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Pages
 Title
 Certain summation & cubature formulas
 Creator
 Northam, Jack Irwin
 Date
 1939
 Collection
 Electronic Theses & Dissertations
 Title
 The origins of connectedness im kleinen
 Creator
 McGrew, John Michael, 1947
 Date
 1976
 Collection
 Electronic Theses & Dissertations
 Title
 A comparative evaluation of programmed and lecture instruction in college business mathematics
 Creator
 Swartz, Manfred E.
 Date
 1985
 Collection
 Electronic Theses & Dissertations
 Title
 Evaluating content validity in crossnational achievement tests
 Creator
 Jakwerth, Pamela M. (Pamela Marie)
 Date
 1996
 Collection
 Electronic Theses & Dissertations
 Title
 The impact of test consequences and response format on performance
 Creator
 DeMars, Christine
 Date
 1998
 Collection
 Electronic Theses & Dissertations
 Title
 The relationship between item format and cognitive processes in widescale assessment of mathematics
 Creator
 Garavaglia, Diane R.
 Date
 2001
 Collection
 Electronic Theses & Dissertations
 Title
 Aristotle as secondary mathematics teacher educator : metaphors and strengths
 Creator
 Johnson, Whitney Pamela
 Date
 2005
 Collection
 Electronic Theses & Dissertations
 Title
 Computations of Floer homology and gauge theoretic invariants for Montesinos twins
 Creator
 Knapp, Adam C.
 Date
 2008
 Collection
 Electronic Theses & Dissertations
 Title
 Elementary teachers' mathematics textbook use in terms of cognitive demands and influential factors : a mixed method study
 Creator
 Son, JiWon
 Date
 2008
 Collection
 Electronic Theses & Dissertations
 Title
 Strategies in repeated games
 Creator
 Li, Mingfei
 Date
 2008
 Collection
 Electronic Theses & Dissertations
 Title
 Learning to anticipate students' mathematical responses in two contexts : the case of one preservice teacher in a university and school setting
 Creator
 Kasten, Sarah Elizabeth
 Date
 2009
 Collection
 Electronic Theses & Dissertations
 Title
 Development of discourse on limits : connecting history and classroom practice through a communicational approach to learning
 Creator
 Güçler, Beste
 Date
 2010
 Collection
 Electronic Theses & Dissertations
 Title
 Placement into first college mathematics course : a comparison of the results of the Michigan State University proctored mathematics placement examination and the unproctored mathematics placement examination
 Creator
 Drake, Samuel
 Date
 2010
 Collection
 Electronic Theses & Dissertations
 Description

The primary purpose of this study was to compare the results of the Michigan State University (MSU) unproctored examination to the results of the proctored examination. Both examinations are used to determine whether first time freshmen at MSU are ready for a standard mathematics course or if a remedial course is necessary. In addition to producing higher placement examination scores, the unproctored examination placed students into higher level courses and a larger proportion of student who...
Show moreThe primary purpose of this study was to compare the results of the Michigan State University (MSU) unproctored examination to the results of the proctored examination. Both examinations are used to determine whether first time freshmen at MSU are ready for a standard mathematics course or if a remedial course is necessary. In addition to producing higher placement examination scores, the unproctored examination placed students into higher level courses and a larger proportion of student who was placed with the proctored examination enrolled in a course at a level lower than the course in which they were placed. Therefore, the first conclusion was that the unproctored examination produced more inappropriate placements than the proctored examination. The second conclusion was that when the mathematics placement examination was considered alone, it was a significant predictor of the log odds of success in Intermediate Algebra (MTH1825), College Algebra (MTH103), and Calculus 1 (MTH132). When ACT Mathematics score, their high school GPA, the type of exam used for placement, whether a student enrolled in mathematics during his or her senior year of high school, and the last high school mathematics course taken were considered, the prediction of the log odds of success was improved for each of these courses. The additional variables improved the "hit rate" of the model containing only placement examination score. In addition, the additional variables decreased the false positive rate of the model containing placement examination only. Therefore, the placement examination alone is not sufficient for placing students into their first college mathematics course. Thirdly, students placed into remedial mathematics less often with the unproctored examination. In fact, the odds of placing into one of MSU's nonremedial mathematics courses with the proctored examination was approximately 1.5 times greater than the odds of placing into a nonremedial mathematics course with the unproctored examination. Therefore, placement into remedial mathematics was dependent on the type of examination used for placement. Finally, there were students who enrolled in courses lower than the level in which they were placed. For example, approximately 30.8% of the students who enrolled in MTH103 and were placed with the proctored examination were eligible to enroll in a higher level course. Approximately 45.9% of the students who enrolled in MTH103 and were placed with the unproctored examination were eligible to enroll in a higher level course. This difference in percentages was significant. It is important to the validity of the placement examination as well as the comparability of the proctored and unproctored placement examinations to determine why students enroll in courses lower than the level in which they were placed. Study limitations are discussed and suggestions for future research are given.
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 Title
 Geometric evolution of singlelayer interfaces in the functionalized CahnHilliard equation
 Creator
 Hayrapetyan, Gurgen Ruben
 Date
 2011
 Collection
 Electronic Theses & Dissertations
 Description

We study the Functionalized CahnHilliard Energy (FCH), which is a higherorder reformulation of the CahnHilliard energy, as a model for network formation in polymersolvent mixtures. The model affords a finite interfacial width, accommodates merging and other topological reorganization, and couples naturally to momentum balance and other macroscopic mass transport equations.The corresponding constrained L
2 gradient flow has a rich family of approximately steadystate...
Show moreWe study the Functionalized CahnHilliard Energy (FCH), which is a higherorder reformulation of the CahnHilliard energy, as a model for network formation in polymersolvent mixtures. The model affords a finite interfacial width, accommodates merging and other topological reorganization, and couples naturally to momentum balance and other macroscopic mass transport equations.The corresponding constrained L2 gradient flow has a rich family of approximately steadystate solutions that include not only the singlelayer heteroclinic front profile seen in gradient flows of the CahnHilliard energy, but also a novel one parameter family of homoclinic bilayer solutions. In this thesis we rigorously derive the geometric evolution of the singlelayer polymersolvent interface.We form a manifold of quasiequilbria by "dressing" a large family of codimension one interfaces immersed in Rd with heteroclinic solutions of a onedimensional equilibrium equation derived from the first variation of the FCH energy. We show that solutions of the gradient flow that start sufficiently close to the manifold remain close, and moreover the flow can be decomposed, at leading order, as a normal velocity for the underlying codimension one interface. Assuming the smoothness of the interface under this flow, we develop rigorous estimates on the proximity of the true solution to the manifold, in an appropriate norm, for long time.
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 Title
 Common and textbook foil groupings : a social network approach to distractor analysis
 Creator
 Pearlman, Leslie
 Date
 2011
 Collection
 Electronic Theses & Dissertations
 Description

"This dissertation examines the patterns and types of mistakes students make on a largescale mathematics assessment, and puts these patterns into perspective based on the textbook used and the specific content covered in a student's classroom."From abstract.
 Title
 Topics in link homology
 Creator
 Jaeger, Thomas Constantin
 Date
 2011
 Collection
 Electronic Theses & Dissertations
 Description

We prove two results about mutation invariance of link homology theories: Weshow that Khovanov's universal sl(2) homology is invariant under mutationand that the reduced sl(n) homology defined by Khovanov and Rozansky isinvariant under componentpreserving positive mutation when n is odd. Wealso give a relationship between the Khovanov homology of a closed positive3braid and the Khovanov homology of the braid after adding a number of fulltwists.
 Title
 The van Hiele theory through the discursive lens : prospective teachers' geometric discourses
 Creator
 Wang, Sasha
 Date
 2011
 Collection
 Electronic Theses & Dissertations
 Description

ABSTRACTTHE VAN HIELE THEORY THROUGH THE DISCURSIVE LENS:PROSPECTIVE TEACHERS' GEOMETRIC DISCOURSES BySasha WangOver the past decade, there has been an increasing trend in the mathematics education research community to study students' reasoning in the teaching and learning of mathematics, and to examine issues emphasizing the use of vocabulary, terminology, and words in the mathematics classroom. In response, this study investigates changes in prospective elementary teachers' levels of...
Show moreABSTRACTTHE VAN HIELE THEORY THROUGH THE DISCURSIVE LENS:PROSPECTIVE TEACHERS' GEOMETRIC DISCOURSES BySasha WangOver the past decade, there has been an increasing trend in the mathematics education research community to study students' reasoning in the teaching and learning of mathematics, and to examine issues emphasizing the use of vocabulary, terminology, and words in the mathematics classroom. In response, this study investigates changes in prospective elementary teachers' levels of geometric thinking, and the development of their geometric discourses in the classification of quadrilaterals. In Sfard's (2008) Thinking as Communicating: Human Development, the Growth of Discourses, and Mathematizing, she introduces her commognitive framework, a systematic approach to analyzing the discursive features of mathematical thinking, including word use, visual mediators, routines, and endorsed narratives. To examine thinking about geometry, this study connects Sfard's analytic framework to another, namely the van Hiele theory (see van Hiele, 1959/1985). The van Hiele theory describes the development of students' five levels of thinking in geometry. Levels 1 to 5 are described as visual, descriptive, theoretical, formal logic and rigor, respectively. This study used the van Hiele Geometry Test from the Cognitive Development and Achievement in Secondary School Geometry (CDASSG) project (Usiskin, 1982) as the pretest and posttest to determine prospective elementary school teachers' van Hiele levels. This study also produces, on the basis of theoretical understandings and of empirical data, a detailed model, namely, the Development of Geometric Discourse. This model translates the van Hiele levels into discursive stages of geometric discourses with respect to word use, visual mediators, routines, and endorsed narratives. This study reveals discursive similarities and differences in participants' geometric discourses at the same van Hiele level, as well as changes in geometric discourse as a result of changes in levels of geometric thinking. The study also investigates the usefulness of a discursive framework in providing "rich descriptions" of participants' thinking processes.
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 Title
 Students' logical reasoning and mathematical proving of implications
 Creator
 Lee, KoSze
 Date
 2011
 Collection
 Electronic Theses & Dissertations
 Description

Students' difficulties in reasoning with logical implication and mathematical proving have been documented widely (Healy & Hoyles, 2000; Knuth, Choppin, & Bieda, 2009). Review of the educational and cognitive science studies of students' reasoning with logical implications and mathematical proving have revealed that their lack of cognizance of counterexamples might be a crucial factor. This study examined the role of logic training and counterexample in enhancing students' logical reasoning...
Show moreStudents' difficulties in reasoning with logical implication and mathematical proving have been documented widely (Healy & Hoyles, 2000; Knuth, Choppin, & Bieda, 2009). Review of the educational and cognitive science studies of students' reasoning with logical implications and mathematical proving have revealed that their lack of cognizance of counterexamples might be a crucial factor. This study examined the role of logic training and counterexample in enhancing students' logical reasoning and various aspects of mathematical proving, namely, Proof Construction, Proof Validation and Knowledge of Proof Method. In particular, the study hypothesized that logic training emphasizing counterexamples was better able to improve students' reasoning of logical implications as well as mathematical proving, in comparison to the other two approaches emphasizing rule violations and truth tables. Using a pretestinterventionposttest experimental design (3 conditions by 2 test trials), students' written and interview data (N = 60) were collected from three Singapore school sites, each over a fourday contact period (including the pretest and posttest administration days). Experimental results showed that logic training emphasizing counterexamples was significantly more effective in improving students' logical reasoning of implication than the other two approaches (p = .0007, large effect size). However, logic training was only similarly effective or ineffective in improving some aspects of students' mathematical proving across conditions. Interview findings from 12 selected students' works on a new proving task conjectured that students improved their use of deductive inferences in all aspects of mathematical proving after logic training. Moreover, their successes in constructing mathematical proofs were also subjected to two conjectured factors, students' interpretation of implication and mathematical knowledge. These findings suggested the importance of logic training and counterexamples in mathematics education and pointed to further inquiry about the role of students' interpretation of implications and mathematical knowledge in mathematical reasoning and proving.
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 Title
 The mathematics textbook as a story : a novel approach to the interrogation of mathematics curriculum
 Creator
 Dietiker, Leslie C.
 Date
 2012
 Collection
 Electronic Theses & Dissertations
 Description

Both the purpose and overarching goal of this dissertation can be summarized with this quote by Buckminster Fuller: "You never change things by fighting the existing reality. To change something, build a new model that makes the existing model obsolete." That is, to enable substantive positive change in mathematics education, this dissertation builds a new curricular model, tackling the question, "When mathematics textbooks are interpreted as art, what can be learned?" Although unconventional...
Show moreBoth the purpose and overarching goal of this dissertation can be summarized with this quote by Buckminster Fuller: "You never change things by fighting the existing reality. To change something, build a new model that makes the existing model obsolete." That is, to enable substantive positive change in mathematics education, this dissertation builds a new curricular model, tackling the question, "When mathematics textbooks are interpreted as art, what can be learned?" Although unconventional, this approach offers new conceptual tools for teachers and curriculum developers to make sense of the way in which mathematical ideas emerge and develop throughout a curricular sequence and to think anew about mathematics curriculum. Specifically, this work reconceptualizes a mathematics textbook as a mathematical story with mathematical characters, action, setting, moral, and plot. Built from literary theory, especially the frameworks of Bal (2009) and Barthes (1974), the mathematical story framework supports a vision of mathematics curriculum as a complex narrative able to stimulate the imagination and curiosity of students and teachers alike. In particular, the notion of mathematical plot offers a new opportunity to articulate the sequential dynamics affecting a reader's aesthetic experience, theorized as a tension between questions pursued by a reader and the revelations enabled by the text as the mathematical story unfolds. Oscillating between the analysis of mathematics textbooks and literary frameworks, the mathematical story constructs were developed and tested. Once stable and consistent, the constructs of mathematical character, action, setting, moral, and plot were carefully defined with examples from written curriculum. In addition, new characteristics of curriculum made visible with this reconceptualization were explored and articulated through the analysis of multiple textbooks, focusing attention on what can be learned about the manifestation of mathematical characters and mathematical plots in textbooks. In part, these analyses reveal how a mathematical character, such as the number zero, is introduced and temporally evolves throughout a sequence of curriculum. This interpretation of mathematics textbooks also exposes how the development of a mathematical object involves not only the identification of the character but also the reader's identification with the character. A representation using Barthes' hermeneutic codes is also introduced to describe the mathematical plots of different mathematical stories, enabling the different experiences of reading these stories to be recognized and understood. As mathematics curriculum broadly affects nearly every aspect of mathematics education (from planning to enacting to assessing), this mathematical story framework supports a renaissance of potential opportunities for mathematics teachers and students. It provides a heuristic for the analysis of math textbooks beyond any specific part (such as a task or a definition) in order to recognize the connective tissue of all the parts and the shape and effect of the whole for a reader. It offers teachers new, yet familiar, language for describing and collaborating on mathematics curriculum such as planned lessons or reflections on enacted lessons, further supporting their curricular design work. In addition, this work offers a conceptual foundation on which designers make important choices regarding the introduction and development of mathematical objects, procedures, and representations. In doing so, this work creates the potential to improve the mathematics curriculum offered to students.
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 Title
 The impact of standardsbased mathematics curricula implemented heterogeneously on high school student achievement
 Creator
 Krantz Selleck, Kari
 Date
 2012
 Collection
 Electronic Theses & Dissertations
 Description

ABSTRACTTHE IMPACT OF STANDARDSBASED MATHEMATICS CURRICULA IMPLEMENTED HETEROGENEOUSLY ON HIGH SCHOOL STUDENT ACHIEVEMENT ByKari Krantz SelleckThis study examined the impact of standardsbased mathematics curricula developed by the National Science Foundation, implemented within heterogeneously grouped, detracked high school classrooms. Four purposefully selected cohorts of high school students participated over a period of eight years. Outcome measures included two coursework measures ...
Show moreABSTRACTTHE IMPACT OF STANDARDSBASED MATHEMATICS CURRICULA IMPLEMENTED HETEROGENEOUSLY ON HIGH SCHOOL STUDENT ACHIEVEMENT ByKari Krantz SelleckThis study examined the impact of standardsbased mathematics curricula developed by the National Science Foundation, implemented within heterogeneously grouped, detracked high school classrooms. Four purposefully selected cohorts of high school students participated over a period of eight years. Outcome measures included two coursework measures (maximum difficulty level of math courses in which students enrolled and total number of math courses enrolled in during high school), and standardized statelevel high school test results. Hierarchical regressions conducted on the sample as a whole showed no significant differences among the cohorts for the highest level of math course taken. The trends were that students in Cohort 2 (the first postreform cohort) took slightly lowerlevel math courses than students in Cohort 1 (prereform), there was then a slight increase in Cohort 3, and finally, students in Cohort 4 took slightly higherlevel math courses than students in Cohort 1. Regarding the number of courses taken, students in Cohorts 2 and 3 took fewer math courses than students in Cohort 1, and students in Cohort 4 took approximately the same number of math courses as students in Cohort 1. The results for Cohorts 2 and 3 were significant. There were negative, significant differences, although slight, for standardized tests. In other words, students postreform performed slightly but significantly worse on standardized tests than students prereform. Further hierarchical regressions on the highest and two lowestachieving quartiles (based on incoming eighthgrade state test results) showed that students at the highest proficiency level within the three postreform cohorts fared slightly worse than those in the prereform cohort (1.35, .84, .67) for highest level math course with Cohort 2 significant (0.36). Highest achieving students performed worse on standardized tests with Cohort 3 and 4 significant (both at p=.001) Students in the lowest proficiency levels across all postreform cohorts fared better than the prereform cohort in terms of level of math courses. Lowperforming students in the fourth cohort (strongest treatment group) took math courses nearly twothirds (.62) of a difficulty level higher than students in the prereform cohort, and this result was significant (p = .010). New state math coursetaking requirements along with changes in content and scale scores of the state assessments during this longitudinal study posed limitations to the study. Implications for national and state mathematics policy included.
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