The study challenges current literature, which views the notion of problem-finding as the initial identification of a problem to be solved. The concept of problem-finding in this study is that problem-finding continues throughout the problem-solving process and is not distinct from it. This thesis aims to develop a better understanding of problem-finding by examining high school students using problem-finding to solve industrial design problems. The study seeks to find out what types of problem-finding exist and what roles they play in solving design problems. To explore problem-finding, this study uses a Think Aloud methodology to examine the thinking of three high school industrial design students and one high school industrial design teacher solving an authentic industrial design problem. Protocol data was gathered from the subjects and then transcribed, segmented and analysed in three ways, each of which became progressively more specific: Firstly, a macroscopic examination which identified problem-finding episodes occurring throughout the design process; secondly, a microscopic examination which identified four categories of problem-finding; and lastly, a microscopic examination which looked at the role played by the different problem-finding categories in solving design problems. The findings of this study are fourfold. Firstly, problem-finding was found to be used throughout the entire design process. Secondly, there were four categories of problemfinding. Thirdly, each category played an important role predominantly through interaction with other categories. Lastly, the more experienced a person was, the more able they were to use problem-finding effectively to solve design problems. Many current practices use trial and error methods to solve design problems. The importance of this study is that through a better understanding of problem-finding, designers may be able to use metacognitive strategies more efficiently in the process. Similarly, in educational practice, high school design students may be able to learn to think about the methods they use to solve design problems, and this may result in more creative designs.

Thesis (M.S.)--Brigham Young University. Dept. of Recreation Management and Youth Leadership, 2005. / Includes bibliographical references (p. 80-90).

Recently there is a lot of interest in the study of Sturm-Liouville problems on graphs, called quantum graphs. However the study on cyclic quantum graphs are scarce. In this thesis, we shall rst consider a characteristic function approach to the spectral analysis for the Schrodinger operator H acting on graphene-like graphs|in nite periodic hexagonal graphs with 3 distinct adjacent edges and 3 distinct potentials de ned on them. We apply the Floquet-Bloch theory to derive a Floquet equation with parameters theta_1, theta_2, whose roots de ne all the spectral values of H. Then we show that the spectrum of this operator is continuous. Our results generalize those of Kuchment-Post and Korotyaev-Lobanov. Our method is also simpler and more direct. Next we solve two Ambarzumyan problems, one for graphene and another for a cyclic graph with two vertices and 3 edges. Finally we solve an Hochstadt-Lieberman type inverse spectral problem for the same cyclic graph with two vertices and 3 edges. Keywords : quantum graphs, graphene, spectrum, Ambarzumyan problem, inverse spectral problem.

This study discusses third grade elementary school children¡¦s growth in mathematics ability through a mathematics curriculum integrated with problem posing. By applying action research method, this study tries to find out the participating teacher¡¦s progress in her teaching method. In particular, also to find out the problems that may arise from carrying out problem- posing instruction, the possible solutions to these problems, and the problem-posing activities that can be readily applied in classroom setting. The time this study takes, from identifying the problem to the point of retreating from the research setting, is about one year. During this year, the investigator used various methods to collect data: interviews, video recordings of class teaching, teachers¡¦ notes and recordings, and children mathematics diaries. He included research-related surveys and triangulation for data analysis. It is found that, the teacher has to do more than having a firm grasp of the teaching materials, but also to attend to the teaching processes, the timing of introducing the critical questions related to the main points, and the ability to conduct a discussion atmosphere that is conducive for the students¡¦ growth. Most important of all, the mindset has to be changed from a teacher-oriented one to a more student-oriented set. Compared to the original teaching without problem posing, it is found that students became more active in class discussions, and showed more logic in their solutions. They debated about mathematics problems instead of aimless quarreling. Moreover, the content of the problem-posing products become more creative and no longer mechanical. In addition, students¡¦ solution processes were no longer by imitation, but instead, showing expressions of elaborated thoughts. All these show that the integration of problem-posing instruction has increased students¡¦ interests and motivation in studying mathematics.

Research study on sixth grade problem-posing instruction: Case of addition, subtraction and number comparison on decimals Abstract The aim of this research project is to investigate the implementation of problem-posing instruction on decimals to one sixth-grade mathematics class. There are four research objectives: 1) design and implement problem-posing instruction on decimals; 2) discuss the status of children¡¦s performance in problem-solving; 3) analyze the type of problems posed by children; and, 4) display categories of misconceptions exhibited when children did problem posing. The stages for instructions were three: 1) children solved the problem given by the instructor; 2) children referred to given problem and posed a problem; and, 3) children solved their own problem. In this study, the type of problem posing chosen for instruction is ¡§similar problem¡¨, which is adapted from Tsubota, a Japan scholar. The researcher collected data by using: own constructed decimal problems question sheet, worksheet on problem solving, worksheet on problem posing, children¡¦s diaries and teachers¡¦ notes on instruction. There are four findings. First, the implementation of sixth grade problem-posing instruction on decimals is feasible. Second, 96.9% of students¡¦ problems are plausible and contain sufficient information for problem solvers. Most students could change the number and content of the question but few revised the structure of the question. There was also multiple development for those problems. Third, children¡¦s performance in posing/solving stage was better than that in problem-solving stage. Finally, the researcher reported that the teacher faced problems such as difficulty in control of time, establishing children¡¦s habit in reporting, and collecting misconceptions of children. Key word : problem solving; problem posing; addition, subtraction and number comparison on decimals

Cracked beam problem is an elliptic boundary value problem with singularity. It is often used as a testing model for numerical methods. We use numerical and symbolic boundary approximation methods and boundary collocation method to compute its extremely high accurate solution with global error $O(10^{-100})$. This solution then can be regarded as the exact solution. On the other hand, we vary the boundary conditions of this problem to obtain several related models. Their numerical solutions are compared to those of cracked beam and Motz problems, the prototypes of singularity problems. From the comparison we can conclude the advantage of each model and decide the best testing model for numerical methods.

The main purpose of this study is to understand the possible effects of the problem-posing teaching technique in an elementary school, grade-two class. With problem-posing teaching technique of twenty-four classes within 12 weeks, the experimenter first used the problem-posing texts to ask students to formulate mathematical problems. After reviewing the problems formulated by students, the necessary interviews were done. The statistical analysis is done on pre-tests and post-tests of mathematical-solving ability. Students¡¦ feedbacks about problem posing teaching technique are collected. There were four stages in this experiment: (1) oral presentation of problem-posing, (2) written presentation of problem-posing, (3) written presentation of problem-posing and problem-solving by the same person, (4) wiitten presentation of problem-posing by one and problem-solving by another. The experimenter explored the following themes during these four stages: (1) the process of problem-posing learning, (2) the characteristics and erroneous types of the students¡¦ opus, (3) the differences on the problem-posing abilities when students faced formulas, pictures and written contexts, (4) the behaviors of the high problem-posing ability group and the low problem-posing ability group, (5) the enhance of problem-solving abilities due to problem-posing teaching technique. From this study, the experimenter found that the majority of the students participated in this study interesting in this teaching technique, and students¡¦ gained confidence in posing and solving mathematical problems. Besides, the experimenter also found that: (1) the students¡¦ ability in posing and solving problems progressed gradually in speed and correctness, (2) the characteristics and erroneous types of the students¡¦ opus were diverse, which included relativeness of situations, students¡¦ interests, school lives, and daily lives, correctness of mathematical logic, ambiguity of language, (3) students were better to pose problems from pictures and written contexts than from formulas, but there was no difference between from pictures and from written contexts, (4) the high problem-posing ability group performs better in speed and correctness to solve problem than the low problem-posing ability group, (5) Comparing the controlled and non-controlled groups, problem-posing teaching technique seems to helpe students to enhance their problem-solving ability.

RENR 405 GIS Environmental Problem Solving is a course offered at Texas A

Thesis (Ph. D.)--University of Missouri-Columbia, 2001. / Typescript. Vita. Includes bibliographical references (leaves 129-136). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2001. / Typescript. Vita. Includes bibliographical references (leaves 249-259). Also available on the Internet.