Developing preschool teachers’ knowledge of students’ number conceptions

This article describes a study that investigates preschool teachers’ knowledge of their young students’ number conceptions and the teachers’ related self-efficacy beliefs. It also presents and illustrates elements of a professional development program designed explicitly to promote this knowledge among preschool teachers. Results indicated that teachers’ knowledge of students’ number conceptions improved and that their related self-efficacy increased. Furthermore, prior to participating in the programs, a significant negative correlation between knowledge and self-efficacy was reported. However, no significant correlation was found after the program.     

Developing culturally responsive mathematics teachers: secondary teachers’ evolving conceptions of knowing students

Research advances in teaching, learning, curriculum, and assessment have not changed the continued underperformance of marginalized students in mathematics education. Culturally responsive teaching is a means of addressing the needs of these students. It is sometimes challenging, however, to convince secondary mathematics teachers about the importance of culture in mathematics education. To contribute to what is known about supporting secondary mathematics teachers in developing a culturally responsive teaching practice, we studied the impacts of a graduate course called Culture in the Mathematics Classroom on 13 teachers enrolled in the course. The course was designed to guide secondary mathematics teachers in understanding and growing their capacity to enact culturally responsive teaching in their classrooms. The purpose of our research was to explore how teachers’ perceptions changed as a result of their engagement in the class with respect to understanding the role of culture in knowing and being responsive to their students. Specifically, we examined how each of the four course projects seemed to individually and collectively influence teachers’ thinking. Overall, teachers appeared to expand their cultural awareness and dispositions for cultural responsiveness that would support them in knowing and supporting their students in the manner of a culturally responsive teacher. Teachers did not, however, develop some more “advanced” understandings related to power and privilege in society. This study provides researchers and mathematics teacher educators with a potential analytic framework for understanding teacher change with respect to culturally responsive teaching.     

Analyzing and attempting to overcome prospective teachers’ difficulties during problem-solving instruction

This article analyzes the experiences of prospective secondary mathematics teachers during a teaching methods course, offered prior to their student teaching, but involving actual teaching and reflexive analysis of this teaching. The study focuses on the pedagogical difficulties that arose during their teaching, in which prospective teachers lacked pedagogical content knowledge and skills. It also analyzes the experience of the course itself, which was aimed at scaffolding the work of prospective teachers on developing their pedagogical content knowledge and skills.     

Examining and elaborating upon the nature of elementary prospective teachers’ conceptions of partitive division with fractions

The purpose of this study was to examine and elaborate upon elementary prospective teachers’ (PSTs) conceptions of partitive division with fractions. We examined the degree to which PSTs’ conceptions were connected (i.e., capable of translating between representations correctly; aware that partitive division generates a unit rate for its quotient) and flexible (i.e., capable of differentiating between opportunities to partition or iterate (or both) when solving a partitive division task; aware that partitioning or iterating (or both) could be associated with the operation of division, as appropriate). Seventeen PSTs participated in task-based interviews prior to instruction in a mathematics content course for teachers. These PSTs demonstrated disconnected conceptions of partitive division with fractions when they incorrectly translated between representations and either inconsistently or did not express awareness that the purpose of the task was to generate a unit rate. These PSTs demonstrated rigid conceptions of partitive division with fractions such that they did not express awareness that the process of iterating could be associated with the operation of division, even when they obtained a correct answer by iterating. Results extend prior research by looking beyond PSTs’ performance on tasks to elaborate upon PSTs’ conceptions of the operation of partitive division. This study contributes new insights into PSTs’ conceptions that can be used by mathematics teacher educators to inform the design of future instructional interventions.     

High-stakes examination preparation that controls teaching: Chinese prospective teachers’ conceptions of excellent teaching and assessment

How prospective teachers conceive of teaching excellence and assessment purposes probably influences how teaching and assessment practices are implemented in the future. This study evaluated, in four ‘normal universities’ in the People’s Republic of China, 765 prospective teachers’ responses to two self-report instruments regarding the nature of excellent teaching and the purpose of assessment. Both questionnaires had previously been developed in Mandarin Chinese and validated with large samples of practicing teachers in China. The original models could not be recovered and with exploratory and confirmatory factor analysis alternative models were found. Excellent teaching was conceived as four inter-correlated factors (i.e. Professional, Model, Examination and Life-long), as also were the purposes of assessment (i.e. Diagnose and Formative, Irrelevant, Control and Life Character). Structural equation modelling showed that the strongest relationship between teaching excellence and assessment began with the examination factor which positively predicted assessment as Irrelevant and for Life Character development and negatively the Diagnose and Formative purpose. Results are consistent with the high-stakes examination system of China and the status of prospective teachers who have only recently stopped being students.     

Text-based writing in elementary classrooms: teachers’ conceptions and practice

Reading and Writing - Writing analytically about text is a valued skill reflected in current academic standards. The quality of text-based writing opportunities in U.S. elementary schools, however,...     

Between teachers’ perceptions and civic conceptions: lessons from three Israeli civics teachers

Building on sociocultural theories of teaching and learning, rooted in constructivist traditions, this study examined the teaching of civics in relation to contextual sociocultural factors in the Israeli educational system. The study focused on ways in which three civics teachers conceptualized and framed notions of good citizenship in relation to the teaching of the civics subject matter, and on the ways in which such notions manifest in their planned teaching. The main finding points to how the teachers framed their civics lessons in a manner that was in congruence with their perceptions of their students’ approaches to citizenship. Thus, the study reaches the conclusion that teachers’ perceptions are a key element in framing and conceptualizing civics lessons, resulting in a reality in which students from different backgrounds may experience significant differences in their orientation to the notion of good citizenship, limiting their exposure to multiple views.     

Teachers’ conceptions of assessment: Comparing two inventories with Ecuadorian teachers

Teacher beliefs about the purpose of assessment matter to how assessment is implemented in classroom settings. Two different teacher conceptions of assessment inventories have originated separately in Spain and New Zealand. This study examined (a) the extent to which the models for each inventory could be recovered and (b) the relationship between inventories. Responses were obtained from 566 Ecuadorian primary and secondary teachers in two rounds of surveying. Results showed that with a few modifications both the Spanish and New Zealand models fit the data. Mean scores were strongest for improvement, caution, and societal control factors. Factor inter-correlations between the Spain and New Zealand models indicated that the teaching, certifying, and accounting domains were moderately correlated with accountability and improvement purposes, while societal control correlated with caution, and formative regulation correlated with irrelevance. These results are consistent with how teachers seem to conceive of assessment within strong examination systems.     

An investigation of prospective secondary mathematics teachers’ conceptual knowledge of and attitudes towards statistics

The development of statistical literacy is fast becoming the focus of a large part of mathematics instruction at primary, secondary and tertiary levels. This broadening of the mathematics curriculum to encompass a focus on statistics makes considerable demands on teachers. Most mathematics teachers acknowledge the practical importance of statistics and are willing to give more relevance to the teaching of statistics; however, many mathematics teachers do not consider themselves well prepared to teach statistics. The aims of this study were to investigate the conceptual understanding of statistics of prospective secondary mathematics teachers; the nature of their attitudes towards statistics and if there was a relationship between attitude towards statistics and conceptual understanding of statistics. Conceptual understanding was measured using a standard assessment instrument (comprehensive assessment of outcomes in a first statistics course) which allows comparison across other disciplines. Despite being very mathematically able and confident, the prospective mathematics teachers in this study do no better in the assessment than students from other (mostly non-quantitative) disciplines. This, perhaps, gives further evidence that statistical thinking is different from mathematical thinking and that a strong background in mathematics does not necessarily translate to statistical thinking. Conceptual knowledge was poor in some fundamental areas of statistics such as being able to properly describe the distribution of a quantitative variable and data production. The attitudes of these teachers towards statistics were measured using a widely used instrument (survey of attitudes towards statistics). The results indicate generally positive attitudes but an acknowledgement that statistics is not a subject quickly learned by everyone and requires discipline to learn. No strong correlation was found between attitudes and conceptual knowledge. It is recommended that in order to improve teacher knowledge, teacher education programmes must include tailored modules in statistics and highlight the differences between mathematical and statistical thinking.     

Teachers’work: Beginning teachers’ conceptions of competence

Worldwide, teachers’ work continues to be the subject of discussion and debate, especially in terms of teacher competence and its appropriate appraisal. Available literature offers a number of perspectives of beginning teacher competence, yet the voices of beginning teachers themselves are not represented. This paper outlines the findings of a phenomenographic study that sought to uncover the conceptions of competence held by beginning teachers. The results of this study suggest that beginning teachers believe that teaching competence requires demonstration of thorough preparation, a sound knowledge base, effective classroom management, professional communication with a range of stakeholders, and an accurate sense of self-awareness in the role of teacher. These conceptions will be compared to a selection of the available literature about teacher competence and associated teaching standards.     

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.     

Improving the judgment of task difficulties: prospective teachers’ diagnostic competence in the area of functions and graphs

To teach adaptively, teachers should be able to take the students’ level of knowledge into account. Therefore, a key component of pedagogical content knowledge (PCK) is the ability to assume the students’ perspectives. However, due to the so-called expert blind spot, teachers tend to misestimate their students’ knowledge, such as when estimating the difficulty of a given task. This empirically well-documented estimation bias is predicted by Nickerson’s anchoring and adjustment model, which generally explains how people take on other people’s perspectives. In this article, we present an intervention study that aims to improve the accuracy of prospective teachers’ judgments of task difficulty in the area of functional thinking. Two types of treatments are derived from Nickerson’s model. In the first condition (PCK group), participants acquire knowledge about task characteristics and students’ misconceptions. The second condition (sensitizing group) serves to control the idea that potential improvements in the PCK group are not merely based on a pure sensitization of the expert’s estimation bias. Accordingly, these participants are only informed about the general tendency of overestimating task difficulties. The results showed that the PCK group improved both in terms of the accuracy of the estimated solution rates and the accuracy of rank order, whereas the sensitizing group only improved in regard to the former. Thus, the study shows that prospective teachers’ diagnostic judgments can be improved by teaching them relevant PCK in a short amount of time.     

A comprehensive model covering prospective teachers’ technology use: the relationships among self,teaching and learning conceptions and attitudes

ABSTRACT

This study was conducted to propose and examine a comprehensive model embracing prospective teachers’ beliefs about self, teaching and learning conceptions, and attitudes towards using instructional technologies. Prospective or inservice teachers’ beliefs (from central to peripheral) and attitudes may empower the support of teacher training related to using instructional technologies. Participants were 1208 Turkish prospective teachers from five different universities who participated voluntarily and were selected using convenience sampling. Structural equation modelling analysis showed that prospective teachers’ beliefs about the autonomous self and autonomous–related self positively related to both their constructivist beliefs about teaching and learning and attitudes towards using instructional technologies, whereas the same beliefs negatively related to traditional conceptions of teaching and learning. Moreover, participants’ constructivist beliefs about teaching and learning positively predicted their attitudes towards using instructional technologies. Furthermore, their beliefs about related self positively and unexpectedly predicted their constructivist conceptions and attitudes. Implications are presented considering these results.     

Fostering Third-Grade Students’ Use of Scientific Models with the Water Cycle: Elementary teachers’ conceptions and practices

Elementary teachers play a crucial role in supporting and scaffolding students’ model-based reasoning about natural phenomena, particularly complex systems such as the water cycle. However, little research exists to inform efforts in supporting elementary teachers’ learning to foster model-centered, science learning environments. To address this need, we conducted an exploratory multiple-case study using qualitative research methods to investigate six 3rd-grade teachers’ pedagogical reasoning and classroom instruction around modeling practices (construct, use, evaluate, and revise) and epistemic considerations of scientific modeling (generality/abstraction, evidence, mechanism, and audience). Study findings show that all teachers emphasized a subset of modeling practices—construction and use—and the epistemic consideration of generality/abstraction. There was observable consistency between teachers’ articulated conceptions of scientific modeling and their classroom practices. Results also show a subset of the teachers more strongly emphasized additional epistemic considerations and, as a result, better supported students to use models as sense-making tools as well as representations. These findings provide important evidence for developing elementary teacher supports to scaffold students’ engagement in scientific modeling.     

Developing prospective elementary teachers’ abilities to identify evidence of student mathematical achievement

This study investigated the effects of a classroom intervention on prospective elementary teachers’ ability to evaluate evidence of student achievement of mathematical learning goals. The intervention was informed by a framework for teacher education which aims to provide prospective teachers (PTs) with the skills needed to systematically learn from their own teaching practice. Prospective teachers (N = 160) participated in an intervention aimed at addressing their misconceptions about evidence of student learning. Results revealed that after the intervention, PTs were less likely to consider teacher behaviors to be evidence of student learning and more likely to discount student responses that were irrelevant to a specified learning goal. However, PTs were still likely to take procedural fluency as evidence of conceptual understanding and may have become overly skeptical of student understanding. Implications of the study suggest new ways of developing prospective teachers’ ability to systematically study and improve their teaching.     

Language teachers’ conceptions of assessment: an Egyptian perspective

The current study investigates the assessment conceptions of both pre-service and in-service English teachers within a high-stakes, test-driven context in Egypt. For this purpose, 170 Egyptian pre-service and in-service teachers completed an assessment conceptions questionnaire. Quantitative and qualitative data analysis were employed to answer the research questions. The results of the study showed in-service teachers preferring a combination of formative and summative assessment practices while pre-service teachers favored a relatively summative paradigm. With regard to functions of assessment, in-service teachers endorsed the improvement function of assessment more than the pre-service group. Both groups had negative perceptions about the effectiveness of teacher training programs. The study provides a number of implications for language teachers, teacher educators, and policy-makers.     

University students’ and teachers’ conceptions of teaching and learning in the biosciences

In this study we compare university teachers’ and first-year students’ conceptions of teaching and learning at the Faculty of Environmental and Biological Sciences. The conceptions were analysed using data from open-ended questionnaires. The results showed that at the beginning of studies the gap between teachers’ and students’ conceptions of teaching and learning is substantial. This finding has important implications for the educational process. In order to enhance successful studying from the beginning of students’ university careers, it is important for teachers to become aware of the differences between students’ and teachers’ conceptions of learning.     

Comparing two constructs for describing and analyzing teachers’ diagnostic processes

Different constructs describe and analyze teachers’ diagnostic processes, in which situation-specific diagnostic skills are utilized to solve challenging situations of teaching and learning in class. This study compares two constructs—professional vision and diagnostic activities—with regard to their suitability for coding and analyzing data collected from interviews using think-aloud protocols with five in-service teachers, who worked in the video-based assessment tool DiKoBi Assess. For data collection, teachers watched a videotaped classroom situation on the biology-specific challenges level of students’ cognitive activities and creation of situational interest that both count as important subject-specific dimensions of instructional quality. Interviews using think-aloud protocols were transcribed and coded with distinct category systems for each construct. Analysis of coded data showed that both constructs covered several aspects of the diagnostic process. A crosstabulation of the coded data revealed that the combination of both constructs was best suited to describe and analyze the diagnostic process.     

Differentiated instruction: Hong Kong prospective teachers’ teaching efficacy and beliefs

Catering for learner diversity is one of the key areas in the recent educational reform in Hong Kong. Pre-service teacher education acts as a fundamental way to equip pre-service teachers ready for accommodating diverse learning needs and to build up pre-service teachers’ self-efficacy. The purpose of the study is to examine prospective teachers’ teaching beliefs toward differentiated instruction and teaching efficacy. Using a sequential mixed methods design that contains a questionnaire, focus group interviews, and individual interviews, prospective teachers undertaking a 13-session course regarding differentiated instruction as offered by a local university in Hong Kong participated in the study from January to April 2013. Changes in teaching beliefs regarding differentiated instruction as well as teaching efficacy levels were found. More positive attitudes toward differentiated teaching were found; however, there existed different concerns including class management and conflicts with personal teaching beliefs. These concerns may be related to practical experiences and confidence as well as expectations upon students. Implications for future course development and research are discussed at the end of the paper.     

Preservice elementary teachers’ conceptions of science: science,theories and evolution∗∗

The intent of the present study is to describe preservice elementary teachers’ understanding of science and how certain contextual variables contribute to this understanding.

Eighty students in three sections of an elementary science methods course participated in the study by completing a questionnaire. Six questions dealt with knowledge of science, theories and evolution. In addition, a 21‐item rating scale covering various aspects of science and science teaching was included.

The major theme arising out of the data is how beliefs affect preservice teachers’ understandings of science. The anthropocentricity in the subjects’ definitions and purposes of science, theories and evolution is the most explicit and pervasive of the beliefs influencing the conceptualizations of science. The often vague and misinformed definitions of theories add a further dimension of how science is perceived. When evolution is introduced, both the anthropocentric view of science and the misunderstood notion of theory come together to confound the subjects’ understanding. When asked about the teaching of evolution, the subjects’ confusion concerning the nature of science becomes strikingly evident.