This research examines problem definition as the first step in a sequential problem solving process. Seventy-seven managers in four diverse organizations were studied to determine common characteristics of problem definers. Among the variables considered as differentiating problem definers from non-problem definers were cognitive style, personal need characteristics, preference for ideation, experience, level of management, and type and level of education. Six hypotheses were tested using the following instruments: the Problem Solving Inventory, the Myers-Briggs Type Indicator Schedule, the Preference for Ideation Scale, the Edwards Personal Preference Schedule, a Problem Definition Exercise, and a Personal Data Questionnaire. Among the managers studied, only twelve were found to be problem definers. Such small numbers severely limit the ability to generalize about problem definers. However, it is possible that problem definers are scarce in organizations. In terms of cognitive style, problem definers were primarily thinking types who preferred evaluation to ideation in dealing with problems, making judgmental decisions on the basis of collected facts. Problem definers were not predominant at lower levels of the organization. One-third of the problem definers held upper level management positions while another one-fourth were responsible for specialized activities within their organizations, overseeing special projects and individuals much like upper level managers. Sixty-eight of the problem definers had non-business educations with none having more than a bachelors degree. As knowledge and judgment on which to base evaluation expands, managers may become less adept at defining problems and more adept at selecting and implementing alternatives. Several tentative hypotheses can be tested in future research including: 1) determining whether problem definers are scarce in organizations, 2) determining whether problem definers are more prevalent in some types of organizations than others, 3) verifying unique cognitive and personal need characteristics, 4) determining whether non-managers rather than managers have problem defining skills.

This thesis investigates two problems that are discrete analogues of two harmonic analytic problems which lie in the heart of research in the field. More specifically, we consider discrete analogues of the maximal Kakeya operator conjecture and of the recently solved endpoint multilinear Kakeya problem, by effectively shrinking the tubes involved in these problems to lines, thus giving rise to the problems of counting joints and multijoints with multiplicities. In fact, we effectively show that, in R3, what we expect to hold due to the maximal Kakeya operator conjecture, as well as what we know in the continuous case due to the endpoint multilinear Kakeya theorem by Guth, still hold in the discrete case. In particular, let L be a collection of L lines in R3 and J the set of joints formed by L, that is, the set of points each of which lies in at least three non-coplanar lines of L. It is known that |J| = O(L3/2) ( first proved by Guth and Katz). For each joint x ∈ J, let the multiplicity N(x) of x be the number of triples of non-coplanar lines through x. We prove here that X x2J N(x)1=2 = O(L3=2); while we also extend this result to real algebraic curves in R3 of uniformly bounded degree, as well as to curves in R3 parametrized by real univariate polynomials of uniformly bounded degree. The multijoints problem is a variant of the joints problem, involving three finite collections of lines in R3; a multijoint formed by them is a point that lies in (at least) three non-coplanar lines, one from each collection. We finally present some results regarding the joints problem in different field settings and higher dimensions.

The purpose of this research was to investigate the differences of using problem decomposition and problem recomposition among dyads of engineering experts, dyads of engineering seniors, and dyads of engineering freshmen. Fifty participants took part in this study. Ten were engineering design experts, 20 were engineering seniors, and 20 were engineering freshmen. Participants worked in dyads to complete an engineering design challenge within an hour. The entire design process was video and audio recorded. After the design session, members participated in a group interview. This study used protocol analysis as the methodology. Video and audio data were transcribed, segmented, and coded. Two coding systems including the FBS ontology and “levels of the problem” were used in this study. A series of statistical techniques were used to analyze data. Interview data and participants’ design sketches also worked as supplemental data to help answer the research questions. By analyzing the quantitative and qualitative data, it was found that students used less problem decomposition and problem recomposoition than engineer experts in engineering design. This result implies that engineering education should place more importance on teaching problem decomposition and problem recomposition. Students were found to spend less cognitive effort when considering the problem as a whole and interactions between subsystems than engineer experts. In addition, students were also found to spend more cognitive effort when considering details of subsystems. These results showed that students tended to use dept-first decomposition and experts tended to use breadth-first decomposition in engineering design. The use of Function (F), Behavior (B), and Structure (S) among engineering experts, engineering seniors, and engineering freshmen was compared on three levels. Level 1 represents designers consider the problem as an integral whole, Level 2 represents designers consider interactions between subsystems, and Level 3 represents designers consider details of subsystems. The results showed that students used more S on Level 1 and 3 but they used less F on Level 1 than engineering experts. The results imply that engineering curriculum should improve the teaching of problem definition in engineering design because students need to understand the problem before solving it.

The main purpose of this research is to explore the implementation of problem-posing teaching activities for fifth grade students in the elementary school. The teaching material is on mixed operations of addition, subtraction, multiplication and division. The method of posing problems is Tsubota¡¦s ¡§Classified Subject¡¨, adopted from Japan. The teaching of posing problems was divided into two phases; one is ¡§problem solving¡¨, the other is ¡§problem posing then solving¡¨. According to this method, students initially solve the problems that the teacher provided. Second, taking this subject as the foundation, students posed the problems by themselves and solved the problems as well. During this research, the researcher utilized a variety of ways to collect data, such as self-construction of instruments on four arithmetic operations, problem-solving worksheets, problem-posing worksheets, learning diaries, and reflective notes. The goals of this research are four: first, analyzing the categories of students¡¦ work and the contents of posing problems that student created; second, investigating into the performance of problem solving; third, probing students¡¦ opinions of problem-posing activities; four, the difficulties the teacher encountered. The results of this research were four. First, it showed that 98.5% of students given problems included sufficient data for solving. Students virtually were able to make feasible problems. Moreover, the majority of students were capable to, not only changing numerals of the problems, but also changing structures of the problems. The tendency of changing structure followed multiple aspects of developments. Second, students¡¦ performance on three steps operations problem solving was low; the performances of problem solving and problem posing then solving were close; students¡¦ performance at problem posing then solving stage was higher; and, the major reason for mistakes was insufficient procedural knowledge. Third, students expressed a liking of problem posing, they thought that the materials were interesting, and showed promising study manner. Fourth, the teacher encountered problems such as time control, the development of in-class presentation culture, and, few students¡¦ lack of concentration while problem posing.

This paper extends respectively Gale-Shapley¡¦s model and Balinski-Sonmez¡¦s model to analyze the college admission problem and the student placement problem in the case of Taiwan. Given the assumption that time is not considered as a critical dimension of this issue, it is argued that Taiwan¡¦s admission mechanism is in accordance with the criterion of the student optimal stable mechanism with number restriction. As well, the outcome of Taiwan¡¦s admission mechanism exhibits features which are similar to that of the student optimal stable matching with number restriction. However, with regard to Taiwan¡¦s student placement mechanism, it is demonstrated that inefficiency may prevail.

Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 177-183). Available also in a digital version from Dissertation Abstracts.

Thesis (Ed. D.)--University of Missouri-Columbia, 2003. / Typescript. Vita. Includes bibliographical references (leaves 112-117). Also available on the Internet.

Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 189-195). Available also in a digital version from Dissertation Abstracts.

Thesis (Ed. D.)--University of Missouri-Columbia, 2003. / Typescript. Vita. Includes bibliographical references (leaves 112-117). Also available on the Internet.

Thesis (Ph. D.)--University of Washington, 2002. / Vita. Includes bibliographical references (leaves 130-146).