Thesis (Ph. D.)--University of Wisconsin--Madison, 1967. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

This thesis is concerned mainly with the interplay between identities involving power series (which are called q-series) and combinatorics, in particular the theory of partitions. The thesis includes new proofs of some q-series identities and some ideas about the generating functions for the rank and crank, a new proof of the triple product identity and a combinatorial proof of a q-elliptic identity.

Thesis (Ph. D.)--Illinois State University, 1996. / Title from title page screen, viewed May 24, 2006. Dissertation Committee: Albert D. Otto (chair), Barbara S. Heyl, Cheryl A. Lubinski, Nancy K. Mack, Jane O. Swafford, Carol A. Thornton. Includes bibliographical references (leaves 188-198) and abstract. Also available in print.

This project investigates primary 4 children's difficulties when solving word problems. It consists of an exploratory study examining the feasibility of using task-based interviews in the school setting; and a main study divided into three phases. The tasks set to the children are selected/adapted word problems from SPNG textbook Stage 2. Phase 1 investigates the difficulties of forty "average" primary 4 children from five different schools. Task-based interviews are used in conjunction with an error analysis. Phase 2 makes structural alterations to six of the most difficult Phase 1 word problems to investigate more closely the possible cause of difficulty. These altered word problems are re-presented to the Phase 1 sample. The original problems are not re-presented to this sample as the task-based interviews allowed for considerable practice of these original problems. Phase 3 took place a year later than Phase 2 and presents the structurally altered word problems alongside the original problems to a different, but similar sample. This sample consists of 126 children from the five schools participating during Phase 1/2. It is suggested that the findings do not support the view that a small unvarying number of variables consistently affect problem difficulty. Rather the sources of difficulty are likely to stem from a number of highly complex interacting sources; and the language itself need not be the block it sometimes appears to be. Informal strategies were evidently important for a significant minority of children, particularly in relation to subtraction problems. This seems well worth investigating further. The use of these strategies suggested that the language of the word problem could be understood when the child could link it to his/her informal strategies. Also, given simpler numbers, the semantic implications of the problem could often be mastered.

My dissertation is mainly focused on work sheets created in Smart notebook 10 which are intended for the third-grade pupils of primary school. At the beginning I am dealing with the didactic part of chosen curriculum in material which was made by me. Futhermore I am comparing available mathematic schoolbooks which are intended for the third grade. The main part contains methodical manual for users of the working sheets which were created in Smart Notebook 10. It is mainly focused on the operation, the usage and the right method of working out the particular tasks. In conclusion of my dissertation I am summarizing my conclusions of hours and I am evaluating my experience gained from teaching at the primary school during which I used the chosen working sheets.