Mathematics anxiety and mathematics teacher efficacy in elementary pre‐service teachers

This study investigated the relationship between mathematics anxiety and mathematics teacher efficacy among 156 elementary pre‐service teachers from a university in the southeastern United States. Data sources included the Mathematics Anxiety Rating Scale (MARS), Mathematics Teaching Efficacy Beliefs Instrument, and pre‐service teacher interviews. Findings revealed a significant, negative relationship between mathematics anxiety and mathematics teachers’ efficacy (r = ?.475, p<.05). Specifically, the pre‐service teachers with the lowest degree of mathematics anxiety had the highest levels of mathematics teacher efficacy. Interviews with pre‐service teachers indicated that their mathematics anxiety is associated with efficaciousness toward mathematics teaching practices and is the basis for their mathematics teaching efficacy beliefs.     

The measurement of teacher efficacy: Hong Kong primary in‐service teachers

This study sought to measure general teacher efficacy levels of in‐service primary teachers in Hong Kong. Participants included 725 Hong Kong in‐service teachers, who were invited to take part in the study. These in‐service teachers came from 28 different primary schools ranging from government, aided, private and direct subsidy schools. The Chinese version of the 12‐item Teachers' Sense of Efficacy (C‐TSE) Scale was applied to investigate the efficacy of the teachers. A factor analysis of these 12 items when male and female datasets were combined led to the extraction of only one factor. But separation of the two datasets led to the extraction of different factor analysis models. This could reflect the different perceptions that male and female teachers had about the formation of teacher efficacy. Overall, this study showed that female teachers were significantly more efficacious than male teachers. Moreover, years of teaching experience showed a weak but significant correlation to levels of general teacher efficacy. Interestingly, educational levels did not have a significant effect on the efficacy of this group of in‐service primary teachers. Overall, the C‐TSE was found to be a valid and reliable scale for measuring the efficacy levels of this particular group of in‐service primary teachers in Hong Kong.     

Raising attainment in mathematics — The story of Wolverton School

This paper has arisen from a case-study undertaken as part of ‘Whole School Action on Numeracy’, one of six linked projects in the Leverhulme Numeracy Research Programme. Studied over four years, ‘Wolverton’ School emerged as a success story in terms of consistently increasing attainment results in mathematics. The research revealed some of the tensions that exist for schools in the current atmosphere of pressure to raise levels of attainment. Decisions have to be made about curriculum coverage, about setting, about teaching to the test. These tensions together with the strategies adopted by the school to promote the development of numeracy form the subject of the paper which draws from teacher and headteacher interviews, followed by analysis by the research team, with an additional section summarising the responses from an LEA primary adviser from a different authority who was interviewed and asked to comment on the first two sections of the paper. The Epilogue brings the story up to date with comments from a recent interview with the Headteacher as he moves on to a new school.     

Using microteaching to enhance teacher efficacy in pre‐service teachers

This study examined pre‐service teachers' efficacy in relation to the utilisation of microteaching as an assessment tool for postgraduate education students in Australia. Three hundred and fifteen pre‐service teachers completed the teacher efficacy survey and additional qualitative questions at Time 1 and 208 completed the survey and questions at Time 2. A principal components analysis conducted on the Time 1 survey data revealed teacher efficacy to be comprised of two components: ‘teacher efficacy in classroom management’ and ‘personal teacher efficacy’. Repeated measures ANOVAs conducted on the 208 participants who completed the survey at Time 1 and 2 revealed that efficacy on both components increased significantly over time, and that internet students had higher efficacy levels than internal students. The qualitative data revealed that pre‐service teachers enter teaching in order to positively impact on children, yet are concerned about behaviour management in the classroom. In addition, this data highlighted the positive impact that microteaching had on their developing teacher identity.     

Formatively assessing prospective teachers’ skills in leading mathematics discussions

Educational Studies in Mathematics - Mathematics discussions are important for helping students to develop conceptual understanding and to learn disciplinary norms and practices. In recent years,...     

The effect of video-based approach on prospective teachers’ ability to analyze mathematics teaching

This is an intervention study that explored the effect of using video lesson analysis methodology (VLAM) on the ability of prospective middle/high school mathematics teachers to analyze mathematics teaching. The sample of the study consisted of 26 female prospective mathematics teachers enrolled in a methods course at the United Arab Emirates University. The participants were divided equally into two groups, experimental and control. The experimental group was involved in video lesson analysis where they analyzed ten video lessons throughout the semester. The group members interacted via discussion forums through Blackboard technology. Both groups wrote analyses of two video lessons, one before the intervention program and another at the end of it. It was found that the intervention remarkably improved the ability to analyze mathematics teaching of the experimental group while little improvement occurred to the control group. Implications for teacher education programs are discussed.     

The teacher‐counselor partnership: Helping effective teachers of the gifted become more affective

A Counselor‐Teacher Education Program provides a workable model for teachers and counselors to integrate their skills and be more effective in programs for the gifted.     

The myth of the research‐led teacher

This paper examines the contention that achievement in research is a prerequisite for effective teaching in higher education. It also explores university level teaching more generally with the purpose of examining the links between teaching and research. Concept mapping, in particular, is described as a means of exploring both the knowledge structures of experts (teachers and researchers) and the cognitive changes that are indicative of meaningful learning among students. We use the approach to suggest that rich and complex networks are indicative of expert status, but that these are seldom made explicit to students in the course of teaching. Instead, simple, linear structures comprise most lesson plans or teaching sequences. This linearity is often made transparent through the lecturers’ use of PowerPoint presentations to structure teaching. Thus the transmission mode of teaching predominates in HE and evidence of authentic research‐led teaching remains scant. This is likely to reinforce surface learning outcomes among university students and be an impediment to the emergence of expert status. The linear chains that are commonly espoused in teaching lend themselves to rote learning strategies rather than to individual meaning making. The approach we describe here has the potential to reinstate expert status as the prime qualification for teaching in higher education. Where concept mapping is used to share and explore knowledge structures between students and experts, then learning can be shown to occur in ways that are synonymous with research and discovery. Using this approach, the teacher–student distinction becomes legitimately blurred so that the sharing and advancement of knowledge are concomitant. In conclusion, we suggest that this is a basis for a pedagogy that is appropriate to HE and distinct from the compulsory sector.     

Using the history of mathematics to induce changes in preservice teachers’ beliefs and attitudes: insights from evaluating a teacher education program

Scholars and teacher educators alike agree that teachers’ beliefs and attitudes toward mathematics are key informants of teachers’ instructional approaches. Therefore, it has become clear that, in addition to enriching preservice teachers’ (PSTs) knowledge, teacher education programs should also create opportunities for prospective teachers to develop productive beliefs and attitudes toward teaching and learning mathematics. This study explored the effectiveness of a mathematics preparatory program based on the history of mathematics that aimed at enhancing PSTs’ epistemological and efficacy beliefs and their attitudes toward mathematics. Using data from a questionnaire administered four times, the study traced the development of 94 PSTs’ beliefs and attitudes over a period of 2 years. The analysis of these data showed changes in certain dimensions of the PSTs’ beliefs and attitudes; however, other dimensions were found to change in the opposite direction to that expected. Differences were also found in the development of the PSTs’ beliefs and attitudes according to their mathematical background. The data yielded from semi-structured follow-up interviews conducted with a convenience sample of PSTs largely corroborated the quantitative data and helped explain some of these changes. We discuss the effectiveness of the program considered herein and draw implications for the design of teacher education programs grounded in the history of mathematics.

The pre-service teachers’ mathematics anxiety related to depth of negative experiences in mathematics classroom while they were students

One of the aims of this study is to examine whether the worst experiences and most troublesome mathematics classroom experience affect mathematics anxiety in pre-service elementary teachers. Another goal is to find out how the causes of their anxiety relate to these negative experiences. The participants were 167 senior elementary pre-service teachers. Three different instruments were used to collect data; Mathematics Anxiety Rating Scale, Worst Experience and Most Troublesome Mathematics Classroom Experience Reflection Test, and Interview Protocol. The findings show that many pre-service teachers have mathematics anxiety and that the worst experience and the most troublesome mathematics classroom experience have a direct influence on mathematics anxiety in pre-service teachers. Also, the majority of instances of participants’ mathematics anxiety are caused by the teachers, their behavior or teaching approaches in their past.     

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.     

Personal variables affecting the perspectives of head‐teachers and teachers towards teacher participation in school decision‐making

The article reviews research which has taken place relating to the influence of certain biographical factors on head‐teacher and teacher perspectives on who should take decisions within schools. The particular biographical factors which are considered are status, sex, age, length of experience and school size. Each is examined independently and shown to have some influence though existing research does not always agree on the type or extent of this influence. The article concludes by stating that whatever this influence might be, it is only one small aspect of the complex decision‐making process.     

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.     

Using teacher ratings of social behavior to differentiate gifted from non‐gifted students

This study investigated the effectiveness of teacher ratings of student social behavior in differentiating a group of 81 elementary‐age gifted students from a control group of 81 age and gender matched non‐gifted students. The School Social Behavior Scales, a recently developed set of rating scales that assesses both social competence and antisocial behavior, was used for the ratings. Gifted students were rated as having significantly higher levels of social competence and lower levels of antisocial behavior than the comparison group, and the individual scores of the gifted students were significantly skewed in the direction of better social‐behavioral adjustment. The findings also indicated the presence of a small subset of gifted students who appeared to have extremely poor social competence and high levels of problem behaviors. The results are compared to previous research on the psychosocial development of gifted children, and important areas for future research on this topic are recommended.     

Exploring the use of concept chains to structure teacher trainees’ understanding of science

This paper reports on a paper and pencil concept‐sorting strategy that enables trainee teachers to restructure their knowledge in any one domain of science. It is used as a self‐study tool, mainly to enable them to break down and understand the progression of concepts beyond the level at which they have to teach. The strategy involves listing key ideas in an increasingly complex and inclusive fashion such that a ‘chain’ is developed where the initial statements are simple and the final ones more complex. Evaluation of the strategy with trainees over a five‐year period revealed promising potential for the strategy as a self‐study tool, as well as an audit tool, enabling tutors to more easily identify misconceptions. There was some evidence that trainees found the strategy useful in preparing themselves to teach in the classroom, possibly by enabling meaningful learning to take place according to the Ausubel–Novak–Gowin theory.     

The premise and promise of inquiry based mathematics in pre‐service teacher education: a poststructuralist analysis

Many teacher educators have recently implemented inquiry based instructional practices into their programs (Crawford & Deer, 1993 Crawford, K and Deer, C. (1993). Do we practise what we preach? Putting policy into practice in teacher education. South Pacific Journal of Teacher Education, 21: 111–121. [Taylor & Francis Online] [Google Scholar]; Foss & Kleinsasser, 1996 Foss, D and Kleinsasser, R. (1996). Pre‐service elementary teachers’ views of pedagogical and ­mathematical content knowledge. Teaching and Teacher Education, 12(4): 429–442. [Crossref], [Web of Science ®] [Google Scholar]; Klein, 1996 Klein M (1996) The possibilities and limitations of constructivist practice in pre‐service teacher education in mathematics Unpublished doctoral dissertation, Central Queensland University, Rockhampton, Australia  [Google Scholar], 1997 Klein, M. (1997). Looking again at the ‘supportive’ environment of constructivist pedagogy. ­Journal of Education for Teaching, 23(3): 277–292. [Taylor & Francis Online] [Google Scholar], 1998 Klein M (1998) New knowledge, new teachers, new times in: C. Kanes, M. Goos & E. Warren (Eds) Teaching mathematics in new times (Brisbane, Mathematics Education Research Group of Australasia) 295 302  [Google Scholar], 2001 Klein M (2001) Correcting mathematical and attitudinal deficiencies in pre‐service teacher education in: J. Bobis, B. Perry & M. Mitchelmore (Eds) Numeracy and beyond (Sydney, Australia, MERGA) 338 345  [Google Scholar]; Schuck, 1996 Schuck, S. (1996). Reflections on the dilemmas and tensions in mathematics education courses for student teachers. Asia‐Pacific Journal of Teacher Education, 24(1): 75–82. [Taylor & Francis Online] [Google Scholar]; Tillema & Knol, 1997 Tillema, M and Knol, W. (1997). Collaborative planning by teacher educators to promote belief changes in their students. Teachers and Teaching: Theory and Practice, 3(1): 29–46. [Taylor & Francis Online] [Google Scholar]). In mathematics education the promise has been that pre‐service teachers’ socialization into new interactive ways of learning will not only lead to the (re)construction of powerful mathematical ideas and relationships, but that it will facilitate the implementation of these inquiry based practices in the classroom. This promise, however, is not often realized (Foss & Kleinsasser, 1996 Foss, D and Kleinsasser, R. (1996). Pre‐service elementary teachers’ views of pedagogical and ­mathematical content knowledge. Teaching and Teacher Education, 12(4): 429–442. [Crossref], [Web of Science ®] [Google Scholar]; Tillema & Knol, 1997 Tillema, M and Knol, W. (1997). Collaborative planning by teacher educators to promote belief changes in their students. Teachers and Teaching: Theory and Practice, 3(1): 29–46. [Taylor & Francis Online] [Google Scholar]). One reading of why this may be so, relying on and made visible through a poststructuralist analytic lens, is (a) that perhaps the pre‐service teachers’ ability to act in inquiry‐based, generative ways in the classroom does not necessarily follow from, but is produced or constituted in, teaching/learning interactions in school and teacher education, and (b) it may be that pedagogic practices in teacher education unintentionally and invisibly reproduce old epistemologies and ontologies that support knowledge transmission and teacher authority over student authored engagement and construction of ideas. In this paper the premise of a rational, autonomous agent of change on which so much of current practice is based is challenged, and the possible implications for teacher education discussed.     

The influence of entry route to teaching on Irish pre-service primary teachers’ attitudes towards mathematics

Abstract

Research examining the characteristics of both qualified and pre-service teachers focuses on traits including gender, socio-economic and socio-demographic background, knowledge and a variety of relevant affective constructs. Studies also investigate such traits among entrants to initial teacher education (ITE). The desire for more diversity within the teaching profession has led to alternative entry routes to the teaching profession (consecutive model for post-graduates) for those who may be unable to gain entry via the traditional concurrent (undergraduate) route. Internationally, there are divergent viewpoints and practices in relation to the value and use of the respective routes. This paper presents a comparative study within the Irish context, examining whether the consecutive model route to ITE promotes diversity in terms of entrants’ attitudes to mathematics. The study examines the entry-level mathematics attitudes of two distinctive groups of ITE entrants, namely 419 concurrent and 59 consecutive elementary pre-service teachers, in one Irish ITE institution prior to engagement with their ITE mathematics education programme. It compares their enjoyment of mathematics as well as their beliefs regarding the value of mathematics and examines the extent to which any distinguishing differences are apparent among the respective cohorts using the Aiken’s Revised Mathematics Attitude Scale. Analyses indicate generally positive attitudes among both cohorts; however, differences are evident between the cohorts with the consecutive route cohort demonstrating particularly apposite attitudes. The findings support the belief that the consecutive ITE route holds merit and prompts further investigation regarding the unique dispositions that these entrants possess.