Patterns of Variation in Teaching the Colour of Light to Primary 3 Students

This paper shows how the patterns of variation created in the teaching were critical in helping a class of Primary 3 students in Hong Kong to learn about the colour of light, so that the students attained conceptual rather than procedural knowledge. A ‘Learning Study’ approach was adopted, which is a Lesson Study grounded in a particular learning theory to improve teaching and learning. This study, based on the learning theory of Variation advanced by Marton and Booth, was premised on three types of variation: variation in students’ ways of experiencing what is to be taught/learnt (V1), variation in teachers’ ways of dealing with the ‘object of learning’ (V2), and the use of ‘pattern of variation’ as a guiding principle of pedagogical design to enhance students’ learning (V3). In planning the lesson, a conscious effort was made to create relevant patterns of variation, i.e. varying certain critical aspect(s) while keeping other aspects of the object of learning invariant in order to help students to discern those aspects. Comparison between the results of the pre- and post-test shows that there was significant gain in the students’ learning outcomes with respect to the intended object of learning. The findings contribute knowledge to how the Theory of Variation can be used in practice. It also illustrates how teachers can make use of this theoretical framework to analyze their own teaching and thereby, develop an analytical awareness of teaching and learning.     

Simulating variation in order to learn classroom management

Classroom management is an important part of learning to be a teacher. The variation theory of learning provides the insight that it is important to vary the critical aspects of any task or subject that is to be learned. Simulation technology is useful in order to provide a controlled environment for that variation, and text as a medium gives the opportunity to control exactly what aspects are presented to the learner. This study shows that text-based simulation has the potential to help the learner discern critical aspects of classroom management.     

On Generalization and Variation Theory

The variation theory developed by Marton has quickly become popular as a framework for providing guidance for making learning possible. However, the epistemological assumption behind the theory is often accepted without critical scrutiny. This paper poses an apparent problem of the possible occurrence of learning in the situation of generalization, where one aspect is kept invariant, while other aspects vary. Eventually some of the learners can learn the invariant aspect. However, variation theory entails that the experience of variation in an aspect is necessary for learners to discern that aspect. How then is it possible for the learners in a situation of generalization to fully discern the invariant aspect? Through scrutinizing the epistemological assumption, I hope to foster discussion toward further improvement of the theory.     

Constructivism-informed variation theory lesson designs in enriching and elevating science learning: Case studies of seamless learning design

The constructivist paradigm opens abundant opportunities for effective knowledge construction in which student build knowledge and continually evaluated and improved their knowledge. The teaching mode under constructivist pedagogy redefines the role of students and the teachers and their interrelationships by creating a nurturing environment. By adapting constructivist framework, this article demonstrates how the variation of learning practices was critical in facilitating Primary 4 students in Singapore to carry out seamless science learning. The variation of learning practices enables the students to explore a particular scientific concept through various learning experience across the contexts. The study adapted the framework of the Objects of Constructivist Learning Model for the improvement of the seamless science learning design. When redesigning the lesson, a conscious effort was made by the teacher to create relevant patterns of variation, that is, varying certain critical aspect(s) while keeping other aspects of the object of learning invariant in order to help students discern those critical aspects. The findings contribute knowledge to how the Theory of Variation can be used in analyzing seamless learning as well as designing for constructivist learning experiences. The findings have also demonstrated that the complementary practice of constructivist pedagogy with variation theory as a viable and effective approach in seamless science learning, at which it deepened students' understanding through constructing the critical aspects of a phenomenon. Engagement with primary school students in experiencing the variations allowed the translation of theory into practice.     

Relating Teaching and Learning of Science Through the Lens of Variation Theory

The relationship between teaching and learning is a most central issue in education research, but it is yet to be fully understood. Variation Theory provides an explanatory account for teaching and learning and offers a specific view on what it means to learn: to discriminate and to discern critical aspects of the object of learning. This paper explores the use of Variation Theory in a case study of two lessons on density in a secondary science classroom. By explicating what was made possible to learn and what was learned this study demonstrates potentials and limitations offered by Variation Theory in enabling a better understanding of the teaching learning relationship.     

Facts,Knowledge, and Skills in the Humanities

Abstract

English language learners (ELL) are students with a primary language spoken other than English enrolled in U.S. educational settings. As ELL students take on the challenges of learning English and U.S. culture, they must also learn academic content. The expectation to succeed academically in a foreign culture and language, while learning to speak and comprehend the language itself, would be a stressful and challenging task for almost anyone. In comparison with non-ELL students, ELL students tend to demonstrate lower levels of academic achievement. The current study examined ELL students' perceptions on teacher power and its' influences on self-perceptions of learner empowerment. Quantitative data was collected measuring perceptions of teacher power use and self-perceptions of learner empowerment. Qualitative data consisted of twenty in-depth interviews with ELL students illuminating their perceptions of teacher power and its relationship to their perceptions of learner empowerment. Differences were found by language in coercive, legitimate, and expert teacher power. Four themes emerged from interviews; what good teachers do, what bad teachers do, what teachers should know, and understanding ELL students. Implications for educators and future research are discussed.     

Learning Theory as Teaching Resource: Enhancing Students’ Understanding of Economic Concepts

A group of experienced secondary school teachers used a novel learning theory as a resource for planning and carrying out their teaching of a difficult economic concept. Their students mastery of this concept after a series of three lessons was compared with the mastery of the same concept by students who were taught by another group of teachers under the same conditions except for the use of the theory. The difference in learning outcomes was extreme. Observations of what was happening in the classrooms showed subtle but decisive differences correlated with the differences in outcome. These differences were interpreted in terms of the theory used by the first group, and the results seem to give support to the theoretical claim that for any specific object of learning there is a necessary pattern of variation and invariance that the learners must experience in order to appropriate the object of learning in question and thus by bringing out that pattern in the learning situation, the likelihood of that object of learning being appropriated is enhanced. Furthermore, this study shows how the understanding of the simultaneous change in the supply of and the demand for a certain good affects its market price can be brought about in a powerful way.     

Structural exclusion through school mathematics: using Bourdieu to understand mathematics as a social practice

Research on learner errors in mathematics education is beginning to focus on how teachers can learn to identify and engage with the reasoning behind these errors. Research on professional learning communities is beginning to show that they present powerful opportunities for on-going teacher collaboration and learning. In this paper, I bring the two areas of research together. Drawing on data from one professional learning community in the Data Informed Practice Improvement Project, I show how teachers in this community came to understand key concepts about learner errors and shifted their ways of talking about learner errors. I identify three important shifts that the teachers made in their learning about learner errors: from identifying to interpreting errors; from interpreting to engaging errors; and from focusing on learner errors to focusing on their own knowledge. I argue that these three shifts suggest a deepening of teachers’ thinking in relation to learner errors.     

在教师专业发展中建构成长型师生关系

师生关系一直是教师专业发展的一个重要方面。为了促进师生关系的和谐发展需要建立成长型的师生关系。成长型的师生关系是指教师和学生在学会终身学习和发展的过程中共历共享成长的一种新型师生关系。建构成长型的师生关系需建立师生间的相互信赖,拓展师生成长的互动层面,建设师生成长的互动环境,丰富师生成长的互动方式等。     

Variatio Est Mater Studiorum

There is no learning without discernment. And there is no discernment without variation. If good teaching is about making learning possible, how do good teachers help students experience variation? In this paper, we argue that they constitute a space of learning which contains those aspects of the object of learning that are subject to variation simultaneously. For learning to occur, whether it be in the formal learning contexts established by these teachers, or in the less formal contexts of participation in social practices, there must necessarily be a certain pattern of variation present to experience, and this pattern must be experienced.     

IMPROVEMENT OF EFFECTIVE COMMUNICATION—THE CASE OF SUBTRACTION

The research study this article is based on aims to implement research knowledge to teaching, that is, the concept of critical aspects and dimensions of variation used in the variation theory. To do this, the researchers worked with willing teachers to explore how to make mathematics teaching more effective. This paper illustrates how teachers make use of a learning theory, the variation theory, as well as their own professional expertise and collaboration to help students improve their mathematical understanding of subtraction as well as their learning of it. The students’ tests, examinations of students’ mathematical work, the teachers’ lessons plan and reports of the instructions for lessons form the data base for the article. The analysis indicates that one of the critical aspects in the process of implementation of the variation theory in the teachers’ practice was to identify the critical aspects in students’ learning. Another critical aspect in the implementation of the variation theory was to open up dimensions of variation in the identified critical aspects of the students. By giving teachers the possibility to develop the ability to identify critical aspects in students’ learning, dimensions of variation are opened up in these aspects, and by applying this knowledge in the daily teaching, they have the possibility to improve students’ learning. The findings suggest that developing an understanding of the students’ critical aspects can be a productive basis in helping teachers make fundamental changes in their instructions and improve students’ learning.     

Informed learning design: teaching and learning through engagement with information

ABSTRACT

While higher education teachers are able to use information in sophisticated ways to learn and communicate within their disciplines, they may not be accustomed to teaching their students to use information creatively and reflectively to support their work in a course. This article introduces informed learning design, a curriculum design model by which teachers specifically enable students to learn course content through intentional engagement with information. Drawing from informed learning pedagogy and the variation theory of learning, the design model outlines an instructional pattern for enabling student awareness of critical aspects and features of the object being studied related to both information use and course content.     

Broadening the horizon: toddlers’ strategies for learning mathematics

The aim of this study is to analyse and discuss those strategies for learning that are essential for toddlers’ development of an understanding of basic aspects of mathematics. Analysis focuses on authentic episodes where toddlers aged one to three are interacting with other people. The settings chosen for the qualitative analysis emanate from a variation theory of learning approach. In such an approach, learning is defined as a change in understanding, and in order to change a person’s understanding of a certain phenomenon, various aspects must be focused on simultaneously. Accordingly, critical aspects that a learner has not been previously able to focus on may emerge during interaction with others since such settings provide an opportunity for the problemisation of differing aspects and perspectives. This study seeks to discern toddlers’ strategies for learning through the observation of those strategies that the toddlers themselves initiate, which may reveal the competence for learning that young children possess.     

基于课程知识结构的网络学习资源建设

本文提出了一种以知识结构为基本框架,建设网络学习环境中的学习资源库的方法.结构化的学习资源库中,首先建立课程的基于知识点的知识结构体系,在此体系中实现以元知识点为最小学习单元,实现对学习者学习过程的控制.建立学习资源与元知识点的关联关系,将学习资源融入课程的知识结构中,从而实现了结构化的学习资源的建设、组织方法.     

Understanding teachers with extreme individual learning differences: developing more effective teachers

Three teachers, who held extreme preferences for the ways they learn, participated in a year‐long professional development course, designed to sensitize teachers to their own and colleagues’ individual learning differences (ILDs). The case study focuses on their extreme learning preferences and discusses the impact of these preferences on their language, beliefs and practice, both before and after the course. The teachers’ learning preferences were determined from their scores on seven learning/cognitive styles tools and understood further from field notes, interviews and pre‐/post‐test responses. The study suggests that teachers with extreme learning preferences tend to: (a) teach the way they prefer to learn; (b) overgeneralize and project their own learning needs onto students; and (c) hold initial pathognomonic (“blame the learner”) beliefs about students mismatched to them. After the course, the teachers changed their language, beliefs and practice in the direction of becoming more effective teachers, e.g., they held more interventionist beliefs (“I can intervene to help the learner”). The three teachers were strong prototypes who can provide insights about the importance of ILDs in learning, practice and professional development.     

Teachers’ learning in a learning study

The point of departure in this study is the question: do teachers who develop theoretical knowledge of the variation theory change the way(s) they offer their pupils the object of learning due to the theoretical framework. The aim of the study is to describe this development, i.e. to find if and how teachers developed theoretical knowledge when planning instruction, and in what way(s) this has an impact on the pupils’ learning outcome when using contrasts in the instruction. The theoretical framework is strongly content related, and by analysing the learning object’s critical aspects the teachers are guided to focus on the content in this particular way. The question “what does it take to develop knowledge about the object of learning?” has to be answered by the teachers before choice of teaching method is made. The research method used is Learning Study, a fusion between lesson study and design experiment. The teachers (6) have carried out nine research lessons in three Learning Study cycles (containing three lessons each). The pupils belong to three different classes and are between 9 and 11 years old. The result shows how the teachers gradually use the variation theory when planning instruction and how the learning outcomes shown by the pupils improve. The developed theoretical insight seems to affect the teachers’ ways of seeing the object of learning, such as subtle changes of how to organize the critical features of the learning object, are discerned. In every learning study cycle contrasts are used in one lesson, and in the analysis of the effect of the contrasts, the two remaining lessons are used as control groups. The results show the impact of contrasts in the pupils’ learning outcomes. The need to complement a lesson study with a theoretical perspective on learning is that the teachers are then given the opportunity to make use of the theory when planning instruction individually, not only in a lesson study. There again, the Learning Study model seems to be a powerful model with which to develop teachers’ understanding of the theoretical framework.     

Exploring mobile learning in the Third Space

Mobile learning is enabling educators and students to learn in ways not previously possible. The ways that portable, multi-functional mobile devices can untether the learner from formal institutional learning give scope for learning to be conceptualised in an expanded variety of places, times and ways. In this conceptual article the authors articulate this notion by using the metaphor of the Third Space to envision what can be achieved with mobile learning. They outline their use of the metaphor, consider how it extends notions of twenty-first century learning and use a previously established Mobile Pedagogical Framework to provide a context for the discussion. They conclude with implications of learning in the Third Space for teachers and students. These implications suggest that roles of teachers and students and structure of the curriculum need to change to ensure we leverage the potential of mobile learning.     

Developing a Data-Driven Assessment for Early Childhood Candidates

ABSTRACT

Decision-making is essential for the work of teaching. Preservice teachers must learn to leverage knowledge about young readers’ strengths, needs, and interests in order to plan and teach guided reading lessons skillfully. However, limited research examines preservice teachers’ decision-making based on what they know about individual children. In this qualitative case study, we report findings from 12 preservice teachers enrolled in a reading methods course who used teacher knowledge to inform their teaching decisions for guided reading lessons with Kindergarteners. Findings reveal how participants used knowledge of learners to make planning as well as in-the-moment teaching decisions. The data show that most of these decisions were lesson planning decisions about text selection and word solving strategies, indicating that participants were beginning to engage in responsive teaching strategies. This study makes a new contribution to early childhood teacher education literature by underscoring the significance of learner knowledge in the context of authentic teaching practice while learning to teach guided reading to young children.     

What matters for students’ learning in the laboratory? Do not neglect the role of experimental equipment!

According to variation theory, it is essential to enable students to focus on the object of learning and discern its critical features, but the features that it is possible to discern often depend on the equipment used. Thus, in labs, the experimental technologies used may shape students’ experience of focal phenomena, in a human–mediating tools–world manner, by placing some aspects of reality in the foreground, others in the background, and visualizing certain aspects that would otherwise be invisible. However, this mediating role is often neglected, and instruments and devices are often seen as having little cognitive value. Hence, the role of experimental technologies in labs as tools for learning is examined here through a case study, in which three sets of students investigated the same physical relationships (Newtonian motion in an inclined plane), but using different measurement technologies. The results demonstrate that what it is possible for students to experience in a laboratory is heavily influenced by the chosen technology. Some technologies do not afford the discernment of features regarded as crucial for students to learn. Furthermore, analysis of video recordings shows that the three sets of students’ discourses differed, although they studied the “same physics”. Hence, the role of experimental technologies in students’ learning in labs should not be neglected, and their courses of action should be seen as material-discursive practice. Moreover, general conclusions about learning in labs should be drawn cautiously, specifying the conditions and technology used, and discussions about learning technologies should not be limited to the use of computers.