External Representations Research Articles

Spatial thinking activities in PK-12 classrooms: Predictors of teachers’ activity use and a framework for classifying activity types

This study examined pre-service and in-service teachers' self-reported use of spatial thinking skills in classroom activities. Additionally, teachers' self-reported spatial anxiety, confidence, and mindset beliefs were examined. Results showed that teachers' confidence for teaching spatial thinking skills significantly predicted their use of spatial thinking activities. Teachers most often reported embedding spatial thinking skills into domain-specific learning activities, utilizing external representations, and engaging students in active and constructive learning opportunities. The findings connect spatial thinking skills research with educational practices to indicate that teachers’ reported spatial thinking classroom activities differ from spatial thinking skills training activities in laboratory settings.

Sensemaking and scientific modeling: Intertwined processes analyzed in the context of physics problem solving

Researchers in physics education have advocated both for including modeling in science classrooms as well as promoting student engagement with sensemaking. These two processes facilitate the generation of new knowledge by connecting to one’s existing ideas. Despite being two distinct processes, modeling is often described as sensemaking of the physical world. In the current work, we provide an explicit, framework-based analysis of the intertwining between modeling and sensemaking by analyzing think-aloud interviews of two students solving a physics problem. While one student completes the task, the other abandons their approach. The case studies reveal that particular aspects of modeling and sensemaking processes co-occur. For instance, the priming on the ‘given’ information from the problem statement constituted the students’ engagement with their mental models, and their attempts to resolve inconsistencies in understanding involved the use of external representations. We find that barriers experienced in modeling can inhibit students’ sustained sensemaking. These results suggest ways for future research to support students’ sensemaking in physics by promoting modeling practices.Received 20 July 2022Accepted 1 February 2023DOI:https://doi.org/10.1103/PhysRevPhysEducRes.19.010118Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasAssessmentEpistemology, attitudes, & beliefsScientific reasoning & problem solvingPhysics Education Research

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.

Improving Students' Mathematical Problem-Solving Ability through the Use of External Representations

This study has the objectives, namely first, to find out whether students' mathematical problem-solving abilities can be improved by using external representations. Second, analyzing student activities in learning mathematics by using external representations. Third, analyzing student responses to learning mathematics by using external representations. This research uses classroom action research (CAR) or classroom action testing (PTK) methods. According to O'Brien in Mulyatiningsih, "action research is carried out when a group of people (students) identify the problem, then the researcher determines an action to overcome it." Classroom Action Research (CAR) seeks to develop and reflect on a learning model with the aim of improving learning processes and outcomes. Based on the results of the research, it can be concluded that: learning using external representations can improve mathematical problem solving abilities; it can be seen that there is an increase in the number of students who score above the KKM in cycle II, with the percentage of students who are declared complete (reaching the KKM) at 71.4%, or as many as 20 students are higher than in cycle I, with a percentage of 53.57%, or as many as 15 students who are declared complete. This means that most students have achieved learning mastery resulting from learning through the use of external representations

Cingulo-Opercular Subnetworks Motivate Frontoparietal Subnetworks during Distinct Cognitive Control Demands.

Cognitive control is the ability to flexibly adapt behavior in a goal-directed manner when habit will not suffice. Control can be separated into distinct forms based on the timescale (present-future) and/or medium (external-internal) over which it operates. Both the frontoparietal network (FPN) and cingulo-opercular network (CON) are engaged during control, but their respective functions and interactions remain unclear. Here, we examined activations in the FPN and CON with fMRI in humans (male and female) during a task that manipulated control across timescales/mediums. The findings show that the CON can be distinguished into the following two separable subnetworks mirroring the FPN: a rostral/ventral subnetwork sensitive to future-oriented control involving internal representations, and a caudal/dorsal subnetwork sensitive to present-oriented control involving external representations. Relative to the FPN, activation in the CON was particularly pronounced during transitions into and out of particular control demands. Moreover, the relationship of each CON subnetwork to behavior was mediated by a respective FPN subnetwork. Such data are consistent with the idea that the CON motivates the FPN, which, in turn, drives behavior. Within the CON, the dorsomedial prefrontal cortex (dmPFC) mediated the relationship between the anterior insula and FPN, suggesting that the dmPFC acts as the crux that links the CON to the FPN. Collectively, these data indicate that parallel CON-FPN subnetworks mediate controlled behaviors at distinct timescales/mediums.SIGNIFICANCE STATEMENT The cingulo-opercular network (CON) and frontoparietal network (FPN) are engaged in diverse, demanding tasks. A functional model describing how areas within these networks can be distinguished, and also interact, would facilitate understanding of how the brain adapts to demanding situations. During a comprehensive control task, fMRI data revealed that the FPN and CON can be fractionated into subnetworks based on control demands that are either externally oriented for use in the present, or control demands that operate internally to guide future behavior. Moreover, we found evidence for a chain of relationships from the CON to FPN to behavior consistent with the idea that the CON drives the FPN to adapt behavior.

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.

The influence of the conceptual structure of external representations when relearning history content

The influence of the conceptual structure of external representations when relearning history content

Inner speech in meaning-making through verbal and artistic discourses

Inner speech plays a significant role in various cognitive processes as internalized social speech and a unique form of sign-using activity. While previous research has already emphasized the role of inner speech in the formation of meanings and interpretation, few attempts have been made to establish a semiotic account of inner speech as a mechanism of meaning-making. The study aims to establish a semiotic account of the concept of inner speech as internalized social speech and as a form of inner communication embodied in artistic discourse. Thus, the paper addresses the meaning-making functions of inner speech at the levels of verbal (inter- and intrapersonal communication) and artistic discourses (manifestation of inner communication in artistic texts). It identifies the role of inner speech in the formation and development of individual meanings that originate from the nature, phenomenology and individual development of internalized verbal language. This development of meanings follows specific laws, which include the internalization of verbal communication, socio-cultural experience and external representations of different modalities. The role of inner speech in meaning-making in artistic narration is addressed by analysing the manifestation of inner communication in artistic discourse and intentional adaptation of the concept of inner speech. The study identifies how the evolution of cultural communication processes shapes the ontology and manifestation of the artistic inner monologue in contemporary culture.

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.

The Complexity of Reasoning about and with Chemical Representations.

External visual representations of chemical entities and processes (chemical representations) play a critical role in chemical thinking and practice. They support reasoning by serving as bridges between the macroscopic world and the chemical models that help us make sense of the properties and behaviors of substances in our surroundings. Consequently, many chemistry education research studies have been carried out to explore and foster students' representational competency in our discipline. Nevertheless, in this Perspective I argue that investigations in this area would benefit from a more in-depth analysis of how the distinctive characteristics of chemical representations affect student reasoning. I identify four dimensions of variation in these representations (iconicity, quantitativeness, granularity, dimensionality) that affect students' ability to interpret, connect, generate, and use chemical representations. I discuss how these features influence the unpacking or packing of information during different types of tasks, affecting sense-making and perceptual competency. Implications for chemistry education research and practice are considered.

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.

On Sense Making and the Generation of Knowledge in Visual Analytics

Interactive visual tools and related visualization technologies, built to support explorative data analysis, ultimately lead to sense making and knowledge discovery from large volumes of raw data. These processes namely rely on human visual perception and cognition, in which human analysts perceive external representations (system structure, dataset, integral data visualizations) and form respective internal representations (internal cognitive imprints of external systems) that enable deeper comprehension of the employed system and the underlying data features. These internal representations further evolve through continuous interaction with external representations. They also depend on the individual’s own cognitive pathways. Currently, there has been insufficient work on understanding how these internal cognitive mechanisms form and function. Hence, we aim to offer our own interpretations of such processes observed through our daily data exploration workflows. This is accomplished by following specific explorative data science tasks while working with diverse interactive visual systems and related notebook style environments that have different organizational structures and thus may entail different approaches to thinking and shaping sense making and knowledge generation. In this paper, we deliberate on the cognitive implications for human analysists when interacting with such a diverse organizational structure of tools and approaches when performing the essential steps of an explorative visual analysis.

Distribution-Sensitive Information Retention for Accurate Binary Neural Network

Model binarization is an effective method of compressing neural networks and accelerating their inference process, which enables state-of-the-art models to run on resource-limited devices. Recently, advanced binarization methods have been greatly improved by minimizing the quantization error directly in the forward process. However, a significant performance gap still exists between the 1-bit model and the 32-bit one. The empirical study shows that binarization causes a great loss of information in the forward and backward propagation which harms the performance of binary neural networks (BNNs). We present a novel distribution-sensitive information retention network (DIR-Net) that retains the information in the forward and backward propagation by improving internal propagation and introducing external representations. The DIR-Net mainly relies on three technical contributions: (1) Information Maximized Binarization (IMB): minimizing the information loss and the binarization error of weights/activations simultaneously by weight balance and standardization; (2) Distribution-sensitive Two-stage Estimator (DTE): retaining the information of gradients by distribution-sensitive soft approximation by jointly considering the updating capability and accurate gradient; (3) Representation-align Binarization-aware Distillation (RBD): retaining the representation information by distilling the representations between full-precision and binarized networks. The DIR-Net investigates both forward and backward processes of BNNs from the unified information perspective, thereby providing new insight into the mechanism of network binarization. The three techniques in our DIR-Net are versatile and effective and can be applied in various structures to improve BNNs. Comprehensive experiments on the image classification and objective detection tasks show that our DIR-Net consistently outperforms the state-of-the-art binarization approaches under mainstream and compact architectures, such as ResNet, VGG, EfficientNet, DARTS, and MobileNet. Additionally, we conduct our DIR-Net on real-world resource-limited devices which achieves \(11.1\times \) storage saving and \(5.4\times \) speedup.

Distortions in Spatial Mental Representation Affect Sketch Maps in Young Adults.

Humans tend to misrepresent spatial information which leads to systematic errors due to distorted organizational processes regarding metric and positional judgments. This study is aimed at analyzing metric and positional distortions in cognitive maps by using external representations, namely sketch maps, in two experiments with young participants. In the first experiment, we use the sketching area of Northern Europe. In the second experiment, the University campus area was used. The first aim was to test the hypothesis that the presence of the sea between the triplet of landmarks generates an overestimation of the distances between them in the case of Northern Europe; and to test the hypothesis that the number of turns in a route influences the overestimation of the distance between landmarks in the case of the campus area. The second aim was to investigate alignment and rotation errors using the same maps. Concerning metric errors, the results showed the overestimation of distances with a geographical gap between the cities (the sea in the Northern European Area), and those with more turns between landmarks (the campus area). The results concerning rotations and alignments were in line with the previous research about positional errors. The present study extended findings on distortions in spatial mental representation as emerging from verbal judgments, to sketch maps: direct visuospatial external representations eluding the conversion into verbal coding of spatial information. The presence of distortions in cognitive maps could be considered the consequence of the encoding of spatial information.

Attention rhythmically samples multi-feature objects in working memory

Attention allows us to selectively enhance processing of specific locations or features in our external environment while filtering out irrelevant information. It is currently hypothesized that this is achieved through boosting of relevant sensory signals which biases the competition between neural representations. Recent neurophysiological and behavioral studies revealed that attention is a fundamentally rhythmic process, tightly linked to neural oscillations in frontoparietal networks. Instead of continuously highlighting a single object or location, attention rhythmically alternates between multiple relevant representations at a frequency of 3–8 Hz. However, attention cannot only be directed towards the external world but also towards internal visual working memory (VWM) representations, e.g. when selecting one of several search templates to find corresponding objects in the external world. Two recent studies demonstrate that single-feature objects in VWM are attended in a similar rhythmic fashion as perceived objects. Here we add to the literature by showing that non-spatial retro-cues initiate comparable theta-rhythmic sampling of multi-feature objects in VWM. Our findings add to the converging body of evidence that external and internal visual representations are accessed by similar rhythmic attentional mechanisms and present a potential solution to the binding problem in working memory.

Focusing with images

ABSTRACT The practise of Focusing with images was the key element of six workshops held for postgraduate research students at the University of East Anglia, UK. Participants were invited both to respond to extant images (including those from the university’s art galleries) as well as to create their own images through working with paint and other art materials. Changes in this highly anxious group’s ability to access and manage inner experiencing as a result of their participation in these workshops was recorded and assessed both qualitatively and quantitatively. Participants completed the Focusing Manner Scale (FMS) at the beginning and at the end of their participation in the workshops and improvement (p = 0.063) was seen in 6 out of 7 participants, indicating a shift in their ability to find ways of processing difficult experiencing. The FMS findings are supplemented by reconstructions of Focusing sessions based on field notes taken during the workshops. Images not only offer external representations of inner experiencing but also provide material for experience to be carried forward.

Enhancing students mathematical thinking using applets

This article presents two different classroom situations in which two pairs of students, one in grade 2 and the other in grade 6, attempted mathematically challenging problems through GeoGebra applets. Their reasoning, conjecture making, and argumentation is analyzed using Pea’s (1985, 1987) theory of technology as amplifier and reorganizer and the notion of internal and external representations. GeoGebra played the role of amplifier and reorganizer in enabling students’ explorations and led them to make conjectures. Furthermore, it was observed that students’ static internal representations were enhanced to more dynamic external representations and this played a significant role in developing students’ thinking. The three aspects of fidelity have been discussed with regard to the use of GeoGebra based applets and how such applets need to be critically designed and assessed in order to support students’ learning.

Analyzing co-design of agroecology-oriented cropping systems: lessons to build design-support tools

If the challenges involved in agroecological transition are to be addressed, cropping systems (CS) need to be changed profoundly, which in turn requires innovative design adapted to local conditions. This is however by no means an easy task since such design activity requires extensive knowledge on objects and processes rarely studied until now, most of which is distributed among numerous stakeholders. Since the 2000s, research on design in agriculture has aimed at developing participatory methods to support on-farm design of new systems, but few studies have focused on the elaboration of design-support tools. With a view to defining the features of tools intended to support the design of agroecology-oriented cropping systems, ergonomists recommended an analysis of the activities of the future users of these tools in their real work situations. We started out by implementing a diagnosis of use situations, based on observations of real collective design activities. To this end, we took part in six design workshops, which differed in terms of goals and of designers participating (i.e., farmers, advisors, students, or scientists). We first identified the diversity of features of these design situations, and then analyzed three processes across the design workshops: (i) the reformulation of the design goal; (ii) the large exploration of candidate solutions; and (iii) the local adaptation of these solutions while anticipating the on-field implementation. Here, we show, for the first time, the type of reasonings and knowledge that designers and facilitators displayed and used throughout the agroecological cropping system design process. We identify the features that future design-support tools should have to guide co-designers of agroecological CS. Such tools should promote several types of design reasoning and allow the development of external representations of the object under design. Our results provide operational guidelines for the elaboration of new design-support tools.

From friction to air resistance

Friction occurs early in our lives. We rub our hands and stamp our feet to get them warm. Another effect of friction is the use of winter tires at cars, new bicycle tires, or special shoes for icy surface. This article discusses how to present the way from friction to air resistance through GeoGebra applets. The approach has been analyzed using the theory of technology as amplifier and reorganizer, theory of variation, and the notion of internal and external representations. The dragging feature of GeoGebra enables students to experience variation and make conjectures. Furthermore, students’ static internal representations will be enhanced to dynamic external representations, which can play an important role in students’ learning. Three aspects of fidelity have been discussed with regard to the use of GeoGebra based applets and how such applets need to be critically designed and assessed in order to support students’ learning.

Integrating external representations and internal patterns into dynamic multiple-criteria decision making

Integrating external representations and internal patterns into dynamic multiple-criteria decision making