The nature and development of middle school mathematics teachers’ knowledge

In this article, we report on the use of a teacher profiling instrument with 62 middle school teachers at the start of a 3-year professional learning programme. The instrument was designed to assess the aspects of teachers’ knowledge identified by Shulman (1987) refined by Ball et al. (2008) and extended to include teachers’ confidence to use and teach various topics in the middle school mathematics curriculum and their beliefs about mathematics teaching and learning. Based on a hierarchical coding of items, the application of the partial credit Rasch model revealed that the profile items were measuring a single underlying construct and suggested that the various facets of teacher knowledge develop together. We describe the characteristics of four levels of the hierarchical construct measuring teacher knowledge and understanding for teaching mathematics in the middle years of schooling, and discuss the unique affordances of a holistic view of teacher knowledge in contrast to considerations of multiple knowledge categories.     

Sharing teacher knowledge at scale: teacher inquiry,learning design and the representation of teachers’ practice

Sharing teachers’ professional knowledge remains challenging. Teachers’ development often remains ad hoc or local, and attempts to scale this up have proved problematic. To address this, research in areas such as ‘learning design’ has explored the use of formal representations of practice. This proposes that educational practice can be improved by documenting, sharing and building on what teachers already do. Whilst this has led to some successes, it has not resulted in the widespread transformation of practice. This paper reviews the literature about sharing teacher knowledge. The challenges of scaling up development are then considered in relation to two theories that help explain the challenges: Communities of Practice and Sociomateriality. This analysis is illustrated through case studies in Norway and the UK. These show that teachers already create and share artefacts that represent their pedagogic knowledge. However, they found formal representations, such as learning designs, difficult to work with. The paper concludes that scaling up teacher development using abstract formalisms is unlikely to succeed. Instead, teachers value stories and the materials they already create in their day-to-day practice. It is this intermediate level of representation, between direct experience and formal abstraction, that offers the most promise for sharing practice.     

The development of student teachers’ research knowledge,beliefs and attitude

This study reports on the development of second-year student teachers’ knowledge of research, and the changes in their beliefs and attitude regarding research during an introductory course at an institute for primary teacher education. Questionnaires and concept maps were administered before and after the course. The results showed that student teachers’ knowledge about research grew during the introductory course and that their positive beliefs about research became more positive, while their negative beliefs about research decreased. A positive change was found concerning the attractiveness of research to student teachers. Furthermore, student teachers’ self-efficacy regarding research appeared related to their beliefs and attitude: the more the student teachers were convinced of their abilities to conduct and use the results of research after the course, the more positive their beliefs and their attitude regarding research were. This study provides guidelines for institutes for teacher education on integrating research activities into their curricula, so that their student teachers develop research knowledge and positive beliefs and attitudes towards research.     

In support of teachers’ learning: specifying and contextualising teacher inquiry as professional practice

Drawing upon research into a case study of teacher inquiry in one school in Queensland, Australia, recent theorising into professional practice, and relevant literature on teachers’ learning, this article reveals the complexity and particularity of teacher inquiry processes in support of teachers’ learning. Specifically, the research reveals how particular actions, dialogue, and relationships collectively constitute a practice of teacher inquiry which seeks to promote substantive teacher-led learning. The research draws upon a group of Year 5 teachers engaged in collective inquiry into their work in what was described as an “Inquiry Cycle” approach in a school in northern Queensland, during a period of support for substantial curriculum reform. The research reveals the Inquiry Cycle approach as characterised by specific actions, dialogue, and relationships – “doings,” “sayings,” and “relatings” – productive of the development of a learning culture focused on significant curriculum reform; overt support for whole-school “explicit” approaches to teachers’ pedagogies; and active/robust critique of data-focused assessment processes. The research reveals necessary texture and detail in support of teachers’ learning, and the specific circumstances and contextual “arrangements” that help constitute this learning.     

The contribution of research to teachers’ professional learning and development

This paper summarises findings from several systematic research reviews about the contribution of research to effective continuing professional development and learning (CPDL) activities and their impact on pupils and teachers. It starts with a review of how teachers engage in and with research as part of CPDL, how teachers and researchers shape professional learning activities and identifies key processes linked to positive outcomes. Finally it explores how different research contributions can be developed to make a more visible contribution to CPDL.The paper highlights common characteristics of effective CPDL, including: sustained collaboration with professional colleagues, including both making use of specialist expertise and structured peer support for embedding specialist contributions; an understanding of and commitment to professional learning, including enquiry-oriented learning and learning to learn from looking; a focus on refining teaching and learning, working towards aspirations for specific pupils side by side with theory; and effective scaffolding and modelling of learning by both teachers and leaders for colleagues and for pupils. The key implications of these findings are explored in the conclusions and include the importance of conceptualising researchers’ contributions to CPDL as specialist expertise and/or researchers and Masters tutors harnessing the potential of peer support between teachers. They also explore overlaps between core research and teaching skills and the need for a shared language between teachers and researchers to enable concepts like analysis, theory and criticality to be valued as practical tools for enhancing professional practice.     

Promoting equity in mathematics teacher preparation: a framework for advancing teacher learning of children’s multiple mathematics knowledge bases

Research repeatedly documents that teachers are underprepared to teach mathematics effectively in diverse classrooms. A critical aspect of learning to be an effective mathematics teacher for diverse learners is developing knowledge, dispositions, and practices that support building on children’s mathematical thinking, as well as their cultural, linguistic, and community-based knowledge. This article presents a conjectured learning trajectory for prospective teachers’ (PSTs’) development related to integrating children’s multiple mathematical knowledge bases (i.e., the understandings and experiences that have the potential to shape and support children’s mathematics learning—including children’s mathematical thinking, and children’s cultural, home, and community-based knowledge), in mathematics instruction. Data were collected from 200 PSTs enrolled in mathematics methods courses at six United States universities. Data sources included beginning and end-of-semester surveys, interviews, and PSTs’ written work. Our conjectured learning trajectory can serve as a tool for mathematics teacher educators and researchers as they focus on PSTs’ development of equitable mathematics instruction.     

Measuring teachers’ knowledge of vocabulary development and instruction

This article describes the development of an instrument to measure teachers’ knowledge of vocabulary development and instruction, the Teacher Knowledge of Vocabulary Survey (TKVS). This type of knowledge has become increasingly important as all classroom teachers are expected to help students meet language and literacy standards that include vocabulary acquisition. While a few studies have measured teacher knowledge of reading, there are no known instruments for measuring teachers’ knowledge of vocabulary development and instruction. However, vocabulary is a crucial determinant of reading comprehension and content area knowledge, particularly for English learners (Graves, August, & Mancilla-Martinez, 2013). Statements about vocabulary development and instruction were gathered from foundational texts, reviewed by subject matter experts, and researched in cognitive labs for possible inclusion as items in the TKVS. The survey’s 52 statements comprise 6 categories, including one section on vocabulary development, four sections on instruction, and one section on instruction specifically for English learners. Ratings of item difficulty by subject matter experts were then used to distinguish three levels of teacher knowledge of vocabulary: emergent, intermediate, and expert. Fifty teachers completed the TKVS, and their performance was found to correlate with the experts’ predicted difficulties of the items. Initial analyses provide evidence for the content and construct validity of the TKVS as a measure of teacher knowledge of vocabulary development and effective instruction. The discussion considers implications for the use of the instrument, including as a needs assessment or guide for professional development for both preservice and inservice teachers.     

Using representations of practice to elicit mathematics teachers’ tacit knowledge of practice: a comparison of responses to animations and videos

This study compared conversations among groups of teachers of high school geometry that had been elicited by a representation of instruction (either a video or an animation) and facilitated with an open-ended agenda. All artifacts used represented instruction scenarios that departed from what, according to prior work, had been hypothesized as normative. We used as the dependent variable the proportion of modal statements about instructional practice made by a group, which we argue is a good quantitative indicator that the statement appeals to the group’s knowledge of the norms of practice. Animations and videos produced similar proportion of modal statements, but the types of modal statements differed—with animations being associated with more statements of probability and obligation and videos being associated with more statements of inclination. Overall, the results suggest that animations are just as useful as videos in eliciting these sorts of orientational meanings.     

Short-term professional learning that focuses on beliefs and practice: Improvements in preschool teachers’ ongoing literacy practice

An intervention study was conducted with preschool teachers to address their beliefs and practice in the area of language and literacy. A total of 27 preschool teachers, each from different early childcare centers, participated in three 1-day professional learning sessions over the course of 9 months. Learning sessions focused on three different language and literacy topics. Study participants completed a pre- and post-session questionnaire and were observed in the classroom before and after each session. Significant differences were observed in both their beliefs and practice after the intervention. Specifically, preschool teachers’ beliefs were related to their practice in two areas: oral language and vocabulary; and book reading. Based on the data, a focus on beliefs and practice in future short-term PL or workshop models may support successful outcomes in teaching practice.     

The impact of educational development workshops on teachers’ practice

Abstract

Workshops are common practice as a staff and educational development tool in higher education around the world, yet while it is common to seek participants’ immediate reactions there been little attempt made to measure their impact. This paper reviews the available literature on the effectiveness of workshops and reports the findings of a study in to the effectiveness of 33 workshops delivered by the Oxford Centre for Staff and Learning Development over a four month period. The study used questionnaires at the end of the workshops and four months later, and these were followed up by telephone interviews with a sample of participants. The study demonstrates that workshops can lead to changes in practice, and that these changes are themselves deemed to be successful by those involved. In addition, where at the end of a workshop participants report that they are likely to make changes this can be used as a reasonably accurate predictor of subsequent change. The features of workshops identified in end‐of‐workshop questionnaires which are linked with likelihood of subsequent change are also reported.     

Constructing constructivism: how student‐teachers construct ideas of development,knowledge, learning,and teaching

This case study investigates the development of the understanding of constructivist theory among students in a Masters level elementary teacher education program within a particular course. The focus of the study is a seminar entitled ‘Advanced Seminar in Child Development’. The questions explored include: How do students’ ideas of teaching, learning and knowledge develop within the context of their experience in this course? How do they come to understand constructivism? What are their definitions of constructivism? What is the course of the development of this understanding? The nature of the students’ learning processes is examined through three sources of data: dialog journals, videotaped sessions and the instructor’s reflective teaching journal. The study looks both at student development and instructional practice to further understanding of how student‐teachers can learn to apply constructivist theory to their teaching and to understand the learning process, both within themselves and their students. Their development is placed in the context of Korthagen and Kessels’s model of teacher understanding and practice, and within a broader context of principles of practice that emphasize a belief in equity and social justice. The case illustrates how the way student‐teachers are taught theory can help them integrate their own ideas of learning and teaching with constructivist theory in order to think critically about their own practice in an ongoing developmental manner.     

The building of pre-service primary teachers’ knowledge of mathematics teaching: interaction and online video case studies

This study explores how preservice primary teachers became engaged in meaning-making mathematics teaching when participating in online discussions within learning environments integrating video-clips of mathematics teaching. We identified different modes of participation in the online discussions and different levels of knowledge-building. The data can be explained by the type of task set in the learning environments and by a gradually improved shared understanding of the teaching. The structure of the learning environments supported inquiry into meaningful topics and knowledge-building through activities like identifying, interpreting and designing. These findings suggest that the different types of task and conditions of online discussion in the learning environments influence the nature of the interaction showing the correspondence between synergistic interaction and higher-order thinking.     

Promoting teachers’ awareness about mathematics,its teaching and learning

Journal of Mathematics Teacher Education -     

The effect of teacher education programs on future elementary mathematics teachers’ knowledge: a five-country analysis using TEDS-M data

This article addresses the problem of how opportunities to learn in teacher education programs influence future elementary mathematics teachers’ knowledge. This study used data collected for the Teacher Education and Development Study in Mathematics (TEDS-M). TEDS-M measured the mathematics content knowledge (MCK) and the mathematics pedagogical content knowledge (MPCK) of future teachers in their final year in teacher preparation programs. The purpose of this study is to explore whether elementary teaching candidates’ MCK and MPCK are associated with their opportunities to learn in mathematics courses and mathematics methods courses in five countries. The results showed that opportunities to learn in some teacher preparation components are more important than in other components.     

Governing teacher learning: understanding teachers’ compliance with and critique of standardization

This paper examines how policy pressure for increased performance on standardised measures of student achievement influenced the teacher learning practices that arose in a school setting in Queensland, Australia. Drawing upon research and theorising of governing by numbers, and applications to the governance of education, and particularly teachers’ learning, the research analyses how a group of Year 3 teachers collaborated to better inform themselves about the nature of their students’ learning. The research reveals that the governance of teachers’ learning under current policy conditions was manifest through both teachers’ compliance with and critique of a strong focus upon school, regional, state and national data – specifically, students’ attainment in ‘leveled’ readers and other school-based standardised measures of reading and mathematics, and school, state and regional results on national literacy and numeracy tests. There is little research that highlights the tensions around these numbers as governing technologies in relation to specific formal, ongoing instances of teacher professional development practices. The research cautions against the influence of such governing processes for how they potentially narrow teachers’ attention to more standardized measures of students’ learning, even as teachers may critique these more reductive effects.     

Accountability conversations: mathematics teachers’ learning through challenge and solidarity

Teacher learning through professional development is a complex process and is not yet well understood. Some features of professional development programs are known to be important, such as a focus on learner needs, design of and reflection on classroom artefacts, and the creation and sustaining of communities of support for teacher professional learning. In this paper, we describe the workings of such communities in a teacher professional development program, which focused on learner errors in a well-researched mathematical topic—the equal sign. Drawing on data from program sessions where teachers discussed their lesson designs and reflections on their teaching with each other, we develop the notions of challenge and solidarity as important in developing accountability conversations among teachers. We show how our program supported teachers to challenge each other and to build solidarity with each other and in so doing to develop accountability to each other and the profession, for their practices and their learning.     

The development of teachers’ knowledge and behaviour in promoting self-discipline: a study of early years teachers in Thailand

The study reported in this paper examines the challenges of developing an in-service training programme for early years teachers in a school in Thailand relating to the topic of enhancing young children’s self-discipline. It is argued that in-service training in Thailand has tended to focus on knowledge acquisition through direct instruction during short courses. By contrast, the training programme developed during the project employed the Socialisation, Externalisation, Combination and Internalisation (SECI) Model, first developed in Japan, that integrates knowledge acquisition with social learning activities. A blended methodology was employed to examine the efficacy of the SECI approach that included interviews with teachers and school leaders, classroom observation, questionnaires and behaviour checklists. Findings suggest that an adapted SECI model is effective in the education of teachers in Thailand and may have relevance more widely in the field of teacher education in other nations.