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The Level Of Teacher Involvement In The Vermont Mathematics Portfolio Assessment Process And Instructional Practices In Grade 4 Classrooms, Carol Anne Fritz

Doctoral Dissertations

The comprehensive assessment system in Vermont includes student mathematics portfolios that are submitted to the state Department of Education for scoring. A student portfolio should include 5--7 pieces of best work selected by the student that can be scored. This alternative assessment process has been in place for ten years, but limited information has been available from classroom teachers about the instructional practices they use when teaching mathematics, or whether or not those practices have been influenced by the portfolio process.

The study was developed to answer questions about the instructional practices used by teachers. Teachers' responses were compared to …

Making Connections: Compartmentalization In Pre -Calculus Students' Understanding Of Functions, Hope H. Gerson

Doctoral Dissertations

Students develop knowledge constructs that they build into concepts through their experiences. Students demonstrate compartmentalization when they understand a construct or concept within one representation, but not another, or when they do not connect mathematically related ideas. For instance, a student may understand f(x) to mean plug x into the function within a symbolic representation, but the same student may understand f(x) to mean f times x within a tabular representation. A student with these understandings has a compartmentalized understanding of function notation.

A two-month study was conducted with a class of pre-calculus students enrolled in a parochial high school. …

A Study Of Mathematics Course Sequence And Student Performance In Mathematics In A Block Scheduled High School, John Harvell Moody

Doctoral Dissertations

The 1983 study of the condition of American Education, A Nation at Risk, brought a significant amount of attention to the way in which schools provided students with the skills necessary to be productive citizens. Many of the recommendations contained in A Nation at Risk focused on the perceived poor performance of American students when compared to their counterparts worldwide. The year after publication of A Nation at Risk, the National Commission on Time and Learning published Prisoners of Time, a report that called for the establishment of high academic standards for students and a major restructuring of the school …

Reflexivity, Elementary Operators And Cohomology, Jiankui Li

Doctoral Dissertations

Let H be a separable complex Hilbert space and let B(H) be the set of all bounded operators on H. In this dissertation, we show that if S is a n-dimensional subspace of B( H), then S is [ 2n ]-reflexive, where [t] denotes the largest integer that is less than or equal to t.

We obtain some lattice-theoretic conditions on a subspace lattice L which imply alg L , is strongly rank decomposable. Let S be either a reflexive subspace or a bimodule of a reflexive algebra. We find some conditions such that T has a rank one summand …

Physics Experiences And Calculus: How Students Use Physics To Construct Meaningful Conceptualizations Of Calculus Concepts In An Interdisciplinary Calculus /Physics Course, Karen Ann Marrongelle

Doctoral Dissertations

The purpose of this study was to investigate the manner by which students enrolled in an integrated Calculus/Physics course use their understanding of physics to inform their conceptualizations of calculus concepts. This study utilized a multiple case study design with analysis by and across cases. The cases represent eight first year students in the College of Engineering and Physical Sciences at the University of New Hampshire who enrolled in an integrated calculus/physics program. Data was gathered in a three-part process: (1) Semi-structured task-based interviews, (2) Participant-observation in the calculus/physics course, and (3) Obtaining copies of students' in-class notes, in-class activities, …

Learning And Understanding In Abstract Algebra, Bradford Reed Findell

Doctoral Dissertations

Students' learning and understanding in an undergraduate abstract algebra class were described using Tall and Vinner's notion of a concept image, which is the entire cognitive structure associated with a concept, including examples, nonexamples, definitions, representations, and results. Prominent features and components of students' concept images were identified for concepts of elementary group theory, including group, subgroup, isomorphism, coset, and quotient group.

Analysis of interviews and written work from five students provided insight into their concept images, revealing ways they understood the concepts. Because many issues were related to students' uses of language and notation, the analysis was essentially semiotic, …