ABSTRACT
As a result of recent developments in information and communication technology (ICT), the use of (external) representations in information processing, communicating, and learning and teaching has increased dramatically. Nowadays, learners must be able to interpret and use a large variety of (external) representational forms and tools both for their own reasoning, problem solving and learning, and for communicating with others. Overviews of state-of-the-art research on the nature and use of (external)
representations can be found in recent (hand)books, including Technologyenhanced Learning: Principles and Products edited by Balacheff et al. (2009), the third edition of the Handbook of Research on Educational Communication and Technology edited by Spector et al. (2007), and the Cambridge Handbook of Multimedia Learning edited by Mayer (2005). In the first and second of these books the issue of (external) representations
is essentially addressed as one element of educational information and communication technology, along with many other issues such as the impact of various kinds of educational software (e.g., drill-and-practice programs) on students’ learning, teachers’ beliefs about and attitudes towards various kinds of educational technology, and the implementation of new forms of information and communication technology in educational settings. Mayer’s (2005) handbook focuses much more on the (educational) use of (external) representations, but this topic is approached from a number of theoretical perspectives that have been typically developed and used within the field of multimedia learning, especially cognitive load theory (Sweller, 1999) and theories of dual coding (Paivio, 1990). Furthermore, given Mayer’s specific definition of multimedia learning
and instruction, the book has a strong emphasis on the issue of textual versus pictorial information. In one chapter in Mayer’s book, Atkinson (2005) notices that the ‘subject-
matter perspective’ is typically missing in current multimedia research, and therefore makes a plea for more research on multimedia learning that is deeply embedded in specific curricular domains such as mathematics or science. In a more recent reflection on the state-of-the-art in multimedia research, Mayer (2010) comments that this research has to address three kinds of questions, namely ‘what works?’, ‘when does it work?’, and ‘how does it work?’; but he also argues that so far research has principally addressed the first two questions and that therefore more work is needed on the analysis and description of the perceptual, thinking, and learning processes that underlie the effectiveness of multimedia materials and techniques. Compared with the above-mentioned volumes, the present book puts a
stronger emphasis on the issue of (external) representations as such, paying ample attention to the similarities and differences between various kinds of (external) representations and to the relationship between external and internal representations. Furthermore, it looks at this representational issue not only from the above-mentioned theoretical perspectives that have been typically applied within the context of multimedia learning, but also from other theoretical perspectives, such as general theories of problem solving and conceptual change, or domain-specific theories of mathematics and science learning. By strictly focusing on (external) representations and by including these addi-
tional theoretical perspectives, we have a dual aim. First, we aim to contribute to a better understanding of how representational forms and tools can – either alone or in combination with others – foster or hinder thinking and learning processes in particular subject-matter domains and instructional settings, that is, the third question emphasised by Mayer (2010). Secondly, we intend to explore how these findings on the relations between (external) representations, the associated thinking and learning processes, and the learning outcomes can be translated into effective and efficient instructional guidelines and methods. In line with this dual goal, Part 1 addresses the analysis of psychological
processes involved in working with (external) representations when reasoning and solving problems, and Part 2 the development of external representational tools and learning environments aimed at the enhancement of the intended reasoning and problem-solving processes. The book grew out an international workshop held in Leuven on September
9-12, 2008, organised by the international scientific network ‘Stimulating critical and flexible thinking’, sponsored by the Research Foundation – Flanders.
Part 1 commences with a chapter in which Schnotz et al. analyse the interplay of external and internal representations in creative thinking and problem solving
from the perspective of semiotics and cognitive psychology, using examples from science and mathematics education. Creative thinking and problem solving are analysed from the perspective of Gestalt psychology and the psychology of information processing, emphasising the roles of structures and procedures. The authors make a distinction between two basic kinds of representations, namely descriptive and depictive, which differ in both representational and inferential power. Their analysis of the use of representations in contexts of science and maths education shows that a close interaction between descriptive and depictive representations is needed in order to make the best use of both kinds of representation for successful thinking and problem solving. In Chapter 2, Vosniadou argues that research on the comprehension of text
and pictures has failed to consider an important distinction between pictures that are perceptually based depictions, on the one hand, and those that represent conceptual models, on the other hand. She addresses differences between these two kinds of external representations and presents some of the difficulties students have when faced with conceptual models. These difficulties arise, she argues, because understanding a conceptual model is an interpretive process that can be seriously hampered by students’ lack of essential domainspecific knowledge and realistic epistemic beliefs. Vosniadou concludes with some recommendations about how pictures representing conceptual models can be helpful in the teaching of science and mathematics. The next chapter by Mason and Ariasi addresses the role of external rep-
resentations in reasoning by examining the epistemic processing of texts and pictures about a biology topic presented on multiple Internet pages. Based on the objective measurement of visual attention through eye-fixations, their study revealed indirect evidence of epistemic processing, that is, processing that takes into account the source, reliability, and accuracy of the informational content. University students were asked to read four web pages differing in authoritativeness, which provided various types of information. The findings showed that participants allocated different amounts of visual attention to different texts and pictures, within and across web pages, according to source credibility. In addition, students’ individual differences regarding prior knowledge, epistemic beliefs, and argumentative reasoning played to some extent a role in epistemic processing. In Chapter 4, Acevedo Nistal et al. report a study in which they examined
students’ ability to make adaptive or flexible representational choices while solving linear-function problems. Two secondary school classes solved problems under a choice condition, where they could choose a table, a graph, or a formula to solve each problem, and three no-choice conditions where a predetermined representation (respectively a table, a graph, or a formula) had to be used. Data concerning representational efficiency (extracted from the no-choice conditions) and frequency of representational choice (extracted from the choice condition) were analysed. Students’ representational flexibility was assessed using two conceptualisations of flexibility. In a purely task-based
conceptualisation choices were considered flexible if they took into account only task characteristics. In a task× student conceptualisation, student characteristics were also brought into the equation. The results obtained from the two approaches are compared. Chapter 5 by Greer, De Bock, and Van Dooren discusses the role of (external)
representations in mathematical proof using the ‘Isis problem’ as a central case. The Isis problem asks: ‘Find which rectangles with sides of integral length (in some unit) have area and perimeter (numerically) equal, and prove the result.’ The problem is notable for the variety of proofs available (empirically grounded, algebraic, geometrical) and the associated representations; moreover, it provides an instrument for probing students’ ideas about proof. First, the authors set out a variety of approaches leading to proofs, showing thereby how proofs can rely on substantially different mathematical representations, each having its affordances differentially clarifying particular aspects of the mathematical situation. They also argue that being involved in making transitions from one representation to another, and linking various representations can provide deeper insight. In the second part of the chapter, they discuss a study with nine American and 39 Flemish future mathematics teachers who first attempted to solve the problem, then studied five given proofs and commented upon them. The results highlight a preference of the more mathematically advanced students for algebraic proofs over empirically grounded and visual (geometric) proofs. In the next chapter, Schneider, Rode, and Stern address the availability and
activation of diagrammatic strategies for learning from texts in secondary school students. The authors’ starting point is that diagrams are powerful tools for learning and reasoning, and that people frequently do not use diagrams even in situations in which they would be very helpful. In two experiments they investigated whether the reason for this is either a lack of availability or a lack of activation of diagrammatic representation strategies. A group of seventh graders and ninth graders read texts which could be summarised by a diagram as well as by keywords. Students were asked to take down notes. The experimental conditions differed as to whether the instructions for note taking explained the diagrammatic strategy or whether they explicitly requested its use. Results revealed that neither availability nor activation was well developed in students. Instructions aimed at increasing availability or activation led to increased diagram use, better memorising of facts, and better inferences. Spontaneous diagram use improved with grade level, but still remained insufficient even in grade nine. The authors argue that instruction should encourage students to use diagrams based on their specific advantages. Part 2 begins with a chapter by Jaakkola, Nurmi, and Lehtinen who
investigated, using video data, the simultaneous use of a computer simulation and real electrical circuits (a hybrid environment). The central question is why simultaneous use in a hybrid environment promotes students’ conceptual understanding of electrical circuits more effectively than the use of the
simulation alone. Elementary school students learnt about electrical circuits in a simulation-alone or a hybrid condition. No differences were found in the amount of cognitive conflicts and self-explanations between the two conditions. However, the video data transcripts from the hybrid environment suggested that analogical encoding of two information resources can improve schema abstraction and deepen students’ conceptual understanding of electrical circuits. The authors conclude that, overall, it seems to be beneficial to try to promote students’ conceptual understanding of electrical circuits at the early elementary school level, because they do not yet have deeply rooted misconceptions that could hamper teaching and learning. Gerjets et al. provide in Chapter 8 an overview of four studies that compared
static and dynamic visualisations in the context of the biological domain of fish locomotion. The different learning objectives addressed in these studies comprise: (1) understanding the physical principles underlying fish locomotion, (2) classifying different fish locomotion patterns, and (3) identifying different fish species based on important static and dynamic features. The results demonstrate that for all three learning objectives dynamic visualisations were superior to static ones. These findings were obtained in laboratory settings as well as in the highly situated learning scenario of using mobile devices during a snorkelling excursion. The authors conclude that their results clearly yield the recommendation to use dynamic instructional visualisations instead of static ones for supporting the comprehension of complex dynamic phenomena in the natural sciences. The next chapter, by Kolloffel, Eysink, and de Jong, reports two stud-
ies in which the effects of external representations on learning combinatorics and probability theory in an inquiry-based learning environment were investigated. In the first study, the effects of five representational formats used to present the domain to students were compared: Tree diagram, Arithmetic, Text, Text+ Arithmetic, or Tree diagram+ Arithmetic. The main finding was that students in the Text+Arithmetic condition obtained the best learning results. Tree diagrams were found to negatively affect learning and to increase cognitive load. The second study examined the effects of providing support tools students could use to construct domain representations. Three formats of such tools (conceptual, arithmetical, or textual) were compared, both in an individual and collaborative learning setting. Format influenced students’ inclination to use a tool, with arithmetical representation being the least popular among the students. Furthermore, the collaborative students obtained better learning outcomes, but if individuals used the support, their learning outcomes equalled those of collaborating students. In Chapter 10, Gravemeijer, Doorman, and Drijvers argue that the problem-
atic character of symbolic representations in mathematics education is tied to what is called the ‘dual nature of mathematics’ – which is procedural as well as structural. Historically, procedural conceptions precede structural conceptions, whereas mathematics education often starts at a structural level, using
concrete representations to introduce those structural conceptions. According to the authors, this is problematic because these representations derive their meaning from structural conceptions that the students still have to appropriate. In the alternative they propose, bottom-up learning processes in which symbols and meaning co-evolve are fostered. They elaborate such an approach known as the ‘emergent modelling instructional design heuristic’ – for the topic of algebraic functions. A brief sketch of a teaching experiment on early algebra elucidates this alternative and suggests that information technology can actually support the transition from a procedural to a structural conception of functions. In Chapter 11, Vamvakoussi reviews a series of studies investigating secondary
students’ understanding of the density of numbers, and attempting to bring this notion within the grasp of students. She presents empirical evidence demonstrating the adverse effect of the multiple symbolic representations of rational numbers, as well as the limited, sometimes adverse, effect of the number line, on students’ judgements on the number of numbers in an interval. Vamvakoussi argues that students’ difficulty with the notion of density relates to a more general problem of conceptual change in the development of the number concept. Cross-domain mapping between number and the line is proposed as a mechanism that could facilitate the restructuring of students’ number concept. This claim is supported by empirical evidence showing that the number line, a representation grounded on the ‘numbers are points’ analogy, can facilitate students’ understanding of density if purposefully employed in instruction. Next, Wetzels, Kester, and van Merriënboer outline a theoretical frame-
work providing insights into the use of external representations of low sophistication during prior knowledge activation in the science domain. This framework distinguishes representations that prompt (i.e., initiate) prior knowledge activation from representations that reinforce (i.e., facilitate) the activation process. Prompts that consist of pictorial representations (e.g., pictures, animations) are regarded as more suitable than verbal representations for activating structural and causal models important for science learning. Furthermore, external representations may reinforce the activation process. There are limits to the amount of information that can be activated simultaneously because of humans’ limited working memory capacity. Self-constructed representations (e.g., note taking) might offload working memory while activating prior knowledge. It is argued that the strength of the prompting and reinforcing effects of external representations during prior knowledge activation is mediated by learners’ level of prior knowledge. An empirical study that provides support for the framework is reported. The final chapter explores the visualisation of argumentation as a shared
activity. Erkens, Janssen, and Kirschner’s starting point is that the use of argumentation maps in computer-supported collaborative learning does not always provide students with the intended support for their collaboration. They compare two argumentation maps from two research projects, both meant to
support the collaborative writing of argumentative essays based on external sources. In the COSAR-project, students could use a Diagram-tool to specify positions, pro-arguments, con-arguments, supports, refutations and conclusions in a free graphical format to write a social studies essay. The tool was highly appreciated by students and teachers, but did not result in better essays. In the CRoCiCL-project, a Debate-tool allowed students to do the same things but in a structured graphical format, meant to visualise the argumentative strength of the positions. This resulted in better history essays. The difference in representational guidance between the tools might explain these distinct effects, with the Debate-tool stimulating students to attend to the justification of positions and their strengths. Implications for research and instruction are discussed at the chapter end.
