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…

This document consists of three papers. The first, "A Parallel Model of (Sequential) Problem Solving," describes a parallel model designed to solve a class of relatively simple problems from elementary physics and discusses implications for models of problem-solving in general. It is shown that one of the most salient features of problem…

Statistical problems were used to test the hypothesis that calculators facilitate problem solution by saving time and increasing accuracy. Manual, basic machine and advance machine methods were used. (MP)

Investigated were the effects on computation performance of amount of prepractice and type of calculator, when students were told to work very fast vs very accurately. (MP)

Three calculation methods--handwork, or simple or advanced calculators--and two levels of difficulty--easy or hard--were used to investigate the effects on computational performance. (MP)

Solving statistical problems using a calculator with sophisticated features was compared to solving the same problems by hand. The calculator group was more accurate and took far less time. (MP)

The calculator is used to solve certain formidable equations, which arise naturally and which may be difficult or impossible to solve by standard methods, by a method of successive approximations. (MP)

Eighteen college students solved addition problems using the Hutchings Low Fatigue Addition Algorithm, which requires a written record of running sums, and the standard algorithm, which does not. Students using the Hutchings algorithm had significantly higher reaction times to a tone, indicating that the Hutchings method requires less cognitive…

Two games and one activity designed to be used with a hand-held calculator are presented. (MK)

Presents a problem of triangular tiles that involves counting and probability. Includes instructor guiding questions. (KHR)

Outlines some directions taken in the United States for mathematics instruction and offers insights for mathematics teaching from research with young children. (ASK)

Given three points in the plane, interest is in the locus of all points for which the sum of the distances to the given points is a prescribed constant. These curves turn out to be sixth degree polynominals in x and y , and thus are complicated. However, it turns out that often there is a point, within the triangle formed by the three given…

Given two circles C 1 and C 2 in a plane such that neither one of the two circles is contained in the other, there are either four common tangents when the circles do not intersect at all or the circles have three common tangents when they touch each other externally or only two common tangents when the circles intersect exactly at two points. The…

An integral, either definite or improper, cannot always be computed by elementary methods, such as reversed usage of differentiation formulae. Graphical properties, in particular symmetries, can be useful to compute the integral, via an auxiliary computation. We present graded examples, then prove a general result. (Contains 4 figures.)

The paper discusses the interaction between intuitive biases of probabilistic thinking and mathematical knowledge. It would appear that students may answer numerical problems correctly but falter on simple descriptive solutions. Students appear to relinquish formal knowledge for simpler heuristics when attempting to describe the outcome of an…