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

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

Teachers learning how to learn

School pupils learning how to learn (LHTL), aimed at helping them develop learning autonomy, requires teachers to develop new classroom practices. Hence teachers LHTL is equally important. The TLRP ‘Learning How to Learn in Classrooms, Schools and Networks’ project researched how practices were developed by teachers in 40 primary and secondary schools in England. Quantitative data were collected using teacher and pupil questionnaires, and qualitative data came from interviews with head teachers, school project co-ordinators and a sub-sample of classroom teachers. Some teachers were also observed and video-recorded. External constraints made it difficult for teachers to promote pupils' learning autonomy, unless they fundamentally changed the nature of classroom tasks and climate. A key factor was teachers' own engagement in collaborative classroom-focused inquiry. However, to be successful, this needed to be supported by school management and leadership. There were strong statistical relationships between school policy, teachers' professional learning and their capacity to promote learning autonomy in their pupils. Teacher learning through networking within their schools, and with other teachers in other schools, was also shown to be important.     

Differences in pedagogical understanding among student–teachers in a four-year initial teacher education programme

As teacher educators, preparing student–teachers who are able to address diverse student needs is our main concern. It has been suggested in the literature that teachers who are adaptive to students’ needs are those who possess adequate pedagogical content knowledge or pedagogical understanding. However, it is not uncommon for teacher educators to find student–teachers with diverse pedagogical understandings even at the point of graduation from the teacher education programme. This paper aims to explain and analyse the development of pedagogical understanding among student–teachers in an initial teacher education programme. The findings are drawn from a study conducted at the Hong Kong Institute of Education where in-depth interviews were carried out during the four-year programme. The findings from the three selected cases provide an explanation for why some individual student–teachers show continuous development, whereas others remain confused in their pedagogical understanding throughout the teacher education programme. While acknowledging individual differences in pedagogical understanding, we attempt to explain such differences by investigating the relationship between different dimensions of the student–teachers’ learning such as the integration of pedagogical understanding with the teaching contexts, integration of feedback from lecturers and supporting teachers, and their focus of concern. The findings reveal that the three cases demonstrate different levels of pedagogical understanding and possess varying ‘senses of agency’. Of the three cases, the first one, Peggy has the strongest sense of agency. Despite influences related to classroom management, diverse learning ability among pupils, and the teaching methods which pupils were accustomed to previously, she actively introduced rhythmic movements into her lessons, developed pupils’ ability to learn gradually and achieved an impact on pupils’ learning which was also recognized by her supporting teacher. The analysis suggests that the second case, Lilian has a weaker sense of agency as she was severely limited by influences in the teaching context in her first teaching practice and resorted to teacher-centered teaching strategies. She improved later on in the programme and started to plan her own learning, drawing on the feedback she received as well as learning from other taught modules, from feedback from various sources, and from her pupils’ responses to her teaching and her own evaluation of her teaching. The third case, Stephanie remained confused throughout the programme and struggled with the implementation of student-centered teaching strategies. The ability to practice one’s own convictions and demonstrate an active sense of agency distinguishes the student–teacher who achieves better pedagogical understanding. Drawing on the findings, the paper concludes that it is crucial for teacher educators to identify ways to nurture a sense of agency among student–teachers. Implications for teacher education programmes are discussed, including providing opportunities for student–teachers to be able to articulate and integrate their pedagogical understandings, as well as negotiate how to accomplish their learning and teaching targets despite complex classroom situations.     

The teacher and the tool: instrumental orchestrations in the technology-rich mathematics classroom

The availability of technology in the mathematics classroom challenges the way teachers orchestrate student learning. Using the theory of instrumental orchestration as the main interpretative framework, this study investigates which types of orchestrations teachers develop when using technology and to what extent these are related to teachers’ views on mathematics education and the role of technology therein. Data consisted of videotapes of 38 lessons taught by three teachers, who also provided information on their views through questionnaires and interviews. Qualitative analysis of these data led to the identification of orchestration types and teacher profiles. The orchestration preferences of the three teachers proved to be related to their views. A detailed analysis of one exemplary episode suggests how other theoretical perspectives might complement the theory of instrumental orchestration.     

Enhancing teachers’ counselling skills: student teachers’ views on a teachers’ education programme

The purpose of this small‐scale study is to investigate the outcomes of a brief teacher education programme by exploring student teachers’ views. The teacher education programme aimed to provide teachers with the opportunity to develop qualities and skills that facilitate communication and to enhance teachers’ competence to apply social and emotional (SEL) programmes’ intervention activities in the classroom. According to student teachers’ estimations, the teacher education programme provided them with new knowledge and experiences in communication and counselling, which they felt they could use in teaching practice. Besides, teachers reported that the programme enabled them to develop their self‐awareness and to adopt a non‐directive attitude during the implementation of SEL programme’s activities.     

The Impact of Reform: Challenges for Mathematics Teacher Preparation

The mathematics education community has been widely recognized as a leader in the standards-based reform movement. Despite the widespread interest and attention that reform documents such as the NCTM Standards have generated, what has yet to be fully understood is the impact of these types of reform documents on the preservice teacher preparation process. This paper examines the state of the standards-based reform effort in mathematics teacher education by presenting the results of a three-year study of six cohorts of secondary mathematics student teachers (n = 63). Examined in particular are the ways in which these student teachers' professed beliefs about and knowledge of the NCTM Standards contrast with their teaching practices. Possible explanations for the mismatch between belief and knowledge statements and teaching practices are examined, along with other implications for mathematics teacher preparation.     

The quality of student ratings of teacher behaviour

In a research project into the effectiveness of mathematics teaching in the first year of secondary education, external observers and students rated teachers' behaviour. The reliability and validity of both methods were established. The results show that teacher behaviour is assessed well when student ratings are aggregated at the classroom level. The quality of aggregated student ratings is as good as the quality of data from external observers. The predictive validity of aggregated student ratings is higher than the predictive validity of external observations when subject motivation is taken as a dependent variable.     

Mentor teachers: Their perceived possibilities and challenges as mentor and teacher

This interview study, including seven case studies of mentor teachers in primary education, explores the possibilities and challenges these mentor teachers perceive when they (sequentially and simultaneously) combine the teacher and mentor roles. Mentor teachers perceive two challenges while simultaneously performing both roles in the same classroom: to transfer (or not) responsibility for the class and pupils to the student teacher and to intervene (or not) in classroom procedures. Mentor teachers felt that being the teacher of the pupils was their primary task, and being a mentor of the student teacher generally was perceived as an aside and additional task.     

Student teachers’ discipline strategies: relations with self-images,anticipated student responses and control orientation

Teacher discipline strategies are well documented when it comes to its effects on students and the working climate in the classroom. Although it is commonly acknowledged that for student teachers classroom management is a major concern, student teachers’ use of discipline strategies is largely unknown. In this paper, we examine student teachers’ beliefs in relation to their discipline strategies. Three clusters of discipline strategies are distinguished: sensitive, directive and aggressive discipline strategies. Beliefs that were taken into account are self-images on control and affiliation, control orientation and anticipated student responses on control and affiliation. All participants were student teachers of a one-year teacher education programme for secondary education in the Netherlands. Student questionnaires were used to measure discipline strategies (n?=?2506). Student teachers’ (n?=?104) self-images, control orientation and anticipated student responses were measured with student teacher questionnaires. Results of the multiple regression analyses showed that student teachers’ sensitive and directive discipline strategies are explained best by self-images on control; aggressive discipline strategies are explained best by self-images on affiliation and by control orientation. Apart from the possible academic interest in these particular findings, results are believed to be useful in a practical sense, in particular for teacher education programmes.     

Associations of newly qualified teachers’ beliefs with classroom management practices and approaches to instruction over one school year

We focus on assessing whether newly qualified teachers’ professional outcome expectations and their beliefs about students’ intellectual potential are associated with teachers’ self-reported classroom management and instructional practices. One hundred and eighteen novice teachers participating in the induction year programme were studied during their first years as full-time teachers. Results attest to a salient association between teachers’ more optimistic views of the malleability of students’ intellectual potential and teachers’ confidence in themselves as positive change agents in student outcomes. Also, teachers’ belief-set in the beginning of their career was shown to be associated with significant differences in the level of using instructional practices promoting mastery goal orientation in the classroom as well as offering students emotional support during the learning process. In the light of the significant belief–behaviour links demonstrated, more explicit attention to the sophistication of teachers’ ability beliefs in teacher education programmes is recommended.     

特殊教育学校数学教师知识结构:现状、成因及对策研究

通过问卷、听课、访谈调查,了解特殊教育学校数学教师知识掌握情况。统计结果表明,特殊教育学校数学教师对知识的掌握程度依次为数学知识、教育学与心理学知识(两者之间没有显著性差异)、其它知识。与普通小学数学教师知识掌握情况进行对比,在数学基础理论、数学思想方法、数学新课程和教学、数学学习认知与心理等方面的知识有显著性差异,知识结构欠合理,深度与广度上存在明显缺失。特殊教育学校数学教师应树立终生教育的理念,顺应特殊教育课程改革的需要,在知识发展的目标、内容、方式、保障机制等方面制定对策,以促进知识的发展。     

Comparing the effectiveness and costs of different approaches for educating primary school teachers in Sri Lanka

The effectiveness and costs of three approaches to elementary teacher education in Sri Lanka — preservice, conventional inservice, and distance inservice — are examined. The effectiveness of these approaches was measured by teachers' theoretical and applied knowledge, classroom performance, and pupil achievement. Costs borne by the sponsoring institution and the teachers were evaluated. Although distance education was the most cost-effective of the approaches, graduates of colleges of education were significantly effective in producing high achievement in their pupils in mathematics and language. This finding is particularly important given the more difficult teaching situations in which they taught.     

'My eyes went wide open'– an evaluation of the special needs education awareness course at Molepolole College of Education, Botswana

This article is an evaluation of the special needs education awareness course run at Molepolole College of Education, Botswana. The course directly reflects the Government of Botswana's policy on special education and seeks to provide students with a wide range of skills and knowledge to help them identify and support pupils with a variety of special needs. It also seeks to examine teachers' attitudes towards the inclusion of children with a wide range of learning support needs in the ordinary school. The evaluation was carried out by Gareth Dart, senior lecturer in the Department of Special Needs Education at Molepolole College of Education, who, in this article, reports the views of the first cohort of student graduates to complete the full course. This account also includes feedback from staff at schools who were involved with supervising the students as they did their special education assignments while on teaching practice. Feedback from the students and teachers is very positive in terms of the content and effect of the course although Gareth Dart suggests that a more thorough evaluation will have to wait until the graduates have been in the field some time. In the future, there will be a need to assess the long-term impact of the course upon the practice of teachers; to review the sustainability of this form of teacher education; and to make judgements about the influence that new generations of teachers have upon schools and policies promoting inclusion.     

Mentor, Mentee and Mathematics: A Story of Professional Development

In this paper, I critically examine my role as a mentor to a group of mid-career mathematics teachers, to better understand how mentoring practices influence teacher learning. The teachers taught mathematics to Grades 5 or 6. They planned and taught lessons to promote conceptual understanding of mathematics through the use of discussions, and reflected on their own and pupils' learning in the process. The study lasted for a year. It draws on qualitative data from sources such as semi-structured interviews, participant observation, and teachers' reflective journals. As a mentor/researcher I found that in the case of mentees' perception of the mentor as a problem solver or evaluator of performance learning was inhibited, whereas mentor and mentee relationships established on mutual trust supported mentees' personal and professional growth. The close work with the teachers also gave me insights into aspects of learning influenced by teachers' beliefs and understanding of mathematics and of how learning takes place. The study has implications for other such teacher education initiatives, particularly in the context of developing countries like Pakistan. This revised version was published online in July 2006 with corrections to the Cover Date.     

Using Tasks to Explore Teacher Knowledge in Situation-Specific Contexts

Research often reports an overt discrepancy between theoretically/out-of context expressed teacher beliefs about mathematics and pedagogy and actual practice. In order to explore teacher knowledge in situation-specific contexts we have engaged mathematics teachers with classroom scenarios (Tasks) which: are hypothetical but grounded on learning and teaching issues that previous research and experience have highlighted as seminal; are likely to occur in actual practice; have purpose and utility; and, can be used both in (pre- and in-service) teacher education and research through generating access to teachers’ views and intended practices. The Tasks have the following structure: reflecting upon the learning objectives within a mathematical problem (and solving it); examining a flawed (fictional) student solution; and, describing, in writing, feedback to the student. Here we draw on the written responses to one Task (which involved reflecting on solutions of $ {\left| x \right|} + {\left| {x - 1} \right|} = 0 $ ) of 53 Greek in-service mathematics teachers in order to demonstrate the range of teacher knowledge (mathematical, didactical and pedagogical) that engagement with these tasks allows us to explore.     

Teacher stress and pupil behaviour explored through a rational-emotive behaviour therapy framework

Using the psychological framework of rational-emotive behaviour therapy, the principal aim of this study was to establish whether irrational beliefs, self-efficacy or pupil behaviour predicted teacher reports of stress. A secondary aim was to establish whether these variables, in addition to teachers’ verbal feedback to pupils in class, predicted on-task pupil behaviour. Participants consisted of 58 teachers from five secondary schools, who completed three self-report questionnaires examining teacher stress, self-efficacy and irrational beliefs. In addition, both teachers and pupils were systematically observed in class using a structured schedule. The results indicated that high self-reported irrational beliefs and low self-efficacy predicted high levels of teacher stress. In addition, high self-efficacy and low levels of negative comments directed at pupils’ social behaviour and academic work in the classroom predicted high levels of on-task pupil behaviour. The implications for supporting teachers in these areas are discussed.     

Mathematics Instruction in Safe Space: Prospective Elementary Teachers' Views of Mathematics Education

This article discusses findings from an investigation into 42 prospective elementary teachers' views of mathematics teaching and learning. The focus is on how the participants saw the roles of teachers, pupils,and mathematics in mathematics classes as they communicated their views in journals written during the study. I argue that some prospective teachers express a tendency to protect and relieve their future pupils from mathematics. I show how this tendency affects a shift from school being the place where teachers teach pupils toward a conception of a safe space where the teachers predominantly care for the children. This revised version was published online in September 2006 with corrections to the Cover Date.     

Educating Student Teachers to Use Small Groups in Secondary‐school Music Classrooms

The use of small groups in teaching classroom music is often accepted in the literature and by expert teachers as a natural part of a music‐education programme. However, research indicates that the classroom teacher commonly does not make use of small‐group activities and that, when small groups are used, the results are not always positive. This article describes a teacher‐education course aimed at developing student teachers’ abilities to manage small groups in the secondary‐school music classroom, and reports the perceptions of both student teachers and teacher‐observers when the students applied their learnings in the practicum setting.