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.     

Using classroom videos to stimulate professional conversations among pre-service teachers: windows into a mathematics classroom

This paper reports on the novel use of classroom videos by 71 pre-service teachers enrolled in a one-year graduate diploma pre-service teacher education program across three Australian universities. The classroom videos were of an experienced teacher delivering a Year-6 mathematics lesson. Students observed, discussed and debated practices that were evident. Data were collected via observation protocols and through recorded focussed discussions. Pre-service teachers, even at the early phase of their course, were able to articulate theoretical explanations for events occurring in the lesson. All students, irrespective of the progression in the course, lamented the absence of prior opportunities to engage in analysis and discussion of classroom lessons. The study reinforces the value of dialectical interactions focussed on authentic teaching scenarios.     

Development of evidence-based,student-learning-oriented rubrics for pre-service science teachers’ pedagogical content knowledge

ABSTRACT

This paper offers pedagogical content knowledge (PCK) rubrics, that is, guides providing criteria for grading that are potentially applicable to a range of science topics and levels of teacher experience. Grading criteria applied in the rubrics are based on qualitative analyses of planned topic-specific professional knowledge (TSPK) and content knowledge (CK). Data were collected via three topic-specific vignettes from 239 pre-service science teachers (PSTs) starting a university-based, full-time, one year teacher education programme in England. The statements were analysed for TSPK and CK. PSTs’ statements proposed instructional strategies comprising demonstrations, explanations, illustrations and analogies, classified as Relevant to the science topics, others Irrelevant. Some Relevant strategies missed an aspect that may, if enacted, help students’ learning, so were judged Incomplete. Statements were also analysed for evidence of relevant and correct CK. CK and TSPK statements are aligned into grids, creating PCK rubrics. These demonstrate the precise nature of knowledge likely to lead to instruction that impacts positively on student learning. The rubrics present the possibility of PCK repertoires that contribute clarity and precision to teaching instruction. Although findings cannot be generalised, the methodology offers a strategy for supporting out-of-field teachers, and those seeking instructional strategies to add to existing repertoires.     

Situated learning in an educational technology course for pre-service teachers

This qualitative study investigated a situated learning environment implemented in an educational technology course where pre-service teachers worked collaboratively on meaningful real-world projects, assuming the role of professional teachers. With a traditional learning environment as a critical frame of reference, we found that the students in the situated learning environment demonstrated sophisticated problem-solving skills, exhibited metacognitive awareness, produced coherent artifacts, and showed high levels of motivation. The findings implied that if we want to successfully implement situated learning, effort should be made to promote a constructive learning culture, improve individual performance, manage students’ perceptions, and foster their positive attitudes.     

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.     

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.     

A new instrument for measuring pre-service biology teachers' pedagogical content knowledge: The PCK-IBI

Teachers' pedagogical content knowledge (PCK) is highly important for effective design and implementation of school teaching. Thus, the current status, development and efficacy of this knowledge, its relationships with teaching quality parameters, and its impact on students' learning processes and success, require rigorous examination. Thoroughly validated, objective and reliable test instruments that are highly sensitive to changes in variables of proven knowledge-related relevance in teacher education are also required. Previous attempts to design such instruments for assessing science teachers' PCK have largely focused on mathematical content. Therefore, here we present an instrument (the pedagogical content knowledge in biology inventory, PCK-IBI), based on conceptualizations of teachers' professional competence, for assessing secondary school pre-service biology teachers' PCK. In a series of three evaluations and refinements it was tested with samples of N = 274 and N = 432 German pre-service as well as one sample of n = 65 German pre-service and n = 35 German in-service biology teachers. Item analysis, scale analysis and empirically obtained indicators of validity suggest that the final 34-item-version of the PCK-IBI is unidimensional, provides objective test scores and enables reliable and valid registration of pre-service biology teachers' PCK. Thus, hypotheses regarding specific aspects of the model on which the PCK-IBI's construction is based on are empirically supported. The results of our study provide empirical support for the instrument's potential utility.     

Examining pre-service elementary mathematics teacher perceptions of parent engagement through a funds of knowledge lens

Missing from the research focusing on preparation of culturally responsive elementary mathematics teachers is an explicit explanation of pre-service teachers’ (PSTs) conceptions of parent engagement. Several authors attest to the importance of teacher preparation programs facilitating change in preconceptions about families and communities in order to build positive relationships. This study uses concept mapping to measure if a one-semester course taught through a funds of knowledge perspective will help pre-service teachers to shift conceptions of parent engagement to reflect a more asset-based orientation towards families. Funds of knowledge is used as both a theoretical and methodological lens for this study.     

Establishing a portfolio assessment framework for pre-service teachers: a multiple perspectives approach

In the field of initial teacher training, portfolios are widely used to assess pre-service teachers' performance as well as the outcomes of university-based teacher preparation programmes. However, little is known about the explicit design of portfolio assessment mechanisms in teacher preparation programmes. Issues related to the design and validation of portfolios for pre-service teacher assessment are a critical area of inquiry for the field of initial teacher training. In this study, perspectives were elicited from school trainee teachers and faculty from a secondary teacher preparation programme to examine the relationships identified among core competencies of a portfolio assessment framework and pre-service candidate learning outcomes. Comparative findings are presented about the relationships identified by the trainee teachers and faculty across the secondary education programme's portfolio core competencies and trainee learning outcomes. A discussion of the findings is presented with implications and future directions highlighted.     

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.     

数学建模思想融入大学数学教学内容的认识与实践

将数学建模思想融入大学数学教学内容之中，能够有效地培养大学生运用数学知识解决实际问题的能力.本文探讨了将数学建模思想融入大学数学教学内容之中应遵循的目标和原则，并介绍了作者的改革实践，以期为高等院校大学数学的教学改革提供参考.     

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.     

The team teaching experiences of pre-service science teachers implementing PBL in elementary school

The current phenomenological-qualitative case study examined the team teaching related experiences of 17 Israeli student teachers in the context of using the project-based teaching method in the course of their pedagogical practicum module conducted in elementary schools. The focus of the study was on participants’ experiences in terms of quality and content. Data collection methods included reflective reports and in-depth interviews. Data analysis was conducted using the qualitative method for content analysis. Findings of the study indicate that during team teaching, the student teachers underwent a process of four qualitatively different experiential stages, each of which is characterised by a unique set of experiences. There was also a qualitative difference at each stage between the experiences of student teachers who emerged with an overall positive assessment and those who emerged with an overall negative assessment of team teaching. The practical implications of the findings are discussed. This research contributes to the professional literature on the team teaching of science courses, and may serve to encourage educators to implement team teaching as part of student teachers‘ practicum involving a project based, student centred methodology.     

潍坊市初中语文骨干教师继续教育考核内容与形式的研究

本文通过对潍坊市初中语文骨干教师继续教育考核实践的回顾 ,对初中语文骨干教师培训考核的内容、形式及管理等方面的问题进行理论上的分析 ,并对如何进一步提高培训质量进行了有益的探索     

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.     

The tensions of preparing pre-service teachers to be assessment capable and profession-ready

There is both a growing appreciation of teacher assessment capability for the improvement of school student learning and achievement and a commensurate drive for graduates in Australian Initial Teacher Education institutions to demonstrate impact on school student learning as part of a national accreditation process. We argue in this article that if institutions are to prepare assessment capable graduates who are “profession-ready”, attention to practice architectures is warranted. Practice architectures are the features in schools that enable and/or constrain practice. Skills, knowledge and understandings do not just cleanly transfer across Initial Teacher Education institutions and practicum contexts into graduate teacher classrooms. Practitioner identities are produced through “relatings” within specific social-political arrangement, “doings” that constitute activities afforded in material-economic conditions, and “sayings” that are a dominating medium in cultural-discursive frameworks.     

A review of ICT related courses in pre-service teacher education programs

This study investigated teacher educators’, prospective teachers’, and K-12 teachers’ opinions about the effectiveness of ICT related courses and the ways to improve the courses in Turkey’s pre-service teacher education programs. The researchers used both quantitative and qualitative research approaches within the data collection and analysis processes. The data were collected from 111 teacher educators, 1,330 prospective teachers, and 1,429 K-12 teachers through questionnaires; and from 6 teacher educators, 6 prospective teachers, and 6 K-12 teachers through interviews. Even though a majority of the participants felt that ICT related courses are effective, most participants recommended that these courses need to be redesigned to be more beneficial in practice.     

Equivalence and relational thinking: preservice elementary teachers’ awareness of opportunities and misconceptions

This study examined awareness of equivalence and relational thinking exhibited by 30 preservice elementary teachers in order to assess their initial preparedness to engage students in these two important aspects of early algebraic reasoning. Findings indicated that preservice teachers collectively demonstrated an awareness of relational thinking both in identifying opportunities offered by tasks to engage students in this thinking and in identifying this thinking in samples of student work. However, in proposing difficulties students might have with selected tasks, few participants demonstrated the understanding that many elementary school students hold misconceptions about the meaning of the equal sign. Implications of these findings for preservice and inservice teacher education are discussed.     

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.