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Analysis on an online placement exam for college algebraOstapyuk, Nina January 1900 (has links)
Master of Science / Department of Mathematics / Andrew G. Bennett / An online placement exam was administered to 2800 entering freshmen, 700 of whom enrolled in College Algebra during the succeeding Fall semester. Problems on the placement exam were clustered using several different techniques including both expert analysis and item response theory. Student scores on these groupings of problems were then compared to their scores on the first two hour exams in the course (representing the first half of the material in the course) and also on ACT data. Based on this comparison, certain problems were selected as more or less informative for purposes of placement. A model was created using previously available ACT data along with the new placement data to predict initial student success in the course. This model explains 50% more of the variance in student scores than the previously available ACT data alone. Suggestions for improvements to the test and the placement methodology are made based on our analysis.
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Using context to enhance students' understanding of decimal fractionsIrwin, Kathryn Cressey January 1997 (has links)
A total of 84 students from a lower economic area, aged 8 to 14, were interviewed about their understanding of decimal fractions. Results showed that most students could give a context in which they saw decimal fractions outside of school. The vast majority could draw a diagram of how a cake or field could be divided equally among 10 or 100 people. However, few students under 14 could give either decimal fraction symbols or common fraction symbols to represent these divisions. Less than half of the students at ages 10, 11 and 12 could visualize what might come between 0 and 1. About half of the students aged 11 and 12 could indicate what 0.1 or 0.01 meant. It was inferred that difficulty in relating these symbols to referents might be an important source of difficulty in understanding decimal fractions. Therefore, these interviews were followed by an intervention study that examined if working with contextualized decimal fractions aided understanding of these numbers when they were presented without context. Half of a group of 16 similar students, aged 11 and 12, were asked to solve problems in which numbers that incorporated decimal fractions were contextualized, and the other half were asked to solve similar problems given in purely numerical form. Students worked in pairs, on problems which incorporated common misconceptions. The group who worked on contextualized problems gained significantly more understanding than did the group that worked on purely numerical problems, as measured by the difference between pretest and posttest scores. Transcripts of the students' discussions were analysed for the effect of prior learning, aspects of peer collaboration that appeared to be beneficial to learning, and the effect of cognitive conflict. The students who gained most from collaboration were not too distant in initial expertise, showed a degree of social equity, and worked on contextualized problems. Much of students' learning appeared to result from needing to reconsider their views following a conflict between their expectations and the results of operating on a calculator or in writing, or hearing an alternative view. / Subscription resource available via Digital Dissertations only.
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Using context to enhance students' understanding of decimal fractionsIrwin, Kathryn Cressey January 1997 (has links)
A total of 84 students from a lower economic area, aged 8 to 14, were interviewed about their understanding of decimal fractions. Results showed that most students could give a context in which they saw decimal fractions outside of school. The vast majority could draw a diagram of how a cake or field could be divided equally among 10 or 100 people. However, few students under 14 could give either decimal fraction symbols or common fraction symbols to represent these divisions. Less than half of the students at ages 10, 11 and 12 could visualize what might come between 0 and 1. About half of the students aged 11 and 12 could indicate what 0.1 or 0.01 meant. It was inferred that difficulty in relating these symbols to referents might be an important source of difficulty in understanding decimal fractions. Therefore, these interviews were followed by an intervention study that examined if working with contextualized decimal fractions aided understanding of these numbers when they were presented without context. Half of a group of 16 similar students, aged 11 and 12, were asked to solve problems in which numbers that incorporated decimal fractions were contextualized, and the other half were asked to solve similar problems given in purely numerical form. Students worked in pairs, on problems which incorporated common misconceptions. The group who worked on contextualized problems gained significantly more understanding than did the group that worked on purely numerical problems, as measured by the difference between pretest and posttest scores. Transcripts of the students' discussions were analysed for the effect of prior learning, aspects of peer collaboration that appeared to be beneficial to learning, and the effect of cognitive conflict. The students who gained most from collaboration were not too distant in initial expertise, showed a degree of social equity, and worked on contextualized problems. Much of students' learning appeared to result from needing to reconsider their views following a conflict between their expectations and the results of operating on a calculator or in writing, or hearing an alternative view. / Subscription resource available via Digital Dissertations only.
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Using context to enhance students' understanding of decimal fractionsIrwin, Kathryn Cressey January 1997 (has links)
A total of 84 students from a lower economic area, aged 8 to 14, were interviewed about their understanding of decimal fractions. Results showed that most students could give a context in which they saw decimal fractions outside of school. The vast majority could draw a diagram of how a cake or field could be divided equally among 10 or 100 people. However, few students under 14 could give either decimal fraction symbols or common fraction symbols to represent these divisions. Less than half of the students at ages 10, 11 and 12 could visualize what might come between 0 and 1. About half of the students aged 11 and 12 could indicate what 0.1 or 0.01 meant. It was inferred that difficulty in relating these symbols to referents might be an important source of difficulty in understanding decimal fractions. Therefore, these interviews were followed by an intervention study that examined if working with contextualized decimal fractions aided understanding of these numbers when they were presented without context. Half of a group of 16 similar students, aged 11 and 12, were asked to solve problems in which numbers that incorporated decimal fractions were contextualized, and the other half were asked to solve similar problems given in purely numerical form. Students worked in pairs, on problems which incorporated common misconceptions. The group who worked on contextualized problems gained significantly more understanding than did the group that worked on purely numerical problems, as measured by the difference between pretest and posttest scores. Transcripts of the students' discussions were analysed for the effect of prior learning, aspects of peer collaboration that appeared to be beneficial to learning, and the effect of cognitive conflict. The students who gained most from collaboration were not too distant in initial expertise, showed a degree of social equity, and worked on contextualized problems. Much of students' learning appeared to result from needing to reconsider their views following a conflict between their expectations and the results of operating on a calculator or in writing, or hearing an alternative view. / Subscription resource available via Digital Dissertations only.
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Using context to enhance students' understanding of decimal fractionsIrwin, Kathryn Cressey January 1997 (has links)
A total of 84 students from a lower economic area, aged 8 to 14, were interviewed about their understanding of decimal fractions. Results showed that most students could give a context in which they saw decimal fractions outside of school. The vast majority could draw a diagram of how a cake or field could be divided equally among 10 or 100 people. However, few students under 14 could give either decimal fraction symbols or common fraction symbols to represent these divisions. Less than half of the students at ages 10, 11 and 12 could visualize what might come between 0 and 1. About half of the students aged 11 and 12 could indicate what 0.1 or 0.01 meant. It was inferred that difficulty in relating these symbols to referents might be an important source of difficulty in understanding decimal fractions. Therefore, these interviews were followed by an intervention study that examined if working with contextualized decimal fractions aided understanding of these numbers when they were presented without context. Half of a group of 16 similar students, aged 11 and 12, were asked to solve problems in which numbers that incorporated decimal fractions were contextualized, and the other half were asked to solve similar problems given in purely numerical form. Students worked in pairs, on problems which incorporated common misconceptions. The group who worked on contextualized problems gained significantly more understanding than did the group that worked on purely numerical problems, as measured by the difference between pretest and posttest scores. Transcripts of the students' discussions were analysed for the effect of prior learning, aspects of peer collaboration that appeared to be beneficial to learning, and the effect of cognitive conflict. The students who gained most from collaboration were not too distant in initial expertise, showed a degree of social equity, and worked on contextualized problems. Much of students' learning appeared to result from needing to reconsider their views following a conflict between their expectations and the results of operating on a calculator or in writing, or hearing an alternative view. / Subscription resource available via Digital Dissertations only.
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Using context to enhance students' understanding of decimal fractionsIrwin, Kathryn Cressey January 1997 (has links)
A total of 84 students from a lower economic area, aged 8 to 14, were interviewed about their understanding of decimal fractions. Results showed that most students could give a context in which they saw decimal fractions outside of school. The vast majority could draw a diagram of how a cake or field could be divided equally among 10 or 100 people. However, few students under 14 could give either decimal fraction symbols or common fraction symbols to represent these divisions. Less than half of the students at ages 10, 11 and 12 could visualize what might come between 0 and 1. About half of the students aged 11 and 12 could indicate what 0.1 or 0.01 meant. It was inferred that difficulty in relating these symbols to referents might be an important source of difficulty in understanding decimal fractions. Therefore, these interviews were followed by an intervention study that examined if working with contextualized decimal fractions aided understanding of these numbers when they were presented without context. Half of a group of 16 similar students, aged 11 and 12, were asked to solve problems in which numbers that incorporated decimal fractions were contextualized, and the other half were asked to solve similar problems given in purely numerical form. Students worked in pairs, on problems which incorporated common misconceptions. The group who worked on contextualized problems gained significantly more understanding than did the group that worked on purely numerical problems, as measured by the difference between pretest and posttest scores. Transcripts of the students' discussions were analysed for the effect of prior learning, aspects of peer collaboration that appeared to be beneficial to learning, and the effect of cognitive conflict. The students who gained most from collaboration were not too distant in initial expertise, showed a degree of social equity, and worked on contextualized problems. Much of students' learning appeared to result from needing to reconsider their views following a conflict between their expectations and the results of operating on a calculator or in writing, or hearing an alternative view. / Subscription resource available via Digital Dissertations only.
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Student response to mathematical concepts in contextMcNaney, Danielle January 1900 (has links)
Master of Science / Department of Mathematics / Andrew G. Bennett / In recent years motivation research has emerged as an area of interest within educational research. Increasing student achievement is not the only aspect of education being studied. Improving the quality of the learning experience and investigating how this improvement affects student achievement is an area of growing interest. Additional investigations also consider what aspects of instruction and teaching affect the quality of the learning experience. Many mathematical organizations have voiced a concern that post-secondary mathematics courses should adapt curriculum and instruction based on results of this research. The current study is an investigation into the effectiveness of suggestions made by these organizations, as well as the effect instructional adaptations have on student attitude and achievement.
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The impact of the infinite mathematics project on teachers' knowledge and teaching practice: a case study of a title IIB MSP professional development initiativeSponsel, Barbara J. January 1900 (has links)
Doctor of Philosophy / Curriculum and Instruction Programs / David S. Allen / Margaret G. Shroyer / Ongoing, effective professional development is viewed as an essential mechanism for eliciting change in teachers’ knowledge and practice in support of enacting the vision of NCTM’s Principles and Standards of School Mathematics. This case study of the Infinite Mathematics Project, a Title IIB MSP professional development initiative, seeks to provide a qualitative examination of the characteristics and strategies used in the project and their impact on teacher learning and practice. The project embodied many features and strategies of effective professional development such as: mathematics content focus; sustained over time; reform activities (e.g., lesson study, teacher collaboration); active learning opportunities (e.g., implementing an action plan; developing differentiated instruction activities for a mathematics classroom); coherence with NCTM and state standards; and collective participation by IHE facilitators and participant K-12 teachers from partner districts. The findings reveal teachers gained both content knowledge (knowledge about mathematics, substantive knowledge of mathematics, pedagogical content knowledge, and curricular knowledge) and pedagogical knowledge (knowledge about strategies for differentiating instruction in a mathematics classroom, for supporting students’ reading in the content area, for fostering the development of number sense, for implementing standards-based teaching, and for critically analyzing teaching). The study also provides some evidence that the project had an impact on teaching practice. In addition, an implication of the study suggests the positive impact of Title IIB MSP partnership requirements.
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Effects of requiring students to meet high expectation levels within an on-line homework environmentWeber, William J. Jr. January 1900 (has links)
Doctor of Philosophy / Curriculum and Instruction Programs / Andrew G. Bennett / On-line homework is becoming a larger part of mathematics classrooms each year. Thus, ways to maximize the effectiveness of on-line homework for both students and teachers must be investigated. This study sought to provide one possible answer to this aim, by requiring students to achieve at least 50% for any on-line homework assignment in order to receive credit. Research shows that students respond well to reasonably set high expectations, and coupling this with one of the primary advantages of on-line homework, the ability to rework assignments, provided the basis for this study. Data for this experimental study was collected from the spring semester of 2008 until the fall semester of 2009, and included student exam scores, the number of on-line assignments above and below the 50% threshold, and the number of times students accessed help features of the on-line homework system when given the ability to do so. Analysis at both the whole-class and cluster levels attempted to discern the effectiveness of the intervention. Results indicated that significantly fewer students settled for on-line homework scores less than 50% in the experimental semesters where the 50% requirement was in place than in the control semesters in which the requirement was absent. Certain clusters of students seemed to benefit even more than others from this higher expectation, leading to the possibility of differentiated instruction or differentiated interventions in the future. In addition to fewer sub-par on-line homework scores, students also demonstrated other positive traits, such as accessing the on-line help links more within the experimental semesters.
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Graphing calculator use by high school mathematics teachers of western KansasDreiling, Keith M. January 1900 (has links)
Doctor of Philosophy / Curriculum and Instruction Programs / Jennifer M. Bay-Williams / Graphing calculators have been used in education since 1986, but there is no consensus as to how, or if, they should be used. The National Council of Teachers of Mathematics and the National Research Council promote their use, and ample research supports the positive benefits of their use, but not all teachers share this view. Also, rural schools face obstacles that may hinder them from implementing technology. The purpose of this study is to determine how graphing calculators are used in mathematics instruction of high schools in western Kansas, a rural region of the state. In addition to exploring the introduction level of graphing calculators, the frequency of their use, and classes in which they are used, this study also investigated the beliefs of high school mathematics teachers as related to teaching mathematics and the use of graphing calculators. Data were collected through surveys, interviews, and observations of classroom teaching. Results indicate that graphing calculators are allowed or required in almost all of the high schools of this region, and almost all teachers have had some experience using them in their classrooms. Student access to graphing calculators depends more on the level of mathematics taken in high school than on the high school attended; graphing calculator calculators are allowed or required more often in higher-level classes than in lower-level classes. Teachers believe that graphing calculators enhance student learning because of the visual representation that the calculators provide, but their teaching styles have not changed much because of graphing calculators. Teachers use graphing calculators as an extension of their existing teaching style. In addition, nearly all of the teachers who were observed and classified as non-rule-based based on their survey utilized primarily rule-based teaching methods.
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