Multiple External Representations Research Articles

Learning with multiple external representations in physics: Concreteness fading versus simultaneous presentation

AbstractMultiple external representations (MERs) are useful for teaching complex content in science education. An open question is whether there is an especially effective way to sequence MERs. On the one hand, the so‐called concreteness fading approach suggests starting instruction with more concrete representations and proceeding stepwise to more idealized representations. The effectiveness of this fading approach is, however, supported mainly by studies in mathematics education, while the results in physics are equivocal. On the other hand, presenting different representations simultaneously may support linking, that is, the comparison and contrast of representations, which may benefit learning. In an experimental classroom study (N = 187), we compared concreteness fading and simultaneous presentation of MERs for learning a challenging physics content in high school, namely, Faraday's law. We found no significant differences between conditions in posttest performance, and an equivalence test with bounds d = −0.5 to 0.5 showed that both approaches performed equally. The results align with previous findings questioning the superiority of concreteness fading over other ways of sequencing MERs. Therefore, facilitating students' understanding of a complex physics content may involve more than determining the optimal order of presenting MERs. We discuss limitations of the present study and implications for future research and practice.

What makes representations good representations for science education? A teacher-oriented summary of significant findings and a practical guideline for the transfer into teaching

Abstract Existing instructional materials for chemistry offer a huge range of different external representations that can be used by chemistry teachers to support students’ understanding of chemical concepts like the concept structure of matter. In science, different kinds of representations are usually combined forming multiple external representations. Examples are combinations of texts, pictures, figures, diagrams, graphs, tables, schemes etc. However, these multiple external representations often have problematic features and/or do not meet students’ subject-related learning needs. For example, many external representations do not take different representational levels into account and/or mix information on the macroscopic level with those from the submicroscopic level. Such representations have the potential to favor students’ misconceptions who often struggle with separating different representational levels. Therefore, it is important to highlight crucial characteristics of external representations that potentially facilitate students’ learning of chemical concepts at lower secondary schools (age group 10–14). When chemistry teachers consider and reflect crucial characteristics of representations and adapt existing external representations or develop new ones, these new representations can become powerful cognitive tools helping to make instruction in chemistry more effective and coherent. This article answers the question What makes representations good representations in science education? by describing features of effective learning with decisive characteristics of multiple external representations and highlighting these characteristics by means of concrete examples from chemistry learning. Finally, an online tool will be outlined that can help teachers to improve multiple external representations for use in chemistry classes.

Bridging Cognitive Science and Teaching Practice: A Proof of Concept Study of the Cognitive Instructional Techniques (CIT) Observation Instrument

This paper presents the Cognitive Instructional Techniques (CIT) observation instrument – a novel tool to assess the degree to which teaching practice is congruent with instructional techniques that have emerged from cognitive science. The paper includes a description of CIT, the process by which it was developed, and initial findings related to its use. CIT includes a 0-4 rating scale (0 = not observed to 4 = high congruence) for eight instructional techniques: Anchoring, Guided Instruction, Multiple Representations, Quizzing, Self-Explanation, Signalling, Variable Practice, and Worked Examples. The instrument was used to code randomly selected videotaped 4th and 5th grade mathematics lessons in the USA (N = 42) selected from the Measures of Effective Teaching Project database (Bill and Melinda Gates Foundation, 2018). Results of this proof-ofconcept study indicated that the CIT instrument captures variability as well as stability in teaching practice. Overall, teaching practice was found to be congruent with some instructional techniques advocated for by cognitive researchers (e.g., testing), but not others (e.g., self-explanation). For instance, half of the instructional lessons in the sample did not use multiple external representations to explain math concepts and less than a quarter demonstrated the use of multiple representations in a manner consistent with what research has identified as most effective. This initial study indicated the potential usefulness of the CIT instrument in determining the extent to which instructional practice is congruent with ideas from cognitive science. The ways in which CIT could create further intersections between cognitive science and education are discussed.

The impact of multiple representations on students' understanding of vector field concepts: Implementation of simulations and sketching activities into lecture-based recitations in undergraduate physics.

Multiple external representations (e.g., diagrams, equations) and their interpretations play a central role in science and science learning as research has shown that they can substantially facilitate the learning and understanding of science concepts. Therefore, multiple and particularly visual representations are a core element of university physics. In electrodynamics, which students encounter already at the beginning of their studies, vector fields are a central representation typically used in two forms: the algebraic representation as a formula and the visual representation depicted by a vector field diagram. While the former is valuable for quantitative calculations, vector field diagrams are beneficial for showing many properties of a field at a glance. However, benefiting from the mutual complementarity of both representations requires representational competencies aiming at referring different representations to each other. Yet, previous study results revealed several student problems particularly regarding the conceptual understanding of vector calculus concepts. Against this background, we have developed research-based, multi-representational learning tasks that focus on the visual interpretation of vector field diagrams aiming at enhancing a broad, mathematical as well as conceptual, understanding of vector calculus concepts. Following current trends in education research and considering cognitive psychology, the tasks incorporate sketching activities and interactive (computer-based) simulations to enhance multi-representational learning. In this article, we assess the impact of the learning tasks in a field study by implementing them into lecture-based recitations in a first-year electrodynamics course at the University of Göttingen. For this, a within- and between-subjects design is used comparing a multi-representational intervention group and a control group working on traditional calculation-based tasks. To analyze the impact of multiple representations, students' performance in a vector calculus test as well as their perceived cognitive load during task processing is compared between the groups. Moreover, analyses offer guidance for further design of multi-representational learning tasks in field-related physics topics.

Augmented reality for chemistry education to promote the use of chemical terminology in teacher trainings.

Chemistry as a whole is divided into three levels. The macroscopic level describes real, observable phenomena of the material world. The submicroscopic level focuses on particles. The representative level includes pictorial and symbolic representations to visualize substance in its nature. Students often have problems separating these levels and conceptually transfer each of the three levels to the other. Therefore, teachers need to use chemical terminology correctly when teaching the substance-particle concept. Augmented reality (AR) connects the real and virtual worlds. The observer physically moves in a real environment that integrates virtual elements. This can be effective for learning when chemical processes that are invisible are made visible. The simultaneous presentation should avoid split attention and offers new possibilities to interactively deal with multiple external representations ((M)ER). The question arises whether AR has a positive effect on the use of technical language. With an AR app on the tablet and on the hololens, chemical processes of a real experiment are represented by AR visualizations. In this study, the chemistry terminology of chemistry teachers (N = 30) was captured using a pre-post survey. Each test includes five tasks elaborated by thinking aloud. Therefore, the AR app was piloted. The thinking-aloud protocols to acquire the use of the chemical terminology are evaluated in MAXQDA.

Measuring the role of spatial ability and multiple external representations in introductory geology students’ knowledge of plate tectonics

Spatial reasoning ability is key to an individual’s understanding of geology and geosciences more broadly. One reason why is because spatial ability allows individuals to use multiple external representations (MERs) to understand information that they cannot normally interact with directly, such as the Earth. This article presents results from two studies that investigate the relationship between students’ understanding of plate tectonics and their use of MERs along with spatial ability more broadly. Students’ spatial ability was measured using the Perspective Taking Spatial Orientation Test, Water Level Task, and Purdue Spatial Visualization Tests: Visualization of Rotations. Students’ understanding of plate tectonics was measured using a variable representation assessment. This type of assessment lets students actively use different MERs as answer options. The results of the two studies suggest that spatial ability did not have a direct relationship with students’ scores on the plate tectonics assessment. Instead, students’ understanding of plate tectonics may be better understood through their prior knowledge of the subject and their use of MERs. Specifically, their collective increased attention in using one particular type of representation. More research should be conducted to further understand what scenarios spatial ability aids students’ understanding of plate tectonics and other areas of geosciences.

Gesticulating Biochemistry: Exploring the Impact of using Augmented Reality Models on Students’ Usage of Gestures when Talking about Biochemistry

There are multiple examples in the literature highlighting the connection between gestures and meaning‐making by students learning chemical concepts in chemistry; however, there is little known about whether this connection extends to student learning in biochemistry. Moreover, learning biochemistry often involves the use and coordination of multiple external representations (ranging from 2D illustrations and physical models to 3D virtual models) of macromolecules. How does use of these external representations impact student gesture production and meaning‐making when learning new biochemical content? In this study, we used a newly developed augmented reality (AR) model of the KscA channel to investigate the influence of external representations on student produced gestures during a discussion on KscA function. We focused on several research questions: what are the different biochemistry content knowledge that students express through gestures? What are the different types of gestures and patterns of gesture production used by students to express content knowledge? What are the differences, if any, in student produced gestures before and after the introduction of an AR model? What are the relationships between student produced gestures and the AR model? Semi‐structured clinical interviews were conducted and recorded through Zoom. Seven undergraduate students who enrolled in an upper‐division biochemistry course participated in the interview. During the interview, participants were presented with an AR model of KcsA channel after proposing a theory of how potassium ions move through the channel. Participants were then asked to modify their theory. In the first stage of analysis, interview participants’ utterances were transcribed and their gestures were described in terms of hand shape and movement. The identification of unique gestures as part of the coding process highlighted the importance of hand shape vs movement vs a combination of both as ways to delineate different gestures. In the second stage of analysis, qualitative and quantitative differences in student gesture production were identified through a comparative analysis of student gestures before and after their exposure to the AR model. Exposure to the AR model resulted in a shift from gestures that were more general (for example, holding two hands parallel to represent the channel) to more specific to the channel representation they say (for example, holding two hands to form a funnel shape or curling one hand into a tube shape). Our findings add to existing literature on the use of external representation in biochemistry education by highlighting the relationships between AR mediated external representations and gesture mediated external representations. Implications for both the development of new external representations and instructor’s choice of external representations are discussed.

Mono- and Multi-Representational Learning of the Covariational Aspect of Functional Thinking

Using multiple external representations is advocated for learning in STEM education. This learning approach assumes that multiple external representations promote richer mental representations and a deeper understanding of the concept. In mathematics, the concept of function is a prototypical content area in which multiple representations are used. However, there are hardly any experimental studies investigating the effect of learning functional thinking with multiple representations compared to learning with only one form of representation. Therefore, this article reports on a quasi-experimental intervention study with students from Grade 7, using three measurement time points. The study compared the multi-representational learning of functional thinking with both tables and graphs with mono-representational learning with either tables or graphs. The results show that multi-representational learning led to advantages in learning qualitative functional thinking. However, in quantitative functional thinking, learning with both graphs and tables did not result in higher learning gains than learning exclusively with graphs. Furthermore, students were better able to transfer their knowledge from graphs to tables than vice versa. The results also indicate that multi-representational learning requires more time than mono-representational learning but can lead to higher learning gains. In sum, the results show that the effect of learning with representations is a complex interaction process between learning content and the forms of representation.

Cognitive Load Implications for Augmented Reality Supported Chemistry Learning

This paper presents a study about augmented-reality-based chemistry learning in a university lecture. Organic chemistry is often perceived as particularly difficult by students because spatial information must be processed in order to understand subject specific concepts and key ideas. To understand typical chemistry-related representations in books or literature, sophisticated mental rotation- and other spatial abilities are needed. Providing an augmented reality (AR) based learning support in the learning setting together with text and pictures is consistent with the idea of multiple external representations and the cognitive theory of multimedia learning. Using multiple external representations has proven to be beneficial for learning success, because different types of representations are processed separately in working memory. Nevertheless, the integration of a new learning medium involves the risk to hinder learning, in case of being not suitable for the learning topic or learning purpose. Therefore, this study investigates how the AR-use affects students’ cognitive load during learning in three different topics of organic chemistry. For this purpose also the usability of AR learning support is considered and the possible reduction of the influence of the mental rotation on learning success will be investigated.

Teaching Transformations of Trigonometric Functions with Technology

Trigonometry is integral to mathematics education. The field of trigonometry plays a crucial role in the study of mathematics and its applications. Despite the importance of the subject, students struggle to understand trigonometric constructs such as angle measure. It has also been noted how students struggle to understand transformations of functions generally. Our review of the literature found few studies specifically on students’ understanding of transformations of trigonometric functions, but evidence exists showing students have difficulties with the concept. Here, a MATLAB program called TrigReps is discussed. TrigReps accepts four inputs for the algebraic representation (a)sin(bx + c) + d, and provides three additional representations as outputs. Students are presented with a graphical representation, an auditory representation, and a dynamic representation of a radius rotating around a unit circle. TrigReps has potential to be a useful tool for teaching transformations of trigonometric functions. In particular, it may be able to help students justify why combinations of horizontal transformations are counterintuitive. TrigReps is analytically sound in its design: it is interactive, dynamic, and displays Multiple External Representations (MERs) simultaneously. Initial data support its usefulness in a trigonometry classroom, but more research must be conducted to draw firm conclusions.

Visual cues improve students’ understanding of divergence and curl: Evidence from eye movements during reading and problem solving

The coordination of multiple external representations is important for learning, but yet a difficult task for students, requiring instructional support. The subject in this study covers a typical relation in physics between abstract mathematical equations (definitions of divergence and curl) and a visual representation (vector field plot). To support the connection across both representations, two instructions with written explanations, equations, and visual representations (differing only in the presence of visual cues) were designed and their impact on students’ performance was tested. We captured students’ eye movements while they processed the written instruction and solved subsequent coordination tasks. The results show that students instructed with visual cues (VC students) performed better, responded with higher confidence, experienced less mental effort, and rated the instructional quality better than students instructed without cues. Advanced eye-tracking data analysis methods reveal that cognitive integration processes appear in both groups at the same point in time but they are significantly more pronounced for VC students, reflecting a greater attempt to construct a coherent mental representation during the learning process. Furthermore, visual cues increase the fixation count and total fixation duration on relevant information. During problem solving, the saccadic eye movement pattern of VC students is similar to experts in this domain. The outcomes imply that visual cues can be beneficial in coordination tasks, even for students with high domain knowledge. The study strongly confirms an important multimedia design principle in instruction, that is, that highlighting conceptually relevant information shifts attention to relevant information and thus promotes learning and problem solving. Even more, visual cues can positively influence students’ perception of course materials.

Engaging Young Children with Mathematical Activities Involving Different Representations: Triangles, Patterns, and Counting Objects

This paper synthesises research from three separate studies, analysing how different representations of a mathematical concept may affect young children’s engagement with mathematical activities. Children between five and seven years old engaged in counting objects, identifying triangles and completing repeating patterns. The implementation of three counting principles were investigated: the one-to-one principle, the stable-order principle and the cardinal principal. Children’s reasoning when identifying triangles was analysed in terms of visual, critical and non-critical attribute reasoning. With regard to repeating patterns, we analyse children’s references to the minimal unit of repeat of the pattern. Results are discussed in terms of three functions of multiple external representations: to complement, to constrain and to construct.

Why do Plants Wilt? Investigating Students’ Understanding of Water Balance in Plants with External Representations at the Macroscopic and Submicroscopic Levels

In order to understand water balance in plants, students must understand the relation between external representations at the macroscopic, microscopic, and submicroscopic levels. This study investigated how Slovenian students (N = 79) at the primary, secondary, and undergraduate tertiary levels understand water balance in plants. The science problem consisted of a text describing the setting, visualizations of the process occurring in a wilted plant stem, and five tasks. To determine students’ visual attention to the various elements of the tasks, we used eye tracking and focused on the total fixation duration in particular areas of interest. As expected, primary school students showed less knowledge and understanding of the process than the secondary school and university students did. Students with correct answers spent less time observing the biological phenomena displayed at the macroscopic and submicroscopic levels than those with incorrect answers, and more often provided responses that combined the macro-, micro-, and submicroscopic levels of thought. Learning about difficult scientific topics, such as the water balance in plants, with representations at the macroscopic and submicroscopic levels can be either helpful or confusing for learners, depending on their expertise in using multiple external representations, which is important to consider in biology and science education.

The effect of multiple external representations (MERs) worksheets toward complex system reasoning achievement

The application of a systems approach to assessing biological systems provides hope for a coherent understanding of cell dynamics patterns and their relationship to plant life. This action required the reasoning about complex systems. In other sides, there were a lot of researchers who provided the proof about the instructional successions. They involved the multiple external representations which improved the biological learning. The researcher conducted an investigation using one shoot case study design which involved 30 students in proving that the MERs worksheets could affect the student's achievement of reasoning about complex system. The data had been collected based on test of reasoning about complex system and student's identification result who worked through MERs. The result showed that only partially students could achieve reasoning about system complex, but their MERs skill could support their reasoning ability of complex system. This study could bring a new hope to develop the MERs worksheet as a tool to facilitate the reasoning about complex system.

Refutational text and multiple external representations as a method to remediate the misinterpretation of box plots

The ability to interpret graphs is highly important in modern society, but has proven to be a challenge for many people. In this paper, two teaching methods were used to remediate one specific misinterpretation: the area misinterpretation of box plots. First, we used refutational text to explicitly state and invalidate the area misinterpretation of box plots. Second, we used multiple external representations (MERs): Histograms were used as an overlay on box plots in order to give students a better insight in the way box plots represent data distributions. Third, we combined refutational text and MERs. We found that refutational text was successful in improving students’ interpretation of box plots, but that the use of MERs did not improve students’ interpretation of box plots. The addition of MERs also did not increase the effect of refutational text.

Applying cognitive psychology based instructional design principles in mathematics teaching and learning: introduction

This special issue comprises contributions that address the breadth of current lines of recent research from cognitive psychology that appear promising for positively impacting students’ learning of mathematics. More specifically, we included contributions (a) that refer to cognitive psychology based principles and techniques, such as explanatory questioning, worked examples, metacognitive training, exemplification, refutational texts, multiple external representations, which are considered as well-established principles or techniques for instructional design in general, and (b) that explore, illustrate and critically discuss the available research evidence for their relevance and efficacy in the specific curricular domain of mathematics teaching and learning. The special issue ends with an interview with Paul Kirchner about the relationships between cognitive psychology, instructional design and mathematics education.

Designing Reciprocative Dynamic Linking to improve learners\u2019 Representational Competence in interactive learning environments

Learning from interactive learning environments enriched with multiple external representations (MERs) is often beneficial. The learning benefits of MERs highly rely on the development of Representational Competence. Representational Competence refers to an ability to translate and see relations between MERs. The relevant research findings have consistently reported learners’ difficulty in relating and translating in MERs due to insufficient development of Representational Competence. Although dynamic linking is one of the strategies recommended to address this issue, it offers mixed results. This paper reports design of a new interaction feature that overcomes some of the limitations of traditional dynamically linked representations. We designed an additional interaction in dynamically linked MERs to support learners’ cognitive demands; we refer to this as Reciprocative Dynamic Linking. The goal of this additional affordance was to strengthen learners’ cross-representation cognitive linkage by promoting Representational Competence. The paper reports the study conducted to investigate effects of Reciprocative Dynamic Linking on students’ Representational Competence. The said study was conducted in a course on Signals and Systems from Electrical Engineering program (N = 24). The subjects were assigned to two conditions: a Simulation and a Simulation with Reciprocative Dynamic Linking. The representation competence was assessed with an instrument for measuring Representational Competence within Signals and Systems domain. The effect of Reciprocative Dynamic Linking on learners’ cognitive load was also investigated. The results confirmed that Reciprocative Dynamic Linking could lead to improvement in Representational Competence and thus, higher learning for “Apply and Analyze Procedural knowledge” categories of tasks. Reciprocative Dynamic Linking also promoted germane cognitive load of learners, as it could offer the required cognitive support to improve learners’ Representational Competence. The findings from semi-structured interviews and screen capture analysis corroborated the results. This paper provides details of how to design Reciprocative Dynamic Linking in interactive learning environments and its effect on learners’ Representational Competence. Apart from establishing learning effectiveness of Reciprocative Dynamic Linking, the study further contributes by confirming the role of cognitive processing of learners while learning from interactive learning environments. The findings from the study suggest designing strategies not for just creating highly interactive learning environments but equipping a given learning environment with conducive interaction features that foster learning.

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.

From learners’ concept maps of their similar or complementary prior knowledge to collaborative concept map: Dual eye-tracking and concept map analyses

The present paper describes the MUPEMURE (Multiple Perspectives on Multiple Representations; Bodemer, Author, Kapur, Rummel, & Weinberger, 2011) model as a conceptual framework for collaborative learning with multiple external representations. Within this framework, a study was conducted to examine how learners working in dyads translated between self-generated concept maps of their own and partner's prior knowledge to create a collaborative concept map. Before individual and collaborative concept mapping (CCM) sessions, prior information on the learning topic was distributed between dyad members in such a way that they had either similar (“same/shared prior knowledge” or SK condition) or different but complementary knowledge (“different/unshared prior knowledge” or DK condition). The dual eye-tracking method was used in this study, and eye movement data was examined in two time periods, the first and second half of the CCM session. Eye movement analysis was complemented with the analysis of concept map measures, such as achievement, individual-to-group transfer and group creativity. In the first half of the CCM session, eye movement behavior across the three maps was interpreted as reflecting initial externalization and divergent processes through which learners mutually compare their knowledge and engage in a process of modeling each other. The second half of the CCM session was identified as a convergent phase characterized by a decrease in eye movement transitions between maps, and a convergence of attention on the collaborative map. The results also showed that in the first half of the collaboration, learners of the DK condition transitioned more between their own and partner maps, and therefore had more difficulty coordinating their respective prior knowledge compared to learners of the SK condition. Participants with different/unshared prior knowledge also focused their attention mainly in their own map and explored less their partner map in the first half of the collaboration. This suggests that they worked in a less collaborative way compared to those with same/shared prior knowledge during the divergent phase.

Digital Games as Multirepresentational Environments for Science Learning: Implications for Theory, Research, and Design

Environments in which learning involves coordinating multiple external representations (MERs) can productively support learners in making sense of complex models and relationships. Educational digital games provide an increasing popular medium for engaging students in manipulating and exploring such models and relationships. This article applies cognitive science research on MERs to a range of popular educational and recreational games that focus on the interpretation and manipulation of models. We leverage the literatures on embodied cognition, adaptive scaffolding, science education, and dynamic visualizations to address the challenges, trade-offs, and questions highlighted by the research. We apply these research-derived design considerations to analyze (a) the extent and forms through which the design considerations are reflected in the design of the games, (b) the implications for designing effective model-based games for learning, and (c) the implications for future research on MERs.