The relationship among elementary teachers’ content knowledge,attitudes, beliefs,and practices

This study investigated 481 in-service elementary teachers’ level of mathematical content knowledge, attitudes toward mathematics, beliefs about the effectiveness of inquiry-based instruction, use of inquiry-based instruction and modeled the relationship among these variables. Upper elementary teachers (grades 3–5) were found to have greater content knowledge and more positive attitudes toward mathematics than primary teachers (grades K-2). There was no difference in teachers’ beliefs about effective instruction, but primary level teachers were found to use inquiry-based instruction more frequently than upper elementary teachers. Consistent with Ernest’s [Ernest (1989). The knowledge, beliefs and attitudes of the mathematics teacher: A model. Journal of Education for Teaching, 15(1), 13–33] model of mathematics teaching, content knowledge, attitudes, and beliefs were all found to be related to teachers’ instructional practice. Furthermore, beliefs were found to partially mediate the effects of content knowledge and attitudes on instructional practice. Content knowledge was found to be negatively related to beliefs in the effectiveness of inquiry-based instruction and teachers’ use of inquiry-based instruction in their classrooms. However, overall, teachers with more positive attitudes toward mathematics were more likely to believe in the effectiveness of inquiry-based instruction and use it more frequently in their classroom. Teacher beliefs were found to have the strongest effect on teachers’ practice. Implications for the goals and objectives of elementary mathematics methods courses and professional development are discussed.

Supporting Teachers’ Use of Technology in Science Instruction Through Professional Development: A Literature Review

Professional development is critical in supporting teachers’ use of technological tools in classrooms. This review of empirical research synthesizes the effective elements of professional development programs that support science teachers in learning about technology integration. Studies are examined that explore how professional development supports technology use within inquiry-based and traditional science instruction. Implications for future research are discussed in four areas: understanding and building on teachers’ beliefs about science and technology; supporting teacher learning by supporting teachers’ examination of students’ work; using technology to support teacher communities and social networks; and sustaining teachers’ learning beyond formal professional development programs.

Meeting the Needs of High School Science Teachers in English Language Learner Instruction

This survey study explored high school science teachers’ challenges and needs specific to their growing English language learning (ELL) student population. Thirty-three science teachers from 6 English as a Second language (ESL)-center high schools in central Virginia participated in the survey. Issues surveyed were (a) strategies used by science teachers to accommodate ELL students’ special needs, (b) challenges they experienced, and (c) support and training necessary for effective ELL instruction. Results suggest that language barriers as well as ELL students’ lack of science foundational knowledge challenged teachers most. Teachers perceived that appropriate instructional materials and pedagogical training was most needed. The findings have implications for science teacher preservice and inservice education in regard to working with language minority students.

Committed for life? Variations in teachers’ work, lives and effectiveness

This paper is based upon a unique mixed methods 4-year research project which focused upon the variations in teachers’ work, lives, and effectiveness of 300 elementary and secondary school teachers in a range of 100 schools across seven regions of England. Its findings challenge linear conceptions of teacher development and expertise and provide new understandings of the effects of personal, school and broader policy contexts upon professional life phase trajectories and teachers’ emotional identities. It finds connections between these and teachers’ commitment, resilience, and effectiveness. This paper discusses these in relation to the school standards and teacher retention agendas.

First grade teachers’ knowledge of phonological awareness and code concepts: Examining gains from an intensive form of professional development and corresponding teacher attitudes

The study examined the efficacy of an intensive form of professional development (PD) for building the knowledge of first-grade teachers in the areas of phonological awareness and phonics. The PD featured frequent in-class support from highly knowledgeable mentors for one school year, in addition to an introductory two-day summer institute and monthly workshops. Pre- and post-assessment of participants on a Teacher Knowledge Survey (TKS) indicated weak knowledge of phonological awareness and phonics concepts prior to PD and large, significant gains in each area by year-end. In addition, to investigate factors potentially associated with teachers’ responses to training, a Teacher Attitude Survey (TAS) was administered before and after the PD. The TAS measured teachers’ attitudes regarding PD, external and internal motivation to participate, intentions to actively engage in learning and implementing new instructional methods, sense of self-efficacy as reading instructors, and premises about reading instruction (e.g., about whole language). Attitudes on a subset of these factors, teachers’ initial knowledge scores on the TKS, and years of teaching experience (estimated by age) accounted for significant portions of the variance in performance on the TKS after training.

The purpose, design and use of examples in the teaching of elementary mathematics

This empirical paper considers the different purposes for which teachers use examples in elementary mathematics teaching, and how well the actual examples used fit these intended purposes. For this study, 24 mathematics lessons taught by prospective elementary school teachers were videotaped. In the spirit of grounded theory, the purpose of the analysis of these lessons was to discover, and to construct theories around, the ways that these novice teachers could be seen to draw upon their mathematics teaching knowledge-base in their lesson preparation and in their observed classroom instruction. A highly-pervasive dimension of the findings was these teachers’ choice and use of examples. Four categories of uses of examples are identified and exemplified: these are related to different kinds of teacher awareness.

Views about Physics held by Physics Teachers with Differing Approaches to Teaching Physics

Physics teachers’ approaches to teaching physics are generally considered to be linked to their views about physics. In this qualitative study, the views about physics held by a group of physics teachers whose teaching practice was traditional were explored and compared with the views held by physics teachers who used conceptual change approaches. A particular focus of the study was teachers’ views about the role of mathematics in physics. The findings suggest the traditional teachers saw physics as discovered, close approximations of reality while the conceptual change teachers’ views about physics ranged from a social constructivist perspective to more realist views. However, most teachers did not appear to have given much thought to the nature of physics or physics knowledge, nor to the role of mathematics in physics.

Challenges in deepening prospective teachers’ understanding of multiplication through justification

This article reports challenges faced by prospective elementary teachers as they revisited whole number multiplication through a sequence of tasks that required them to develop and justify reasoning strategies for multiplication. Classroom episodes and student work are used both to illustrate these challenges, as well as to demonstrate growth over time. Implications for the design of mathematics courses for prospective teachers’ are discussed. Although the study is situated in the context of multiplication, it has implications for teachers reasoning and justification in other areas of mathematics.

Teaching the Standards is Developmentally Appropriate Practice: Strategies for Incorporating the Sociopolitical Dimension of DAP in Early Childhood Teaching

Many early childhood practitioners in the U.S. are experiencing tension between their desire to offer students developmentally appropriate learning experiences and their obligation to teach the academic knowledge and skills mandated by their states. However, careful examination of the DAP guidelines’ definition of culturally appropriate practice reveals a significant sociopolitical dimension that has been obscured by the field’s tight focus on the sociocultural dimension. Because standards-based education is an explicit feature of the sociopolitical landscape of U. S. public education, teaching the standards is developmentally appropriate practice. Implementation of this broadened understanding of DAP adds new complexity to early childhood teachers’ work. This article offers ideas drawn from Bronfenbrenner, Vygotsky, and Dewey as sources of theoretical support and provides examples of strategic decision making—illustrated with examples drawn from Texas kindergartens—that can assist teachers in managing the curricular and instructional complexities that accompany the broadened understanding of DAP.

Exploration of the contribution of teachers’ knowledge about reading to their students’ improvement in reading

Recent studies of elementary teachers’ knowledge about reading have been built on the premise that teachers need thorough knowledge about language and reading processes, but these studies have provided only limited evidence that teachers’ performance on tests of such knowledge contributes to their students’ reading achievement. The present study was designed to examine the contribution of first- through third-grade teachers’ knowledge about early reading to their students’ improvement on tests of word analysis and reading comprehension, controlling for socio-demographic characteristics of students, their prior reading achievement, and teachers’ educational attainment, professional experiences, and socio-demographic characteristics. Preliminary analyses indicated that the test of teachers’ knowledge had adequate psychometric characteristics. However, performance on this measure of teachers’ knowledge did not significantly explain students’ improvement on the two reading subtests. The complexity of the factors that influence teachers’ knowledge acquisition and the context in which the study was carried out offer possible explanations for these results. In addition, teachers’ content knowledge about reading might not be closely associated with the practices they use in reading instruction, and therefore might not be significantly related to their students’ improvement in reading over a year.

Tracing the development of preservice teachers’ efficacy beliefs in teaching mathematics during fieldwork

This paper focuses on efficacy beliefs with respect to teaching mathematics; it aims at testing and validating an existing scale for measuring efficacy beliefs in the domain of mathematics, examining the development of preservice teachers’ efficacy beliefs in mathematics during fieldwork, and identifying factors that contribute to the development of these beliefs. Exploratory factor analysis applied to longitudinal data collected through a questionnaire administered to almost 90 preservice teachers elicited a two-factor model, reflecting efficacy beliefs in mathematics instruction and classroom management. Using cluster analysis, we found four patterns in the development of preservice teachers’ efficacy beliefs regarding these two factors. Our analysis of semi-structured interviews with eight participants representing these four patterns suggested that preservice teachers’ efficacy beliefs were mainly informed by experimentation with teaching and interaction with mentors, tutors, peers, and pupils. Based on our findings, we draw implications for mathematics preservice teacher education and provide suggestions for future research.

Improving mathematics instruction through lesson study: a theoretical model and North American case

This article presents a theoretical model of lesson study, an approach to instructional improvement that originated in Japan. The theoretical model includes four lesson study features (investigation, planning, research lesson, and reflection) and three pathways through which lesson study improves instruction: changes in teachers’ knowledge and beliefs; changes in professional community; and changes in teaching–learning resources. The model thus suggests that development of teachers’ knowledge and professional community (not just improved lesson plans) are instructional improvement mechanisms within lesson study. The theoretical model is used to examine the “auditable trail” of data from a North American lesson study case, yielding evidence that the lesson study work affected each of the three pathways. We argue that the case provides an “existence proof” of the potential effectiveness of lesson study outside Japan. Limitations of the case are discussed, including (1) the nature of data available from the “auditable trail” and (2) generalizability to other lesson study efforts.

Using the history of mathematics to induce changes in preservice teachers’ beliefs and attitudes: insights from evaluating a teacher education program

Scholars and teacher educators alike agree that teachers’ beliefs and attitudes toward mathematics are key informants of teachers’ instructional approaches. Therefore, it has become clear that, in addition to enriching preservice teachers’ (PSTs) knowledge, teacher education programs should also create opportunities for prospective teachers to develop productive beliefs and attitudes toward teaching and learning mathematics. This study explored the effectiveness of a mathematics preparatory program based on the history of mathematics that aimed at enhancing PSTs’ epistemological and efficacy beliefs and their attitudes toward mathematics. Using data from a questionnaire administered four times, the study traced the development of 94 PSTs’ beliefs and attitudes over a period of 2 years. The analysis of these data showed changes in certain dimensions of the PSTs’ beliefs and attitudes; however, other dimensions were found to change in the opposite direction to that expected. Differences were also found in the development of the PSTs’ beliefs and attitudes according to their mathematical background. The data yielded from semi-structured follow-up interviews conducted with a convenience sample of PSTs largely corroborated the quantitative data and helped explain some of these changes. We discuss the effectiveness of the program considered herein and draw implications for the design of teacher education programs grounded in the history of mathematics.

Assessing Teachers’ Beliefs to Facilitate the Transition to a New Chemistry Curriculum: What Do the Teachers Want?

In this article, we describe the results of a study of chemistry high school teachers’ beliefs (N = 7) of the chemistry curriculum and their roles, their beliefs on the teacher as developer of materials, and their beliefs about professional development. Teachers’ beliefs influence the implementation of a curriculum. We view the use of a new curriculum as a learning process, which should start at teachers’ prior knowledge and beliefs. The results reveal that it is possible to develop a new curriculum in which teachers’ beliefs are taken as a starting point. Promising approaches to prepare teachers for a new curriculum is to let them (co)develop and use curriculum materials: It creates ownership, and strengthens and develops teachers’ pedagogical content knowledge (PCK).

Towards new documentation systems for mathematics teachers?

We study in this article mathematics teachers’ documentation work: looking for resources, selecting/designing mathematical tasks, planning their succession, managing available artifacts, etc. We consider that this documentation work is at the core of teachers’ professional activity and professional development. We introduce a distinction between available resources and documents developed by teachers through a documentational genesis process, in a perspective inspired by the instrumental approach. Throughout their documentation work, teachers develop documentation systems, and the digitizing of resources entails evolutions of these systems. The approach we propose aims at seizing these evolutions, and more generally at studying teachers’ professional change.

Explanations of attitudes to change: Colombian mathematics teachers’ conceptions of the crucial determinants of their teaching practices of beginning algebra

This article arises from a study whose overall purpose was to investigate the relationship between Colombian mathematics teachers’ conceptions of beginning algebra and their conceptions of their own teaching practices. The teachers’ understandings of their teaching practices were explored with a view to unravelling their conceptions of change in their teaching. Focusing on the perspectives of teachers afforded opportunities that exposed the powerful role that the teachers’ conceptions of social/institutional factors of teaching played in their conceptions of their practices. The degree to which the teachers attributed these (external) factors as crucial reasons for what they do in their teaching was the basis of a categorisation of their conceptions of the crucial determinants of their teaching practices into three types. The findings are particularly relevant to our understanding of the stability of mathematics teaching approaches in the Colombian context but have likely implications for a range of international education contexts. Specific implications for the development of the research into teachers’ conceptions of mathematics and its teaching, and for teacher education programmes are presented.

Learning to observe: using video to improve preservice mathematics teachers’ ability to notice

Video has assumed an increasingly prominent role in teacher education, particularly in the form of the viewing of videotaped class lessons by preservice teachers. Yet there is little research that confirms whether preservice teachers attend to the aspects of the video(s) that teacher educators anticipate or desire. This article explores this issue and reports on the impact of video viewing as a means to improve teachers’ ability to be observers of classroom practice. We utilized a pre- and post-test design to measure the quantity and type of classroom events that preservice mathematics teachers noticed before and after a teaching methods course where improving observation skills was an explicit goal. The results of the pre-assessment suggest that preservice teachers generally do not enter teaching methods courses with well-developed observation skills. The post-assessment indicates that the course led to significant increases in preservice teachers’ observation skills, particularly in teachers’ ability to notice features of the classroom environment, mathematical content of a lesson, and teacher and student communication during a lesson.

Forms of mathematical interaction in different social settings: examples from students’, teachers’ and teacher–students’ communication about mathematics

The study presented in this article investigates forms of mathematical interaction in different social settings. One major interest is to better understand mathematics teachers’ joint professional discourse while observing and analysing young students mathematical interaction followed by teacher’s intervention. The teachers’ joint professional discourse is about a combined learning and talking between two students before an intervention by their teacher (setting 1) and then it is about the students learning together with the teacher during their mathematical work (setting 2). The joint professional teachers’ discourse constitutes setting 3. This combination of social settings 1 and 2 is taken as an opportunity for mathematics teachers’ professionalisation process when interpreting the students’ mathematical interactions in a more and more professional and sensible way. The epistemological analysis of mathematical sign-systems in communication and interaction in these three settings gives evidence of different types of mathematical talk, which are explained depending on the according social setting. Whereas the interaction between students or between teachers is affected by phases of a process-oriented and investigated talk, the interaction between students and teachers is mainly closed and structured by the ideas of the teacher and by the expectations of the students.

Characteristics of teachers’ choice of examples in and for the mathematics classroom

The main goal of the study reported in our paper is to characterize teachers’ choice of examples in and for the mathematics classroom. Our data is based on 54 lesson observations of five different teachers. Altogether 15 groups of students were observed, three seventh grade, six eighth grade, and six ninth grade classes. The classes varied according to their level—seven classes of top level students and six classes of mixed—average and low level students. In addition, pre and post lesson interviews with the teachers were conducted, and their lesson plans were examined. Data analysis was done in an iterative way, and the categories we explored emerged accordingly. We distinguish between pre-planned and spontaneous examples, and examine their manifestations, as well as the different kinds of underlying considerations teachers employ in making their choices, and the kinds of knowledge they need to draw on. We conclude with a dynamic framework accounting for teachers’ choices and generation of examples in the course of teaching mathematics.

The power of Colombian mathematics teachers’ conceptions of social/institutional factors of teaching

In this paper I shall discuss data from a study on Colombian mathematics teachers’ conceptions of their own teaching practices of beginning algebra, which led to the development of a theoretical model of teachers’ thought structures designed as a thinking tool at the initial stage of the study. With a focus on the perspectives of teachers, the study investigated the relationship between the teachers’ conceptions of beginning algebra and their conceptions of their own teaching practices, with a view to unravelling their conceptions of change in their practices. Significant findings which threw light on the aforementioned relationship have been presented in Agudelo-Valderrama, Clarke and Bishop (2007), highlighting a direct association between a teacher’s conceptions of the nature of beginning algebra, the crucial determinants of her/his teaching practice, and her/his attitude to change. After an overview of the study, this paper focuses on specific evidence which clearly shows that in contrast to the strong relationship between a teacher’s conceptions of mathematics and her/his teaching practice, assumed in the theoretical model of teachers’ thought structures, the teachers see a strong relationship between their conceptions of social/institutional factors of teaching and what they do in their teaching. Implications of the findings for teacher education in Colombia are identified.