Source: Dissertation Abstracts International, Volume: 38-05, Section: A, page: 2626. / Thesis (Ph.D.)--The Florida State University, 1977.

Source: Dissertation Abstracts International, Volume: 38-05, Section: A, page: 2628. / Thesis (Ph.D.)--The Florida State University, 1977.

Understanding children's construction of rational number knowledge is important to both mathematics educators and researchers. The study presented investigated how children's concepts of units might influence their construction of rational numbers. The research questions addressed are: (1) What is the nature of a child's concepts of one as a composite whole, that is, divisible whole? (2) How does a child's experiences such as sharing influence this construction? / Four second graders participated in the study. Each child was interviewed individually four times. Additionally, the children were paired and each group participated in four problem solving sessions. / The analyses of the data showed that children's schemes to coordinate units play an important role in their understanding of fractional quantities. Four schemes to coordinate units were identified: one-as-one, one-as-many, many-as-one, and many-as-many. The one-as-one scheme is the most basic scheme involved in counting. When a child considers a unitary item as a multiplicity of another unit, he/she is considered to have the one-as-many scheme. The many-as-one scheme coordinates a multiplicity of a unit with another unit. Finally, the many-as-many scheme coordinates a multiplicity of a unit with a multiplicity of another unit. / These schemes form a basis for the levels of sophistication in a child's ability to coordinate units. In level one, the child has not constructed relationships between units, and his/her coordination scheme is limited to one-as-one. Level two is divided into two sub-levels. In sub-level one, the child's coordination schemes include one-as-many and/or many-as-one. In sub-level two, the child is able to coordinate many-as-many. / The many-as-many coordination scheme is conjectured to influence children's construction of multiplicative understanding, including proportional reasoning and rational numbers. Furthermore, the many-as-many scheme is conjectured to be a prerequisite for construction of abstract fractional units. / Source: Dissertation Abstracts International, Volume: 52-10, Section: A, page: 3550. / Major Professor: Grayson H. Wheatley. / Thesis (Ph.D.)--The Florida State University, 1991.

Source: Dissertation Abstracts International, Volume: 38-05, Section: A, page: 2633. / Thesis (Ph.D.)--The Florida State University, 1977.

Source: Dissertation Abstracts International, Volume: 39-11, Section: A, page: 6610. / Thesis (Ph.D.)--The Florida State University, 1978.

Source: Dissertation Abstracts International, Volume: 25-09, page: 5295. / Thesis (Ph.D.)--The Florida State University, 1964.

The purposes of the study were: (1) to develop a remedial instruction program based on an error type model; and (2) to compare its effectiveness with that of a general re-teaching model in remediating students who had not mastered a mathematics objective of the state assessment program. / Subjects were 44 fifth grade students enrolled in a local public elementary school. Subtraction of 4-digit numbers with one regrouping was the skill chosen for use in the study. From pretest results, students were assigned to one of three error categories: (a) algorithm errors, (b) reversal errors, and (c) fact errors. Random assignment of students within each category was made to either control group (general re-teaching model) or experimental group (error type model). / After one week of instruction, a posttest was administered. After a three-week maintenance period, a second posttest was administered. After four weeks of no further intervention, a third posttest was administered. Using the Wilcoxon Rank Sum Test, no significant difference between experimental group and control group mean scores was found on any of the three posttests. An informal analysis found the maintenance period to be only somewhat effective in maintaining the posttest score and extinguishing the diagnosed specific error. / A proposed model for remedial instruction which combined elements from both models used in the present study was offered by the researcher for further investigation. / Source: Dissertation Abstracts International, Volume: 46-06, Section: A, page: 1549. / Thesis (Ph.D.)--The Florida State University, 1985.

The purpose of the study was to determine whether a state of physiological arousal induced by an episode of moderate physical exercise serves to improve problem solving ability in high school Algebra II students. / Forty-eight students were pretested for 15 minutes with a test of non-routine problems. The students were then exposed to one of two treatments. The experimental treatment consisted of running in place for four minutes at an individual pace aimed at maintaining a heart rate of 130-150 beats per minute. The control treatment consisted of reviewing Algebra II concepts. After the treatment, the subjects were posttested with a different form of the problem solving test. / A posttest-pretest difference was computed for each subject and an analysis of covariance was performed on the differences with pretest scores as the covariate. The F value obtained was F = 7.85, which is significant at the (alpha) = .01 level. It was concluded that the exercise effect was significant. / Three related hypotheses were also investigated. / Source: Dissertation Abstracts International, Volume: 46-09, Section: A, page: 2605. / Thesis (Ph.D.)--The Florida State University, 1985.

Solving proportion problems in schools is a difficult task for most children. Often techniques for solving fractions are utilized in teaching ratio and proportion. These techniques may prove useful for obtaining a solution, they do not provide rich learning opportunities for students to construct proportional relationships. / Researchers have studied proportional reasoning and have described the developmental stage at which individuals are able to solve proportional reasoning tasks, as well as the individual solution strategies. While this body of research has provided information for examining children's proportional reasoning, these studies do not provide us with insights into the constructions the children make when they are trying to make sense of proportional tasks. / 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 component in observing and interacting with the participants. The tasks used during these problem solving episodes included scaling furniture, mixing paint, and a giant's footprint. A detailed description and analysis of the tasks is included. / 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. Another outcome of this study was the importance of finding meaningful and doable proportion tasks. 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. / Source: Dissertation Abstracts International, Volume: 53-07, Section: A, page: 2282. / Major Professor: Grayson H. Wheatley. / Thesis (Ph.D.)--The Florida State University, 1992.

Many authorities have recommended that estimation be a regular part of the elementary and secondary curriculum. Prior research has indicated that elementary school students can learn to estimate sums, differences, and products of whole numbers, but no research has been carried out for estimation of quotients. / This study investigated whether seventh graders can learn to estimate decimal quotients mentally, which of two quotient-estimation techniques might be more suitable, and what effect having learned to estimate might have upon calculation errors. / This research used two seventh-grade classes in one school as the population sample. Through computer selection, this school randomly selected its students so that they represented the entire Tallahassee, Florida community in race, sex, and ability. Each class was randomly divided into three equal groups: the first was randomly assigned to a quotient-estimation technique based directly upon a previously learned place-value long division strategy; the second to a more universally applicable technique; the third to a control (no-estimation) group. / Following instruction in the long-division strategy, a decimal-division achievement pretest (O(,1)) was administered to all students a week before the estimation instruction. While both experimental groups were taught the estimation instruction within 3 days, the control group was given a fraction review not related to decimal division. An estimation achievement test (O(,2)) was administered to all groups on the day following the instruction, with each question shown with overhead projection for fifteen seconds. A decimal-division achievement posttest (O(,3)) took place the day following the estimation test. / Analysis of covariance was used to test whether there were any differences among the three groups on the estimation test. Scores on test O(,1) served as the covariate. A null hypothesis of no difference was rejected at the 0.05 level. Using the Newman-Keuls range test it was found that the first quotient-estimation technique was more effective than either the second quotient-estimation technique or the control. Gain scores from O(,1) to O(,3) were used to determine whether being a successful decimal-quotient estimator could have any effect upon student ability to compute; no significant effect was found. / Source: Dissertation Abstracts International, Volume: 46-06, Section: A, page: 1548. / Thesis (Ph.D.)--The Florida State University, 1985.