Examining instructional practices in Core-Plus lessons: implications for professional development

In the research reported in this article, we sought to understand the instructional practices of 26 secondary teachers from one district who use a problems-based mathematics textbook series (Core-Plus). Further, we wanted to examine beliefs that may be associated with their instructional practices. After analyzing data from classroom observations, our findings indicated that the teachers’ instructional practices fell along a wide continuum of lesson implementation. Analysis of interview data suggested that teachers’ beliefs with regard to students’ ability to do mathematics were associated with their level of lesson implementation. Teachers also differed, by level of instructional practices, in their beliefs about appropriateness of the textbook series for all students. Results strongly support the need for professional development for teachers implementing a problems-based, reform mathematics curriculum. Further, findings indicate that the professional development be designed to meet the diverse nature of teacher needs.     

Teacher tensions: expectations in a professional development institute

The purpose of this study was to better understand teacher tensions in professional development. The population under study was practicing mathematics teachers engaged in a week-long professional development institute. Data sources included observations, interviews, and teacher products (such as registration forms, surveys, journals, and notebooks). The data were analyzed to determine what tensions were evident in the institute and how those tensions arose. In this paper, we examine participants’ tensions in a professional development situation when their expectations did not match reality. We have done so by presenting a theoretical model of professional development based on an instructional rhombus that illuminates the actual and applicatory aspects of teachers’ professional development experiences. The main tensions expressed by the teachers were related to the content and pedagogy of the institute. This study points toward the importance of teachers’ expectations in professional development.     

Using comparison to develop flexibility for teaching algebra

In this paper, we describe a one-day professional development activity for mathematics teachers that promoted the use of comparison as an instructional tool to develop students’ flexibility in algebra. Effective use of comparison in mathematics instruction involves using side-by-side presentation of problems and solution methods and subsequent student discussion of these multiple solution methods to highlight the similarities and differences among problem-solving techniques. The goals of the professional development activity were to make teachers aware of how to use comparison effectively in their instruction, as well as to impact teachers’ own flexibility in algebra by using comparison instructionally during the professional development. Our analysis of teachers’ experiences in the professional development activity suggests that when teachers were presented with techniques for effective use of comparison, their own understanding of multiple solution methods was reinforced. In addition, teachers began to question why they relied exclusively on one familiar method over others that are equally effective and perhaps more efficient and started to draw new connections between problem-solving methods. Finally, as a result of experiencing instructional use of comparison, teachers began to see value in teaching for flexibility and reported changing their own teaching practices.     

A Mathematics Teachers’ Perspective and its Relationship to Practice

In this paper we try to characterize the pedagogical approaches that mathematics teachers are developing to meet the challenges posed by education reforms. A key aspect is the identification of the perspectives that underlie those pedagogical approaches, using the term perspective to include a broad pedagogical structure composed of multiple conceptions that are related to some aspects of a teacher’s practice. Through the study of the practice of a secondary mathematics teacher, we try to explore how his/her pedagogical approaches on mathematics, mathematics learning, and mathematics teaching are related to the relational architecture that is established in the classroom during the development of an instructional unit of similarity at a secondary school level, and we examine if that relationship can be explained in terms of the underlying perspective. The results of the study have shown the characteristics of that relationship, and the important role that the teacher’s knowledge of the students’ difficulties plays both in making decisions and in developing the teachers’ actions.     

‘The conference was awesome’: social justice and a mathematics teacher conference

Professional development comes in many forms, some of which are deemed more useful than others. However, when groups of teachers are excluded, or exclude themselves, from professional development opportunities, then there is an issue of social justice. This article examines the experiences of a group of teachers from a Māori-medium school who attended a mathematics teacher conference. By analysing the teachers’ sense of belonging through their ideas about engagement, alignment and imagination, we are able to describe how different kinds of relationships influence the inclusion/exclusion process. This leads to a discussion about what can be done by the teachers as well as conference organisers to increase these teachers’ likelihood of attending further conferences in the future.     

Qualified Pedagogical Reflection as a Way to Improve Mathematics Education

All changes of the character of education and improvement of its quality depend, in our view, particularly on the teacher. To be able to do their work efficiently, teachers have to be equipped with professional skills and dispositions, with “teachers’ competence”. For their professional growth, we consider indispensable competence in reflection, which is aimed at the teacher’s activities with regard to aspects of pedagogy and/or subject-didactics. From the point of view of the goals and content of their teaching and the methods of work (and their realisation), the development of teachers’ conscious self-reflection on their own teaching and systematic pursuance of joint reflection with other teachers and/or researchers can promote the teacher’s professional growth. In this paper, we show how a selected group of elementary school teachers reflected on their competence in the course of preparing, carrying out and analysing several instruction experiments. The paper is based on samples of teachers’ reflections and their gradual development from mere simple conversations based on intuitive perceptions, through searching for effective teaching approaches, to the deep assessment of mathematics teaching from the point of view of topics and their didactic elaboration and to suggestions for the teachers’ own experiments. May the teacher know what he teaches. May the teacher know how to teach. May the teacher be sincerely interested in teaching. Comenius     

Teaching experiments and professional development

The challenge that we address concerns teachers’ shifts toward student-centered instruction. We report on a yearlong professional development study in which two United States elementary school teachers engaged in a teaching experiment, as described by Steffe and Thompson (in: Lesh and Kelly (eds) Research on design in mathematics and science education, 2000). The teaching experiment involved close mathematical interactions with a pair of students after school, in the context of solving fractions tasks. By conducting a teaching experiment, we anticipated that each teacher would have more opportunity to develop insight into students’ mathematics. We also anticipated that these insights would influence the teachers’ classroom practice, even without explicit support for such a shift. Indeed, the teachers found that they began asking more probing questions of their students and spending more time listening to students’ explanations, but shifts to classroom practice were limited by constraining factors such an inflexible curriculum.     

Alignment, cohesion, and change: Examining mathematics teachers’ belief structures and their influence on instructional practices

This collective case study reports on an investigation into the relationship between mathematics teachers’ beliefs and their classroom practices, namely, how they organized their classroom activities, interacted with their students, and assessed their students’ learning. Additionally, the study examined the pervasiveness of their beliefs in the face of efforts to incorporate reform-oriented classroom materials and instructional strategies. The participants were five high school teachers of ninth-grade algebra at different stages in their teaching career. The qualitative analysis of the data revealed that in general beliefs were very influential on the teachers’ daily pedagogical decisions and that their beliefs about the nature of mathematics served as a primary source of their beliefs about pedagogy and student learning. Findings from the analysis concur with previous studies in this area that reveal a clear relationship between these constructs. In addition, the results provide useful insights for the mathematics education community as it shows the diversity among the inservice teachers’ beliefs (presented as hypothesized belief models), the role and influence of beliefs about the nature of mathematics on the belief structure and how the teachers designed their instructional practices to reflect these beliefs. The article concludes with a discussion of implications of teacher education.     

Reversing the Downward Spiral of Science Instruction in K-2 Classrooms

This study investigated the extent to which teacher professional development led to changes in science instruction in K-2 classrooms in rural school districts. The research specifically examined changes in (a) teachers’ content knowledge in science; (b) teachers’ self-efficacy related to teaching science; (c) classroom instructional time allotted to science; and (d) instructional strategies used in science. The study also investigated contextual factors contributing to or hindering changes in science instruction. Data sources included a teacher survey, a self-efficacy assessment, content knowledge tests, interviews, and classroom observations. After one year in the program, teachers showed increased content knowledge and self-efficacy in teaching science; they spent more instructional time on science and began using different instructional strategies. Key contextual factors included curricular demands, resources, administrative support, and support from other teachers.     

Mathematics, computers, and young children as a research-oriented learning environment for a teacher candidate

The advent of computer technology in the classroom raised the issue of its appropriate use by teachers and their students alike. It has been recommended that teacher education programs provide more opportunities for teacher candidates’ use of technology including teaching their own technology-enhanced lessons. With a goal of integrating scholarship into student teaching, a teacher candidate enrolled in a graduate program in childhood education carried out a technology-enhanced research project within a professional development school. Examining the impact of the project on the teacher candidate, this article describes how one’s pedagogical content knowledge and technological competence can be developed through a research-oriented teaching experience. The article also demonstrates the emergence of a community of practice that shares the goal of providing learning spaces for the teacher candidate and young children in the context of mathematics enrichment with computers.     

Using concept maps to assess change in teachers’ understandings of algebra: a respectful approach

The purpose of this study was to explore teachers’ growth in understanding of algebra using concept maps. The study was set in the context of a five-year National Science Foundation funded teacher retention and renewal professional development project. In this project both beginning and experienced teachers are supported as they increase their understanding about mathematics, their ability to implement effective mathematics practices in their classrooms, and their knowledge of working with English Learners. Results indicate that teachers’ algebraic knowledge structures became more complex and connected as a result of their professional development. In addition, they were able to adapt their knowledge networks to incorporate important aspects of algebra into them. Concept maps are recommended to other leaders of mathematics professional development as a means of assessing change.     

Reconsidering the Study of Mathematics Instructional Practices: The Importance of Curricular Context in Understanding Local and Global Teacher Change

This paper discusses the case of one teacher, Jackie, whose instructional practices illuminate the importance of textbooks and student/parent expectations in shaping pedagogy. Jackie teaches in the Plainview district, which offers parents and students a choice between a reform-oriented, integrated curriculum (Core Plus) and a more conventional algebra sequence (the University of Chicago series). Each day, Jackie teaches two very different sections of accelerated eighth-grade mathematics using each of these curricular materials. Drawing from students’ survey responses, classroom observations, and teacher interview data, we show ways in which Jackie’s pedagogy differs considerably between the two courses and we shed light on reasons underlying this variation.By examining one teacher who enacts different practices in each of the two curricular contexts, this paper highlights factors that contribute to teachers’ enacted curricula – factors that have been understated in previous mathematics education research on teacher development. The study establishes the importance of distinguishing between global and local teacher change, and suggests implications for future studies of teaching and reform.     

Mediators of a Preservice Teacher’s Use of the Inquiry-Application Instructional Model

This paper reports on one preservice teacher’s use of the Inquiry-Application Instructional Model (I-AIM) to plan and teach an instructional sequence on photosynthesis to 5th-grade students. Analysis of the preservice teacher’s planned and enacted instructional sequences and interviews shows that the preservice teacher was successful in leveraging the conceptual change but not the inquiry aspects of the I-AIM. The mediators of this preservice teacher’s use of the I-AIM included her approach to teaching science, the curriculum materials she had available, and the meanings she made of the underlying frameworks. Understanding the mediators of preservice teachers’ uses of instructional models can inform teacher educators’ approaches to supporting preservice teachers in using instructional models for organizing science instructional sequences.     

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.

Assessment Practices: Empowering Mathematics and Science Teachers in Rural Secondary Schools to Enhance Student Learning

Aligned with recent changes to syllabuses in Australia is an assessment regime requiring teachers to identify what their students ‘know’ and ‘can do’ in terms of the quality of understanding demonstrated. This paper describes the experiences of 25 secondary science and mathematics teachers in rural schools in New South Wales as they explore the changing nature of assessment and its implications on their classroom practice. To help reconceptualise these changes, teachers were introduced to a cognitive structural model as a theoretical framework. Throughout the 2-year study, teachers attended a series of professional development sessions and received ongoing consultative support. Each session was taped and transcribed while interviews were conducted with each teacher at the end of both years. Analysis of these data using a grounded theory approach identified seven major components of teacher practice impacted by the study. The core component was questioning while the six contributing components were teachers’ pedagogical practices, attention to cognition, teaching strategies, assessment linked to pedagogy, classroom advantages for students, and classroom advantages for teachers. These findings represent a major shift in teachers’ perceptions of assessment from a focus on the accumulation of students’ marks to one of diagnosis as a means of directing teaching to enhance students’ scientific and mathematical understandings.     

面向技术时代的教学设计与教师专业发展

从技术理性与教师主体性行为的角度可以看出整学设计的发展经历了规定性、权威性、参与性、使用性四个阶段。新技术时代,教学设计与技术、教师及其专业发展之间相互影响,教学设计可以促进教师专业发展。当前我国教师专业发展在理论研究方面缺乏技术视角、在发展模式上内涵发展不足,新媒体技术时代教学设计是促进教师专业发展的重要途径,教师及教育管理部门应积极推动教师专业的发展。     

Underpinnings of teachers’ professional development-a new conceptualization of field experience

Many researchers have addressed the professional development of teachers and the importance of the field experience component in the process of teaching effectiveness (Kowalchuk, 1999). A phased development model or paradigm used to address teachers’ professional development and stages of effectiveness have been noted. Conceptual models of Field Experience have been developed in accordance to the paradigms addressed the professional development of teacher effectiveness, basing on no matter external forces or internal reflective capability that will change a teacher. Simply put, a focus is placed upon teachers to change and grow. Field experience is not equivalent to student placement or teaching supervision, but is a device for teacher change at various professional stages. This implies the need for a re-thinking of teacher education preparation.     

Factors Affecting Teachers’ Adoption of Technology in Classrooms: Does School Size Matter?

Researchers in educational technology have searched for factors to explain teachers’ acceptance and resistance to using technology for instruction. Among the many identified factors, however, organizational and school factors have not yet been explored and discussed. This study investigates the effects of school size on science and mathematics teachers’ adoption of technology in classrooms. Using national survey data collected from 940 science and mathematics teachers at junior high schools in Taiwan, we employed factor analyses, log-linear analyses, and three-way ANOVA techniques to examine interactions among school factors and teacher factors. Results obtained from the log-linear analyses suggested that both the interactions of school region with school size and school size with technology users were needed to explain teachers’ use of educational technology in classrooms. It appears that teachers at small schools were more likely to use technology for instructional purposes. Additionally, results of the study revealed that teachers at small schools tended to have positive attitudes toward technology use and that among users of educational technology in southern Taiwan, teachers at small schools designed and used significantly more instructional activities with technology. This study suggests that small schools provide a better environment for science and mathematics teachers to implement educational technology in instruction.     

Challenges of critical colleagueship: examining and reflecting on mathematics teacher study group interactions

This article examines mathematics teacher collegiality by focusing on both the ways in which teachers interacted as critical colleagues in a long-term professional development project and the evolving role of the teacher–educator–researcher as the facilitator of this project. The professional development collaboration comprised two phases: one focused on reading classroom discourse literature and one focused on supporting each other through cycles of action research related to mathematics classroom discourse. Lord’s (1994) critical colleagueship framework is used to examine how a study group of middle-grades (ages 11–16) mathematics teacher–researchers took (or did not take) a more critical stance toward their own teaching practice and that of their colleagues. We found that challenging interactions were related to instances in which the teachers interacted as critical colleagues and were marked by particular features including the use of particular words and the use of personal experience as a form of evidence. We present the ways in which we came to understand what it might look like to scrutinize one’s practice and findings related to the development of this type of collegiality across the two different phases of this project. We end with a section in which the teacher–educator–researcher who facilitated the professional development project reflects on the ways in which the analysis caused her to reconsider both the nature of argumentation in mathematics study group settings and what implications this has with respect to her own practice as a facilitator.     

THE ROLE OF TEACHER CHARACTERISTICS AND PRACTICES ON UPPER SECONDARY SCHOOL STUDENTS�� MATHEMATICS SELF-EFFICACY IN NYANZA PROVINCE OF KENYA: A MULTILEVEL ANALYSIS

The study identified two dimensions of teacher self-efficacy and practices and five dimensions of students’ mathematics self-efficacy and sought to determine the extent to which teacher characteristics and practices can enhance secondary school students’ self-efficacy. Data were collected from 13,173 students in 193 teachers’ classrooms from 141 schools in the 10 districts of Lake Victoria Region of Kenya. Two-level hierarchical linear model revealed that teachers’ frequent use of mathematics homework, their level of interest and enjoyment of mathematics, as well as their ability and competence in teaching mathematics were found to play a key role in promoting students’ mathematics self-efficacy. Teachers’ ability and competence in teaching were also found to be effective in narrowing the gender gap in students’ self-confidence and competence in mathematics. The study recommends that teacher training colleges emphasize such teacher practices and values in order to enhance students’ mathematics self-efficacy, reduce their level of anxiety and fear of mathematics, and consequently, enhance their achievement in mathematics. Professional development opportunities should also be made available to in-service teachers to continually update their knowledge and skills and develop new strategies for teacher effectiveness.