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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.

Conceptual change theories assume that knowledge structures grow during the learning process but also get reorganized. Yet, this reorganization process itself is hard to examine. By using concept maps, we examined the changes in students’ knowledge structures and linked it to conceptual change theory. In a longitudinal study, thirty high-achieving students (M = 14.41 years) drew concept maps at three timepoints across a teaching unit on magnetism and electrostatics. In total, 87 concept maps were analyzed using betweenness and PageRank centrality as well as a clustering algorithm. We also compared the students’ concept maps to four expert maps on the topic. Besides a growth of the knowledge network, the results indicated a reorganization, with first a fragmentation during the unit, followed by an integration of knowledge at the end of the unit. Thus, our analysis revealed that the process of conceptual change on this topic was non-linear. Moreover, the terms used in the concept maps varied in their centrality, with more abstract terms being more central and thus more important for the structure of the map. We also suggest ideas for the usage of concept maps in class.

Luonnontieteiden kouluopetuksen tavoitteita on jo pitkään laajennettu tieteellisen sisältötiedon ulkopuolelle. Perinteisen sisältötietopainotuksen sijaan on alettu korostaa luonnontieteellistä lukutaitoa (engl. scientific literacy), jonka tavoitteena on antaa oppilaille valmiuksia osallistua tieteeseen ja teknologiaan liittyvään keskusteluun ja päätöksentekoon henkilökohtaisissa, yhteiskunnallisissa ja globaaleissa kysymyksissä. Suomen tuoreen opetussuunnitelmauudistuksen painotukset ja ilmiöpohjaisuus ovat osa tätä maailmanlaajuista kehitystä. Tässä artikkelissa esitämme, että luonnontieteellisen lukutaidon opettamiseen ja ilmiöoppimiseen liittyy ratkaisemattomia jännitteitä. Vaikka nykyisissä tavoitteissa korostuu opetuksen relevanssi oppijan ja yhteiskunnan kannalta, sisältötieto määritellään edelleen pitkälti oppiainelähtöisen autenttisuuden näkökulmasta. Me argumentoimme, että opetusmenetelmien ja kontekstien lisäksi myös sisältötieto on uudelleenmääriteltävä muuttuneiden tavoitteiden mukaiseksi. The goals of science education expand beyond traditional scientific content knowledge. Scientific literacy has become an important goal, offering students knowledge and skills to engage in public discussion and decision making in personal, societal and global issues related to science and technology. The recent changes in Finnish Core Curricula towards phenomenon-based learning represent these global trends in science education. In this paper, we argue that there are unresolved tensions in the the pursuit for scientific literacy and phenomenon-based learning. While the current aims of science education emphasize relevance for the student and the society, content knowledge is still defined on the basis of disciplinary authenticity. We argue that in addition to the teaching methods and contexts also content knowledge needs to be redefined to reflect the changing goals of science education.

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The process of learning scientific knowledge from the dynamic systems viewpoint is studied in terms probabilistic learning model (PLM), where learning accrues from foraging in the epistemic landscape. The PLM leads to the formation of attractor‐type regions of preferred models in an epistemic landscape. The attractor‐type states correspond to robust learning outcomes which are more probable than others. These can be assigned either to the high confidence in model selection or to the dynamic evolution of a learner's proficiency, which depends on the learning history. The results suggest that robust learning states are essentially context dependent, and that learning is a continuous development between these context dependent states. © 2016 Wiley Periodicals, Inc. Complexity 21: 259–267, 2016

Model-based learning (MBL) has an established position within science education. It has been found to enhance conceptual understanding and provide a way for engaging students in authentic scientific activity. Despite ample research, few studies have examined the cognitive processes regarding learning scientific concepts within MBL. On the other hand, recent research within cognitive science has examined the learning of so-called relational categories. Relational categories are categories whose membership is determined on the basis of the common relational structure. In this theoretical paper, I argue that viewing models as relational categories provides a well-motivated cognitive basis for MBL. I discuss the different roles of models and modeling within MBL (using ready-made models, constructive modeling, and generative modeling) and discern the related cognitive aspects brought forward by the reinterpretation of models as relational categories. I will argue that relational knowledge is vital in learning novel models and in the transfer of learning. Moreover, relational knowledge underlies the coherent, hierarchical knowledge of experts. Lastly, I will examine how the format of external representations may affect the learning of models and the relevant relations. The nature of the learning mechanisms underlying students' mental representations of models is an interesting open question to be examined. Furthermore, the ways in which the expert-like knowledge develops and how to best support it is in need of more research. The discussion and conceptualization of models as relational categories allows discerning students' mental representations of models in terms of evolving relational structures in greater detail than previously done.

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