Leader noticing of facilitation in videocases of mathematics professional development

In this article, we report on Researching Mathematics Leader Learning (RMLL), a project designed to support leaders in learning how to facilitate robust opportunities for teachers’ mathematical learning. Our two-phase research design allowed us to construct a set of videocase seminars, enact the seminar design with leaders, analyze these data, refine our seminar design, and implement a second set of seminars with a new group of leaders. We drew on the noticing literature to examine leaders’ pedagogical reasoning as they discussed videocases of professional development. In this article, we demonstrate how changes in our framework for leader development and the resulting changes in the prompts and tasks shaped leader noticing in three ways: (a) accounting for the mathematical work of the facilitator and teachers in the videocase; (b) linking the mathematical work to goals for teacher learning; and (c) reasoning around the facilitator’s work in advancing those learning goals. Analysis indicates that in Phase II, leader discussions were more focused on the mathematical and pedagogical work needed to advance teacher learning. Based on our research and development work with over 70 leaders, we offer a set of design principles for leader professional development.     

Students' Understanding of the Objectives and Procedures of Experimentation in the Science Classroom

As part of a project to identify opportunities for reasoning that occur in good but typical science classrooms, this study focuses on how sixth graders reason about the goals and strategies of experimentation and laboratory activities in school. Collaborating with teachers, we explore whether reasoning can be deepened by developing instruction that capitalizes more effectively on the classroom opportunities that arise for fostering complex thinking and understanding. The design of the study includes (a) a baseline interview probing students' understanding of experimentation in the context of a standard, 40-min "hands-on" activity that is part of the standard sixth-grade curriculum; (b) a 3-week teaching study, in which five teachers, informed by the cognitive science research concerning the development of scientific reasoning, designed and taught a special experimentation unit in their classrooms; and (c) a series of follow-up interviews, in which students' understanding of experimentation was reexamined. The findings from the two learning contexts-one more supportive of student reasoning than the other-inform us about the kinds of reasoning that are developing in middle-school students and the forms of instruction best suited to exercising those developing skills.     

Design approach of mathematics learning activities in a digital environment for children with autism spectrum disorders

Learning environment on mathematics for autistic children is a prototype of a digital environment with dynamic adaptation features designed to offer activities towards the development of mathematical reasoning in children aged 6–12 years, diagnosed with autism spectrum disorders (ASD), a neurodevelopmental disorder characterized by deficits in social communication and social interaction as well as restricted and repetitive patterns of behaviour, interests or activities. This paper, with a primarily conceptual and analytical scope, discusses the mathematical difficulties that some children with ASD have, and presents strategies that can be used to overcome them. Based on a literature review and on the results of a preliminary study already conducted, we present results concerning the proposal of a set of learning activities for the prototype under development, specifically targeted to promote mathematical reasoning in students with ASD. Guidelines for future research are also discussed.     

Annual Index Volume 75, 1981-82

Abstract

This study was designed to investigate whether teachers who receive training and then implement more effective instructional practices change in terms of the reasons they offer for their effectiveness. Comparisons were made between 46 teachers who were trained in and implemented mastery learning techniques and 50 similar teachers who could not be included in the training. The results of a multivariate analysis of variance showed that the mastery learning teachers attached increased importance to teaching practices and behaviors in explaining their effectiveness after they had implemented these techniques. Furthermore, there was a significant reduction in the importance mastery learning teachers attached to personality factors. The implications of these findings for staff development are discussed.     

Four Student Teachers' Pedagogical Reasoning on Functions

This study attempts to identify theinfluence of student teachers' subject matterknowledge for teaching on the process ofpedagogical reasoning. This influence isstudied through the way in which the concept offunction is presented to pupils in teachingthrough the textbook problems. Our findingsshow that the four student teachers in ourstudy differed in their subject-matterknowledge for teaching both in the differentaspects of concepts they emphasised and in theuse of a representation repertoire to structurelearning activities. All of this conditionedthe use of graphical and algebraic modes intheir planning of subject matter to bepresented to pupils. We explored also theinfluence of images of mathematics,teaching and learning on student teachers'organisation of the subject matter forteaching, but found this only slight. Finally,regarding the relationship between subjectmatter knowledge and pedagogical contentknowledge in student-teachers' ways of knowingthe subject matter, we offer some implicationsof these findings for mathematics teachereducation programmes.     

Cycles of Research and Application in Education: Learning Pathways for Energy Concepts

ABSTRACT— We begin this article by situating a methodology called developmental maieutics in the emerging field of mind, brain, and education. Then, we describe aspects of a project in which we collaborated with a group of physical science teachers to design developmentally informed activities and assessments for a unit on energy. Pen-and-paper assessments, called teasers , were employed, along with interviews, to study how students learned about the physics of energy. Results were used to describe students' learning pathways and to design a scoring rubric for teacher use. We hypothesized that (a) teasers, by themselves, could be used effectively to evaluate the developmental level of students' reasoning about energy and (b) teachers could employ the scoring rubric with minimal instruction. Encouraged by our findings, we went on to create a freely available online version of the energy teaser , including a new rubric designed to improve the accuracy with which teachers can assess the developmental level of students' energy conceptions.     

Teacher question and student response with regard to cognition and language use

In the current study, we focus on teacher-student discourse in Pre-K science activities, with particular attention to teacher questioning. Videotaped classroom observations and teacher interviews served as the corpus of data. Overall, teachers asked mostly closed-ended questions, but used more open-ended questions when experiments were being conducted. During experiments, teachers?? questions were aimed at prediction and reasoning. In contrast, teachers used primarily closed-ended questions when science skills were being practiced and during science book readings, when their questions were oriented toward recognition and recall of factual information. The effects of the teachers?? questions can be seen in the students?? responses. When questions were open-ended, students employed a more varied vocabulary and more complex sentence structures. When teachers?? questions were oriented toward prediction and reasoning, students practiced these higher level cognitive skills in responding. Based on these findings, we provide recommendations for teaching practice in early childhood science education.     

Teacher support for collective argumentation: A framework for examining how teachers support students’ engagement in mathematical activities

We propose a framework for examining how teachers may support collective argumentation in secondary mathematics classrooms, including teachers’ direct contributions to arguments, the kinds of questions teachers ask, and teachers’ other supportive actions. We illustrate our framework with examples from episodes of collective argumentation occurring across 2 days in a teacher’s classroom. Following from these examples, we discuss how the framework can be used to examine mathematical aspects of conversations in mathematics classrooms. We propose that the framework is useful for investigating and possibly enhancing how teachers support students’ reasoning and argumentation as fundamentally mathematical activities.     

From visual reasoning to logical necessity through argumentative design

Our main goal in this study is to exemplify that a meticulous design can lead pre-service teachers to engage in productive unguided peer argumentation. By productivity, we mean here a shift from reasoning based on intuitions to reasoning moved by logical necessity. As a subsidiary goal, we aimed at identifying the kinds of reasoning processes (visual, inquiry-based, and deductive) pre-service teacher's students adopt, and how these reasoning processes are interwoven in peer-unguided argumentation. We report on a case study in which one dyad participating in a pre-service teachers program solved a mathematical task. We relied on three principles to design an activity: (a) creating a situation of conflict, (b) creating a collaborative situation, and (c) providing a device for checking hypotheses/conjectures. We show how the design afforded productive argumentation. We show that the design of the task entailed argumentation which first relied on intuition, then intertwined the activities of conjecturing and checking conjectures by means of various hypotheses-testing devices (measurement, manipulations, and dynamic change of figures with Dynamic Geometry software), leading to a conflict between conjectures and the outcome of the manipulation of DG software. Peer argumentation then shifted to abductive and deductive considerations towards the solution of the mathematical task. These beneficial outcomes resulted from collaborative rather than adversarial interactions as the students tried to accommodate their divergent views through the co-elaboration of new explanations.     

The internet as a tool to learn a second language in a technical environment

Second language acquisition is a hard task for teachers, since to achieve the motivation from students to practice a language simulating a real context is very difficult. On the one hand, students are often influenced by their mother tongue and more when they are practising a second language with a partner from the same nationality. On the other, technology is part of our lives and teachers should use all the tools in order to motivate students to learn any topic. So, if we integrate technology in the methodology we use when teaching a second language and students can practise with international partners, the results can be surprising. Chats, scanning texts, games, filling forms, etc. are just some of the activities our students can do in order to improve their command of a second language and also these activities can be used by content teachers in order to complement content learning. In the present paper, we provide some examples of activities designed by collaborating with content teachers based on websites, and then we analyse the effect they produced on students. We contrast the methodology used to propose tasks based on websites and those based on texts, and finally, evaluate their effect on the motivation of students.     

Scaffolding the development of effective collaboration and learning

Research in Mexican and British schools provides an empirical basis for arguing that, by the use of certain kinds of interactional strategies, teachers can enable children to become more able in managing individual and joint reasoning and learning activities in the classroom.The research described is based on a sociocultural conception and analysis of education, which focuses on the ways that children can be inducted into the communicative and intellectual activities of the classroom as a ‘community of enquiry’. The research has provided (a) an account of strategies teachers use, and for relating teacher’s scaffolding to the interactive process of knowledge construction; (b) an analysis of ways that children talk when working together on joint activities; and (c) a practical method for promoting children’s effective collaboration, communication, reasoning and learning, successfully tested with British and Mexican primary school children. The results of the research are discussed in relation to a Vygotskian conception of the relationship between ‘intermental’ (social) and ‘intramental’ (psychological) development.     

How education policy is made meaningful – a narrative exploration of how teachers show autonomy in the development of teaching and learning

This study addresses how the autonomy of teachers in higher education, in relation to education policy and reform, can be understood. By taking a narrative-in-action approach, we studied health profession teachers’ activities and reasoning within their ongoing practice during one year. The findings show how the teachers created their own policies and in what way these policies became meaningful. As teachers in this study continuously made changes, the joint creation of policies contributed to their sense of togetherness and the re-building of a community of practice. In parallel, they increased the evidence-based standards related to their discipline and experienced a shift in perspective concerning teaching and learning. The importance of their jointly made policies can be explained by how they learned a student-learning view together, and built on their own ideas of what educational matters needed to be developed. At the same time, their activities and reasoning mirror ‘a debated but yet prevailing view’ on the discourse of quality and a number of ideals thereof such as transparency and standardisation, effective teaching and increased academisation.     

Do expert clinical teachers have a shared understanding of what constitutes a competent reasoning performance in case-based teaching?

To explore the assessment challenge related to case based learning we study how experienced clinical teachers—i.e., those who regularly teach and assess case-based learning—conceptualize the notion of competent reasoning performance for specific teaching cases. Through an in-depth qualitative case study of five expert teachers, we investigate whether they share a common concept of what constitutes a good reasoning performance for a set of three teaching cases. We ask expert teachers to reflect on their problem-solving performances to extract specific expectations regarding the assessment of learners. Using visual representations of their performance, experts inspect and identify whether key elements are considered critical, necessary, and useful for the assessment of learners’ performance. Findings indicate that despite solving cases differently, expert teachers share a common concept regarding the key elements that demonstrate good clinical reasoning for specific cases. These results and methods used to trigger assessment criteria from expert clinical teachers show potential for the development of process measures in the assessment of clinical reasoning.     

Reasoning as a scientist: ways of helping children to use language to learn science

Sociocultural researchers have claimed that students' learning of science is a discursive process, with scientific concepts and ways of reasoning being learned through engagement in practical enquiry and social interaction as well as individualized activity. It is also often claimed that interacting with partners while carrying out scientific investigations is beneficial to students' learning and the development of their understanding. The research we describe investigated the validity of these claims and explored their educational implications. An experimental teaching programme was designed to enable children in British primary schools to talk and reason together and to apply these skills in their study of science. The results obtained indicate that (a) children can be enabled to use talk more effectively as a tool for reasoning and (b) talk‐based activities can have a useful function in scaffolding the development of reasoning and scientific understanding. The implications of the findings for educational policy and practice are discussed.     

Teacher knowledge,curriculum materials,and quality of instruction: Lessons learned and open issues

This paper draws on four case studies to perform a cross-case analysis investigating the unique and joint contribution of mathematical knowledge for teaching (MKT) and curriculum materials to instructional quality. As expected, it was found that both MKT and curriculum materials matter for instruction. The contribution of MKT was more prevalent in the richness of the mathematical language employed during instruction, the explanations offered, the avoidance of errors, and teachers' capacity to highlight key mathematical ideas and use them to weave the lesson activities. By virtue of being ambitious, the curriculum materials set the stage for engaging students in mathematical thinking and reasoning; at the same time, they amplified the demands for enactment, especially for the low-MKT teachers. The analysis also helped develop three tentative hypotheses regarding the joint contribution of MKT and the curriculum materials: when supportive and when followed closely, curriculum materials can lead to high-quality instruction, even for low-MKT teachers; in contrast, when unsupportive, they can lead to problematic instruction, particularly for low-MKT teachers; high-MKT teachers, on the other hand, might be able to compensate for some of the limitations of the curriculum materials and offer high-quality instruction. This paper discusses the policy implications of these findings and points to open issues warranting further investigation.     

The Role of Teacher Leadership in Professional Learning Community (PLC) in International Baccalaureate (IB) Schools: A Social Network Approach

This study aims to illuminate how professional interactions among teachers form different types of teacher leadership in schools, which, in turn, shape different levels of teachers’ involvement in activities related to their professional learning community (PLC). To investigate certain patterns of teachers’ interactions that contribute to the formation of teacher leadership and thereby the development of PLC, two international schools that offer a full continuum of three International Baccalaureate (IB) programs were purposively chosen. The schools have similar numbers of students and are located in two different countries in East Asia. Using a mixed-methods research approach, the patterns of teacher professional interactions were first examined using social network analysis. Next, the degree to which teachers in the case study schools enact practices related to PLCs was assessed and compared through a multivariate analysis of variance (MANOVA) test. Further, based on findings from social network analysis, in-depth semistructured interviews were conducted with selected key participants to understand the linkage between teacher leadership and teachers’ involvement in their PLC in each case school. From the findings, we propose four conceptual types of teacher leadership that explain how teacher leadership shapes different levels of teachers’ engagement in PLC in the two case schools.     

Professional Development of Physics Teachers in an Evidence-Based Blended Learning Program

The present study examined continuity of learning between face-to-face and online environments in a “blended” professional development program designed for 16 physics teachers. The program had nine face-to-face meetings as well as continuous online exchanges between them through a website. The program focused on “knowledge integration” (KI) innovative activities in physics classes using an “evidence-based” approach: The teachers implemented the activities, collected and analyzed data about their practice and their students’ learning, and reflected on the evidence with their peers. Five reflective tools were used to promote continuity: Your Comments, Hot Polls, Smashing Sentences, Hot Reports, and Mini Research. Continuity was assessed with regard to the ideas discussed by the teachers and the reasoning patterns that they employed. Analysis of the online exchanges in relation to teachers’ face-to-face discourse revealed that the teachers discussed the same ideas (KI, evidence and learner-centered pedagogies), employed the same reasoning patterns (e.g., forming generalizations), and extended ideas in re-visitation. The online and face-to-face environments played different and complementary roles in the teachers’ learning. This study shows that appropriate use of an online environment in a blended program can lead to a continuous course of learning and can transform a “9 once-a-month-meetings” workshop into a “9-month” workshop.     

Discerning student thinking: a practical theoretical framework for recognising or informally assessing different ways of thinking

We expect our students to learn different ways of thinking, such as historical empathy or scientific reasoning, reflection, critical analysis, or clinical reasoning. But how do we discern if they have learned these ways of thinking when thinking is often abstract, tacit and seemingly invisible? In this conceptual and theoretical article, I argue that we can discern any kind of thinking, however we define it, if we focus on the observable actions or thinking behaviours associated with that thinking. Based on this argument, I then offer a theoretical framework for teachers so they might recognise and informally assess the particular kind of student thinking they want to cultivate. This framework synthesises several important theories about how we learn to think, and distinguishes six general features a teacher might look for to be more discerning about any kind of thinking: visibility, complexity, frequency, flexibility, independence, and application of the thinking behaviours.     

Developing preservice teachers' pedagogical reasoning ability

Teachers not only need to develop a knowledge base for teaching, but also should be able to make reasoned decisions regarding their classroom science teaching. Preservice teachers need opportunities to begin developing their pedagogical reasoning ability as part of their undergraduate education so that science teaching in primary schools is based on sound reasoning. This paper, using a case study methodology, reports on the initial pedagogical reasoning ability of second-year preservice primary teachers. By completing a problem-based science education topic, these preservice teachers had the opportunity to explore all stages in the pedagogical reasoning process. Preservice teachers initially demonstrated limited pedagogical reasoning ability, but as a result of the framework provided in the problem-based approach, they were able to refine their reasoning ability. Through a combination of group work and individual research, the preservice teachers were able to integrate their science knowledge, curriculum knowledge and knowledge of learners and apply this to a peerteaching situation and in the process develop their pedagogical reasoning skills.