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Prior research shows the importance of external representations in learning physics at school. This research often focuses on the teaching of as well as learning with different forms of representations, such as graphs and tables, and their impact on understanding professional content. Teachers’ and students’ perception and the matching of both have not been in the focus of previous research. One open question in this regard is, how teachers estimate the adequacy of how they use external representations to teach physics compared to how students perceive it. To investigate this question, we conducted a survey of teachers as well as students of 6th, 8th, and 10th grade in German schools. The development and validation of the questionnaire is part of the research method. The results show differences between how teachers estimate the frequency and adequacy of the representations they use and how adequate students perceive this to be. As a practical consequence, these insights could be used for teachers to reflect upon the materials they use to teach physics.

Visual representations play a critical role in enhancing science, technology, engineering, and mathematics (STEM) learning. Educational psychology research shows that adding visual representations to text can enhance students' learning of content knowledge, compared to text-only. But should students learn with a single type of visual representation or with multiple different types of visual representations? This article addresses this question from the perspective of the representation dilemma, namely that students often learn content they do not yet understand from representations they do not yet understand. To benefit from visual representations, students therefore need representational competencies, that is, knowledge about how visual representations depict information about the content. This article reviews literature on representational competencies involved in students' learning of content knowledge. Building on this review, this article analyzes how the number of visual representations affects the role these representational competencies play during students' learning of content knowledge. To this end, the article compares two common scenarios: text plus a single type of visual representations (T+SV) and text plus multiple types of visual representations (T+MV). The comparison yields seven hypotheses that describe under which conditions T+MV scenarios are more effective than T+SV scenarios. Finally, the article reviews empirical evidence for each hypothesis and discusses open questions about the representation dilemma.

Why do people create extra representations to help them make sense of situations, diagrams, illustrations, instructions and problems? The obvious explanation—external representations save internal memory and computation—is only part of the story. I discuss seven ways external representations enhance cognitive power: they change the cost structure of the inferential landscape; they provide a structure that can serve as a shareable object of thought; they create persistent referents; they facilitate re-representation; they are often a more natural representation of structure than mental representations; they facilitate the computation of more explicit encoding of information; they enable the construction of arbitrarily complex structure; and they lower the cost of controlling thought—they help coordinate thought. Jointly, these functions allow people to think more powerfully with external representations than without. They allow us to think the previously unthinkable.

The dynamic multiple-criteria decision-making (MCDM) approach has drawn immense attention in the decision analysis domain over recent years. An essential problem of this dynamic process is how to retrieve the utmost from historical data. Although most previous dynamic MCDM studies process historical data only with external representatives, namely scores given to alternatives on each criterion, we argue that internal patterns of historical data are also essential to achieve a more comprehensive evaluation of alternatives. Nevertheless, a data-driven methodology aiming to capture internal patterns of historical data and consequently provide decision-makers with meaningful insights is still lacking. In this paper, we propose a framework that serves as integration within which both external representations and internal patterns are used to make a more comprehensive evaluation. Then we apply our framework to student evaluations and country-level risk assessments in the contexts of additive and fuzzy measures, respectively. Both cases show that either using external representatives or internal patterns alone leads to entirely different and even biased results. On the contrary, integrating external representations and internal patterns can offer more flexibility and higher interpretation power.

In the field of biochemistry, the use of external representations such as static diagrams and animations has increased rapidly in recent years. However, their effectiveness as instructional tools can be hindered if students lack the visual literacy and cognitive skills necessary for processing and interpreting such representations. We aimed to identify and assess visualisation skills necessary for effective processing of external representations in biochemistry. We used a modified Bloom's taxonomy to identify the cognitive skills essential for optimal visual literacy, and designed probes based on those skills to develop a test instrument. Student responses to the probes were scored and processed with the Rasch model. This approach enabled us to rate the degree of difficulty of each visualisation skill on a linear logit scale, and to generate a person-item map to measure biochemistry students' level of visual literacy. The results showed that the identified visualisation skills could be measured reliably, and the Rasch model was effective both for ranking the skills according to level of difficulty and for estimating a student's relative level of visual literacy.

To help students acquire mathematics and science knowledge and competencies, educators typically use multiple external representations (MERs). There has been considerable interest in examining ways to present, sequence, and combine MERs. One prominent approach is the concreteness fading sequence, which posits that instruction should start with concrete representations and progress stepwise to representations that are more idealized. Various researchers have suggested that concreteness fading is a broadly applicable instructional approach. In this theoretical paper, we conceptually analyze examples of concreteness fading in the domains of mathematics, physics, chemistry, and biology and discuss its generalizability. We frame the analysis by defining and describing MERs and their use in educational settings. Then, we draw from theories of analogical and relational reasoning to scrutinize the possible cognitive processes related to learning with MERs. Our analysis suggests that concreteness fading may not be as generalizable as has been suggested. Two main reasons for this are discussed: (1) the types of representations and the relations between them differ across different domains, and (2) the instructional goals between domains and subsequent roles of the representations vary.

Digital learning environments are dynamic systems that require learning designers to leverage environmental conditions and the needs of their learners. While many frameworks and studies have explored pedagogical reasoning, little emphasis has been placed on the dynamic decision-making processes of learning designers. To advance the exploration of pedagogical reasoning and dynamic decision-making in digital learning environments, we proffer a conceptual framework that supports these practices through the promotion of reflection-in-action, external representations, and the use of conjecturing strategies to maneuver through the learning design space. Theoretical and practical implications are considered for how pedagogical reasoning and dynamic decision-making can be integrated into learning design curricula and educational policy.

The present article reviews 42 studies investigating the role of sequencing of text and pictures for learning outcomes. Whereas several of the reviewed studies revealed better learning outcomes from presenting the picture before the text rather than after it, other studies demonstrated the opposite effect. Against the backdrop of theories on memory representations, these results are explained by a recency effect: that is, recall of information should be superior for the medium (text or picture) presented second, and thus, in closer temporal proximity to the assessment. As a consequence, the type of knowledge assessed (text-based vs. picture-based) and its congruence with the more recent medium should determine whether better learning results are found when presenting the picture or text first. Against the backdrop of theories on mental model construction, results were explained by a facilitation effect for the medium (text or picture) presented second. As a consequence, the relative complexity of information conveyed by the picture and by the text should determine which medium is better to be processed first, with less complex information being processed first leading to better comprehension. To conclude, the review suggests that it is not so much the sequence of text and pictures per se that affects learning outcomes than these boundary conditions (i.e., type of assessed knowledge, relative complexity of text, and picture). Accordingly, the present review seeks to stimulate further research along the boundary conditions to better understand the processes involved when learning with text and pictures.

BackgroundRepresentational competence is commonly considered a prerequisite for the acquisition of conceptual knowledge, yet little exploration has been undertaken into the relation between these two constructs. Using an assessment instrument of representational competence with vector fields that functions without confounding topical context, we examined its relation with N = 515 undergraduates’ conceptual knowledge about electromagnetism.ResultsApplying latent variable modeling, we found that students’ representational competence and conceptual knowledge are related yet clearly distinguishable constructs (manifest correlation: r = .54; latent correlation: r = .71). The relation was weaker for female than for male students, which could not be explained by measurement differences between the two groups. There were several students with high representational competence and low conceptual knowledge, but only few students with low representational competence and high conceptual knowledge.ConclusionsThese results support the assumption that representational competence is a prerequisite, yet insufficient condition for the acquisition of conceptual knowledge. We provide suggestions for supporting learners in building representational competence, and particularly female learners in utilizing their representational competence to build conceptual knowledge.

(Series Information) European Papers - A Journal on Law and Integration, 2024 9(1), 121-129 | European Forum Insight of 18 June 2024 | (Table of Contents) I. Introduction. - II. Signature of international agreements: the (in)consistent practice. - III. Solving the indeterminacy of art. 218 TFEU. - iii.1. Scope, institutional balance and sincere cooperation. - iii.2 Signature of non-binding agreements. - IV. Case C-551-21: insights and commentaries. - iv.1. Understanding the arguments. - iv.2. The Court’s Findings. - V. Conclusions | (Abstract) The current Insight analyses the judgment of the European Court of Justice in Case C-551/21, which up-held the Commission's claim regarding its right to exercise the external act of treaty signature. The deci-sion sheds light on the signature procedure outlined in art. 218 TFEU and adds to previous cases, clari-fying the proper contours and roles of each institution in relation to the procedure set in the article. An initial observation of the practice appears to indicate the Permanent Representative of the country holding the Council's presidency as the responsible party to sign international agreements with third parties representing the Union. However, a more in-depth analysis reveals a lack of consistent and standardised practice. The judgment correctly recalibrates the institutional balance and is coherent with the reforms of the Lisbon Treaty, which sought to bring about an evolution of the principles of the Treaties without a formal amendment process.