Infusing assessment into mathematics content courses for pre-service elementary school teachers

The present study aims to explore the use of assessment in mathematics content courses for future elementary school teachers. Analysis of self assessment data on mathematical understanding and peer assessment data on oral mathematical presentation showed that pre-service teachers had a balanced understanding of procedural knowledge and problem solving. Conceptual understanding was not in the structure of pre-service teachers’ mathematical knowledge. Understandings of conceptual knowledge, procedural knowledge, and problem solving had no meaningful effects on gains in mathematics performance. Aspects of oral mathematical presentation were associated with improved understanding of procedural knowledge and in particular conceptual knowledge. The result of the study calls for a conceptual approach to mathematical knowledge and sufficient mathematical problem solving in college-level mathematics content courses and in particular the infusion of assessment into college-level mathematics education for pre-service teachers.     

Developing assessment literacy through approximations of practice: Exploring secondary mathematics pre-service teachers developing criteria for a rich quadratics task

This study draws on a theoretical model for teacher assessment literacy to investigate the process of how secondary mathematics pre-service teachers (PSTs) might develop theirs through experiencing an approximation of practice. Sixty PSTs participated in designing and then refining assessment criteria for a rich open-ended quadratics task using real student example responses. Data analysis examined variations in the PSTs’ attention to quadratic features and mathematical language as assessment criteria for the task throughout the activity. This paper discusses evidence suggesting that the collaborative analysis of example student responses can make certain, but not all, assessment criteria salient to PSTs.     

Traditional vs. innovative uses of computers among mathematics pre-service teachers in Serbia

This study examined pre-service teachers’ intentions to use computers in traditional and innovative teaching practices in primary mathematics classrooms. It extended the technology acceptance model (TAM) by adding as external variables pre-service teachers’ experience with computers and their technological pedagogical content knowledge (TPCK). Data collected from 226 participants revealed that the proposed model had a good fit for both traditional and innovative uses of computers. Structural equation modelling suggested that the established TAM variables, together with TPCK and experience, were significant determinants of pre-service teachers’ intentions to use computers in teaching mathematics at both levels. The most dominant determinant of behavioural intention was TPCK, followed by attitude. The proposed model explained 22.7% of the variance in the use of computers in traditional teaching practices and 27.6% of the variance in the use of computers in innovative teaching practices. The implications for mathematics teaching are discussed in the final section.     

Reflection on the teaching-learning process in the initial training of teachers. Characterization of the issues on which pre-service mathematics teachers reflect

Our aim was to highlight the issues of the reflections of pre-service mathematics teachers in their learning portfolio about the teaching-learning process taking place in a university teacher-training classroom. Category systems were designed which, together with the analysis system used, could provide a method helpful to teacher educators, teachers and to future research. The pre-service teachers showed difficulty in considering themselves as ‘authentic’ mathematics teachers. The study revealed that the preparation of a portfolio can help pre-service teachers learn more about themselves and provide educators insight into how to help pre-service mathematics teachers engage in the teaching-learning process.     

Producing caring qualified teachers: An exploration of the influence of pre-service teacher concerns on learner-centeredness

In a time where students in the United States academic performance continues to lag behind in the international rankings, a disconcerting phenomenon in concerns literature indicates that pre-service and in-service teachers report low levels of concerns regarding the effect implementation of educational innovations have on students. This study explored the relationship of pre-service teachers' learner-centeredness and their concerns related to how learner-centered education affects students. Results indicated that as learner-centeredness increased, so did concerns about student outcomes. Implications for teacher education programmes in the US and abroad will be discussed.     

Pedagogical content knowledge of French as a foreign language: differences between pre-service and in-service teachers

Pedagogical content knowledge (PCK) is an important predictor of educational quality. PCK develops from various sources, such as teaching experience. Studies investigating the effects of teaching experience on PCK development mainly focus on the question whether experienced teachers differ from novices in the amount of PCK. In a mixed methods study, we study both quantitative and qualitative differences between pre-service and in-service teachers’ PCK. Total scores on a paper-and-pencil instrument are used as a measure of French PCK. To analyse the participants’ PCK in a qualitative way, answers are coded in four categories and the prevalence of answers in each category is compared between groups. Furthermore, the nature of answers is studied. No differences on our quantitative PCK measure are observed. The qualitative analysis shows that in-service teachers have more difficulties with conceptual knowledge, while showing more practical knowledge of students’ understanding than pre-service teachers.     

Assessing pre-service teachers’ skills for analyzing teaching

This study investigated the learning-from-practice skills that pre-service teachers possess when they enter teacher preparation programs in the United States. Two subskills were hypothesized to represent, at least in part, what is required to learn from practice: (1) the ability to collect evidence about students’ learning in order to analyze the effects of instruction, and (2) the ability to use the analysis to revise the instruction. Because it seems likely that different teaching situations and contexts reveal these learning-from-practice skills in different ways and to different degrees, this study examined the skills that pre-service teachers exhibited under two experimental conditions. Thirty pre-service teachers were asked to analyze the effects of a videotaped mathematics lesson on student learning, to support their analysis with evidence, and to use their analysis to revise the lesson. Based on the results, it appears that many entry level pre-service teachers can carry out a cause-effect type of analysis of the relationships between specific instructional strategies and students’ learning, and can use this analysis to make productive revisions to the instruction. However, prospective teachers’ ability to collect evidence that supports their analysis appears to be less developed. In addition, the type of analysis that prospective teachers carried out about the effects of instruction on students’ learning differed dramatically across the two experimental task conditions.Preparation of this article was supported by the National Science Foundation (Grant #0083429 to the Mid-Atlantic Center for Teaching and Learning Mathematics). The opinions expressed in the article are those of the author and not necessarily those of the Foundation. Thanks to James Hiebert for his comments on earlier drafts of the paper.     

Physics teachers: a holistic plan for professional education during both the pedagogical stage and the probation year

Despite the Bologna agreement implementation in 2008, teachers' education in Portugal has not changed significantly from earlier practice. The major modification in the requirements of master’s level teacher education programmes was the introduction of a strong component of educational research in a master’s degree; this is designed to replace an educational monograph in the typical 5-year ‘Licenciatura’. Both a professional one-year in-school pedagogical stage and a fifth year as a university student continue to be mandatory, as well as the stage co-supervision of the university and the school. However, existing government regulations imply that in the very near future the full professional education of teachers will have to be complemented with an in-service probation year conducted under the supervision of a school mentor. The current study has been designed to try to determine: (a) how the activities of the probation year should be organised in order to improve this stage of professional education; and (b) how probation years could be used to promote school–university partnerships that could provide for more effective in-service teacher education and/or possible shared educational action research. Drawing on the survey data from pre-service students from four different universities, novice teachers, stage supervisors and school principals, information was collected on the perceptions of the quality and scope of the professional education of future teachers from the beginning of their programmes through their pedagogical stage. A high degree of agreement among all the respondents enables us to point towards the perceived high quality of several components of the teacher education programmes, e.g, teachers’ ability to plan a lesson using different teaching strategies and the high value-accorded school–university collaborations. The results also show the weaknesses of other components, e.g, teachers’ skill with controlling badly behaved students and their ability to capture students’ attention and motivation. Based on these results and on our knowledge about the type of professional support needed to promote teaching practice, we conclude with a holistic plan designed for teachers’ professional education during the pre-service pedagogical stage and the in-service probation year.     

Developing and validating a competence framework for secondary mathematics student teachers through a Delphi method

Initial teacher education programmes provide student teachers with the desired competences to develop themselves as teachers. Although a generic framework for teaching competences is available covering all school subjects in Spain, the initial teacher education programmes curriculum does not specify which competences secondary mathematics student teachers should acquire during their initial teacher education. This explains why this study aimed at developing and validating a competence framework for secondary mathematics student teachers in Spain. Building on existing models and international frameworks, a preliminary list of competences was drawn up. The validation process was based on a Delphi method. In addition experts expressed their opinions about the formulation of the chosen competences. A comprehensive framework of 33 competences for secondary mathematics student teachers could then be validated.     

Developing a communal identity as beginning teachers of mathematics: Emergence of an online community of practice

The aim of this study is to investigate how a community of practice focused on becoming a teacher of secondary school mathematics emerged during a pre-service teacher education programme and was sustained after students graduated and began their first year of full-time teaching in schools. Bulletin board discussions of one pre-service cohort are analysed in terms of Wenger’s (1998) three defining features of a community of practice: mutual engagement of participants, negotiation of a joint enterprise, and development of a shared repertoire for creating meaning. Emergence of the online community was associated with our own role in facilitating professional dialogue, the voluntary and unstructured nature of participation, initial face-to-face interaction that created familiarity and trust, and the convenience of using email rather than logging on to a website. The study shows that the emergent design of the community contributed to its sustainability in allowing the pre-service and beginning teachers to define their own professional goals and values.

Teacher efficacy of pre-service teachers in Taiwan: The influence of classroom teaching and group discussions

The greatest benefit of teacher preparation programs is field-related training where pre-service teachers contextualize the learned knowledge and theories with tasks and students during training. This preliminary study is based on the collaboration between a teacher training program and an elementary school to investigate the effect that exposure to various sources of teacher efficacy has on pre-service teachers in Taiwan. The results of this study show some influences of classroom experience and group discussions on the teaching efficacy of this group of pre-service teachers. Pre-service teachers demonstrated a higher level of PTE after the classroom experience and group discussions.     

The multimedia case as a tool for professional development: an analysis of online and face-to-face interaction among mathematics pre-service teachers, in-service teachers, mathematicians, and mathematics teacher educators

In this study, we consider the potential of multimedia cases as tools for teacher professional development. Specifically, we examined online and face-to-face discussions that occurred within groups composed of pre-service mathematics teachers, in-service mathematics teachers, mathematicians, and mathematics teacher educators. Discussions within these heterogeneous groups tended to focus on issues of classroom implementation of the tasks shown in the multimedia case. Secondary foci of discussion included task characteristics and appropriateness of tasks for engaging students in thinking about mathematical concepts and processes. Analysis of contributions to discussions across group member type revealed differences that suggest that the variety of backgrounds and experiences of group members can blend in ways that support rich and critical discussions of mathematics, teaching, and learning.     

Challenges faced by pre-service chemistry teachers teaching in a laboratory and their solution proposals

This study examines the challenges faced by pre-service chemistry teachers teaching in a laboratory and their proposed solutions to these challenges. The study was conducted in a 13-week-long methodology course. Written statements from participants and observations from researchers were used as data sources. From these data, it was found that the participants faced challenges related to content knowledge and connections, laboratory and experiments, students, planning and implementing instruction and general teacher qualifications. In terms of solutions, various ideas were proposed, such as improved development of content knowledge, pre-lesson preparation and the acquisition of professional experience. The challenges expressed by participants differed from those observed by the researchers and increased during the length of the course. In addition, their proposed solutions were not sufficient, coherent or explicit.     

Windows into teaching and learning: professional growth of classroom teachers in an online environment

The Windows into Teaching and Learning (WiTL) project was developed by researchers at one large urban institution in the southeast region of the United States as a way to facilitate online clinical experiences for content area methods students during summer coursework. Utilising both synchronous and asynchronous elements, WiTL addressed the issue of students gaining meaningful clinical experiences in coursework offered during the summer. Though the purpose of WiTL was initially for methods students to engage in observations of and conversations with practising classroom teachers, an unanticipated outcome occurred. In this paper, the authors describe the WiTL process and discuss the impact it had on the professional growth of the practising classroom teachers. The results indicate that WiTL encouraged teachers to utilise reflective practice in rethinking their pedagogy and used technology to facilitate professional learning community among classroom teachers.     

Cultivating critical thinkers: Exploring transfer of learning from pre-service teacher training to classroom practice

This study explores the transfer of critical thinking skills and dispositions from pre-service teacher training to classroom practice and student achievement in the cases of two graduates from a course on critical thinking-integrated instruction. Two 7th and two 8th grade classes were randomly assigned as experimental (CT-integrated instruction), or comparison (traditional instruction) groups. Empirical results demonstrated that, in these two cases, the teachers successfully developed CT-integrated instruction for effectively fostering students' CT skills and dispositions, while improving student achievement. Future research should include larger and more representative samples to avoid bias and reliably evaluate CT-based teacher training initiatives.     

Using a video-based curriculum to develop a reflective stance in prospective mathematics teachers

Although video cases are increasingly being used in teacher education as a means of situating learning and developing habits of reflection, there has been little evidence of the outcomes of such use. This study investigates the effects of using a coherent video-case curriculum in a university mathematics methods course by addressing two issues: (1) how the use of a video-case curriculum affects the reflective stance of prospective teachers (PTs); and (2) the extent to which a reflective stance developed while reflecting on other teachers’ practice transfers for reflecting on one’s own practice. Data sources include videotapes of course sessions and PTs’ written work from a middle school mathematics methods course that used a video-case curriculum as a major instructional tool. Both qualitative and quantitative analytical methods were used, including comparative and chi-square contingency table analyses. The PTs in this study showed changes in their level of reflection, their tendency to ground their analyses in evidence, and their focus on student thinking. In particular, they began to analyze teaching in terms of how it affects student thinking, to consider multiple interpretations of student thinking, and to develop a more tentative stance of inquiry. More significantly, the reflective stance developed via the video curriculum transferred to the PTs’ self-reflection in a course field experience. The results of this study speak to the power of using a video-case curriculum as a means of developing a reflective stance in prospective mathematics teachers.

Reconceptualising professional experiences in pre-service teacher education…reconstructing the past to embrace the future

This paper provides a conceptual framework for developing high-quality professional experiences for pre-service teachers. The paper begins with a discussion of how professional experiences are conceptualised, structured and supervised in each of three orientations, which we have termed traditional, reflective and learning communities. We then describe a number of professional experience initiatives at two Australian universities, which are being reconceptualised around the notion of learning communities. We argue that framing professional experience around the notion of learning communities has the potential to support pre-service teachers to work with their peers and mentor teachers in more collegial and reciprocal ways.     

Designing and implementing authentic investigative proportional reasoning tasks: the impact on pre-service mathematics teachers’ content and pedagogical knowledge and attitudes

In this study we created, implemented, and evaluated the impact of proportional reasoning authentic investigative tasks on the mathematical content and pedagogical knowledge and attitudes of pre-service elementary and middle school mathematics teachers. For this purpose, a special teaching model was developed, implemented, and tested as part of the pre-service mathematics teacher education programs conducted in Israeli teacher colleges. The conclusion of the study is that application of the model, through which the pre-service teachers gain experience of and are exposed to authentic investigative proportional reasoning tasks with incorporation of theory (reading and analyzing relevant research reports) and practice, leads to a significant positive change in the pre-service teachers’ mathematical content and pedagogical knowledge. In addition, improvement occurred in their attitudes and beliefs towards learning and teaching mathematics in general, and ratio and proportion in particular.