Macro-Situation and Numerical Knowledge Building: The Role of Pupils’Didactic Memory in Classroom Interactions

This paper is based on a long-term didactic engineering about division problems (only in a numerical setting) at primary school. Situations and students’ work are analyzed by means of a double theoretical framework: the theory of situations and the theory of conceptual fields (Vergnaud 1991). The analysis focuses mainly on classroom interactions and on the didactic memory from both the teacher perspective and the learner perspective: in particular, it not only investigates how didactic memory is managed by the teacher, but also how students recall past events or reread those events in a-didactic situations.     

What Can the Teacher Learn in the Classroom?

Our research is concerned with teacher’s knowledge, and especially with teacher’s processes of learning, in the classroom, from observing and interacting with students’ work. In the first part of the paper, we outline the theoretical framework of our study and distinguish it from some other perspectives. We argue for the importance of distinguishing a kind of teacher’s knowledge, which we call didactic knowledge. In this paper, we concentrate on a subcategory of this knowledge, namely observational didactic knowledge, which grows from teacher’s observation and reflection upon students’ mathematical activity in the classroom. In modeling the processes of evolution of this particular knowledge in teachers, we are inspired, among others, by some general aspects of the theory of didactic situations. In the second part of the paper, the model is applied in two case studies of teachers conducting ordinary lessons. In conclusion, we will discuss what seems to be taken into account by teachers as they observe students’ activity, and how in-service teacher training can play a role in modifying their knowledge about students’ ways of dealing with mathematical problems.     

When Classroom Situation is the Unit of Analysis: The Potential Impact on Research in Mathematics Education

In this commentary, I will critically elaborate on the potential impact of the coordinated papers of this volume on further development of research in mathematics education. The papers, which share common theoretical frameworks, will be categorized into three different classes: ‘demolishers of illusions’, ‘economizers of thought’ and ‘energizers of practice’. I will analyze the role played by psychology and related sciences as a possible enrichment of the frameworks, especially where technologies are concerned. Finally, I will discuss the possible conflict between the need to consider the phenomena elicited in this kind of studies and the sophistication required by the theoretical constructs, which makes the results of these studies very difficult to communicate to the international community.     

Characterization of an Ordinary Teaching Practice with the Help of the Theory of Didactic Situations

In this paper, we use the theory of didactic situations to characterize a mathematics teaching practice, currently used in secondary schools in France, which we have called interactive synthesis discussion. We have studied this practice in ordinary classes, i.e. classes where the researcher intervenes neither in the preparation nor in the management of the lessons. We have looked at the didactic situations the teacher chooses, and how he manages his teaching project, the students’ work in the classroom and at home, and classroom interactions. We present two case studies of experienced teachers, one in grade 8, and the other in grade 10.     

LISTEN TO THE SILENCE: THE LEFT-BEHIND PHENOMENON AS SEEN THROUGH CLASSROOM VIDEOS AND TEACHERS’ REFLECTIONS

This study uses classroom videotapes to examine the phenomenon of students who are left behind during whole-class teaching. Zooming in via these videos enabled us to analyze these classroom situations by means of a compact, multi-perspective set of theories – van Hiele theory, conceptualization, and visual perception. The analysis provided a picture of the classroom interaction in which the sound of silence of those students who might not share understanding during the class discourse is ignored. Based on a sample of Taiwanese junior high school geometry classes, the study demonstrated how investigating situations of silence uncovered the possibility of teachers’ unawareness of student difficulties or their unsuccessful efforts to cope with them. Teachers’ post-lesson interviews and questionnaires shed additional light on the perspective of left-behind students. Implications of this method for pre- and in-service teachers’ programs are briefly discussed, and some recommendations for change are proposed. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

实践教学论:回归课堂生活的研究

实践教学论是与理论教学论相对的教学理论,所谓理论教学论是指以教学理论为研究对象的教学论,其实质是一种教学理论的再研究,是一种书斋文献式的研究。而实践教学论是指以教学生活本身为研究对象的教学论,其实质是一种教学研究,是一种深入“课堂田野”的实践研究。实践教学论正在逐渐发展成为一种主流教学理论。     

政治理论课“1＋1＋1=45”的课堂教学模式研究

教学模式一直都是政治理论课能否取得课堂实效性的关键,因此,对政治理论课课堂教学模式的研究与探索也从未中断,人们关注的视角从知识课堂到生本课堂,从填鸭课堂到和谐课堂,但如何在课堂四十五分钟内真正实现教师、学生与知识的价值,使学生对于政治理论知识的追求变成自身的意念行为,形成长效机制,则成为本文探索与关注的焦点。     

实践教学论论纲

实践教学论是与理论教学论相对的教学理论 ,所谓理论教学论是指以教学理论为研究对象的教学论 ,其实质是一种教学理论的再研究 ,是一种书斋文献式的研究。而实践教学论是指以教学生活本身为研究对象的教学论 ,其实质是一种教学研究 ,是一种深入“课堂田野”的实践研究。实践教学论的提出与完善动摇了传统主流的理论教学论“一枝独秀”的局面。     

Secondary students’ modelling conceptualisation in situations related to particle dynamics: a clinical perspective

This study investigates the modelling conceptualisation of secondary school students in two situations related to particle dynamics: pendulum’s motion and horizontal motion. We performed in-depth clinical interviews with secondary school students (N?=?10). Participants’ ideas about properties which are not ‘given’ in empirical observations were explored in order to investigate signs of abstractions and idealisations in their reasoning processes. We proposed contributions to modelling in science education based on Mario Bunge’s epistemology and we employed his basic concepts as the axis to analyse our results: (1) abstractions and idealisations, considered as thought processes required to build conceptual counterparts of concrete objects; (2) theoretical models, meaning hypothetico-deductive systems concerning those conceptual objects; and (3) general theoretical frameworks that allow us to derive those theoretical models. We developed our analysis viewing the ideas presented by participants as concepts-in-action and theorems-in-action as regarded by Gérard Vergnaud’s Theory of Conceptual Fields. Results indicated a gradation in the concepts-in-action mobilised in terms of levels of idealisation and showed that participants do not spontaneously recognise the use of a general theory as a possible way to obtain a theoretical model. These results suggest that science education practices must pay better attention to make abstractions and idealisations explicit in scientific concepts formation, as well as to the heuristic role of theories in model construction.     

‘Yes,but . . .’: rhetoric,reality and resistance in teaching assistants' experiences of inclusive education

This research examines the role of teaching assistants (TAs) working with children with special educational needs (SEN) in an increasingly complex and diverse context. The role of the TA has been given more attention recently, partly due to the increased focus on their effectiveness within an inclusive education system in a time of workforce reform. The research takes a life history approach to examining the experiences of TAs within inclusive contexts and focuses upon how their backgrounds impact upon their role within the classroom, as well as how their experiences demonstrate ambiguity, tension and contradictions. Rather than a focus on pupil and institutional outcomes, the article analyses the tensions between the policy and institutional frameworks of inclusion and how TAs experience this. TAs' contradictions, tensions, resistance and also pleasures within their work are explored from their own perspectives. The personal interpretations, understandings and day‐to‐day implementation of inclusion are the focus.     

当前教学论研究:热点与沉思

教学世界自身的演变发展历程决定了教学世界不能简单地回归生活世界,而是在生活世界的基础上超越生活世界。因此,作为教学世界核心的课堂既要传承知识,更要激扬生命,即由知识课堂走向生命课堂。与此相适应,当前教学论研究范式不能迷恋书斋文献,而是要热衷于课堂实践,即研究范式从"文本式"向"田野式"转向;教学理论来源不要仅停留在思辨演绎层面,而是要实践生成,即从理论教学论到实践教学论;研究取向不应只追求宏大理论,而是要关注教学生活,即研究取向由"科学泛化"趋向"泛学科化"。     

职业教育教科书的科学理论探求——基于康德的范畴框架

目前职业教育教科书科学理论并不算完善,即便整个教科书领域也是如此,总体而言存在“功能与目标”“过程与结果”“方法与程序”等三个思维框架下的碎片化探索,这不利于职业教育教科书研究的系统化积累。为了探求职业教育教科书的科学理论,应基于康德的范畴理论,建立教科书科学理论形式框架,汇总、归类已有教科书研究思维,并建构出更为系统的职业教育教科书研究的科学理论。具体行动包括:基于范畴框架阐释教科书以便系统性整合三种理论思维;基于范畴框架重新建立职业教育教科书科学理论的发展框架;职业教育教科书的科学理论建构不能脱离实践的需要。     

The Adidactic Interaction with the Procedures of Peers in the Transition from Arithmetic to Algebra: A Milieu for the Emergence of New Questions

The purpose of the present article is to give an account of the emergence of knowledge pertaining to the transition from arithmetic to algebra in the course of a debate in a grade 7 classroom. This debate follows two other instances of work: (1) the adidactic interaction between each student and a given problem, (2) the adidactic interaction of each student with the procedures generated by other students during stage 1. The two kinds of processes – adaptation to a milieu and social interactions – play a critical role in the change of “rationality” required for the move from arithmetic to algebra. Both the design of the initial mathematical problem given to the students and the organization of the interactions leading to the debate under study in this article are based on this hypothesis. The research presented in this article is set in a broader work of didactic engineering that aims at studying didactic conditions for making a connection between arithmetic practices and algebraic practices.     

Noticing Children’s Learning Processes – Teachers Jointly Reflect on Their Own Classroom Interaction for Improving Mathematics Teaching

One could focus on many different aspects of improving the quality of mathematics teaching. For a better understanding of children’s mathematical learning processes or teaching and learning in general, reflection on and analysis of concrete classroom situations are of major importance. On the basis of experiences gained in a collaborative research project with elementary school teachers, several ideas about a professional reflection on one’s own instruction activities are explained. The paper focuses on joint reflection between teachers and researchers on the participating teacher’s own classroom interaction by means of concrete examples. It becomes clear that changes of one’s own interaction behavior will take place only in the long-term. Nevertheless such a joint professional reflection should be an essential component of teachers’ professional knowledge in a natural way. An erratum to this article can be found at     

‘What makes her succeed?’ Children's interpretations of their peers' successes in learning situations

Previous research has shown that observing peers' success in learning is important for the development of children's belief in themselves as learners. However, in research, these observations are seldom made in actual classroom learning activities. This study investigated how children explain factors that lead to their peers' successes in classroom learning activities. Seventeen elementary school children from first, second and third grade participated in a ‘detective course’ in which they needed to capture moments of success using a mobile camera device. The pictures were used for photo-elicitation interviews (n?=?28) in order to find out children's views on the reasons for their peers' successes in learning situations. Pictorial data (n?=?361) were coded with data-driven categories to see what kind of situations children considered successful. The results show that the reasons given for peers' successes dealt with situation-specific information, such as mastery and quality of performance. Findings indicate that children explain peers' successes through the actions that their peers made during the situations, rather than by comparison between the abilities of their classmates. The results provide information for practitioners and teachers on how to promote children to use the example of their peers to recognise and explain successful learning situations in the classroom.     

论21世纪中国教学论发展趋向

中国的教学论发展面临人主义和创新教育的巨大冲击,其发展应避免走向三个误区：（一）从研究“教”向研究“学”转变;（二）从注重理论体系建构的学科重心向注重教学实践的问题中心转变;（三）从教学论研究向元教学论研究转变。     

理论联系实际：马克思主义理论课教学的基本原则

理论联系实际是马克思主义理论课教学的基本原则。坚持这一原则是加强和改进马克思主义理论课教学,增强教学实效性的必然要求。正确掌握马克思主义理论是理论联系实际的首要条件,全面把握社会实际和学生特点是理论联系实际的必要条件。深入贯彻这一原则应立足于教学目的的实现,选取典型性的材料,运用社会实践等多种教学方式和坚持实事求是的态度,把理论和实际有机结合。     

Evaluating student engagement and experiential learning in global classrooms: A qualitative case study

The global classroom is an emerging technology-based pedagogy used internationally by educational institutions. To evaluate a global classroom, we conducted a qualitative study using written reflections and semi-structured interviews of global classroom participants, based on two theoretical frameworks: Kearsley and Shneiderman’s engagement theory and Kolb’s experiential learning theory. We analyzed student reflections and transcribed interviews, using the software package, NVivo, with two objectives: (1) to evaluate if global classroom is engaging and experiential to students and (2) to elucidate how student engagement is fostered in the global classroom through experiential learning. Results illustrated a complex relationship between student engagement and experiential learning. During the experiential learning cycle, engagement theory (relate-create-donate) principles contributed to student engagement at varying levels and for different purposes. Based on the results of this study, we created a framework that demonstrates the interactivity of engagement theory and experiential learning theory to describe how student engagement featured in experiential learning during this global classroom, with strategies to maximize student engagement in experiential learning.     

教学认识论与教学实践论——关于教学本质的两种不同观点

关于教学的本质,长期以来教育理论界一直存在争议。教学认识论认为,教学是一种特殊的认识过程,这一观点在特殊的历史时期发挥了积极的作用,但由于缺乏科学的立论基础,导致课堂教学存在诸多弊端。在课程改革的背景下,教学实践论得到了人们的普遍认可。教学实践论是对教学本质的再认识,该观点认为教学是学生学习知识的实践过程,强调学生实践的突出意义,有利于改革传统课堂教学的弊端,建立新的课堂教学观。