Thesis (Ph. D.)--Oregon State University, 2007. / Printout. Includes bibliographical references (leaves 160-168). Also available on the World Wide Web.

Thesis (M.Ed.)--Memorial University of Newfoundland, 2000. / Bibliography: p. 52-57.

Thesis (M.A.)--York University, 2008. Graduate Programme in Psychology. / Typescript. Includes bibliographical references (leaves 195-208). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:MR38747

Thesis (Ed. D.)--University of Kentucky, 2002. / Title from document title page. Document formatted into pages; contains xix, 175 p. : ill. Includes abstract. Includes bibliographical references (p. 160-173).

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This dissertation reports the results of a three-phase study on the learning of algebra. The first phase involved interviews with ten seventh graders (12 and 13 years of age) to uncover some of their pre-algebraic notions on equations and equation solving. Six of these novice subjects were kept on for the second phase: a two-month teaching experiment on equation solving which emphasized the symmetric procedure of performing the same operation on both sides. The pretest and two posttest interviews of the second phase included both equation-solving and equivalent-equations tasks. The third phase involved interviews with nine more-experienced algebra students from grades eight to eleven, to investigate their equation-solving procedures, errors, and methods of determining the equivalence of equation-pairs. Their approaches were compared with those of the novices on the same tasks. / The study uncovered two distinct paths followed in the learning of equation solving: one by those already predisposed toward inversing; the other by those with a predisposition toward using surface operations. The latter group was more receptive to the procedure taught during the teaching experiment. A relationship was found to exist between subjects' view of the literal term in equations and their preferred equation-solving method. Novices with an inversing preference applied learned principles to equivalence tasks, but not to equation solving. More-expert subjects relied on inversing for both. / Theoretical implications of these findings concern: the processes used in the early stages of learning a new domain, the modeling of the procedures used to determine equivalence, the relationship between errors and structural knowledge, and the representation of word problems by equations. Finally, the characterization of an arithmetic approach and an algebraic approach to the learning of equation solving is used to suggest a basis for a theory of algebra learning.

The purpose of this study was to investigate the effectiveness of two different methods of teaching learning disabled middle school students (6th, 7th, and 8th grades) how to solve one-step addition and subtraction mathematics story problems. This study also compared the generalization of the two instructional methods to problems written in simple syntax which required the performance of two mathematics operations, addition and subtraction, in order to obtain the correct written solution.Teachers were randomly assigned to one of the two instructional methods. The students in the experimental and control classrooms were administered the The Mathematics Computation Screeninq Test, the One-step Story Problem-Solving Test of Mathematics Reasoninq and the Two-step Story Problem-Solving Test of Mathematics Reasoninq. Students who obtained above 80% mastery on the The Mathematics Computation Screening Test and at or below 67% mastery on the pretest of the One-step Story Problem-Solving Test of Mathematics Reasoning were included in the experimental and control groups. Students in the experimental and control groups who meet the above criteria and were at or below the 60% mastery level on the pretest of the Two-step Storv Problem Solving Test of, Mathematics Reasoning were included in the analysis of two-step problems. There were 70 students who meet these criteria. Following administration of the tests, students received 17 days of instruction in one of the two instructional methods.Previous research has shown that good problem-solvers initially have a mental representation of a story problem prior to solving the problem and that accurate performance may be increased by teaching students to generate diagrammatic representations of the problems. Based on this research it was hypothesized that learning disabled students who receive instruction in generating diagrammatic representations would have a higher mean performance on a linear composite of writing number sentences and solving one-step addition and subtraction story problems than learning disabled students who did not receive this instruction when pretest performance on one-step written solutions was held constant. It was also hypothezied that when presented with two-step addition and subtraction story problems learning disabled students who receive instruction in how to generate diagrammatic representations for various one-step addition and subtraction story problems would have a higher mean performance than learning disabled students who do not receive this instruction when pretest one-step and two-step written solutions were held constant.A 2 X 2 X 2 X 2 hierarchical multivariate analysis of covariance mixed effects design followed by examination of step down F ratios was used to test the one-step hypotheses. Analysis of the data indicated no significant difference between the groups on number sentence writing and on solving one-step addition and subtraction story problems varying in syntactic complexity and position of the unknown term. The data did indicate a significant interaction between the within subject factors of syntax, position of the unknown term, and mathematics operation.A 2 X 2 hierarchical analysis of covariance design was used to test the hypotheses regarding generalization of the two instructional methods to two-step story problems of addition and subtraction. Analysis of the data indicated no significant difference between the problem-solving performance of students taught with the diagrammatic instructional method and those taught in the control group. / Department of Special Education

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Thesis (Ph. D.)--University of Wyoming, 2005. / Title from PDF title page (viewed on March 4, 2008). Includes bibliographical references (p. 141-152).