A hierarchy of skills in the measurement topic of area was validated on three-hundred and six students between grades six and nine. The hierarchy of skills was based on the rules underlying the individual skills. When a rule for one skill was considered a component of a rule for another skill, then the two skills were hypothesized to be hierarchically ordered. In addition, if a simple rule for a particular skill was replaced by a more complex rule, resulting in a different skill, then these two skills were hypothesized to be hierarchically ordered. The physical representations of the area tasks, as well as the shapes of the area figures were hypothesized as influencing the skill orderings. The use of Latent-class analysis revealed that seven of the nine skill orderings analyzed were hierarchically ordered based on difficulty level and not prerequisiteness. The other two skill orderings indicated equaprobable partial mastery classes. In addition to Latent-class analysis, the incorrect processes used by the students were coded and tabulated. The results revealed that (1) nonstandard shaped area problems were the most difficult for this sample, (2) the most frequent process associated with incorrect responses involved the addition of numbers shown in area problem figures, (3) the second most frequent process involved some form of multiplication, without regard to the area concepts inherent in the task, and (4) students beyond the sixth grade made more errors involving multiplication processes than errors involving addition processes. The study revealed that the use of rules, representations and shapes as the basis for a hierarchy does appear to have merit. In addition, process analysis revealed that students respond in a large variety of ways when they do not know the correct process for area tasks.

Solving proportion problems in schools is a very difficult task for most children. Too often children are taught to use techniques for solving fractions when working with ratio and proportion problems. Although these techniques may prove useful for obtaining a solution to a proportion problem, they do not provide rich learning opportunities for students to construct proportional relationships. Individual interviews, problem solving episodes, and personal journals were the primary tools used in collecting data for this study. The problem solving episodes became the key components in observing and interacting with the participants as they solved ratio and proportion problems. The researcher found that individuals must have many elaborated constructions to solve proportion tasks. Without these elaborated constructions the individual is unable to effectively coordinate the information needed to solve proportion tasks. That is, the individual is unable to reason proportionally. Another outcome of this study was the importance of finding meaningful and doable proportion tasks for the informants to complete. Unexpected outcomes of the study included the effect of engaging in problem solving on the identity of the child and the role of language in giving meaning to the tasks. / Typescript. / "Summer Semester, 1992." / "Submitted to the Department of Curriculum and Instruction in partial fulfillment of the requirements for the degree of Doctor of Philosophy." / Advisor: Grayson H. Wheatley, Professor Directing Dissertation. / Includes bibliographical references.

Thesis (Ph.D.)--University of Delaware, 2007. / Principal faculty advisor: James Hiebert, School of Education. Includes bibliographical references.

Thesis (M.A.)--Brigham Young University. Dept of Mathematics Education, 2006. / Includes bibliographical references (p. 65-66).

Thesis (EdD.)--Open University.

Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 141-169). Available also in a digital version from Dissertation Abstracts.

The purpose of this study was to develop, implement, and evaluate a comprehensive interpersonal problem solving training program with four and five year old children. The goal of the program was to teach children the necessary skills to successfully resolve problems with their peers. The interpersonal problem solving training program consisted of the following core components: language, perception, problem identification, empathy, alternative generation, consequential thinking, and integration. The sample consisted of 46 children, 23 children in the experimental group and 23 children in the control group. Both experimental and control group subjects met for ten weeks (15-20 minutes a day) with trained graduate students. Control group subjects participated in reading story sessions while experimental group subjects participated in the interpersonal problem solving training sessions. Experimental and control group subjects were assessed at pretest and posttest on two measures. The BPIPS (a behavioral assessment of interpersonal problem solving ability) and the BOS (a behavioral observation scale). Analysis of variance of gain scores demonstrated significant differences between experimental group subjects and control group subjects on: (a) ability to generate solutions in interpersonal problem solving situations and (b) frequency of positive verbal and nonverbal interaction with peers. Analysis of variance of gain scores indicated no significant differences between experimental and control groups on: (a) the frequency of positive interactions with adults or (b) the frequency of negative interactions with either peers or adults. Discussion focused on the measured and observed results from training in the interpersonal problem solving program, possible explanations for insignificant differences relative to adult interactions, and program generalizability.

No description available.

This study examines the effects of maternal teaching style on the developing problem-solving abilities of deaf and hearing preschool children. Mothers and children from three matched groups, hearing mother-deaf child, hearing mother-hearing child, and deaf mother-deaf child, were videotaped while the mother taught the child to construct a small pyramid from 21 interlocking blocks and again when the child attempted the task independently. The tapes were coded and analyzed to examine maternal instructional style and subsequent independent child performance. The mothers in the deaf mother-deaf child and hearing mother-hearing child dyads used appropriate scaffolding behavior significantly more often than the other mothers; their children were significantly more adept and independent problem-solvers than the deaf children of hearing mothers. The more contingent the mother's instructions, the more independent and successful child. Scaffolding is discussed in terms of its benefits for instructing deaf children.

This dissertation describes the personal problem-solving language used by grade five students as they solve mathematical problems. Student classroom interactions were audio-taped and filmed during the course of the 199711998 school year. Ethnographic methods and a qualitative research approach were used for gathering, analyzing and interpreting the data. The questions that guided the study were: (1) how children solve problems and (2) what tools and symbols systems do they use. The purpose was to understand the problem-solving process better. The underlying assumptions were that: (1) most students can generate their own strategies and problem-solving theories; (2) many students can solve complex mathematical problems. The findings revealed that students generate problem-solving strategies and symbol systems that resemble the tools that they chose to use and their individual learning styles. Most students needed to talk about their proceedings and often used a personalized language form and nomenclatures that were uniquely creative as place holders for the more exact terminology, which replaced the invented language. The data also captured highly creative moments when the students experienced a heightened sense of awareness and sensibility while they explored their problem spaces. It was also evident that there is a transfer from the child's personal problem-solving style, choice of tools and creative symbol systems into his unique representation of the problem's solution. This transfer supports Vygotskian notions that language mediates thought and that social interaction mediates language.