Matching Items (3)
Filtering by
- All Subjects: Problem Solving
- Creators: Goldinger, Stephen
Description
A sample of 127 high school Advanced Placement (AP) Calculus students from two schools was utilized to study the effects of an engineering design-based problem solving strategy on student performance with AP style Related Rate questions and changes in conceptions, beliefs, and influences. The research design followed a treatment-control multiple post-assessment model with three periods of data collection. Four high school calculus classes were selected for the study, with one class designated as the treatment and three as the controls. Measures for this study include a skills assessment, Related Rate word problem assessments, and a motivation problem solving survey. Data analysis utilized a mixed methods approach. Quantitative analysis consisted of descriptive and inferential methods utilizing nonparametric statistics for performance comparisons and structural equation modeling to determine the underlying structure of the problem solving motivation survey. Statistical results indicate that time on task was a major factor in enhanced performance between measurement time points 1 and 2. In the experimental classroom, the engineering design process as a problem solving strategy emerged as an important factor in demonstrating sustained achievement across the measurement time series when solving volumetric rates of change as compared to traditional problem solving strategies. In the control classrooms, where traditional problem solving strategies were emphasized, a greater percentage of students than in the experimental classroom demonstrated enhanced achievement from point 1 to 2, but showed decrease in achievement from point 2 to 3 in the measurement time series. Results from the problem solving motivation survey demonstrated that neither time on task nor instruction strategy produced any effect on student beliefs about and perceptions of problem solving. Qualitative error analysis showed that type of instruction had little effect on the type and number of errors committed, with the exception of procedural errors from performing a derivative and errors decoding the problem statement. Results demonstrated that students who engaged in the engineering design-based committed a larger number of decoding errors specific to Pythagorean type Related Rate problems; while students who engaged in routine problem solving did not sustain their ability to correctly differentiate a volume equation over time. As a whole, students committed a larger number of misused data errors than other types of errors. Where, misused data errors are the discrepancy between the data as given in a problem and how the student used the data in problem solving.
ContributorsThieken, John (Author) / Ganesh, Tirupalavanam G. (Thesis advisor) / Sloane, Finbarr (Committee member) / Middleton, James (Committee member) / Arizona State University (Publisher)
Created2012
Description
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.
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.
ContributorsEllis, Derek M (Author) / Brewer, Gene A. (Thesis advisor) / Homa, Donald (Committee member) / Goldinger, Stephen (Committee member) / Arizona State University (Publisher)
Created2019
Description
Individuals encounter problems daily wherein varying numbers of constraints require delimitation of memory to target goal-satisfying information. Multiply-constrained problems, such as compound remote associates, are commonly used to study this type of problem solving. Since their development, multiply-constrained problems have been theoretically and empirically related to creative thinking, analytical problem solving, insight problem solving, intelligence, and a multitude of other cognitive abilities. Critically, in order to correctly solve a multiply-constrained problem the solver must have the solution available in memory and be able to target and access to that information. Experiment 1 determined that the cue – target relationship affects the likelihood that a problem is solved. Moreover, Experiment 2 identified that the association between cues and targets predicted inter- & intra-individual differences in multiply-constrained problem solving. Lastly, Experiment 3 found monetary incentives failed to improve problem solving performance likely due to knowledge serving as a limiting factor on performance. Additionally, problem solvers were shown to be able to reliably assess the likelihood they would solve a problem. Taken together all three studies demonstrated the importance of knowledge & knowledge structures on problem solving performance.
ContributorsEllis, Derek (Author) / Brewer, Gene A (Thesis advisor) / Homa, Donald (Committee member) / Blais, Chris (Committee member) / Goldinger, Stephen (Committee member) / Arizona State University (Publisher)
Created2021