THE RELIGIOUS EXPERIENCE OF THE HOME

The process of sophisticated theological thinking in children begins at an early age. Thinking deeply about the ultimate concerns of life is inherent in human beings. This paper, based on the author's conversations with his children, explores the profound processes of theological reflection in playground songs sung by children in public elementary schools, informal conversations with children about prayer and religious insight, and the place of paradox and play in the theological reflection of children. Drawing on the works of such scholars as Winnicott, Gerkin, Rizzutto, and Stivers, the author charts intriguing areas for reflection as well as needed areas for future research.     

The role of teacher instructional practices in student collaboration

Prior research on collaborative learning identifies student behaviors that significantly predict student achievement, such as giving explanations of one’s thinking. Less often studied is the role of teachers’ instructional practices in collaboration among students. This article investigates the extent to which teachers engage in practices that support students’ explanations of their thinking, and how these teacher practices might be related to the nature of explanations that students give when asked by the teacher to collaborate with each other. The teachers observed here, all of whom received specific instruction in eliciting the details of student thinking, varied significantly in the extent to which they asked students to elaborate on their suggestions. This variation corresponded to variation across classrooms in the nature and extent of student explanations during collaborative conversations and to differences in student achievement.     

Using a Field Trip Inventory to Determine If Listening to Elementary School Students' Conversations,While on a Zoo Field Trip,Enhances Preservice Teachers' Abilities to Plan Zoo Field Trips

This study investigated whether listening to spontaneous conversations of elementary students and their teachers/chaperones, while they were visiting a zoo, affected preservice elementary teachers' conceptions about planning a field trip to the zoo. One hundred five preservice elementary teachers designed field trips prior to and after listening to students' conversations during a field trip to the zoo. In order to analyze the preservice teachers' field trip designs, we conducted a review of the literature on field trips to develop the field trip inventory (FTI). The FTI focussed on three major components of field trips: cognitive, procedural, and social. Cognitive components were subdivided into pre-visit, during-visit, and post-visit activities and problem-solving. Procedural components included information about the informal science education facility (the zoo) and the zoo staff and included advanced organizers. Social components on student groups, fun, control during the zoo visit, and control of student learning. The results of the investigation showed that (a) the dominant topic in conversations among elementary school groups at the zoo was management, (b) procedural components were mentioned least often, (c) preservice teachers described during-visit activities more often than any other characteristic central to field trip design, (d) seven of the nine characteristics listed in the FTI were noted more frequently in the preservice teachers' field trip designs after they listened to students' conversations at the zoo, and (e) preservice teachers thought that students were not learning and that planning was important.     

Qualified Pedagogical Reflection as a Way to Improve Mathematics Education

All changes of the character of education and improvement of its quality depend, in our view, particularly on the teacher. To be able to do their work efficiently, teachers have to be equipped with professional skills and dispositions, with “teachers’ competence”. For their professional growth, we consider indispensable competence in reflection, which is aimed at the teacher’s activities with regard to aspects of pedagogy and/or subject-didactics. From the point of view of the goals and content of their teaching and the methods of work (and their realisation), the development of teachers’ conscious self-reflection on their own teaching and systematic pursuance of joint reflection with other teachers and/or researchers can promote the teacher’s professional growth. In this paper, we show how a selected group of elementary school teachers reflected on their competence in the course of preparing, carrying out and analysing several instruction experiments. The paper is based on samples of teachers’ reflections and their gradual development from mere simple conversations based on intuitive perceptions, through searching for effective teaching approaches, to the deep assessment of mathematics teaching from the point of view of topics and their didactic elaboration and to suggestions for the teachers’ own experiments.     

The family car as a “vehicle” for children's use of distant time referents

The conversations of nine preschool-aged children (C.A. 4:0–5:2) were tape-recorded as they interacted with teachers and with peers at preschool, as they traveled home from school with their parent in the family car, and as they engaged in routine home activities. The speech samples were coded to identify the time referents the children used in their topics of conversation in the three settings. The study sought to explore suggestions that young children, although generally context-bound in their talk at home and school, are capable of decontextualized talk when settings and conversational partners are familiar and supportive, and when contexts are transitional and prompt talk about other than the here-and-now.Significant differences were found in the children's use of present, past and future time referents in the three settings. Overall, the children spoke most often about the here-and-now, making frequent references to the present activities or to people in each setting. References to past and future events, however, were significantly more frequent in the car setting than in the home or school talk. Most references to the past occurred during the first 5 min of travel and were often prompted by the presence of a project remnant in the car or parents' questions or comments. References to future events occurred more frequently during the latter portion of the car trip. Differences in the children's proportional use of fantasy time referents were not significant. Possible implications for teachers and parents are discussed along with suggestions for future research.     

Promoting a willingness to wonder: moving from congenial to collegial conversations that encourage deep and critical reflection for teacher educators

There is an inherent expectation that educators will work towards continuously improving their practice and quality of teaching. Underpinning this expectation is an assumption that educators also engage in the process of reflection. In this article, we begin by outlining the current tensions in the field of education that relate to managerialist concerns of the measurement and monitoring of quality teaching and effectiveness. We then contextualise our particular circumstances and provide an account of a collaborative action research project we initiated to examine our team-teaching practices in a graduate entry pre-service teacher education programme. In the project, we initially focused on how we might provide for pre-service teachers’ learning while they were undertaking an internship in the final semester of their programme. Factors that required consideration included the use of face-to-face and synchronous online forms of interaction. Having experienced the powerful influence of using protocols to structure professional learning conversations with the pre-service teachers with whom we were working, we also decided to extend the conversations we were having with each other to conversations with our colleagues. Taken together, the action research framework and the processes afforded by protocols provided a structured approach for our inquiry. Conversing with the pre-service teachers involved in the programme, with each other and with our peers at a faculty-level seminar and an international conference were the main sources of data gathered during the research project. The collegial conversations that occurred when using protocols also provided a way to move to the level of critical reflection. Rather than discuss the outcomes of our project in the remainder of the article, we elected to scrutinise and theorise the significant elements that were germane to our project – the three Cs: collegiality, conversation and critical reflection. We conclude by realising that to learn about ourselves as teachers and as learners, we need to move beyond routine and technical aspects of reflection, to a level that is critical and transformative, and that this can be achieved through the use of protocols in purposeful and collaborative conversations with others.     

Informal formative assessment: The role of instructional dialogues in assessing students’ learning

This paper focuses on an unceremonious type of formative assessment - informal formative assessment - in which much of what teachers and students do in the classroom can be described as potential assessments that can provide evidence about the students’ level of understanding. More specifically, the paper focuses on assessment conversations, or dialogic interactions or exchanges, which continuously happen in the classroom and that are at the center of informal formative assessment. It is argued that assessment conversations make students’ thinking explicit in an unobtrusive manner, and when students’ thinking is explicit, it can be examined, questioned, and shaped as an active object of constructive learning. The paper conceptualizes informal formative assessment at the center of effective instructional activities with the use of instructional dialogues as assessment conversations, a typical informal formative assessment practice. The paper then presents a discussion about the evidence on the effect of assessment conversations on student learning.     

Trade Union Education in Canada

Encouraging adults to undertake critical reflection is one of the most frequently espoused aims of graduate programmes of adult education. A considerable body of adult educational literature has been produced in this area, most of it focusing on conceptual analysis or on debate reflecting the strains between progressive, humanistic and liberal interpretations of these processes and radical, critical, socialist interpretations. Missing from the debate surrounding critical reflection as an adult capacity has been attention to the way adults feel their way through critically reflective episodes ‐ to understanding the visceral, emotive dimensions of this process. This paper uses Marton's concept of phenomenography ‐ the exploration and portrayal of how learners experience and interpret learning ‐ to outline a phenomenography of critical reflection as it pertains to one group of adults who happen to be adult educators. Five themes emerge from journals, conversations and autobiographies: impostorship (the sense that participating in critical thought is an act of bad faith), cultural suicide (the recognition that challenging conventional assumptions risks cutting people off from the cultures that have defined and sustained them up to that point in their lives), lost innocence (the move from dualistic certainty toward dialectical and multiplistic modes of reasoning), roadrunning (the incrementally fluctuating flirtation with new modes of thought and being) and community (the importance of a sustaining support group to those in critical process). The paper elaborates these themes and describes how developmental activities for adult educators in critical process can be grounded in participation in critical conversations within learning communities.     

Observing young children's creative thinking: engagement,involvement and persistence

This paper looks at young children's creative thinking as inferred through observations of their activities. A total of 52 episodes of child-initiated and adult-initiated activities in 3- to 4-year-olds in an English Children's Centre were analysed using the Analysing Children's Creative Thinking (ACCT) Framework. Results showed that activities such as gardening and construction were as valuable for supporting creative thinking as ones traditionally associated with creativity, for example, music and painting. Outdoor play of all kinds and socio-dramatic play were particularly effective contexts. All adults played a significant role in facilitating children's initial engagement in activities, and at supporting their speculative thinking and use of prior knowledge. Teachers were often more successful than other adults in supporting the acquisition of new knowledge. Child-initiated activities featured the highest levels of involvement, and were associated with trying out and analysing ideas, flexibility and originality, imagining and hypothesising. This was particularly evident in group or pair play. Children were also more persistent in child-initiated activities. Evidence of risk-taking behaviour was low, although more apparent in child-initiated activities than adult-initiated activities, or activities in which adults were present.     

Closing the gap on the map: Davydov’s contribution to current early algebra discourse in light of the 1960s Soviet debates over word-problem solving

Recent scholarship around teaching elementary mathematics supports the learning of early algebra with 5- to 12-year olds. However, in spite of the recognition of the affordances of early algebra, issues about how to introduce it remain open. Within this context, Davydov’s work is often cited as a source of impressive demonstration of young learners’ capacity for algebraic thinking. This work requires further exploration in order to yield a clearer picture of a very particular teaching approach, which focuses on early abstractions and symbolic language. We argue that in order to fully understand how Davydov’s work contributes to current conversations and what Davydov was trying to do, we need to shed light on the context- and time-specific discourse of the 1960 Soviet educational reforms that made it possible for Davydov to develop his vision about algebraic thinking and to set in motion appropriate teaching approaches for young learners. In this paper, we look back to the Soviet debates that unfolded in Russia on the integration of early algebra in elementary school word-problem solving. Drawing on these debates and the results of Davydov’s school experiments, we lay out the developmental axes of capacity building. This can be done by emphasizing ascent from the abstract to the concrete using a variety of representational modeling tools to support the emergence of algebraic thinking while targeting particular habits of mind within carefully designed learning activities. We conclude with some insights about current arithmetic-algebra debates, and how these could be enriched and deepened by Davydov’s work, which yet remains open to future discussion and reflection.

     

A multiple-perspective analysis of learning in the presence of technology

This paper presents an inquiry into students' conceptual development of a graphics calculator function for direction. The focus is primarily on one student. Her understanding is seen to be constituted and evidenced by her actions, including writing, frequent conversations with a peer, occasional contributions to class discussion and sustained use of her graphics calculator. The analysis is in terms of reflective thinking and reflexive enculturation, operational and structural understanding, and situated abstraction. Tracking the dynamics of students' learning over one month led us to explore a range of issues associated with technology-based learning and to the conclusion that, in accordance with the literature, a key aspect of long-term mathematical advancement, with or without the presence of technology, is reflection on prior activities.This revised version was published online in September 2005 with corrections to the Cover Date.     

The interplay between reflective thinking,critical thinking,self-monitoring,and academic achievement in higher education

The present study assessed the associations among higher-order thinking skills (reflective thinking, critical thinking) and self-monitoring that contribute to academic achievement among university students. The sample consisted of 196 Iranian university students (mean age = 22.05, SD = 3.06; 112 females; 75 males) who were administered three questionnaires. To gauge reflective thinking, the “Reflective Thinking Questionnaire” designed by Kember et al. (Assess Eval High Educ 25(4):380–395, 2000) was utilized. It includes 16 items measuring four types of reflective thinking (habitual action, understanding, reflection, and critical reflection). To assess critical thinking, the “Watson–Glaser Critical Thinking Appraisal”(2002) was utilized. It comprises 80 items and consists of 5 subtests (inference, recognizing unstated assumptions, deduction, interpretation, and evaluation). Self-monitoring was measured via 8 items of the self-regulation trait questionnaire designed by O’Neil and Herl (Paper presented at the annual meeting of the American Educational Research Association, San Diego, CA, 1998). The results demonstrated that critical thinking and all components of reflective thinking positively and significantly predicted achievement with habitual action having the lowest impact and reflection exhibiting the highest influence. Self-monitoring indirectly exerted a positive influence on achievement via understanding and reflection. It was also found that among the four subscales of reflective thinking, reflection and critical reflection predicted critical thinking positively and significantly. Self-monitoring had a positive and significant impact on critical thinking. It also significantly and positively influenced understanding as well as reflection.     

A dynamic learning concept in early years’ education: a possible way to prevent schoolification

In early childhood education and care, Nordic social pedagogy approach is challenged by a learning orientation that often results in unproductive ‘either/or’ thinking. Therefore, based on the two approaches and by analysing several dimensions of Froebel’s ideas and prevailing social-historical activity (play) theory, the author deduces four generally accepted play criteria that form the basis for the construction of a dynamic and play-based learning concept that has the three following cornerstones as focal points: (1) learning happens in activities where the child is an active participant and interacts and communicates with other people; (2) meaningful activities pave the way for children’s learning; these are activities where the child’s motive aligns with the goal of the activity; and (3) learning is seen as a productive and creative activity characterised by imagination.     

The construction of word meaning in a multicultural classroom. Mediational tools in peer collaboration during mathematics lessons

In this article, we examine the construction of word meaning by students during collaborative activities in a multicultural classroom at a Dutch primary school. The analysis is based on recordings of student talk in small groups of four or five students during mathematics lessons. Difficulties with specific terms and expressions frequently arose during group work. Students could easily ask each other about the meaning of difficult words as a part of the collaborative activities they were accustomed to. In the groups with both Dutch and minority children, the minority students addressed their Dutch classmates as language experts. Conversations about language difficulties also occurred in the groups with only minority students. The conversations about word meaning revealed four patterns: (1) ignoring a question about the meaning of a word, (2) showing the meaning using gestures, (3) explaining, or (4) discussing word meaning. In none of the cases were the language problems solved by referring to the everyday meaning of the word. Instead, the conversations focussed directly on the specialised meaning which the word had in the context of the mathematics lesson. This means that the children used the mathematical discourse as a mediational tool for constructing a mathematical meaning of the words.     

Problem posing based on investigation activities by university students

This paper reports a classroom-based study involving investigation activities in a university numerical analysis course. The study aims to analyse students' mathematical processes and to understand how these activities provide opportunities for problem posing. The investigations were intended to stimulate students in asking questions, to trigger their thinking processes, to promote their ability to investigate and to support them in learning numerical analysis' concepts and procedures. The results show that the investigations provided opportunities for students to experience mathematical processes, including posing questions, formulating and testing conjectures and, to some extent, proving results. They also provide some understanding about the role of problem posing in these processes. Posing questions occurred mainly in an implicit way, in the interpretation of tasks and in identifying regularities, analysing graphs and testing cases. The conjectures were often based on pattern identification or data manipulation, and the students tended to accept them without testing or proving. The students also proposed alternative formulations for the initial questions and posed new problems from their explorations and attempts to refine previous conjectures.     

禅门机缘语与中唐的尚奇之风

禅门机缘语的产生有其历史渊源和现实背景。从历史上说 ,魏晋清谈的“赌理”,是禅家机缘对话的滥觞。禅门的一些基本辩论方式以及所辩论的内容 ,在魏晋清谈之中早有端倪。从中唐以后的社会状况来看 ,由于战乱频仍 ,大量流民涌入禅门 ,迫使禅门授徒方针由原来的招揽改为拒斥 ,所以也就造成了机缘语的隐晦与诡怪。此外 ,中唐以后 ,由于社会和人们心态的变化 ,整个文化界出现一种尚奇和“解构”之风 ,机缘语的奇特 ,也是这种思潮的反映 ,它是与当时的文化语境密切相关的。     

Teacher‐involved conversations with young children during small group activity

This qualitative study examines the conversations of two preschool teachers with two‐ and three‐year‐old children during small‐group activity settings in two high‐quality child development centers. Using interviews, observations and videotaping of small‐group activities, the conversations are characterized in terms of the kind and function of language, the usage of cognitive demands and the reciprocal nature of these conversations. The findings indicate that teachers use declarative statements primarily to manage instruction and encourage language development. While teachers control most conversations, teacher–child reciprocity is evident and more genuine in authentic, teacher‐guided activities. In both classrooms, the language during small‐group activities is characterized as having low cognitive demands. Teachers and teacher educators need to be more cognizant of their language, including its purpose and opportunities to facilitate cognitively challenging conversations with young children. Recommendations for practice are provided.     

The process of understanding the task: how is agency distributed between students, teachers and representations in technology-rich learning environments?

In this article, we explore how students’ agency relates to both highly structured and open-ended learning environments. This is done by analysing how students’ understanding of tasks evolves through their activities in relation to the representations inscribed in two technology-rich learning environments. Based on the sociocultural approach to thinking, reasoning and learning we argue that it is necessary to include activities, artefacts and aspects of the knowledge domain in order to understand how and what the students’ learn. We conclude by arguing that the process of understanding a task is often complex and ongoing through the activity.     

Qualified Pedagogical Reflection as a Way to Improve Mathematics Education

All changes of the character of education and improvement of its quality depend, in our view, particularly on the teacher. To be able to do their work efficiently, teachers have to be equipped with professional skills and dispositions, with “teachers’ competence”. For their professional growth, we consider indispensable competence in reflection, which is aimed at the teacher’s activities with regard to aspects of pedagogy and/or subject-didactics. From the point of view of the goals and content of their teaching and the methods of work (and their realisation), the development of teachers’ conscious self-reflection on their own teaching and systematic pursuance of joint reflection with other teachers and/or researchers can promote the teacher’s professional growth. In this paper, we show how a selected group of elementary school teachers reflected on their competence in the course of preparing, carrying out and analysing several instruction experiments. The paper is based on samples of teachers’ reflections and their gradual development from mere simple conversations based on intuitive perceptions, through searching for effective teaching approaches, to the deep assessment of mathematics teaching from the point of view of topics and their didactic elaboration and to suggestions for the teachers’ own experiments. May the teacher know what he teaches. May the teacher know how to teach. May the teacher be sincerely interested in teaching. Comenius     

Three dimensions of reflective thinking in solving design problems: a conceptual model

Design tasks are omnipresent in our everyday lives. Previous research shows that reflective thinking is one of the critical factors in solving design problems. Related research has attempted to capture designers’ reflective thinking process. Yet a close inspection of designers’ reflective thinking taking place during their design process demands further effort. To understand designer’s reflective practice and to find better ways to promote novices’ reflective thinking in solving real-world design problems, a comprehensive model was developed. This model identified three dimensions to guide the understanding of designers’ reflective thinking during a design process: (1) the timing of reflection, indicating the points in the process where reflective thinking occurs, (2) the objects of reflection, showing the different types of objects that designers may reflect upon, and (3) the levels of reflection, referring to the different levels of designers’ reflection. This model provides for meaningful aspects of reflective thinking to be situated in a design process, which can guide educators and instructional designers in developing appropriate learning environments for facilitating novice and practicing designers’ reflective thinking. Moreover, the model can serve as a stepping stone for further research.