A transfer advantage of learning diagrammatic representations of mathematics
نویسنده
چکیده
This study examined learning and transfer of a simple mathematical concept when learning a symbolic sentential format versus learning a diagrammatic format. Undergraduate college students learned an instantiation of a cyclic group and were then given a test of a novel isomorphic group of the same order followed by a test of a novel non-isomorphic group of a higher order. The results were that both the sentential and the diagrammatic formats led to successful learning and transfer to the novel isomorphic group. However, only learning from the diagrammatic representation produced successful transfer to the non-isomorphic group. These findings suggest that learning a diagrammatic representation of a mathematical concept can have transfer advantages over learning strictly sentential formats.
منابع مشابه
Image Classification via Sparse Representation and Subspace Alignment
Image representation is a crucial problem in image processing where there exist many low-level representations of image, i.e., SIFT, HOG and so on. But there is a missing link across low-level and high-level semantic representations. In fact, traditional machine learning approaches, e.g., non-negative matrix factorization, sparse representation and principle component analysis are employed to d...
متن کاملHierarchical Functional Concepts for Knowledge Transfer among Reinforcement Learning Agents
This article introduces the notions of functional space and concept as a way of knowledge representation and abstraction for Reinforcement Learning agents. These definitions are used as a tool of knowledge transfer among agents. The agents are assumed to be heterogeneous; they have different state spaces but share a same dynamic, reward and action space. In other words, the agents are assumed t...
متن کاملAbstraction , Visualisation and Graphical Proof
In this paper we investigate the process of learning and verifying graphical theorems through abstraction and visualisation. First, the notion of effectiveness of a representation is discussed from both a computational and a cognitive perspective; the nature of the relation between external representations and abstraction in these two views, and its implications for diagrammatic reasoning in AI...
متن کاملUse of the Shearlet Transform and Transfer Learning in Offline Handwritten Signature Verification and Recognition
Despite the growing growth of technology, handwritten signature has been selected as the first option between biometrics by users. In this paper, a new methodology for offline handwritten signature verification and recognition based on the Shearlet transform and transfer learning is proposed. Since, a large percentage of handwritten signatures are composed of curves and the performance of a sig...
متن کاملA Universal Investigation of $n$-representations of $n$-quivers
noindent We have two goals in this paper. First, we investigate and construct cofree coalgebras over $n$-representations of quivers, limits and colimits of $n$-representations of quivers, and limits and colimits of coalgebras in the monoidal categories of $n$-representations of quivers. Second, for any given quivers $mathit{Q}_1$,$mathit{Q}_2$,..., $mathit{Q}_n$, we construct a new quiver $math...
متن کامل