Mathematics teachers’ values about teaching mathematics

Not much is known about mathematics teachers’ values, and no assessment tool is available for measuring these to get more insight into their perspectives. The goals of this study are to construct the Mathematics Teachers’ Values Questionnaire (MTVQ) and to determine mathematics teachers’ values about teaching mathematics using the MTVQ. In order to do this, data have been gathered for exploratory factor analysis (n = 637) and confirmatory factor analysis (n = 573) while developing the instrument, and a proportional stratified random sample has been formed consisting of 2226 Turkish middle and high school mathematics teachers working at schools that provide more religious education than other middle and high schools. Five components have been extracted: relevance (C1), practice (C2), information and communications technology (ICT; C3), teaching approach (C4), and consolidating (C5). One result of the study reveals the mathematics teachers emphasize the least ICT value and the most consolidating value.     

Mathematics teaching life histories in the study of teachers’ perceptions of change

The aim of this paper is to discuss teachers’ perceptions of change in their thought and/or practice over time and their perceptions of what kind of experiences or challenges might have influenced those changes. Two mathematics teaching life histories of Brazilian teachers are examined, considering a context of curriculum development in the state of São Paulo, Brazil. Reflection on teachers’ thought and practice and interest in their own development, including interest in their own learning of mathematics, seemed to be the most important internal aspects influencing change and development. Close support seemed to be the most important external aspect. The retrospective analysis put a good face on personal change and development.     

Mathematics teachers’ learning: a conceptual framework and synthesis of research

How do practicing mathematics teachers continue to develop the knowledge and habits of mind that enable them to teach well and to improve their teaching over time? The question of how (and what) teachers learn lies at the crux of any effort to provide high-quality mathematics teaching for all students. This article reviews 106 articles written between 1985 and 2008 related to the professional learning of practicing teachers of mathematics. We offer a synthesis of this research, guided by Clarke and Hollingsworth’s (Teach Teach Educ 18(8):947–967, 2002) dynamic model of teacher growth. Their model emphasizes the recursive nature of teachers’ learning and suggests that growth in one aspect of teachers’ knowledge and practice may promote subsequent growth in other areas. We report the results in six major areas of teacher learning, identify several crosscutting themes in the literature, and make recommendations for future research aimed at understanding teachers’ professional learning.     

Mathematics teachers’ self-captured video and opportunities for learning

Numerous video-based programs have been developed to support mathematics teachers in reflecting on and examining classrooms interactions without the immediate demands of instruction. An important premise of such work is that teacher learning occurs at the time that the video is viewed and discussed with teachers. Recent advances in technology, however, offer new approaches for the use of video with teachers. We claim that these new technologies provide important opportunities for teacher learning prior to the viewing and discussion of video with colleagues. In particular, we believe that important teacher learning can occur from the activities of (1) capturing video from one’s own classroom and (2) selecting clips to share with others. The goal of this article is to introduce key strategies that three groups of middle and high school mathematics teachers use prior to, during, and after instruction as they engage in this work. We believe that increased attention to these strategies is necessary in order to better understand how to support teacher learning in the context of new digital technologies.     

The influence of textbooks on teachers’ knowledge of chemical bonding representations relative to students’ difficulties understanding

Background: Textbooks are integral tools for teachers’ lessons. Several researchers observed that school teachers rely heavily on textbooks as informational sources when planning lessons. Moreover, textbooks are an important resource for developing students’ knowledge as they contain various representations that influence students’ learning. However, several studies report that students have difficulties understanding models in general, and chemical bonding models in particular, and that students’ difficulties understanding chemical bonding are partly due to the way it is taught by teachers and presented in textbooks.

Purpose: This article aims to delineate the influence of textbooks on teachers’ selection and use of representations when teaching chemical bonding models and to show how this might cause students’ difficulties understanding.

Sample: Ten chemistry teachers from seven upper secondary schools located in Central Sweden volunteered to participate in this study.

Design and methods: Data from multiple sources were collected and analysed, including interviews with the 10 upper secondary school teachers, the teachers’ lesson plans, and the contents of the textbooks used by the teachers.

Results: The results revealed strong coherence between how chemical bonding models are presented in textbooks and by teachers, and thus depict that textbooks influence teachers’ selection and use of representations for their lessons. As discussed in the literature review, several of the selected representations were associated with alternative conceptions of, and difficulties understanding, chemical bonding among students.

Conclusions: The study highlights the need for filling the gap between research and teaching practices, focusing particularly on how representations of chemical bonding can lead to students’ difficulties understanding. The gap may be filled by developing teachers’ pedagogical content knowledge regarding chemical bonding and scientific models in general.     

Mathematics and science teachers’ pedagogical orientations and their use of ICT in teaching

The key concern driving policy and community interest in the pedagogical integration of ICT is the premise that ICT is important for bringing changes to classroom teaching and learning, so as to foster the development of students’ 21st century skills. An important concept underpinning the design of the SITES 2006 study is the pedagogical orientation of the teacher, which can be broadly conceptualized as traditionally important or 21 ^st century oriented. The latter can be further differentiated into lifelong learning and connectedness oriented. Indicators were created to measure teachers’ pedagogical orientation based on their espoused curriculum goals, teacher practices and student practices. Results from this study shed light on whether there is evidence that 21st century pedagogy as identified in the literature and in innovative practices can be found more generally in random samples of teachers in countries participating in SITES 2006. Relationship between ICT use and pedagogical practice in mathematics and science classrooms is reported and the associated policy implications are discussed.     

Mathematics teachers’ knowledge and skills about questioning in the context of modeling activities

Asking effective questions has been considered to be one of the most important indicators of good teaching since questioning is an important instructional tool and the ability to ask effective questions requires sophisticated pedagogical reasoning. Teachers can facilitate students’ higher-level thinking through effective questions. However, teachers’ utilization of effective and higher-level questions is usually limited in traditional settings. The goal of this study is to investigate how secondary mathematics teachers’ knowledge and skills of questioning change when they are engaged in professional development activities based on the modeling perspective. The program included five cycles each of which lasted a month. Each cycle consisted of meetings before and after the implementation of a model-eliciting activity and its implementation. The results showed that the professional development program had a positive effect on teachers’ ability to ask qualitatively different questions in order to move students’ thinking forward.     

Mathematics student teachers’ views on tutor feedback during teaching practice

A group of students studying to become mathematics teachers were asked to comment on the tutor feedback they received during teaching practice (TP) and to offer suggestions aimed at improving this feedback. Analysis of the written data – which was collected through emails – suggests the need for: (i) all TP tutors to provide good quality feedback; (ii) action aimed at deepening students’ understanding of feedback; and (iii) feedback improvement strategies that take into consideration the students’ sense of practicality. The ensuing discussion serves to promote the idea that teachers-to-be can learn a lot about the constructive role of feedback when they observe their tutors managing successfully during TP the inherent tensions between the formative and summative dimensions of assessment. This would require however a shift in pre-service teacher education from simply ‘teaching by telling’ to also ‘teaching by example’.     

Pre-service Mathematics Teachers’ Knowledge of History of Mathematics and Their Attitudes and Beliefs Towards Using History of Mathematics in Mathematics Education

This study examined pre-service mathematics teachers’ knowledge of history of mathematics and their attitudes and beliefs towards using history of mathematics in mathematics education based on year level in teacher education program and gender. The sample included 1,593 freshman, sophomore, junior, and senior pre-service middle school (grades 4–8) mathematics teachers from nine universities in Turkey. Data were collected through Knowledge of History of Mathematics Test and Attitudes and Beliefs towards the Use of History of Mathematics in Mathematics Education Questionnaire. Results indicate that pre-service teachers have moderate knowledge of history of mathematics and positive attitudes and beliefs towards using history of mathematics. Their knowledge scores increase as the year level in teacher education program advanced. Males’ knowledge scores are significantly higher than females’ scores in the first 2 years. This situation reverses in the last 2 years, but it is not statistically significant. Pre-service teachers have more positive attitudes and availing beliefs towards using history of mathematics as they progress in their teacher education program. Females have greater attitudes and beliefs mean scores than males in each of the years. The results indicate that the teacher education program may have enhanced the pre-service teachers’ knowledge of history of mathematics by related courses. However, the moderate knowledge scores indicate that there is a need for revision of these courses. The pre-service teachers’ positive attitudes and beliefs towards using history of mathematics stress the importance of teacher education program in order to prepare them for implementing this alternative strategy in the future.     

Screens of disorder: English cinema’s representation of teachers’ responses to challenges to their authority in the 1960s

Change across wider English society in the 1960s was characterised by a managed and relatively consensual social liberalism. There was a discernible cultural shift toward greater personal and sexual freedom. Within education in England, a revisionist approach sought to extend traditional education to a wider constituency, in particular incorporating the sometimes disaffected and unskilled working class. This context presented new challenges for 1960s teachers in their relationships with pupils. Through the 1950s and 1960s, English cinema portrayed England’s changing teacher–pupil relations. This article examines the nature of change in teacher–pupil relations, with particular regard to its impact upon teachers’ authority. English cinema’s representation is located within English societal change in the 1960s in relation to youth culture, education and attitudes to authority.

Several themes are identified. Teacher status appeared to contribute rather less to 1960s teachers’ authority and teachers’ personalities rather more. 1960s teacher–pupil relations were somewhat volatile. Relationships began to take place beyond the school gates. Films depicted greater diversity in teachers’ strategies to maintain their authority, with some teachers making concessions to pupils to preserve harmonious relations. A more prominent approach was teachers’ still more firm imposition of traditional discipline, attempting to hold back the tide of increased pupil hostility in classrooms, which more frequently featured the particular challenges posed by girls.

The analysis has relevance beyond England and beyond the 1960s. It explores the variety and fragility of teacher authority, highlights the pressure that maintaining discipline places upon individual teachers and recognises the appeal of classroom conservatism.     

Opportunities and challenges in the development of teachers’ knowledge: the development of narrative authority through knowledge communities

This work examines generative approaches to teacher professional development that pay attention to how personal, interpersonal, contextual and situational factors influence teacher knowledge developments over time. Using examples from our research programs, we show how critical it is to intentionally account for how teachers filter their professional development experiences through their personal practical knowledge expressed in community. By featuring Pat (the pre-service case) and Liz (the in-service case), we illustrate how teachers develop their narrative authority in knowledge communities and show why knowledge communities are critical to the sustained development of narrative authority. We argue that attending to these critical matters creates opportunities for understanding that can lead to confirmation of, refinement in, or transformation of present practices.     

Investigating teachers’ images of mathematics

Research suggests that understanding new images of mathematics is very challenging and can contribute to teacher resistance. An explicit exploration of personal views of mathematics may be necessary for pedagogical change. One possible way for exploring these images is through mathematical metaphors. As metaphors focus on similarities, they can be used to express already-held perceptions about the nature of mathematics. In addition to providing a way of talking about current views of mathematics, the analogous dimensions of metaphors can prompt new ways of thinking about these images. In this article, I consider the use of metaphors as a strategy for explicating elementary teachers’ views of mathematics. I claim that the investigation of metaphors of mathematics helped create a shared communicative space and enhanced the quality of the discussion with the teachers. In particular, our exploration of the metaphor mathematics is a language encouraged a consideration of the humanistic dimensions of mathematics and contributed to a varied re-imaging of mathematics.     

Mathematics education as sociopolitical: prospective teachers’ views of the What,Who, and How

In this article, I introduce a framework—the What, Who, and How of mathematics—that emerged from studying my teaching of prospective teachers and their views of the social and political dimensions of mathematics teaching and learning. The What, Who, How framework asks us to consider What messages we send about mathematics and the world, Whose perspectives are represented in mathematics, and How mathematical concepts and our world are related. I situate each aspect of the framework in the literature on social justice and critical mathematics and provide examples of prospective teachers’ views. The What, Who, How serves as a tool to understand prospective teachers’ views, to navigate a broad range of literature on social justice mathematics, and a means of informing the practice of teachers and teacher educators.     

Understanding teachers’ ‘levels of use’ of learnscapes

All eight teachers and their principal, at an Australian regional primary school in New South Wales (NSW) accredited for its ongoing ‘learnscape’ developments, were interviewed. This was to ascertain their perceptions about the role of learnscapes and their self‐reported use of such outdoor areas to assist in the achievement of their State’s syllabus and environmental education learning outcomes. Teachers at the school (6) and their principal were (re)interviewed a year later to determine if changes in perceptions and practice had occurred and why. This paper interprets narratives derived from the combined interviews of these latter teachers and their principal from an educational change perspective in order to gain insight into their level of use of learnscapes. Teachers’ learnscape and environmental education content and pedagogical knowledge, their focus on the consequences of learnscape use for student learning, and awareness of multiple learning outcomes, including social learning, when using learnscapes, were among interdependent change factors identified which may assist in understanding why teachers embraced learnscapes to different degrees. Consequent avenues for increasing the future use of learnscapes for syllabus and environmental purposes are suggested.     

Trainee teachers’ experience of reflection

This article reports an investigation of trainee teachers’ experience of reflection whilst undertaking a teaching qualification for the post-compulsory sector. The study used a sequential, mixed-methods design, employing a structured questionnaire and a semi-structured interview; 127 individuals completed the questionnaire about their experience of reflection and keeping a reflective journal. The questionnaire responses were used to select a sample of 15 individuals for interview. The findings indicate that, whilst the majority value reflection and believe keeping a journal is useful, finding time to reflect can be problematic. Two potential areas of difficulty are identified, namely, individual preferences for engagement with reflection and the use of reflective journals. Where course requirements are at variance with an individual’s preferred approach, difficulties with reflection may be experienced. Therefore this article recommends that course requirements need to allow flexibility to enable individuals to try different techniques and adopt whichever they are most comfortable with.     

Being professional: accountability and authority in teachers’ responses to science curriculum reform

The science curriculum is a focus of repeated reform in many countries. However, the enactment of such reforms within schools rarely reflects the intended outcomes of curriculum designers. This review considers what we know about the experiences and reflections of teachers in the enactment of externally driven school science curriculum reform. ‘Externally driven’ signals a focus on studies of teachers who did not make a proactive choice to adopt a particular curriculum reform initiative. This is a very common experience for teachers in many school systems, and one likely to highlight issues of professionalism and authority that are central to the work of teachers. The review analyses 34 relevant studies. These include studies of teachers’ experiences of national curriculum reform, and also studies focusing on more regional or local curriculum reform activities. The studies examine individual teachers’ beliefs, practices and reflections associated with curriculum reform, the response of teacher communities to reform (e.g. within school departments), and teachers’ (and other stakeholders’) experiences across school systems. A wide range of factors influencing teachers’ responses are identified. These are characterised in terms of personal, internal and external contexts of teachers’ work. The review also highlights issues of authority, professionalism and the process of meaning-making in response to external curriculum reform. The discussion section identifies important areas for future research and gives recommendations for the design of curriculum policies that recognise and support the professionalism of science teachers.     

Using representations,decomposition, and approximations of practices to support prospective elementary mathematics teachers’ practice of organizing discussions

This paper examines a series of instructional activities that provide prospective elementary teachers with an opportunity to engage in one of the more difficult practices to learn within mathematics teaching—organizing a mathematical discussion. Within a mathematics methods course, representations and decomposition of practice built from the Five Practices framework (Smith and Stein in Five practices for orchestrating productive mathematics discussions. Corwin Press, Thousand Oaks, CA, 2011) were implemented and studied to examine how prospective elementary teachers set goals, selected and sequenced available student work, and planned questions within a mathematical discussion. We examined prospective elementary teachers’ strengths and weaknesses in these facets through an approximation of practice set in a lesson context familiar to the prospective elementary teachers. Our results demonstrated that although prospective elementary teachers set varying goals for a discussion, their pedagogical choices in planning their discussion tended to be consistent with the goals they have set. These results support the focused development of prospective elementary teachers’ goal setting as an implication for mathematics teacher educators.     

Socio-cultural factors of teachers’ conceptions of knowledge: epistemic beliefs of Arab teachers

This research investigates aspects of epistemic beliefs of pre-service and in-service teachers in the United Arab Emirates, and how these beliefs might be related to factors such as teachers’ gender, location (where they live), and the subject they teach (humanities vs. science). A standardized Arabic version of the Epistemic Belief Inventory was administered to a group of 35 pre-service teachers and 52 in-service teachers. The results indicated that in-service teachers had more sophisticated beliefs than pre-service teachers on Certainty of Knowledge, Omniscient Authority, and Innate Ability dimensions. Also, male teachers were found to be less sophisticated than female teachers and teachers from rural areas tended to think in a simpler way than teachers from urban areas. Although there was no main effect of subject, it significantly modified the effects of gender and location. The data showed the multidimensional nature of epistemic beliefs, and were discussed in the context of Arab/Emirati culture.