abstract: In the daily life of an individual problems of varying difficulty are encountered. Each problem may include a different number of constraints placed upon the problem solver. One type of problem commonly used in research are multiply-constrained problems, such as the compound remote associates. Since their development they have been related to creativity and insight. Moreover, research has been conducted to determine the cognitive abilities underlying problem solving abilities. We sought to fully evaluate the range of cognitive abilities (i.e., working memory, episodic and semantic memory, and fluid and crystallized intelligence) linked to multiply-constrained problem solving. Additionally, we sought to determine whether problem solving ability and strategies (analytical or insightful) were task specific or domain general through the use of novel problem solving tasks (TriBond and Location Bond). Results indicated that multiply-constrained problem solving abilities were domain general, solutions derived through insightful strategies were more often correct than analytical, and crystallized intelligence was the only cognitive ability that provided unique predictive value. / Dissertation/Thesis / Masters Thesis Psychology 2019

This thesis describes changes in the spatial thinking of Year 2 and Year 4 students who participated in a six-week long spatio-mathematical program. The main investigation, which contained quantitative and qualitative components, was designed to answer questions which were identified in a comprehensive review of pertinent literatures dealing with (a) young children's development of spatial concepts and skills, (b) how students solve problems and learn in different types of classrooms, and (c) the special roles of visual imagery, equipment, and classroom discourse in spatial problem solving. The quantitative investigation into the effects of a two-dimensional spatial program used a matched-group experimental design. Parallel forms of a specially developed spatio-mathematical group test were administered on three occasions—before, immediately after, and six to eight weeks after the spatial program. The test contained items requiring spatial thinking about two-dimensional space and other items requiring transfer to thinking about three-dimensional space. The results of the experimental group were compared with those of a ‘control’ group who were involved in number problem-solving activities. The investigation took into account gender and year at school. In addition, the effects of different classroom organisations on spatial thinking were investigated~one group worked mainly individually and the other group in small cooperative groups. The study found that improvements in scores on the delayed posttest of two-dimensional spatial thinking by students who were engaged in the spatial learning experiences were statistically significantly greater than those of the control group when pretest scores were used as covariates. Gender was the only variable to show an effect on the three-dimensional delayed posttest. The study also attempted to explain how improvements in, spatial thinking occurred. The qualitative component of the study involved students in different contexts. Students were video-taped as they worked, and much observational and interview data were obtained and analysed to develop categories which were described and inter-related in a model of children's responsiveness to spatial problem-solving experiences. The model and the details of children's thinking were related to literatures on visual imagery, selective attention, representation, and concept construction.

The purpose of this research is to use Schoenfeld¡¦s mathematics problem-solving model to analyze processes, strategies, and affective characteristics of children in a gifted primary program, and then, to propose concrete suggestions for gifted class and general class teachers. Participants were six third-grade gifted children who were great in articulation, and enrolled in one primary school in Kaohsiung. The investigator analyzed think-aloud protocols of them who solved four non-routine problems selected by several expert teachers. The findings of this study were three. First, all six gifted students' thought processes mostly conformed to Schoenfeld¡¦s problem-solving model, though with various differences by individuals, and by problems. One of them provided two correct answers, having no verification stage in all problems. And one only provided one correct answer, had less analysis, exploration, design, and verification stage in solving all problems. Second, children exhibited diversified and flexible strategies. They used representing, drawing figures, working backward, introducing auxiliary element, and attempting mistakes to solve four non-routine mathematical problems. Last, the affective characteristics of students were positive. They were patient and perseverant and showed personal mathematics curiosity, excitement, and confidence, which were given as creative characteristics by Sternberg, and as mathematical talent or characteristics by Krutetskii. The investigator concluded that not all gifted students possessed meta-cognition ability: including exploration, design, and verification. The gifted class teachers could use non-routine mathematics problems to discipline students' meta-cognitive ability, including exploration, design, and verification, and encourage them to generate more solving strategies by group discussion in class. Finally, the general class teachers could adopt problem-solving characteristics of gifted students as materials for gifted students and general students to learn together in class.

Teaching mathematics is now gaining more importance, as the new elementary mathematics school curriculum has been adapted to Turkish Educational System. One of the main goals of the curriculum reform is to increase elementary school students&rsquo / problem solving abilities in mathematics (Ko&ccedil / , ISiksal &amp / Bulut / 2007). In this study, the aim is to investigate the change in sixth grade students&rsquo / problem solving abilities, attitude towards problem solving and attitude toward mathematics after mathematics instruction based on Polya&rsquo / s problem solving steps. The sample of this study consisted of 53 sixth grade students from an elementary school in Istanbul. The participants consist of a class selected conveniently among all the sixth grade classes in the school. In these selected classes, mathematical problems are solved according to the Polya&rsquo / s problem solving steps by following different problem solution techniques during the semester.At the end of this study, the three main results were found: 1) Instruction based on Polya&rsquo / s step has significantly affected students&rsquo / problem solving abilities in a positive way, 2) students&rsquo / attitudes towards problem solving has changed in a positive way, 3) students&rsquo / attitudes towards mathematics is enhanced by the instruction based on Polya&rsquo / s problem solving steps.

The purpose of this study was to investigate the prospective elementary mathematics teachers&rsquo / use of strategies and their achievement levels in solving mathematical problems with respect to year level. The data were collected from 250 prospective elementary mathematics teachers enrolled in an elementary mathematics education program from a state university in Central Anatolian Region. Problem Solving Test (PST) was used to accomplish the purpose of the study. The data collection tool adapted by the researcher included nine open ended problems. In this study, item based in-depth analysis was employed to determine a variety of problem solving strategies used by prospective teachers.The frequencies and percentages of categories were gathered for each item and for each year level. The results of this study revealed that prospective elementary mathematics teachers&rsquo / problem solving achievement was moderately high. Prospective elementary mathematics teachers in each year level were able to use various problem solving strategies to a certain extent. More specifically, the results indicated that &lsquo / making a drawing&rsquo / and &lsquo / intelligent guessing and testing&rsquo / strategies were among the most prominent strategies frequently used by prospective teachers. Setting up an equation and using a formula was other strategies used by prospective teachers. On the other hand, finding a pattern strategy was the least frequent strategy used by prospective teachers.

Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 143-150). Available also in a digital version from Dissertation Abstracts.

Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 143-150). Available also in a digital version from Dissertation Abstracts.

Thesis (M. Sc.)--University of Hong Kong, 2002. / Includes bibliographical references (leaves 116-119).

published_or_final_version / Education / Master / Master of Education

Problem solving has been a core theme in education for several decades. Educators and policy makers agree on the importance of the role of problem solving skills for school and real life success. A primary purpose of this study was to investigate the influence of cognitive abilities on mathematical problem solving performance of students. The author investigated this relationship by separating performance in open-ended and closed situations. The second purpose of this study was to explore how these relationships were different or similar in boys and girls. No significant difference was found between girls and boys in cognitive abilities including general intelligence, general creativity, working memory, mathematical knowledge, reading ability, mathematical problem solving performance, verbal ability, quantitative ability, and spatial ability. After controlling for the influence of gender, the cognitive abilities explained 51.3% (ITBS) and 53.3% (CTBS) of the variance in MPSP in closed problems as a whole. Mathematical knowledge and general intelligence were found to be the only variables that contributed significant variance to MPSP in closed problems. Similarly, after controlling for the influence of gender, the cognitive abilities explained 51.3% (ITBS) and 46.3% (CTBS) of the variance in mathematical problem solving performance in open-ended problems. General creativity and verbal ability were found to be the only variables that contributed significant variance to MPSP in open problems. The author concluded that closed and open-ended problems require different cognitive abilities for reaching correct solutions. In addition, when combining all of these findings the author proposed that the relationship between cognitive abilities and problem solving performance may vary depending on the structure (type) and content of a problem. The author suggested that the content of problems that are used in instruments should be analyzed carefully before using them as a measure of problem solving performance.