6447408
Tuning of Search of the Problem Space for Geometry Proofs
In planning a proof, a student searches through a space of inferences leading forward from the givens of the problem and backward from the to-be-proven statement. One dimension of growth of expertise is that students become more tuned in the search of this problem space. This can be shown to result from the application of various learning operators to production embodiments of the inference rules. Rules are evaluated after the solution of a problem according to whether they led to or led away from the solution. Rules that contributed to a solution are strengthened and an attempt is made to formulate general versions of these rules that will apply in other situations. Rules that led away from the solution are weakened and a discrimination process is evoked to try to add features to the rules that will try to restrict them to the correct circumstances of application. Composition is a learning process that collapses successful sequences of rule operations into single macro-rule productions. There is also a process that converts the backward reasoning rules formed by composition into forward reasoning rules. The effect of these learning processes is to put into production conditions tests for problem features that are heunstically predictive of the rule's success.
195901903
Integrating analogical mapping and general problem solving: the path-mapping theory
This article describes the path-mapping theory of how humans integrate analogical mapping and general problem solving. The theory posits that humans represent analogs with declarative roles, map analogs by lower-level retrieval of analogous role paths, and coordinate mappings with higher-level organizational knowledge. Implemented in the ACT-R cognitive architecture, the path-mapping theory enables models of analogical mapping behavior to incorporate and interface with other problem-solving knowledge. Path-mapping models thus can include task-specific skills such as encoding analogs or generating responses, and can make behavioral predictions at the level of real-world metrics such as latency or correctness. We show that the path-mapping theory can successfully account for the major phenomena addressed by previous theories of analogy. We also describe a path-mapping model that can account for subjects' incremental eye-movement and typing behavior in a story-mapping task. We discuss extensions and implications of this work to other areas of analogy and problem-solving research.
1998598
Dynamic Student Modelling in an Intelligent Tutor for LISP Programming
We describe an intelligent tutor for LISP programming. This tutor achieves a set of pedagogical objectives derived from Anderson's (1983) learning theory provide instruction in the context of problem-solving, have the student generate as much of each solution as possible, provide immediate feedback on errors, and represent the goal structure of the problem-solving. The tutorial interface facilitates communication and prevents distracting low-level errors Field tests of the tutor in college classes demonstrate that it is more effective than conventional classroom instruction.
12617679
Human Symbol Manipulation Within an Integrated Cognitive Architecture
This article describes the Adaptive Control of Thought-Rational (ACT-R) cognitive architecture (Anderson et al., 2004; Anderson & Lebiere, 1998) and its detailed application to the learning of algebraic symbol manipulation. The theory is applied to modeling the data from a study by Qin, Anderson, Silk, Stenger, & Carter (2004) in which children learn to solve linear equations and perfect their skills over a 6-day period. Functional MRI data show that: (a) a motor region tracks the output of equation solutions, (b) a prefrontal region tracks the retrieval of declarative information, (c) a parietal region tracks the transformation of mental representations of the equation, (d) an anterior cingulate region tracks the setting of goal information to control the information flow, and (e) a caudate region tracks the firing of productions in the ACT-R model. The article concludes with an architectural comparison of the competence children display in this task and the competence that monkeys have shown in tasks that require manipulations of sequences of elements.
8794180
The generality/specificity of expertise in scientific reasoning
Previous research on scientific reasoning has shown that it involves a diverse set of skills. Yet, little is known about generality or domain specificity of those skills, an important issue in theories of expertise and in attempts to automate scientific reasoning skills. We present a study designed to test what kinds of skills psychologists actually use in designing and interpreting experiments and contrast expertise within a particular research area with general expertise at designing and interpreting experiments. The results suggest that psychologists use many domain-general skills in their experimentation and that bright and motivated Carnegie Mellon undergraduates are missing many of these skills. We believe that these results have important implications for psychological and artificial intelligence models of expertise, as well as educational implications in the domain of science instruction.
17702751
The Geometry Tutor
The tutor for doing proofs in high school geometry consists of a cot of ideal and buggy rules (IRR), a tutor, and an interface. The IBR is responsible for ehiuertly computing matcher, to all the correct and incorrect rules The interface is responsible for interacting with the student and graphically representing the proof. The tutor is responsible for directing the IBR and interface to achieve a current tutorial strategy. The strategy wo employ involves tracing the student's behavior in terms of what rules in the IBR it instantiates, correcting the student when behavior deviates below a minimum threshold, and helping the student over hurdles. While incomplete, current evidence indicates the geometry tutor is guite effective. 
 
The Advanced Computer Tutoring Project has been working on the development of intelligent computerhased tutors for mathematics and science subjects in the range of senior high-school to junior college. This paper describes the general framework that we have developed and its instantiation in the case of a tutor tor generating proofs in geometry. First, we will describe the general philosophy of out tutoring efforts. Second, we will describe the basic structure of the geometry tutor that we have built. Third, we will describe the ongoing efforts to evaluate the tutor.
7659346
Skill Acquisition and the LISP Tutor
An analysis of student learning with the LISP tutor indicates that while LISP is complex, learning it is simple. The key to factoring out the complexity of LISP is to monitor the learning of the 500 productions in the LISP tutor which describe the programming skill. The learning of these productions follows the power-law learning curve typical of skill acquisition. There is transfer from other programming experience to the extent that this programming experience involves the same productions. Subjects appear to differ only on the general dimensions of how well they acquire the productions and how well they retain the productions. Instructional manipulations such as remediation, content of feedback, and timing of feedback are effective to the extent they give students more practice programming, and explain to students why correct solutions work.
41957373
'Model': a POPLOG package to support model-based vision
Abstract A software package to support model-based vision in the poplog environment is described. The package contains a constructive solid geometry instantiated in an extended-depth buffer to yield a representation of the spatial properties of the viewed scene. The geometry constrains its geometrical transformations to make visual search more efficient.
529922
Mace: language support for building distributed systems
Building distributed systems is particularly difficult because of the asynchronous, heterogeneous, and failure-prone environment where these systemsmust run. Tools for building distributed systems must strike a compromise between reducing programmer effort and increasing system efficiency. We present Mace, a C++ language extension and source-to-source compiler that translates a concise but expressive distributed system specification into a C++ implementation. Mace overcomes the limitations of low-level languages by providing a unified framework for networking and event handling, and the limitations of high-level languages by allowing programmers to write program components in a controlled and structured manner in C++. By imposing structure and restrictions on how applications can be written, Mace supports debugging at a higher level, including support for efficient model checking and causal-path debugging. Because Mace programs compile to C++, programmers can use existing C++ tools, including optimizers, profilers, and debuggers to analyze their systems.
17909219
Robot Free Will
We introduce the perspex machine which unifies projective geometry and Turing computation and results in a supra-Turing machine. We show two ways in which the perspex machine unifies symbolic and non-symbolic AI. Firstly, we describe concrete geometrical models that map perspexes onto neural networks, some of which perform only symbolic operations. Secondly, we describe an abstract continuum of perspex logics that includes both symbolic logics and a new class of continuous logics. We argue that an axiom in symbolic logic can be the conclusion of a perspex theorem. That is, the atoms of symbolic logic can be the conclusions of sub-atomic theorems. We argue that perspex space can be mapped onto the spacetime of the universe we inhabit. This allows us to discuss how a robot might be conscious, feel, and have free will in a deterministic, or semi-deterministic, universe. We ground the reality of our universe in existence. On a theistic point, we argue that preordination and free will are compatible. On a theological point, we argue that it is not heretical for us to give robots free will. Finally, we give a pragmatic warning as to the double-edged risks of creating robots that do, or alternatively do not, have free will.
6600453
The nature of indexing: how humans and machines analyze messages and texts for retrieval - Part I: Research, and the nature of human indexing
Abstract Does human intellectual indexing have a continuing role to play in the face of increasingly sophisticated automatic indexing techniques? In this two-part essay, a computer scientist and long-time TREC participant (Perez-Carballo) and a practitioner and teacher of human cataloging and indexing (Anderson) pursue this question by reviewing the opinions and research of leading experts on both sides of this divide. We conclude that human analysis should be used on a much more selective basis, and we offer suggestions on how these two types of indexing might be allocated to best advantage. Part one of the essay critiques the comparative research, then explores the nature of human analysis of messages or texts and efforts to formulate rules to make human practice more rigorous and predictable. We find that research comparing human vs automatic approaches has done little to change strongly held beliefs, in large part because many associated variables have not been isolated or controlled. Part II focuses on current methods in automatic indexing, its gradual adoption by major indexing and abstracting services, and ways for allocating human and machine approaches. Overall, we conclude that both approaches to indexing have been found to be effective by researchers and searchers, each with particular advantages and disadvantages. However automatic indexing has the over-arching advantage of decreasing cost, as human indexing becomes ever more expensive.