Exploring prospective teachers’ noticing of students' understanding through micro-case videos

This paper explores the nature of prospective teachers’ noticing of students’ understanding as they analyze and discuss middle school students’ understandings of trapezoids in micro-case videos in the context of geometry. In this exploratory study, the data were obtained from eight prospective middle school mathematics teachers through individual video analysis, reflection papers, and group discussions. The results indicated that the use of purposeful micro-case video designs based on prospective teachers’ background knowledge of quadrilaterals allowed them to be productive in video analyses and discussions. In individual video analyses, prospective teachers attended to various mathematical elements to identify students’ responses but did not always use them to make interpretations of each student’s understanding of trapezoid. In the group discussions of the micro-case videos, in contrast, prospective teachers could provide alternative interpretations of students’ understanding by identifying links between the mathematical elements in students’ responses and the characteristics of students’ understandings. In the group discussions, they provided more detailed and specific instructional actions to support each student’s understanding of trapezoid than their individual video analyses. This study suggests practical implications for teacher education programs on how to use video cases (e.g., firstly, working individually and then having group discussions about the videos) to explore prospective teachers’ professional noticing skills. Considering prospective teachers’ background knowledge of related mathematical contents, this study can also inspire future studies on how to design effective videos about students’ mathematical understanding.

     

Inquiry-Based Professional Development: What does it take to support teachers in learning about inquiry and nature of science?

This study examined the geologic and evolutionary subject matter and views of inquiry and nature of science (NOS) of a group of 5th–9th grade teachers, and a comparison group, before and after participating in an inquiry-based professional development (PD) experience. Project teachers participated in an intensive, week-long, resident institute where they learned about geology, evolutionary concepts, NOS, and inquiry while engaging in an authentic scientific investigation. They were also given support in how to teach these topics using an inquiry-based approach. Analyses of data indicate that project teachers showed greater gains in subject matter than comparison teachers and the relative change was significantly different statistically. Furthermore, most project teachers demonstrated a shift from less informed to more informed views of inquiry and NOS and the relative change between participant and comparison teachers was significantly different statistically. These gains are promising because they suggest that short-term and intensive PD can support teachers in enhancing their knowledge and views. Moreover, analysis of post-programme questionnaires and interviews indicated that supporting teachers in reflecting on the relationship between their former classroom teaching practice, and new knowledge acquired during PD, may be an important link in enhancing teacher knowledge and supporting change in practice. This suggests that enhanced knowledge and views may not be the only factor contributing to changing one's practice. The study points to the importance of reflection in promoting teacher change. Results from this study add insights to supporting teachers in enacting inquiry-based instruction and teaching about NOS in their classrooms.     

The hyperkinetic child: What do teachers know?

School personnel are involved in the diagnosis and treatment of hyperkinetic children in many important ways: (a) schools identify and refer the hyper-kinetic child to the physician, who then relies on behavioral reports provided by teachers and parents in making a formal diagnosis and in evaluating treatment; and (b) more recently, schools have begun to administer behavioral intervention programs which may well be as effective as drug treatment in reducing the off-task classroom behavior of many hyperkinetic children. There are many hyperactive children in classrooms who are not referred for medical evaluation and treatment. A group of teacher-identified hyperactive boys was rated significantly higher on the Hyperkinesis Index of the Conners Teacher's Questionnaire than a group of non-hyperactive classmate control boys, but the mean Hyperkinesis Index scores of teacher-identified hyper-actives and clinic-diagnosed hyperkinetics did not differ from each other. The teacher-identified hyperactive boys were observed to be off-task 33% of the time in their classrooms, and the clinic-diagnosed hyperkinetic boys were off-task a comparable 37% of the time. It was suggested that if school personnel use their expertise to identify hyperactive children in the classroom and begin behavioral intervention programs at the earliest possible time, medical referral and treatment will be unnecessary for many children.     

What sort of science education do we really need?

The research aims to explore the role of science for employees in science-based industries and for members of the public interacting with science in their everyday lives. Case studies were carried out in a small sample of industries, in community action groups and in personal decision making. The methodology, informed by a tentative model of science, included scrutiny of available relevant documentation and semi-structured interviews. The findings suggest that procedural understanding was essential in the higher levels of industry and in interacting effectively with everyday issues, while conceptual understanding was so specific that it was acquired in a need-to-know way. The implications for science education hinge on a substantial reduction in the conceptual content and the explicit teaching of the nature of evidence (procedural understanding). The authors suggest building on primary pupils' enthusiasm for investigative work at UK Key Stage 3 (11-14 years) and developing an issues-based curriculum at Key Stage 4 (14-16 years).     

What does the teacher do?: Constructivist pedagogies and prospective teachers’ beliefs about the role of a teacher

The constructivist pedagogies that are increasingly part of teacher education course work and expectations emerge from an intellectual world where knowledge is seen as created rather than received, mediated by discourse rather than transferred by teacher talk, explored and transformed rather than remembered as a uniform set of positivistic ideas. Increasingly, teacher educators ask new teachers to learn how to elicit and then use students’ existing ideas as a basis for helping them construct new, more reasoned, more accurate or more disciplined understandings. While the role a teacher plays in developing or shaping students’ thinking via constructivist pedagogies is obvious to teacher educators who advocate such strategies, the case of Taylor, a prospective English teacher, suggests that the role a teacher plays when using these strategies may not be at all clear to prospective teachers. Rather than understanding constructivist pedagogies as techniques for thinking with learners, for teaching them, Tayor saw these strategies as ends in themselves. Faced with models of constructivist pedagogies, Taylor concluded that the teacher's role ends when she has activated learners, invited them to talk, successfully engaged their participation. This article describes how she reached this conclusion and explores the ways in which constructivist pedagogies can lead prospective teachers to project a thin vision of their role as a teacher.     

Coordinating multiple representations of polynomials: What do patterns in students' solution strategies reveal?

We investigate the strategies used by 64 advanced secondary mathematics students to identify whether a given pair of polynomial representations (graphs, tables, or equations) corresponded to the same function on an assessment of coordinating representations. Participants also completed assessments of domain-related knowledge and background skills. Cluster analysis of strategies by representation pair revealed patterns in the participants' strategy use. Two clusters were identifiable on tasks that required matching equations to graphs and graphs to tables. We identified overlap between these two clusters, suggesting that while the representation pair influenced strategy choice, there was also a general distinction between students who used more and less sophisticated strategies. However, students who used more sophisticated coordination strategies were similar to the others on measures of domain-specific knowledge or background skills. We consider implications for future investigations testing interventions to promote coordinating representations.     

Challenges in deepening prospective teachers’ understanding of multiplication through justification

This article reports challenges faced by prospective elementary teachers as they revisited whole number multiplication through a sequence of tasks that required them to develop and justify reasoning strategies for multiplication. Classroom episodes and student work are used both to illustrate these challenges, as well as to demonstrate growth over time. Implications for the design of mathematics courses for prospective teachers’ are discussed. Although the study is situated in the context of multiplication, it has implications for teachers reasoning and justification in other areas of mathematics.

What do we know and where do we go? Formative assessment in developing student teachers’ professional learning of teaching science

In the context of teacher education, it could well be suggested that assessment activities that build on formative interactions between student teachers and teacher educators might offer new windows into better understanding teaching and learning. This paper presents findings from a study into a primary science teacher education initiative that seeks to build the foundations on which 24 primary science student teachers, through the use of formative assessment of their science teaching and learning, can begin developing their pedagogical content knowledge (PCK). In the project, formative assessment consists of activities used by teacher educators to stimulate interactions, self- and peer-assessment in order to provide insights into how student teachers develop their PCK during a semester. Content Representations (CoRes), were used as a tool to unpack the student teachers’ approach to teaching a science topic and the reasons for that approach. The results indicate that the use of CoRes, together with subsequent self-assessment and formative interactions with teacher educators and peers, do have the potential for PCK development for student teachers. The results further highlight the need for developing reliable and valid tools for capturing and assessing student teachers’ PCK in pre-service teacher education.     

Arab prospective science teachers’ world view: presuppositions towards nature

This study investigated the nature of Arab prospective science teachers’ world view presuppositions towards nature. An instrument was developed and administered to 117 prospective science teachers. The instrument covers four world view presuppositions in a bipolar form. They are safety and fear, order and chaos, aesthetic and materialistic, special and mundane. The results showed that the prospective teachers mostly felt safe towards nature. They considered nature orderly, beautiful and special. More importantly, their presuppositions were mostly religious. Although many of them would be science teachers within a few months they lacked the usual scientific presuppositions. The study concludes that science education programmes in the Arab culture should be culturally sensitive.     

The I files,the truth is out there: science teachers’ constructs of inquiry

This article is concerned with the personal constructs of science teachers about inquiry in selected schools in the Yorkshire and the Humber region of England. While there is a large volume of existing literature which advocates the use of inquiry in the science classroom to enhance students' engagement with, and learning of science, relatively few of these studies represent teachers' voice. Therefore, we believe that it is important and distinctive to report teachers' constructs of inquiry and related concerns regarding its use in the science classroom. We identify the key constructs from 10 participating teachers and discuss these amongst a backdrop of policy implications for inquiry approaches in English secondary school science classrooms. Personal Construct Theory was used to underpin the study and frame data collection and analysis. Key findings show that the teachers identify an inquiry approach as being effective in stimulating students' independent learning and interest in science but issues such as time and confidence inhibit their deployment of inquiry approaches.     

Conceptualizing a basis for understanding: What differences do differences make?

The purpose of our commentary is to offer ways of understanding the differences in theoretical positions and of exploring what difference the differences make. To conceptualize a basis for understanding the theoretical transformation currently taking place in the field of educational psychology, we bring two constructs from the philosophy of science to bear. We suggest that one way to understand the differences is to consider the expressive potential of the research programs. In so doing, we suggest that the research programs be seen as intellectual ecologies created by members within these traditions. We argue that to understand the emic point of view of a tradition, one must become initiated into the discourse within that community and understand the historical development of the ideas within that intellectual ecology.     

What do science teachers think about developing scientific competences through context-based teaching? A case study

ABSTRACT

In this paper we explore the views and opinions of four secondary education science teachers regarding the teaching of scientific competences. Their views were gathered in the context of a training programme in which they had to design, implement, and assess their own teaching unit for developing students’ scientific competences by means of context-based learning. Analysis of the data yielded a set of 14 categories distributed across 5 areas: scientific competence and context-based teaching; the teacher and his/her professional environment; implementation in the classroom; development of the teaching unit; and assessment. This process also identified the aspects which teachers believed either facilitated or acted as an obstacle to the development of scientific competences through context-based teaching. We discuss the implications of our findings and suggest ways in which a shift towards a context-based approach to teaching scientific competences can best be achieved, and consider a series of factors related to teachers’ professional identity that may influence this process.     

What is science in preschool and what do teachers have to know to empower children?

In this article we problematize the purpose of teaching science in preschool and the competences preschool teachers need in order to conduct science activities in the classroom. The empirical data were collected through an action research project with five preschool and primary school teachers (K-6). In the first section of this paper we use one situation, a floating–sinking experiment, as an illustration of how two different epistemological perspectives generate different foci on which kind of science teaching competences can be fruitful in preschool settings. In the first perspective, the central goal of science teaching is the development of the children’s conceptual understanding. With this perspective, we found that the science activities with children were unsuccessful, because their thoughts about concepts did not develop as expected, the situation even enhanced a “misconception” concerning density. Moreover, the teacher was unsuccessful in supporting the children’s conceptual learning. The second perspective uses a feminist approach that scrutinizes science, where we investigate if the floating–sinking activity contributes to a feeling of participation in a scientific context for the children and if so how the teacher promotes this inclusion. This second perspective showed that the children’s scientific proficiency benefited from the situation; they had a positive experience with density which was reinforced by the teacher. The children discovered that they had power over their own learning by using an experimental approach. On the basis of these findings, we conclude that there are competences other than subject matter knowledge that are also important when preschool teachers engage children in scientific activities. Through process-oriented work with the teacher group, we identified four concrete skills: paying attention to and using children’s previous experiences; capturing unexpected things that happen at the moment they occur; asking questions that challenge the children and that stimulate further investigation; creating a situated presence, that is, “remaining” in the situation and listening to the children and their explanations. We discuss possible ways to move preschool teachers away from their feelings of inadequacy and poor self-confidence in teaching science by reinforcing this kind of pedagogical content knowledge.     

What can teachers do to raise pupil achievement?

Improving weak teaching may be one of the most effective means of raising pupil achievement. However, teachers’ classroom practices and the teaching ‘process’ may matter more to student learning than teachers’ observed résumé characteristics (such as certification and experience). There may also be important differences in teacher characteristics across government and private schools which may help explain the large documented public-private achievement differences often found in studies. This paper delves into the black-box representing ‘teaching’ to uncover the teacher characteristics and teaching practices that matter most to pupil achievement. This is done using unique school-based data, collected in 2002-2003 from government and private schools from one district in Punjab province in Pakistan. The data allow exploitation of an identification strategy that permits the matching of students’ test scores in language and mathematics to the characteristics of teachers that teach those subjects. Within pupil (across subject rather than across time) variation is used to examine whether the characteristics of different subject teachers are related to a students’ mark across subjects. The data are also unique in asking all subject teachers questions pertaining to their teaching practices and these, often unobserved, ‘process’ variables are included in achievement function estimates. Our pupil fixed-effects findings reveal that the standard résumé characteristics of teachers do not significantly matter to pupil achievement. Perversely, however, teachers are found to be rewarded with higher pay for possessing these characteristics, highlighting the highly inefficient nature of teacher pay schedules. Our findings also show that teaching ‘process’ variables matter significantly to student achievement. There are important differences across school-types.     

What do students think when teachers make adaptations?

Eight hundred and seventy-six high school and middle school students provided information on their perceptions of adaptations teachers may make to accommodate the individual needs of their students. Additionally, achievement and social alienation were examined to determine the extent to which these variables relate to students' perceptions of teacher adaptations. Overall, students preferred teachers who made adaptations; however, item analyses revealed that students find some adaptations more desirable than others. Students felt positively about many adaptations that promote learning, but preferred that no adaptations be made to textbooks and materials, tests, and homework. While students' perceptions followed the same overall pattern for low and high achieving students, those students who preferred adaptations demonstrated significantly higher reading and mathematics achievement scores. Students who felt more alienated (less socially accepted) from their teachers were more likely to view favorably teachers who made adaptations. Students' comments about teachers who make adaptations indicate that they perceive these teachers as better able to meet the individual needs of students, caring and understanding of students, and willing to provide extra help.     

Pre-K-8 prospective teachers’ understanding of fractions: An extension of fractions schemes and operations research

In an effort to expand our knowledge base pertaining to pre-K-8 prospective teachers’ understanding of fractions, the present study was designed to extend the work on fractions schemes and operations to this population. One purpose of our study was to validate the fractions schemes and operations hierarchy with the pre-K-8 prospective teacher population to determine whether this population follows the same trajectory as upper elementary and middle school students. A second purpose of our study was to identify which of the fractions schemes and operations our sample of prospective teachers demonstrated evidence of having constructed along with what this tells us about prospective teachers’ understanding of fractions. We were able to validate the hierarchy for this population, meaning that each lower-level fraction scheme/operation appeared to be a prerequisite to the higher-level schemes/operations. We found that although most of the prospective teachers had constructed the lower-level schemes and operations, less than half had constructed the more sophisticated ones. An unexpected result related to the association between the coordination of three levels of units and the iterative fraction scheme is addressed. Prospective teachers’ reliance on procedural knowledge related to fractions also presented a challenge to assessing, in particular, their ability to coordinate three levels of units. We conclude with implications for research and practice in mathematics courses intended for pre-K-8 prospective teachers.     

Using process drama to enhance pre-service teachers’ understanding of science and religion

I report an action research study that aimed at improving Thai pre-service teachers’ understanding of the relationship between science and religion and at assisting them to respond to this issue in a science classroom. The participants were twelve post-grad students pursuing Master of Art in Teaching Science at Kasetsart University. They took a course, Philosophy of Science, taught by the researcher in Semester A, academic year 2007. Process drama is the teaching strategy employed. The students were fully engaged in the process drama; doing research, producing, distributing, and criticizing the drama. Focus group, student journal, and observation were used to gather the data and the data was analyzed using qualitative analysis techniques. The focus groups revealed that the drama could help students reflect on the complexity and sensitivity of the issue. They found there was no inherent conflict between science and religion since they answered different questions and used different methods to achieve their results. However, the conflicts occurred when people were not aware of the basic differences between the two so they justified one on the basis of purpose and method of one another. The pre-service teachers also found consistency between science and Buddhism. They thought that the teachers of science should respond to the conflicts in a respectful, compromising, and neutral manner.