Spatial information in science is often expressed through representations such as diagrams and models. Learning the strengths and limitations of these representations and how to relate them are important aspects of developing scientific understanding, referred to as representational competence. Diagram translation is particularly challenging for students in organic chemistry, and although concrete models greatly help in solving diagram translation problems, most students do not use models spontaneously. In 2 experiments, we examined the effectiveness of instructional interventions for teaching diagram translation using models. In Experiment 1. students drew diagrams and checked their accuracy by attempting to match concrete models to their solutions (model-based feedback). The instruction helped students in the experimental group to identify their mistakes, understand the usefulness of concrete models, and led to large improvements in performance, compared with a control group. To examine whether feedback, the opportunity to match models, or both was the critical aspect of the intervention, in Experiment 2, 1 group was provided only verbal feedback (by a tutor) and another group matched diagrams and concrete models, but not in the context of receiving an evaluation of their pretest performance. Feedback alone did not improve performance relative to a control group, but the oppor tunity to match models and diagrams improved performance relative to control. The results indicate that using models as feedback is an effective way of training representational competence in the domain of organic chemistry and more generally in science, technology, engineering, and mathematics disciplines.Spatial information, such as shape, size, structure, and motion, is particularly important in the natural sciences, and certain branches of science are devoted to studying spatial properties. For example, anatomy is the study of the structure of living things, geology is the science of the structure of the earth, and stereo chemistry is the study of the structure of compounds. Understand ing spatial information is particularly challenging when the rele vant structures are not directly observable, for example, because they occur at a scale of space that is not visible (e.g., molecules) or are internal to some three-dimensional (3-D) structure that we typically only see from the outside (e.g., internal anatomy). In these cases, spatial information is represented most directly through spatial representations such as diagrams, concrete and virtual models, and animations; it is also represented using nonspatial representations such as text, symbols, and formulae.Scientists are facile in using a range of different representations of spatial phenomena that vary in their dimensionality (e.g., twodimensional [2-D] vs. 3-D), abstraction (e.g., diagrams vs. equa tions), and spatial perspective (e.g., orthographic vs. isometric projections, cross-sections) to represent, reason, and communicate about different spatial phenomena (Ainsworth, 2006;Kozm...

Mastering the many different diagrammatic representations of molecules used in organic chemistry is challenging for students. This article summarizes recent research showing that manipulating 3-D molecular models can facilitate the understanding and use of these representations. Results indicate that students are more successful in translating between diagrams when they have models available, that using a model to enact the translation process in the world is predictive of learning, and that using models as feedback (to check the accuracy of diagram translation) is particularly effective. Model-based feedback is superior to verbal feedback alone, models scaffold learning rather than act as a crutch, learning with model-based instruction is resilient over a delay of several days, and learning with models transfers to performance when models are no longer available. Finally, virtual models are equivalent to hand-held models in promoting learning in the studied contexts.

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We make a case for using gestures and actions to understand and convey spatial and dynamic properties of systems. Problems in learning elementary astronomy are analysed in the context of demands of spatial thinking, in a system which is not amenable to direct perception, namely, the sun-earth-moon (SEM) system. We describe a pedagogy which uses gestures (most often in combination with concrete models and diagrams) to facilitate the visualisation and simulation required in elementary astronomy. These gestures are presented in terms of their purpose in pedagogy: to internalise a natural phenomenon, or an astronomical model, or general properties of space. In terms of design these pedagogical gestures mediate between concrete models of the SEM system and related spatial configurations on the one hand, and their corresponding abstract diagrammatic representations on the other: called here the modelgesture-diagram pedagogical link. Next we present some video data on students' gestures observed during collaborative problem-solving which took place in the course of our pedagogic intervention. Implications of these results are drawn for embodiment and multimodality of thought.