey—with various levels of sophistication, transformation, application, and integration. We introduce the concept of mindshifts to represent the developing and nascent epistemological viewpoints and instincts that are strengthened while becoming a design thinker. We review designs for tools that were based on the concept of mindshifts that include reflective and performance assessments and an assessment dashboard.
Three principles from brain research - emotional safety, appropriate challenge, and self-constructed meaning - suggest that a one-size-fits-all approach to classroom teaching is ineffective for most students and harmful to some.
Supporting Teacher Design Teams (TDTs) during local curriculum development efforts is essential. To be able to provide high-quality support, insights are needed about how TDTs carry out design activities and how support is valued by the members of TDTs and how it affects their design expertise. In this study, the design and support processes of two TDTs assisted by an external facilitator were investigated using a case study approach. The results revealed that support offered to TDTs depended on the contextual boundaries and the focus of the design process. The focus, coherence and form of support affected the opportunities for developing teachers’ design expertise. In both cases, teachers’ curriculum design expertise had grown, whereas their pedagogical content knowledge and subject matter knowledge were hardly developed. Findings show that the most conducive support activities and materials were those that could directly be applied in the design process.
ZET: Disiplinlerarası öğretirnin önemi, etkili ve anlamlı öğrenmeye olan katkısı her geçen gün daha fazla vur-gulanmaktadır. Bu yaklaşım yeni olmamakla birlikte ken-dini hem literatürde hem de okullardaki uygulamalarda daha fazla hissettirmeye başlamıştır. Öğretmen eğitimi pro-gramları, grupla öğretim ve problemlere dayalı öğretim gibi uygulamalarla disiplinlerarası öğretimi ön plana çıkarmakta ve geleceğin öğretmenlerini bu yönde hazırlamaktadırlar. Disiplinlerarası öğretim, farklı disiplinlere ait bilgi ve be-cerileri anlamlı bir biçimde biraraya getirme ve kullanma yönünde etkili bir strateji olarak görülmektedir. Bu yak-laşım aynı zamanda bütüncül olan doğal düşünme bi-çimimizle tutarlılık göstermektedir. Bu çalışma, disiplinlerarası yaklaşımın temellerini göz-den geçirmekte ve program geliştirme yönünden ortaya çı-kan bir takım sonuçları tartışmaktadır. Ayrıca, pratik ve et-kili olabilecek disiplinlerarası bir program geliştirme modeli tanımlanmakta ve okullarımızda disiplinlerarası öğretirnin uygulanması yönünde bazı önerilere yer verilmektedir. ANAHTAR SÖZCÜKLER: Disiplinlerarası öğretim, di-siplinlerarası program. ABSTRACf: The importance of interdisciplinary teaching in causing meaningful and effective learning in students is emp-hasized increasingly both in the literature and in schools. Teacher education programs attempt to explore ways to in-tegrate different subject areas in a meaningful way to pre-pare their students as future teachers so that they them-selves can utilize the same approach in their teaching practices in schools. Interdisciplinary approach is viewed as a way of bringing together different disciplines in a me-aningful and practical manner so that students perceive knowledge and skills as a whole rather than discrete pi-eces. This approach is consistent with our natural way of thinking, that is halistic most of the time.
Teachers and educationalists working together in curriculum development is still rather unusual. The article reports on a project of collaborative curriculum development and uses it as a case‐study that reveals more general insights. The authors describe and interpretatively analyse collaborative curriculum development as the encounter of different professional knowledge systems. This encounter implies certain tensions and specific difficulties, but at the same time it offers rich opportunities to benefit from the ‘complementary competence’ of the different collaborating professionals. The authors conclude that collaborative curriculum development not only improves the quality of the curriculum outcomes, but at the same time constitutes a powerful means for teachers' professional development. The article is intended to contribute to a more balanced understanding of collaborative curriculum development, by explicitly describing its positive potential and its eventual pitfalls.
Studies of student learning have shown that students' conceptions of learning are strongly correlated with their approaches to study. Students who consider learning in quantitative terms are likely to find it very difficult to adopt a deep approach to learning. This study looks at the parallel situation for teachers. It looks at the conceptions of teaching and learning of a group of first year science lecturers, and how those conceptions relate to their approaches to teaching. The results also parallel those found for students. Strong relations are found between conceptions of teaching and approaches to teaching. Relations between conceptions of teaching and conceptions of learning were not so strong, but lecturers with highly developed conceptions of teaching differentiated between teaching and learning in quite different ways to those with less well-developed conceptions. The implications of these results for the practice and development of teaching in higher education are discussed.
The No Child Lett Behind legislation, with its emphasis on conducting scientifically based research, has reopened the door to a set of instructional and curricular practices left for dead in light of the scathing criticism of Oakes and Slavin in the 1980s, mainly ability grouping. This article represents a review of the literature of best practices, both instructional and curricular, that may lead to increased achievement among America's gifted and talented youth, whether they reside in an enrichment or resource room or the regular classroom. The review suggests that flexible ability grouping, combined with appropriate curricular revision or differentiation, may result in substantial achievement gains both for average and high ability learners. It is imperative that researchers in the field of gifted education take the lead in this endeavor so that no child, including the gifted and talented, will be left behind.
Subject matter and pedagogy have been peculiarly and persistently divided in the conceptualization and curriculum of teacher education and learning to teach. This fragmentation of practice leaves teachers on their own with the challenge of integrating subject matter knowledge and pedagogy in the contexts of their work. Yet, being able to do this is fundamental to engaging in the core tasks of teaching, and it is critical to being able to teach all students well. This article proposes three problems that would have to be solved to bridge this gap and to prepare teachers who not only know content but can make use of it to help all students learn. The first problem concerns identifying the content knowledge that matters for teaching, the second regards understanding how such knowledge needs to be held, and the third centers on what it takes to learn to use such knowledge in practice.
Curriculum materials for Grades K–12 that are intended to promote teacher learning in addition to student learning have come to be called educative curriculum materials. How can K–12 curriculum materials be designed to best promote teacher learning? What might teacher learning with educative curriculum materials look like? The authors present a set of design heuristics for educative curriculum materials to further the principled design of these materials. They build from ideas about teacher learning and organize the heuristics around important parts of a teacher’s knowledge base: subject matter knowledge, pedagogical content knowledge for topics, and pedagogical content knowledge for disciplinary practices. These heuristics provide a context for a theoretically oriented discussion of how features of educative curriculum materials may promote teacher learning, by serving as cognitive tools that are situated in teachers’ practice. The authors explore challenges in the design of educative curriculum materials, such as the tension between providing guidance and choice.
Lee S. Shulman builds his foundation for teaching reform on an idea of teaching that emphasizes comprehension and reasoning, transformation and reflection. "This emphasis is justified," he writes, "by the resoluteness with which research and policy have so blatantly ignored those aspects of teaching in the past." To articulate and justify this conception, Shulman responds to four questions: What are the sources of the knowledge base for teaching? In what terms can these sources be conceptualized? What are the processes of pedagogical reasoning and action? and What are the implications for teaching policy and educational reform? The answers — informed by philosophy, psychology, and a growing body of casework based on young and experienced practitioners — go far beyond current reform assumptions and initiatives. The outcome for educational practitioners, scholars, and policymakers is a major redirection in how teaching is to be understood and teachers are to be trained and evaluated.
This article was selected for the November 1986 special issue on "Teachers, Teaching, and Teacher Education," but appears here because of the exigencies of publishing.
The purpose of this study was to examine the effects of curricular (textbook, revised, and differentiated) and grouping (whole, between, and within-class) practices on intermediate students' achievement in mathematics. A pretest-posttest, quasi-experimental design using a stratified random sample of 31 teachers and their students (N = 645) was used in this study. Achievement data were collected using a curriculum-based assessment. Repeated measures analysis of variance was employed to investigate the effects of grouping arrangements and curricular design on the treatment and comparison group posttest scores. Results indicated significant differences, F (5, 246) = 22.618, p less than 0.001, between comparison and revision treatment groups on the posttest after adjusting for grade level (4 or 5). Further results indicated significant differences, F (11, 673) = 41.548, p less than 0.001, among all treatment groups after adjusting for grade level. Comparison of Textbook, Revised, and Differentiated Unit is appended. (Contains 6 tables.)
The International School of Kuala Lumpur in Malaysia, which serves international students in preschool through middle school, focused a great deal of professional attention on differentiation. The administrators in Malaysian school, by making rounds of classrooms, raised teachers' awareness of differentiated instruction.
There has been some debate about the extent to which contextual'stories' and graphical images can help pupils to think their way through numerical problems. The degree to which contexts stimulate useful'models to think with' may vary considerably. Some contexts seem to encourage children to reason more effectively, but others have little impact either on pupils'performance, or on the way in which they tackle the computations required. In this study three sets of four questions involving subtraction and division were trialled with a total sample of 1795 Year 6 to 9 pupils. In each comparison, about a quarter of the pupils could answer the question only when it was presented in context, or only out of context, but not both. Pupils' methods of working were analysed to reveal differences in their approach to the different questions.
This article articulates what might be called a value-based argument, a philosophical statement, one that emphasizes principles and perspectives that have remained precious to the author throughout 40 years in the field of education. It is the author's perspective on research and the school experience rather than a review of the research literature and, as such, strongly reflects a point of view. The author argues that heterogeneous classrooms and differentiated instruction must form the core of the classroom experience for students in a democracy that works.
The need to differentiate or adapt curriculum and instruction to meet special needs continues to challenge educators of students with high-incidence disabilities. The current emphasis on teaching and assessing standards requires knowledge and skills to differentiate standards-based education to successfully meet diverse needs in the classroom.
Major changes have taken place in Russian education during the past eight years: new openness, new approaches, new recognition of deficiencies and needs. As teachers sought to throw of the regimentation of the past, they turned to the newly republished works of L. S. Vygotsky and his followers for ideas. This article contrasts the differing perspectives on a number of critical issues in Vygotsky's cultural-historical theory (zone of proximal development, action/act/activity, element/unit analysis, social situation of development/contextualism). The recent effort to design a teacher developmental education program based on the principles of Vygotsky's cultural-historical concept put the concept itself in question. The principles of such a program will be discussed, particularly the idea of teacher self-identification in culture. The aim of this article is to facilitate the debate about these important issues and to define the international perspectives in the development of the cultural-historical concept.
Case studies were conducted to investigate the conceptions of mathematics and mathematics teaching held by three junior high school teachers. Examination of the relationship between conceptions and practice showed that the teachers' beliefs, views, and preferences about mathematics and its teaching played a significant, albeit subtle, role in shaping their instructional behavior. Differences among the teachers in their conceptions and practices are explained followed by a discussion of properties of their conceptual systems.
These five chapters address important issues on mathematics teaching and learning. They include, amongst others, how Applications
and Modelling help students learn mathematics in ways that result in a deep and holistic understanding; are central to the
development of Mathematical Literacy, and; are enriched by the creative use of technology.
In this article, we report on an 18-month longmathematics professional development projectwith elementary school teachers. Using a modelwe developed, three participant case studieswere analyzed with respect to not only theprofessional development milieu, but also howthese teachers interacted with the professionaldevelopment experience. In particular we foundthat having teachers reflect on new, authenticreform-oriented mathematics learningexperiences leads some teachers to take aninquiry stance concerning their own teaching,resulting in self-sustaining changes in theirmathematics instructional practices. Thisimplies that professional development forelementary mathematics teachers should includechallenging mathematics learning experiencescomplete with opportunities to reflect on personal and professional implications.
This paper analyses the difficulties which Spanish student teachers have in solving the PISA 2003 released items. It studies
the role played by the type and organisation of mathematical knowledge in the activation of competencies identified by PISA
with particular attention to the function of contextual knowledge. The results of the research lead us to conclude that the
assessment of the participant’s mathematical competencies must include an assessment of the extent to which they have school
mathematical knowledge (contextual, conceptual and procedural) that can be productively applied to problem situations. In
this way, the school knowledge variable becomes a variable associated with the PISA competence variable.
The article is based on a research and development project conducted in a Norwegian lower secondary school. The purpose of the text is to show how a project involving a researcher and a teacher team encourages the teachers to reflect on teaching processes, and, furthermore, to show what the form and content of such reflection processes could be. Theories on reflection are presented as the framework in which illustrations from practice are analysed. Findings from the project show that when teachers question their own practice, they can transcend their teaching, meaning they can think of and see new things. In connecting theory and practice, the article concludes that teachers are shown in this way how to reflect before action, reflecting on prior experiences by using theory, and how they can reflect in action and on action, connecting theoretical concepts to their teaching practice. In this way theories can serve as a tool in reflection processes.