Computational learning theory studies the design and analysis of learning algorithms, and it is integral to the foundation of machine learning. In the modern era, classical computational learning theory is growingly unable to catch up with new practical demands. In particular, problems arise in the following aspects: i). "scalability":…

The past thirty years have shown a rise in models of language acquisition in which the state of the learner is characterized as a probability distribution over a set of non-stochastic grammars. In recent years, increasingly powerful models have been constructed as earlier models have failed to generalize well to increasingly complex and realistic…

We report on an innovative design of algorithmic analysis that supports automatic online assessment of students' exploration of geometry propositions in a dynamic geometry environment. We hypothesized that difficulties with and misuse of terms or logic in conjectures are rooted in the early exploration stages of inquiry. We developed a generic…

This research revealed promising results by merging old principles to new approaches in visual design education. Initial empirical analysis of participants who tested the "mDes" application applying four of the principles of design in comparison to conventional methodologies showed the most significant results of retention for the…

Computer task automation is part of the natural progression of encoding information. This thesis considers the automation process to be a question of whether it is possible to automatically learn the encoding based on the behavior of the system to be described. A variety of representation languages are considered, as are means for the learner to…

The purpose of this paper is to distinguish several different ways in which phonemic information might be employed in spelling, to examine some empirical data on the consequences of using these different information sources, to formulate hypotheses about the underlying processes involved, and to suggest possible implications for the learning and…

A new heuristic factorization scheme uses learning to improve the efficiency of determining the symbolic factorization of multivariable polynomials with interger coefficients and an arbitrary number of variables and terms. The factorization scheme makes extensive use of artificial intelligence techniques (e.g., model-building, learning, and…

Demonstrates that an elementary understanding of computer programing and the development and illustration of the structure of computer program analysis will be valuable assets in the understanding and teaching of mathematics and may be used as modeling devices to simulate the stages of learning. (Author)

This paper is a theoretical discussion of several functions of knowledge systems based on the idea of partial matching, that is, comparison of two or more descriptions by identification of their similarities. Several knowledge system functions are described in terms of partial or best matchings including analogical reasoning, inductive inference,…

The hypothesis investigated is that understanding of the long division algorithm requires a higher cognitive level than understanding of fundamental division concepts. Sixth-grade children were tested on performance and understanding of a given algorithm and concepts of division. (MP)

A process for helping students in the elementary grades develop their own algorithms for subtraction with carrying is described. Pupils choose their own times and ways to move from manipulative materials to written notation. (MP)

The time at which component skills are taught is studied to see whether it is a significant instructional variable. This research involved the instruction of a multiplication algorithm to 15 below-average first graders. (MP)

This thesis addresses problems from two areas of theoretical computer science. The first area is that of computational learning theory, which is the study of the phenomenon of concept learning using formal mathematical models. The goal of computational learning theory is to investigate learning in a rigorous manner through the use of techniques…