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The Role Of Error Analysis, Diagnostic Grading Procedures, And Student Reflection In First Semester Calculus Learning (Epistemology, Metacognition, Inquiry), Karen Jean Geuther
The Role Of Error Analysis, Diagnostic Grading Procedures, And Student Reflection In First Semester Calculus Learning (Epistemology, Metacognition, Inquiry), Karen Jean Geuther
Doctoral Dissertations
The present study is an integrative study designed to explore the nature of student difficulties within the context of a first semester college calculus course. The techniques of error analysis were used to identify and categorize the student difficulties. Insights gained from this categorization served as the basis for the design and development of calculus grader preparation materials implemented with a subgroup of undergraduate calculus graders. These grader preparation materials emphasized grader diagnosis of student difficulties and student reflection on errors and process. Current preparation procedures served as the control on the basis of which comparisons and evaluations were made. …
Operator Ranges Of Shifts And C*-Algebras (Strange Range, Quasi-Similarity, Lattice), Charles Lucien Roy
Operator Ranges Of Shifts And C*-Algebras (Strange Range, Quasi-Similarity, Lattice), Charles Lucien Roy
Doctoral Dissertations
It is shown that Lat(, 1/2)(H('(INFIN))(S)), the invariant operator ranges of the commutant of the unilateral shift, is a proper sub-lattice of the lattice of invariant operator ranges of the unilateral shift, S. The notion of a strange operator range for S of order n where n (ELEM) is introduced and it is demonstrated that there exist strange ranges for S of every order. This is done by deriving an operator range condition which is sufficient to insure that a pair of quasi-similar compressions of shifts really be similar. A set of operator ranges which forms a sub-lattice of Lat(, …