Browsing by Subject "Problem Solving"
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Item A CASE STUDY ON USING GIS AS A TOOL TO ENABLE LEARNING OF SPATIAL PROBLEM SOLVING ABILITIES IN AN ONLINE ENVIRONMENT(2010-01-16) Ball, Kendall C.RENR 405 GIS Environmental Problem Solving is a course offered at Texas AItem An analysis of incubation effects in problem solving using a computer-administered assessment tool(2009-05-15) Yoo, Sung AeAn insightful solution to a problem may be promoted by temporarily being away from the problem at hand and engaging in other tasks or problems. Wallas (1926) conceptualized such an interruption period between problem solving activities as an incubation period. The present study examines the effect of such activities that are provided as an incubation period in computer-based problem solving tasks. In addition, this study explores the potential interaction between the type of problems and the type of interruption tasks involving two types of problems (verbal and spatial) and two types of interruption activities (verbal and spatial). One hundred eighty five undergraduate volunteers participated. The participants were randomly assigned to one of the six conditions, Spatial Problems: No-Interruption Task, Spatial Problems: Verbal Interruption Task, Spatial Problems: Spatial Interruption Task, Verbal Problems (Anagrams): No-Interruption Task, Verbal Problems (Anagrams): Verbal Interruption Task, and Verbal Problems (Anagrams): Spatial Interruption Task. A computerized technique was developed and incorporated for data collection and material presentation. This technique was considered to have advantages over the conventional data collection format because of its ability to (1) standardize the presentation and assessment of problem solving tasks, (2) allow subjects to manipulate the problem components as they desire, simulating real world problem solving approaches, and (3) monitor the subjects? on-going interactions through the use of intricate, covert, data collection techniques. Regression analyses were employed to analyze the data collected using this computerized technique. The findings from the present study partially support the view that problem solvers can benefit from a temporary interruption task in a problem solving sequence. The participants resolved the problems more quickly when distracted by an intervening simple cognitive task than when allowed to work continuously. It was implied that a problem solver could benefit from an interruption that involves stimuli changing visually and spatially and that also demands some degree of cognitive involvement. Although the present study did not demonstrate effects of interaction between the problem types and interruption types, the findings suggested that in the case of spatial problems, engaging in an incubation activity is likely to result in more efficient performance.Item They Must Be Mediocre: Representations, Cognitive Complexity, and Problem Solving in Secondary Calculus Textbooks(2012-12-03) Romero, Christopher 1978-A small group of profit seeking publishers dominates the American textbook market and guides the learning of the majority of our nation?s calculus students. The College Board?s AP Calculus curriculum is a de facto national standard for this gateway course that is critically important to 21st century STEM careers. A multi-representational understanding of calculus is a central pillar of the AP curriculum. This dissertation asks whether this multi-representational vision is manifest in popular calculus textbooks. This dissertation began with a survey of all AP Calculus AB Examination free response items, 2002-2011, and found that students score worse on items characterized by numerical anchors or verbal targets. Based on previously elucidated models, a new cognitive model of five levels and six principles is developed for the purpose of calculus textbook task analysis. This model explicates complexity as a function of representational input and output. Eight popular secondary calculus textbooks were selected for study based on Amazon sales rank data. All verbally anchored mathematical tasks (n=555) from sections of those books concerning the mean value theorem and all AP Calculus AB prompts (n=226) were analyzed for cognitive complexity and representational diversity using the model. The textbook study found that calculus textbooks underrepresented the numerical anchor and verbal target. It found that the textbooks were both explicitly and implicitly less cognitively complex than the AP test. The article suggested that textbook tasks should be less dense, avoid cognitive attenuation, move away from the stand-alone item, juxtapose anchor representations, scaffold student solutions, incorporate previously considered overarching concepts and include more profound follow-up questions. To date there have been no studies of calculus textbook content based on established research on cognitive learning. Given the critical role that their calculus course plays in the lives of hundreds of thousands of students annually, it is incumbent upon the College Board to establish a textbook review process at the very least in the same vain as the teacher syllabus auditing process established in recent years.