Secondary mathematics cooperating teachers’ perceptions of the purpose of student teaching

This article reports on the results of a survey of 45 secondary mathematics cooperating teachers’ perceptions of the primary purposes of student teaching and their roles in accomplishing those purposes. The most common purposes were interacting with an experienced, practising teacher, having a real classroom experience, and experiencing and learning about classroom management. The most common roles were providing the space for experience, modeling, facilitating reflection, and sharing knowledge. The findings provided insights into the cooperating teachers’ perceptions about both what should be learned through student teaching and how it should be learned. These findings paint a picture of cooperating teachers who do not see themselves as teacher educators—teachers of student teachers. Implications for mathematics teacher educators are discussed.     

Students’ conception of infinite series

This is a report of a study of students’ understanding of infinite series. It has a three-fold purpose: to show that students may construct two essentially different notions of infinite series, to show that one of the constructions is particularly difficult for students, and to examine the way in which these two different constructions may be built so that we may uncover ways to help students improve their understanding. The theoretical framework consists of action–process–object–schema theory and the specific model of conceptions in Balacheff’s theory of conception, knowing, and concept. Approaching the problem from these two different theoretical perspectives allows us to provide different and at the same time complementary explanations of observed phenomena. The two different infinite series constructions are, briefly stated, series as an infinite unending process of addition and series as a sequence of partial sums. Students are found to have difficulty building an understanding of series as a sequence of partial sums and thus tend to have difficulty in problem situations that require this interpretation. The study uses semi-structured interviews with 10 graduate students. The interviews explore situations that might give insight into students’ notion of the sequence of partial sums.     

Studying culturally valued texts: teachers’ conception vs. students’ conceptions

This study is based on in-depth interviews with Israeli teachers and students studying culturally valued texts and focuses on their respective conceptions of Bible studies. The findings indicate that the students see their encounter with the Bible as first and foremost a process of cultural encounter with the text. On the other hand, teachers see their role as one of imparting knowledge and one which is almost devoid of any cultural dimension. The paper concludes that the teachers of Bible and other culturally valued texts should change their conception of their role from one focusing on the transmitting of knowledge to one focusing on intercultural mediating.     

Secondary teachers’ knowledge of elementary number theory proofs: the case of general-cover proofs

In light of recent reform recommendations, teachers are expected to turn proofs and proving into an ongoing component of their classroom practice. Two questions emerging from this requirement are: Is the mathematical knowledge of high school teachers sufficient to prove various kinds of statements? Does teachers’ knowledge allow them to determine the validity of an argument made by their students? The results of this study, in which 50 secondary school teachers participated, point to a positive answer to the first question in the framework of elementary number theory (ENT). However, the picture is more complex with respect to the second one. Results indicated that some teachers may over-value the generality of symbolic mode of representation and under-value the generality of verbal ones. Possibly, the verbal representation of an argument is less transparent and more difficult to understand.     

Investigating further preservice teachers’ conceptions of multidigit whole numbers: refining a framework

This study was designed to investigate preservice elementary school teachers’ (PSTs’) responses to written standard place-value-operation tasks (addition and subtraction). Previous research established that PSTs can often perform but not explain algorithms and provided a four-category framework for PSTs’ conceptions, two correct and two incorrect. Previous findings are replicated for PSTs toward the end of their college careers, and two conceptions are further analyzed to yield three categories of incorrect views of regrouped digits: (a) consistently as 1 value (all as 1 or all as 10), (b) consistently within but not across contexts (i.e., all as 10 in addition but all as 1 in subtraction), and (c) inconsistently (depending on the task).     

Dewey’s conception of vocation: existential,aesthetic, and educational implications for teachers

I offer a close reconstruction of John Dewey’s account of vocation in Democracy and Education, bringing out the existential and aesthetic dimensions of Dewey’s idea that vocations constitute perceptual environments for their practitioners. Although Dewey offers this idea to teachers only as an insight about student development, I contend that its most powerful educational implication concerns the growth of teachers. Picking up where Dewey left off, I investigate to what extent teaching constitutes an educative environment for teachers. I conclude that, while the environment of teaching is an exceedingly rich one, the basic working conditions of teachers and the ethos of education often frustrate their attempts to interact with this environment. I conclude with a critique of some of the forces that narrow the range of what teachers notice, feel, and learn in the course of their work.     

Secondary science teachers’ implementation of CCSS and NGSS literacy practices: a survey study

Most middle and high school students struggle with reading and writing in science. This may be because science teachers are reluctant to teach literacy in science class. New standards now require a shift in the way science teachers develop students’ literacy in science. This survey study examined the extent to which science teachers report implementing science literacy practices from the Common Core Literacy in Science and Technical Subjects and the Next Generation Science Standards with their students. A survey detailing these practices was emailed to all secondary science teachers (N = 2519) in one northeastern state and 14% of them (n = 343) responded. Practices that aligned more closely with disciplinary literacy skills and strategies were implemented more often when compared to the practices aligned with intermediate literacy skills and strategies. Since the development and intermediate skills are important to support students’ literacy progression from foundational to disciplinary, secondary science teachers may not be providing enough support for their students to be competently literate in science, in a fundamental literacy sense. This, in turn, impacts students’ ability to use fundamental literacy skills toward knowledge-building in science, achieving a derived sense of science literacy.     

Levels of students’ “conception” of fractions

In this paper, we examine sixth grade students’ degree of conceptualization of fractions. A specially developed test aimed to measure students’ understanding of fractions along the three stages proposed by Sfard (1991) was administered to 321 sixth grade students. The Rasch model was applied to specify the reliability of the test across the sample and cluster analysis to locate groups by facility level. The analysis revealed six such levels. The characteristics of each level were specified according to Sfard’s framework and the results of the fraction test. Based on our findings, we draw implications for the learning and teaching of fractions and provide suggestions for future research.     

Stimulating pre-service teachers’ content and pedagogical content knowledge on rational numbers

This study explored the perspectives of mathematics teacher educator-researchers (MTE-Rs) on the use of theory in facilitating teacher growth. We adopted the framework of the theory-centered scholarship triangle (Silver & Herbst, 2007) to probe the underlying meanings of perspectives on theory use expressed by MTE-Rs. Qualitative analysis revealed three distinct types of perspectives: a perspective focusing on research, a perspective focusing on practice, and a perspective on the connection between research and practice. For the perspective on the connection between research and practice, two sub-categories were identified: connection with consideration of context and that without consideration of context. Different perspectives that MTE-Rs possess may influence their actions taken in professional development and consequently influence teachers’ learning of theory. Specifically, the cyclic process of decontextualizing and recontextualizing theory between research and practice domains is the key to the development of MTE-Rs’ educative power so that they can better facilitate teachers in learning theory.     

Secondary school teachers’ perceptions of adolescent social anxiety and learning and development in the classroom

Social anxiety has been linked with adverse consequences for adolescents in education, including low self-efficacy, poor academic attainment and difficulties with social functioning. However, studies have not considered the phenomenon from an educator’s point of view. We set out to explore the perceptions of secondary school teachers concerning socially anxious adolescents and the implications of social anxiety for their learning and development. Seven secondary school teachers in the north west of England took part in semi-structured interviews focused on their lived experiences of supporting socially anxious adolescents. The findings suggest that educators perceive social anxiety to have the potential to be persistent and debilitating, impeding learning and development. The findings also demonstrate that teachers are aware of social anxiety and supportive strategies, but face difficulties in disentangling different anxious behaviours and providing differentiation. Conclusions indicate that recurring professional development and teacher training surrounding anxieties and comorbid behaviour may alleviate negative consequences for learning and development.     

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.     

Mathematics teachers’ representations of authority

Issues of authority abound in education and schooling but have not been interrogated sufficiently. We describe a tool that we have developed to initiate dialogue with teachers about authority in their classrooms—using a diagram to represent authority in their classrooms. Our analysis of the diagrams mathematics teachers created and discussed in our work with them illustrates the importance of understanding teachers’ perspectives about authority. To understand better how mathematics teachers think about the authority in their classrooms, we investigated what sources of authority they represented in their diagrams, and how the teachers related these sources to each other. The diversity in the teachers’ representations exceeded our anticipations, indicating that research on authority in classrooms has merely scratched the surface of understanding the ways mathematics teachers think about authority in their classrooms.     

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.     

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.     

Struggling to balance various stakeholders’ perceptions: the work life of ideo-political education teachers in China

As a compulsory course at universities throughout the Chinese Mainland, ideo-political education aims to safeguard university students’ political loyalty to the Communist Party. By employing a qualitative research method, this study investigated a renowned comprehensive university in southern China. The case study found that students expressed strong resistance to compulsory ideo-political courses. From the outset, teachers had to work to change students’ overwhelmingly negative perceptions of ideo-political education. Informants found that they could not attract student interest if they only strictly followed the state designed textbook, and therefore chose instead to cover topics they found more interesting and to discuss social issues in their lectures. However, the new curriculum reform and teaching quality assurance mechanism placed further restrictions on teaching and learning. Whether teachers could maintain enough autonomy to make the above adjustments depended on the understanding and support of key senior academics.     

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.     

Secondary teachers’ experiences with students with disabilities: examining the global landscape

This study contributes to the international conversation about the education for students with disabilities at the secondary level by providing some international data about secondary teachers’ training and experiences with inclusive practices. Teacher leaders from 20 different countries participated in this exploratory survey research about the context in which they work, their experiences and their training as related to their efficacy to educate individuals with disabilities. We acknowledge that efficacy and teacher training for inclusion are predominated by a discourse defined through Western best practice. We learned that despite variations in the countries’ concept of disability and their implementation of inclusive educational systems, the teachers had moderately high self-efficacy for inclusive practices yet had limited training and experience with students with special needs. Results are discussed in relation to the preparation of secondary teachers for educating students with special needs.     

Expressions of agency within complex policy structures: science teachers’ experiences of education policy reforms in Sweden

We explore the experiences of school science teachers as they enact three linked national curriculum and assessment policy reforms in Sweden. Our goal is to understand teachers’ differing responses to these reforms. A sample of 13 teachers engaged in 2 interviews over a 6–9-month period. Interviews included exploration of professional background and school context, perceptions of the aims of the policy reforms and experiences of working with these reforms in the classroom. Analysis was guided by an individual-oriented sociocultural perspective on professional agency. Here teaching is conceptualised as an ongoing interplay between teachers’ knowledge, skills and personal goals, and the characteristics of the social, institutional and policy settings in which they work. Our analysis shows that navigating the ensuing continuities and contradictions results in many different expressions of teacher agency, e.g. loss of autonomy and trust, pushing back, subversion, transfer of authority, and creative tensions. Typically, an individual teacher’s enactment of these reforms involved several of these expressions of agency. We demonstrate that the sociocultural perspective provides insights into teachers’ responses to education policy reform likely to be missed by studies that focus largely on individual teacher knowledge/beliefs about reform or skills in ‘implementing’ reform practices.