Let’s Draw a Picture

In an undergraduate analysis course taught by one of the authors, three prompts are regularly given: (i) What do we know? (ii) What do we need to show? (iii) Let’s draw a picture. We focus on the third prompt and its role in helping students develop their confidence in learning how to construct proofs. Specific examples of visual models and their impact on student work are presented.     

External and internal representations in the acquisition and use of knowledge: visualization effects on mental model construction

This article investigates whether different formats of visualizing information result in different mental models constructed in learning from pictures, whether the different mental models lead to different patterns of performance in subsequently presented tasks, and how these visualization effects can be modified by further external representations during task performance. A total of 80 university students learned from an illustrated text different day times and different dates exist simultaneously on the earth. One half of the participants received the text combined with pictures visualizing the earth as a kind of carpet (carpet pictures), whereas the other half received the text combined with pictures visualizing the earth surface as a circle (circle pictures). After learning, the participants received a test including different kinds of tasks. In both visualization groups, one half of the participants solved the tasks with an additional external representation, whereas the other half solved the tasks without an external representation. The findings indicate that the form of visualization affects the structure of mental models. Different structures of mental models result in different patterns of performance, when individuals solve tasks based only on their mental representations acquired during their previous learning. However, these effects decrease, when further external representations are made available to the learners. The findings are discussed within a broader framework of learning with multiple external representations.     

空间生产理论视域下的文庙教育空间实践

文庙是中国古代重要的官方教育机构。本文以江阴文庙为例,运用法国哲学家列斐伏尔的社会空间生产理论,对古代中国教育空间的生产进行分析。研究发现:文庙作为一个教育空间,其物理空间的生产实践是在国家制度、权力意志、经济资本和地理环境等多重因素相互作用下的结果;通过相关建筑物的命名与空间环境的营造,文庙空间有效地表征了儒家的教育理想与追求;并且通过官员谒庙、授业课试和定期祭祀等教化活动,文庙所表征的教育空间也得到了儒家知识分子与社会的广泛认同。以史为鉴,江阴文庙空间的生产也为现代教育空间的改造提供了一定的借鉴与启示。     

Representational Classroom Practices that Contribute to Students’ Conceptual and Representational Understanding of Chemical Bonding

Understanding bonding is fundamental to success in chemistry. A number of alternative conceptions related to chemical bonding have been reported in the literature. Research suggests that many alternative conceptions held by chemistry students result from previous teaching; if teachers are explicit in the use of representations and explain their content-specific forms and functions, this might be avoided. The development of an understanding of and ability to use multiple representations is crucial to students’ understanding of chemical bonding. This paper draws on data from a larger study involving two Year 11 chemistry classes (n = 27, n = 22). It explores the contribution of explicit instruction about multiple representations to students’ understanding and representation of chemical bonding. The instructional strategies were documented using audio-recordings and the teacher-researcher’s reflection journal. Pre-test–post-test comparisons showed an improvement in conceptual understanding and representational competence. Analysis of the students’ texts provided further evidence of the students’ ability to use multiple representations to explain macroscopic phenomena on the molecular level. The findings suggest that explicit instruction about representational form and function contributes to the enhancement of representational competence and conceptual understanding of bonding in chemistry. However, the scaffolding strategies employed by the teacher play an important role in the learning process. This research has implications for professional development enhancing teachers’ approaches to these aspects of instruction around chemical bonding.     

Representational competence: towards a distributed and embodied cognition account

Multiple external representations (MERs) are central to the practice and learning of science, mathematics and engineering, as the phenomena and entities investigated and controlled in these domains are often not available for perception and action. MERs therefore play a twofold constitutive role in reasoning in these domains. Firstly, MERs stand in for the phenomena and entities that are imagined, and thus make possible scientific investigations. Secondly, related to the above, sensorimotor and imagination-based interactions with the MERs make possible focused cognitive operations involving these phenomena and entities, such as mental rotation and analogical transformations. These two constitutive roles suggest that acquiring expertise in science, mathematics and engineering requires developing the ability to transform and integrate the MERs in that field, in tandem with running operations in imagination on the phenomena and entities the MERs stand for. This core ability to integrate external and internal representations and operations on them – termed representational competence (RC) – is therefore critical to learning in science, mathematics and engineering. However, no general account of this core process is currently available. We argue that, given the above two constitutive roles played by MERs, a theoretical account of representational competence requires an explicit model of how the cognitive system interacts with external representations, and how imagination abilities develop through this process. At the applied level, this account is required to develop design guidelines for new media interventions for learning science and mathematics, particularly emerging ones that are based on embodied interactions. As a first step to developing such a theoretical account, we review the literature on learning with MERs, as well as acquiring RC, in chemistry, biology, physics, mathematics and engineering, from two perspectives. First, we focus on the important theoretical accounts and related empirical studies, and examine what is common about them. Second, we summarise the major trends in each discipline, and then bring together these trends. The results show that most models and empirical studies of RC are framed within the classical information processing approach, and do not take a constitutive view of external representations. To develop an account compatible with the constitutive view of external representations, we outline an interaction-based theoretical account of RC, extending recent advances in distributed and embodied cognition.     

Convergence of sequences and series: Interactions between visual reasoning and the learner's beliefs about their own role

This paper examines part of a set of students who were followed during their first-term, first-year studies in formal definition-based real analysis at a British university. It explores the approaches to problems about convergence of sequences and series made by students who have a tendency to include visual imagery in their reasoning. We explore links between the students' mathematical behavior in solving these problems and their perception of their roles as learners. We develop a theory in which the tendency to visualize, coupled with the students' view of their role, can be used to account for their mathematical behavior. This revised version was published online in July 2006 with corrections to the Cover Date.     

The influence of textbooks on teachers’ knowledge of chemical bonding representations relative to students’ difficulties understanding

Background: Textbooks are integral tools for teachers’ lessons. Several researchers observed that school teachers rely heavily on textbooks as informational sources when planning lessons. Moreover, textbooks are an important resource for developing students’ knowledge as they contain various representations that influence students’ learning. However, several studies report that students have difficulties understanding models in general, and chemical bonding models in particular, and that students’ difficulties understanding chemical bonding are partly due to the way it is taught by teachers and presented in textbooks.

Purpose: This article aims to delineate the influence of textbooks on teachers’ selection and use of representations when teaching chemical bonding models and to show how this might cause students’ difficulties understanding.

Sample: Ten chemistry teachers from seven upper secondary schools located in Central Sweden volunteered to participate in this study.

Design and methods: Data from multiple sources were collected and analysed, including interviews with the 10 upper secondary school teachers, the teachers’ lesson plans, and the contents of the textbooks used by the teachers.

Results: The results revealed strong coherence between how chemical bonding models are presented in textbooks and by teachers, and thus depict that textbooks influence teachers’ selection and use of representations for their lessons. As discussed in the literature review, several of the selected representations were associated with alternative conceptions of, and difficulties understanding, chemical bonding among students.

Conclusions: The study highlights the need for filling the gap between research and teaching practices, focusing particularly on how representations of chemical bonding can lead to students’ difficulties understanding. The gap may be filled by developing teachers’ pedagogical content knowledge regarding chemical bonding and scientific models in general.     

不同迁移方式与不同学习“方式”对知觉运动序列学习的影响——一项ERP研究

拟采用迁移范式,以事件相关电位(ERP)成分N2、P3作为主要指标,结合不同迁移方式和不同学习"方式"探讨学习者的知识表征方式的差异。结果发现:内隐组和外显组被试在习得了一定的序列知识后,相对于标准序列的反应时,效应器迁移序列的反应时明显变慢;在脑电数据中,以N2的平均波幅作为指标,不管是内隐组还是外显组,标准序列与刺激迁移序列不存在区别,而与效应器迁移序列却差异显著。对于P3的平均波幅的分析得出:在内隐组,标准序列与效应器迁移序列不存在区别;而在外显组,两者却差异显著。该结果说明:效应器水平的编码机制是参与序列知识的学习的;且相对于知觉编码,不管以何种"方式"学习,效应器编码起的作用都要更大。     

‘The funeral’: a study of children's shared meaning‐making and its developmental significance

This article argues the need to examine communication in joint play situations rather than individual assessments in solitary play situations when children's development is focused. Informed by Bakhtin's dialogical and Moscovici's interactionist perspectives, observations were made of the interaction between two girls, aged 3½ and 4, playing at holding a funeral ceremony, in the setting of a Swedish pre‐school. The analysis shows that new knowledge occurred through negotiations of appropriate actions in play. The children's interactions resulted in shared meaning‐making of the funeral as a ritual of revival.