A self-administered problem-solving skill training video for nonclinical families with teens is evaluated. The study focuses on the generalization of skills to naturalistic family conversations and the program's social validity: potential iatrogenic aggravation of family problems, perceived effectiveness, and program enjoyment. Seventy families with young teens were randomly assigned to two treatment groups. One group (skill) viewed a skill training program that included information about the human immunodeficiency virus (HIV). Another group (control) viewed a similar program that lacked the skill training component. Family conversations were recorded in the families' homes before (pretest), two weeks after (posttest), and four months after (follow-up) the families received the programs. In an associated study, the skill group demonstrated greater levels of skill than controls in role-plays. In the present study, skill families demonstrated greater knowledge of problem-solving than controls at posttest and follow-up (p < .001). Analysis of the conversations revealed generally superior skill performance in the skill group. Significant group differences in skill were found in naturalistic conversations about previously discussed problems at posttest (p < .05). Performance differences in conversations about novel topics were not significant. No significant skill differences were observed at follow-up. Correlations of skill measures from the role-play and conversation assessments revealed moderate behavioral consistency (r = -.02 to .37). The conversation analysis revealed no significant group differences in the number of families showing increases or decreases in their use of degrading comments after program exposure, but a somewhat significantly greater number of skill families demonstrated a reduction in the number of additional problems raised in their conversations at posttest and follow-up (p = .06). No significant group differences were found in observer ratings of problem-solving effectiveness, measures of parent problem-solving confidence, family ratings of the program's effects on their ability to cope with family problems, program enjoyment, or satisfaction with the management of family problems. Implications for the development of effective, socially valid, self-help, media programs are discussed. / Ph. D.

Perspective and Purpose Recent investigations by Steffe, Richards, and von Glasersfeld (1979) have indicated that addition and subtraction problem-solving competencies are developmental in nature and that these competencies build upon counting abilities. They postulate that, in beginning addition and subtraction, a type of problem-solving strategy termed counting-all develops prior to another kind of strategy termed counting-on (for addition) and counting-back (for subtraction). If these tasks are developmental, one may assume that students approach the tasks in qualitatively different ways based upon their developmental levels. Neo-Piagetian researchers have postulated that a quantitative measure of development explains the qualitatively different ways in which children react to the same cognitive task at different stages of development. The measure, termed mental space or M-Space, describes the number of schemes which may be coordinated at one time. First graders, the majority of whom have an M-Space of a+2 or a+3, are capable of solving addition and subtraction word problems by utilizing the counting-all and/or the counting-on (back) strategies. Given this information, the purpose of this study was to determine what effect M-Space level has on the strategy a subject uses to solve problems when he is trained on a strategy which either matches or mismatches his M-Space level. Design To determine whether a match between M-Space and strategy demand is necessary or whether instruction will facilitate the chunking of schemes which allows the developmental task to be solved by a strategy which would otherwise be above the subject's M-Space level, the following steps occurred: one hundred thirty-nine first graders were pretested to identify those who could count to sixteen, perform numeral/number correspondence to sixteen, but could not solve addition and subtraction number fact problems to sixteen. One hundred fifteen subjects meeting these criteria were given the Cucumber Test and Backward Digit Span Test to assess their M-Space levels. After eliminating subjects before and during training, 50 subjects remained. Twenty-six subjects with an a+2 M-Space were divided into two training groups. Approximately half of the group was trained to use an a+2 strategy (the count-all strategy) to solve addition and subtraction word problems and the other half of the group was trained to use an a+3 strategy (the count-on (back) strategy). The same training procedure was used for the twenty-four subjects with an M-Space of a+3. Four to five weeks later, a delayed posttest consisting of four addition and four subtraction problems and one each of three types of transfer problems was presented. Results Mann-Whitney test results indicated that there were significantly fewer a+3 responses by the subjects with an a+2 M-Space who were trained to use an a+3 strategy than there were for subjects with an a+3 M-Space trained to use an a+3 strategy. However, there was no significant difference between those with an a+2 M-Space trained on an a+2 strategy and those with an a+2 M-Space trained on an a+3 strategy. Results of other research questions indicated that subjects gave similar responses to transfer problems which varied by material or additional variable; for subjects with an a+3 M-Space trained on an a+3 strategy, there were significantly more a+3 addition responses than subtraction responses; the implied comparison subtraction problem was answered incorrectly more often than straight take-away subtraction problems, and students tended to devise simple addition and subtraction problems and solve them by using memorized number facts. Discussion The findings indicate that more study is warranted for the application of the M-Space construct to a theory of how mathematical knowledge develops sequentially, the different ways in which addition and subtraction tasks can be conceptualized, and the instructional implications of applying a developmentally based theory of instruction to mathematics problem-solving. / Ph. D.

published_or_final_version / abstract / Education / Master / Master of Education

Thesis (Ph. D.)--University of California, Riverside, 2009. / Includes abstract. Includes bibliographical references (leaves 83-98). Issued in print and online. Available via ProQuest Digital Dissertations.

M.Ed. (Psychology of Education) / Please refer to full text to view abstract

This thesis examines whether problem solving strategies develop and improve through working in a collaborative environment and, if so, how. The study explored the way peer-topeer discussions which are focussed on finding solutions to mathematical problems might shape learners' attitudes and participation in mathematical problem solving. I use the Vygotskian (1978) socio-cultural perspective where the process of learning takes place within the Zone of Proximal Development (ZPD). Polya's problem solving heuristics (Polya, 1973) and Kilpatrick's "Instructional Triangle" (Kilpatrick, Swafford & Findell, 2001) provided the analytical framework for the study. Seven grade 7 learners from a Ex-Model C school, volunteered to participate in the study. The data gathering process involved an initial problem solving assessment, a written questionnaire, observations and video recordings of the seven learners during a series of after school problem solving sessions and post intervention learner interviews. The study showed that group discussion can have a positive impact on learners' problem solving in several respects: My key findings point to: Mathematical communication does play a role in development of problem solving strategies. A more knowledgeable other, with regards to Vygotsky's (1978) ZPD and Kilpatrick et al's (2001) instructional triangle is a critical factor in the development of problem solving strategies. All five strands of Kilpatrick et al., (2001), strands for mathematical proficiency are required for correct solutions to be calculated. At times Polya's (1973) steps for problem solving move at a rapid pace and are difficult to notice. These steps develop at different speeds for different people.

The focus of this study is to explore three key aspects of learners’ multiplicative proficiency: the nature of learners’ conceptual understanding of multiplication, the nature of learners’ numeracy dispositions (in the context of learning multiplication), and the relationship between conceptual understanding and productive dispositions in the context of multiplication. The study used a qualitative case study approach to gather rich data in relation to these. In the study a purposively selected sample of six Grade 4 learners was used from the same school: two high, two average, and two low performers. Kilpatrick, Swafford, and Findell (2001) define conceptual understanding as a functional grasp of mathematical ideas and its significant indicator is being able to represent mathematical situations in different ways and knowing how different representations can be useful for different purposes. They then refer to productive disposition as the ‘tendency to see sense in mathematics, to perceive it as both useful and worthwhile, to believe that steady effort in learning mathematics pays off, and to see oneself as an effective learner and doer of mathematics’ (p.131). Individual interviews were conducted using Wright, et al.’s (2006) instrument for exploring the nature of students’ conceptual understanding of multiplication. Wright, et al. (2006) argue that the topics of multiplication and division build on the students’ knowledge of addition and subtraction, and also multiplication and division provide foundational knowledge for topics such as fractions, ratios, proportion and percentage, all of which are core and essential areas of mathematical learning typically addressed in the primary or elementary grades. Researchers agree that learners have to be exposed to various strategies so that they are able to see that there is a difference between additive reasoning and multiplicative reasoning. In order to classify learners’ conceptual understanding of multiplication an analysis of the data was done and learners were allocated levels according to the Wright, et al. (2006) levels of achievement. For the classification of learner dispositions, the data was analysed in terms of the elements of productive disposition as defined by Kilpatrick, et al. (2001) and Carr and Claxton (2002). The key findings of the study indicate that for conceptual understanding most of the learners depended on using concrete materials in solving multiplication and they also used basic strategies and methods. The findings for productive dispositions were that most of the learners saw themselves as competent in doing multiplication but the aspect of sense making and steady effort was less developed. The findings for the relationship between conceptual understanding and productive disposition were that both strands have a mutual relationship in which one helped the other to develop.

Please read the abstract in the 00front part of this document. See also General Summary and Opsomming after chapter 7 (pp162-165) / Dissertation (DPhil (Communication Pathology))--University of Pretoria, 2006. / Speech-Language Pathology and Audiology / Unrestricted

The purpose of the study was to explore the effects that individual vs. collective structured creative musical problem solving tasks had on students' compositional products. Subjects in a convenience sample of 32 fourth-graders and 32 fifth-graders were randomly assigned to either the individual or collective condition. The 3 treatment sessions were characterized by an open-ended creative problem solving task, which included questions intended to guide subjects through 3 stages of the creative problem solving process: Understanding the Problem, Generating Ideas, and Planning for Action. Subjects participated in the pre- and posttest individually. Three experienced music educators assessed the compositional products in terms of pattern use, cohesiveness, and creativity. The originally intended MANCOVAs could not be carried out because the data did not meet the necessary assumptions. Pretest and posttest scores were explored with individual ANOVAs. The Bonferroni technique was used to adjust the alpha level. The statistical analyses showed that subjects exposed to the individual condition obtained higher scores than subjects exposed to the collective condition on six of the eight explored subtests, but these differences were not significant. The level of interjudge reliability decreased at each of the three measurements of the study: pilot test, pretest, and posttest. The study's results suggest that music educators interested in observing specific characteristics of individual students' compositional products, such as the levels of cohesiveness, creativity, and pattern use, could do so regardless of the condition under which students were exposed to compositional tasks, either individually or collectively. Recommendations for future research include the use of a measurement instrument specifically designed for open-ended tasks, and the exploration of the current study's measurement instrument with closed-ended tasks. The study highlights the need for appropriate measurement instruments designed for the compositional tasks at hand, and the need for research results reported clearly, so that more advancement of this field is possible.

The problem of this study was to determine the effects of computer programming instruction on fifth graders, as measured by gains, if any, on tests of logic and problem solving.