Exploring the episodic structure of algebra story problem solving

This paper analyzes the quantitative and situational structure of algebra story problems, uses these materials to propose an interpretive framework for written problem-solving protocols, and then presents an exploratory study of the episodic structure of algebra story problem solving in a sizable group of mathematically competent subjects. Analyses of written protocols compare the strategic, tactical, and conceptual content of solution attampts, looking within these attempts at the interplay between problem comprehension and solution. Comprehension and solution of algebra story problems are complimentary activities, giving rise to a succession of problem solving episodes. While direct algebraic problem solving is sometimes effective, results suggest that the algebraic formalism may be of little help in comprehending the quantitative constraints posed in a problem text. Instead, competent problem solvers often reason within the situational context presented by a story problem, using various forms of "model-based reasoning" to identify, pursue, and verify quantitative constraints required for solution. The paper concludes by discussing the implications of these findings for acquiring mathematical concepts (e.g., related linear functions) and for supporting their acquisition through instruction

Exploring the episodic structure of algebra story problem solving

This paper analyzes the quantitative and situational structure of algebra story problems, uses these materials to propose an interpretive framework for written problem-solving protocols, and then presents an exploratory study of the episodic structure of algebra story problem solving in a sizable group of mathematically competent subjects. Analyses of written protocols compare the strategic, tactical, and conceptual content of solution attempts, looking within these attempts at the interplay between problem comprehension and solution. Comprehension and solution of algebra story problems are complimentary activities, giving rise to a succession of problem solving episodes. While direct algebraic problem solving is sometimes effective, results suggest that the algebraic formalism may be of little help in comprehending the quantitative constraints posed in a problem text. Instead, competent problem solvers often reason within the situational context presented by a story problem, using various forms of "model-based reasoning" to identify, pursue, and verify quantitative constraints required for solution. The paper concludes by discussing the implications of these findings for acquiring mathematical concepts (e.g., related linear functions) and for supporting their acquisition through instruction

Situational reasoning for road driving in an urban environment

Robot navigation in urban environments requires situational reasoning. Given the complexity of the environment and the behavior specified by traffic rules, it is necessary to recognize the current situation to impose the correct traffic rules. In an attempt to manage the complexity of the situational reasoning subsystem, this paper describes a finite state machine model to govern the situational reasoning process. The logic state machine and its interaction with the planning system are discussed. The approach was implemented on Alice, Team Caltech’s entry into the 2007 DARPA Urban Challenge. Results from the qualifying rounds are discussed. The approach is validated and the shortcomings of the implementation are identified

Philosophical Dialogue and Military Decision Making

Abstract: The military establishment plays an important role in society, not only because it is pivotal in securing the state from external and internal threats but also because the conduct of soldiers affect the fortunes of the state both fiscally and morally. Early in their career, soldiers are trained to be irreproachable in their loyalty, unquestioning in their obedience and unthinking in their pursuit of military objective. This, however changes as they move up into command positions and are required to decide on objectives as well as give orders for others to obey. For many officers, this is usually a difficult transition to make even though Staff School training is supposed to enable them to make this transition. This paper is based on an attempt to introduce philosophical dialogue to student officers of a military academy to help them make this difficult transition. It discusses the use of philosophical dialogue in facilitating officers’ understanding of important issues in the military, including military decision making. It highlights the procedure, difficulties and dangers of facilitating philosophical dialogue between soldiers especially as it relates to the corporate unity and command structure of the military. The paper also reflects on the efficacy and desirability of involving soldiers in a dialogue process. Keywords: Decision making, Military training, MDMP (Military Decision Making Process), Philosophical Dialogue, Resumen: La institución militar y juega un papel importante en la sociedad, no sólo porque es una base crucial para la seguridad del estado frente a amenazas internas y externas sino porque la conducta de los soldados afecta al destino del estado tan física como moralmente. Al comienzo de sus carreras, los soldados son entrenados en el desarrollo de una lealtad indubitable, evitando el cuestionamiento y la crítica para incentivar el desarrollo de los objetivos militares. Esta situación cambia cuando asciende a posiciones superiores, donde se requiere que decidan sobre la consecución de ciertos objetivos y que den órdenes a otros. Para muchos oficiales, esto supone una difícil transición a pesar de que la escuela de oficiales se supone que los capacita para realizar esta transición. Este artículo pretende explicar cómo introducir el diálogo filosófico a los estudiantes que se preparan para ser oficiales en la academia militar, actividad que les ayudará a desenvolver esta complicada transición. El trabajo discute el uso del diálogo filosófico para facilitar a los oficiales la comprensión de los asuntos militares importantes, lo cual abarca la toma de decisión militar. Subrayará, el procedimiento, las dificultades y los peligros de facilitar un diálogo filosófico entre los soldados, particularmente cuando se dirige a la unidad militar y a la estructura de órdenes delejército. Además, esta investigación reflexiona sobre la eficacia y deseabilidad de incorporar a los soldados en un proceso dialógico. Palabras clave: Toma de decisión, entrenamiento militar, Proceso de toma de decisión militar (PTDM), diálogo filosófico

Learning-assisted Theorem Proving with Millions of Lemmas

Large formal mathematical libraries consist of millions of atomic inference steps that give rise to a corresponding number of proved statements (lemmas). Analogously to the informal mathematical practice, only a tiny fraction of such statements is named and re-used in later proofs by formal mathematicians. In this work, we suggest and implement criteria defining the estimated usefulness of the HOL Light lemmas for proving further theorems. We use these criteria to mine the large inference graph of the lemmas in the HOL Light and Flyspeck libraries, adding up to millions of the best lemmas to the pool of statements that can be re-used in later proofs. We show that in combination with learning-based relevance filtering, such methods significantly strengthen automated theorem proving of new conjectures over large formal mathematical libraries such as Flyspeck.Comment: journal version of arXiv:1310.2797 (which was submitted to LPAR conference

Decision Taking for Selling Thread Startup

Decision Taking is discussed in the context of the role it may play for a selling agent in a search market, in particular for agents involved in the sale of valuable and relatively unique items, such as a dwelling, a second hand car, or a second hand recreational vessel. Detailed connections are made between the architecture of decision making processes and a sample of software technology based concepts including instruction sequences, multi-threading, and thread algebra. Ample attention is paid to the initialization or startup of a thread dedicated to achieving a given objective, and to corresponding decision taking. As an application, the selling of an item is taken as an objective to be achieved by running a thread that was designed for that purpose

STOP-IT: strategic, tactical, operational protection of water infrastructure against cyberphysical threats

Water supply and sanitation infrastructures are essential for our welfare, but vulnerable to several attack types facilitated by the ever-changing landscapes of the digital world. A cyber-attack on critical infrastructures could for example evolve along these threat vectors: chemical/biological contamination, physical or communications disruption between the network and the supervisory SCADA. Although conceptual and technological solutions to security and resilience are available, further work is required to bring them together in a risk management framework, strengthen the capacities of water utilities to systematically protect their systems, determine gaps in security technologies and improve risk management approaches. In particular, robust adaptable/flexible solutions for prevention, detection and mitigation of consequences in case of failure due to physical and cyber threats, their combination and cascading effects (from attacks to other critical infrastructure, i.e. energy) are still missing. There is (i) an urgent need to efficiently tackle cyber-physical security threats, (ii) an existing risk management gap in utilities’ practices and (iii) an un-tapped technology market potential for strategic, tactical and operational protection solutions for water infrastructure: how the H2020 STOP-IT project aims to bridge these gaps is presented in this paper.Postprint (published version