Browsing by Subject "problem solving"
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Item Considering representational choices of fourth graders when solving division problems(Texas A&M University, 2007-09-17) Gilbert, Mary ChilesStudents need to build on their own understanding when problem solving. Mathematics reform is moving away from skill and drill types of activities and encouraging students to develop their own approaches to problem solving. The National Council of Teachers of Mathematics emphasizes the importance of representation by including it as a process standard in Principles and Standards for School Mathematics (2000) as a means for students to develop mathematically powerful conceptualization. Students use representation to make sense of and communicate mathematical concepts. This study considers the way fourth grade students view and solve division problems and whether problem type affected the choice of strategy. This study also looked at factors that affect students' score performance. Students in extant classrooms were observed in their regular mathematics instructional settings. Data were collected and quantified from pretests and posttests using questions formatted like students see on the state assessment. The results indicate that students moved from pre-algorithmic strategies to algorithmic strategies between pretest and posttest administration. The results also indicate that problem type did not predict students' choice of strategy and did not have an affect on the students' ability to arrive at a correct solution to the problem. This study found that the students' choice of strategy did play a significant role in their quest for correct solutions. The implication is that when students are able to make sense of the problem and choose an appropriate strategy, they are able to successfully solve division problems.Item Expert-novice interaction in problematizing a complex environmental science issue using web-based information and analysis tools(Texas A&M University, 2006-08-16) Schroeder, Carolyn M.Solving complex problems is integral to science. Despite the importance of this type of problem solving, little research has been done on how collaborative teams of expert scientists and teams of informed novices solve problems in environmental science and how experiences of this type affect the novices?? understandings of the nature of science (NOS) and the novices?? teaching. This study addresses these questions: (1) how do collaborative teams of scientists with distributed expertise and teams of informed novices with various levels of distributed expertise solve complex environmental science issues using web-based information and information technology (IT) analysis tools? and, (2) how does working in a collaborative scientific team improve informed novices?? understandings of the nature of authentic scientific inquiry and impact their classroom inquiry products? This study was conducted during Cohort II of the Information Technology in Science project within the Sustainable Coastal Margins scientific group. Over two summers, four environmental scientists from various disciplines led ten science teacher and graduate student participants in learning how each discipline approaches and solves environmental problems. Participants were also instructed about NOS by science educators and designed an inquiry project for use in their classroom. After performing a pilot study of the project, they revised it during the second summer and the entire experience culminated with diverse teams problematizing and solving environmental issues. Data were analyzed using statistical and qualitative techniques. Analysis included evaluation of participants?? responses to a NOS pre- and posttest, their inquiry projects, interviews, and final projects. Results indicate that scientists with distributed expertise approach solving environmental problems differently depending on their backgrounds, but that informed novice and expert teams used similar problem-solving processes and had similar difficulties. As a result of the project, I developed a model of distributed group problem solving for environmental science. Participants?? understandings of NOS improved and matured after instruction and experience working with scientists. The level of most instructional products was ??guided inquiry.?? The implications are that working with scientists along with direct NOS instruction is beneficial for teachers and science graduate students for their understanding of scientific problem solving, but that much more work needs to be done to achieve authentic inquiry in science classrooms at both secondary and post-secondary levels.Item Middle school students' representational understandings and justification schemes: gleanings from cognitive interviews(2009-05-15) Matteson, Shirley MarieThis dissertation investigated several aspects of middle graders? mathematical understanding based on representational models. Twenty (11 male, 9 female) sixth grade students were interviewed about their solution strategies and answer justifications when solving difficult mathematics problems. The interview participants represented a stratified demographic sampling of the student body of a culturally diverse middle school in a suburban school district in the southwestern United States. Data from the interviews were analyzed qualitatively. This involved ?chunking? cognitive interview transcripts into sections. Major themes were identified and manuscripts were developed around those themes. One theme examined the interviewers? ethic of care behaviors. Carol Gilligan noted differences in male and female ethic of care behaviors, but it was Nel Noddings who discussed the importance of such behaviors in the educational community. So what impact could the gender of the interviewer have on cognitive interviews? After considering ethic of care behaviors explicated by Hayes, Ryan and Zseller?s (1994) study with middle grades students, the interview transcripts were examined for specific positive and negative ethic of care behaviors. The theme of students? justifications of mathematical solutions was also selected. The major undertaking involved developing a justification scheme applicable across mathematical strands and grade levels. The justification scheme that emerged was based on the work of Guershon Harel and Larry Sowder. The first-level schemes of Language, Mechanistic, Authoritarian, and Visual were used to classify and define the justifications. Several second-level schemes were also defined. The justification scheme framework was applied to students? cognitive interview responses on four difficult mathematics problems. The third theme investigated the symbiosis of justification schemes with mathematical representations. This study examined possible links between representational formats and justification scheme categories. The premise of this study was that representations ?trigger? students? choices of justification schemes. Student responses were analyzed as to which aspect of the mathematical representation received the students? initial attention. The students? understanding of the representation was pivotal to their solution, as well as the students? reasoning, or justification, of the answer. Students focused on key aspects of the problem and developed solutions based on that information.Item Problem based learning for police recruit training(Law Enforcement Management Institute of Texas (LEMIT), 2011) Ragsdale, RussellItem The influence of contextual teaching with the problem solving method on students' knowledge and attitudes toward horticulture, science, and school(Texas A&M University, 2006-10-30) Whitcher, Carrie LynnAdolescence is marked with many changes in the development of higher order thinking skills. As students enter high school they are expected to utilize these skills to solve problems, become abstract thinkers, and contribute to society. The goal of this study was to assess horticultural science knowledge achievement and attitude toward horticulture, science, and school in high school agriculture students. There were approximately 240 high school students in the sample including both experimental and control groups from California and Washington. Students in the experimental group participated in an educational program called ??????Hands-On Hortscience?????? which emphasized problem solving in investigation and experimentation activities with greenhouse plants, soilless media, and fertilizers. Students in the control group were taught by the subject matter method. The activities included in the Hands-On Hortscience curriculum were created to reinforce teaching the scientific method through the context of horticulture. The objectives included evaluating whether the students participating in the Hands-On Hortscience experimental group benefited in the areas of science literacy, data acquisition and analysis, and attitude toward horticulture, science, and school. Pre-tests were administered in both the experimental and control groups prior to the research activities and post-tests were administered after completion. The survey questionnaire included a biographical section and attitude survey. Significant increases in hortscience achievement were found from pre-test to post-test in both control and experimental study groups. The experimental treatment group had statistically higher achievement scores than the control group in the two areas tested: scientific method (p=0.0016) and horticulture plant nutrition (p=0.0004). In addition, the students participating in the Hands-On Hortscience activities had more positive attitudes toward horticulture, science, and school (p=0.0033). Students who were more actively involved in hands-on projects had higher attitude scores compared to students who were taught traditional methods alone. In demographic comparisons, females had more positive attitudes toward horticulture science than males; and students from varying ethnic backgrounds had statistically different achievement (p=0.0001). Ethnicity was determined with few students in each background, 8 in one ethnicity and 10 students in another. Youth organization membership such as FFA or 4-H had no significant bearing on achievement or attitude.