The role of strategy choice and working memory capacity in arithmetic acquisition in third grade primary school children

This review examines the question of what determines arithmetic ability in primary school children. It has been suggested that arithmetic ability is mediated by many factors such as developmental factors, exposure to arithmetic facts, selection and utilisation of various strategies when solving arithmetic problems, and individual differences in working memory capacity. Some theories suggest that factors such as the complexity of a problem affect the selection of strategies when solving simple arithmetic problems such as addition, whereas other theories propose that individual differences in working memory capacity play a prominent role in arithmetic ability. Research is discussed that provides support for both theories. Further research is proposed that would reconcile these apparent contradictions. This project was focused on how children come to understand basic arithmetic rules and acquire strategies and principles that help them to resolve arithmetic problems. Research conducted by Siegler (1987) indicated that children use multiple strategies such as counting and retrieval from memory. Other research also indicated that a larger working memory capacity is more likely to result in better academic achievement in areas such as language and mathematics (Gathercole, Pickering, Knight & Stegmann, 2004). In order to test previous results and expand knowledge of arithmetic skills this research investigated strategies used by 52 third grade children, their working memory capacity in the domains of sentences, digit span forward and object search, and their ability to solve multiplication problems. Analysis indicated the children who utilised retrieval strategy when adding were able to solve more multiplication problems than children who utilised other strategies; counting all and min strategy. The three domains of working memory were also positively correlated with the number of correctly solved addition and multiplication problems. The strategy selected when solving the most complex addition problem was a significant predictor of the ability to correctly solve multiplication problems. Implications for future research and the implementation of these findings aiming at enhancing teaching of arithmetic in primary school were discussed

A Stochastic Continuous Optimization Backend for MiniZinc with Applications to Geometrical Placement Problems

International audienceMiniZinc is a solver-independent constraint modeling language which is increasingly used in the constraint programming community. It can be used to compare different solvers which are currently based on either Constraint Programming, Boolean satisfiability, Mixed Integer Linear Programming, and recently Local Search. In this paper we present a stochastic continuous optimization backend for MiniZinc models over real numbers. More specifically, we describe the translation of FlatZinc models into objective functions over the reals, and their use as fitness functions for the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) solver. We illustrate this approach with the declarative modeling and solving of hard geometrical placement problems, motivated by packing applications in logistics involving mixed square-curved shapes and complex shapes defined by Bézier curves

Reformulation in planning

Reformulation of a problem is intended to make the problem more amenable to efficient solution. This is equally true in the special case of reformulating a planning problem. This paper considers various ways in which reformulation can be exploited in planning

Visualization of database structures for information retrieval

This paper describes the Book House system, which is designed to support children's information retrieval in libraries as part of their education. It is a shareware program available on CD‐ROM or floppy disks, and comprises functionality for database searching as well as for classifying and storing book information in the database. The system concept is based on an understanding of children's domain structures and their capabilities for categorization of information needs in connection with their activities in schools, in school libraries or in public libraries. These structures are visualized in the interface by using metaphors and multimedia technology. Through the use of text, images and animation, the Book House encourages children ‐ even at a very early age ‐ to learn by doing in an enjoyable way, which plays on their previous experiences with computer games. Both words and pictures can be used for searching; this makes the system suitable for all age groups. Even children who have not yet learned to read properly can, by selecting pictures, search for and find those books they would like to have read aloud. Thus, at the very beginning of their school life, they can learn to search for books on their own. For the library community, such a system will provide an extended service which will increase the number of children's own searches and also improve the relevance, quality and utilization of the book collections in the libraries. A market research report on the need for an annual indexing service for books in the Book House format is in preparation by the Danish Library Centre A/S

Building and Refining Abstract Planning Cases by Change of Representation Language

ion is one of the most promising approaches to improve the performance of problem solvers. In several domains abstraction by dropping sentences of a domain description -- as used in most hierarchical planners -- has proven useful. In this paper we present examples which illustrate significant drawbacks of abstraction by dropping sentences. To overcome these drawbacks, we propose a more general view of abstraction involving the change of representation language. We have developed a new abstraction methodology and a related sound and complete learning algorithm that allows the complete change of representation language of planning cases from concrete to abstract. However, to achieve a powerful change of the representation language, the abstract language itself as well as rules which describe admissible ways of abstracting states must be provided in the domain model. This new abstraction approach is the core of Paris (Plan Abstraction and Refinement in an Integrated System), a system in which abstract planning cases are automatically learned from given concrete cases. An empirical study in the domain of process planning in mechanical engineering shows significant advantages of the proposed reasoning from abstract cases over classical hierarchical planning.Comment: See http://www.jair.org/ for an online appendix and other files accompanying this articl

Progress in AI Planning Research and Applications

Planning has made significant progress since its inception in the 1970s, in terms both of the efficiency and sophistication of its algorithms and representations and its potential for application to real problems. In this paper we sketch the foundations of planning as a sub-field of Artificial Intelligence and the history of its development over the past three decades. Then some of the recent achievements within the field are discussed and provided some experimental data demonstrating the progress that has been made in the application of general planners to realistic and complex problems. The paper concludes by identifying some of the open issues that remain as important challenges for future research in planning