Thesis (M.S.)--Central Connecticut State University, 2000. / Thesis advisor: Phillip Halloran. " ... in partial fulfillment of the requirements for the degree of Master of Science in Mathematics." Includes bibliographical references (leaves [26]-[27]).

Thesis (Ph. D.)--Florida State University, 2004. / Advisor: Dr. Marcy P. Driscoll, Florida State University, College of Education, Dept. of Educational Psychology and Learning Systems. Title and description from dissertation home page (viewed Jan. 18, 2005). Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1974. / Typescript. Vita. Includes bibliographical references.

Thesis (M. Ed.)--University of Hong Kong, 2005. / Title proper from title frame. Also available in printed format.

Thesis (Ph. D.)--Ohio State University, 1984. / Includes bibliographical references (leaves 183-188). Available online via OhioLINK's ETD Center

While mathematical problem solving and problem posing are central to good mathematics teaching and mathematical learning, no criteria exist for what makes a good mathematics problem. This grounded theory study focused on defining attributes of good mathematics problems as determined by students, teachers, and mathematicians. The research questions explored the similarities and differences of the responses of these three populations. The data were analyzed using the grounded theory approach of the constant comparative method. Fifty eight students from an urban private school, 15 teachers of mathematics, and 7 mathematicians were given two sets of problems, one with 10 algebra problems and one with 10 number theory problems, and were asked choose which problems they felt were the “best” and the “least best”. Once their choices were made, they were asked to list the attributes of the problems that lead to their choices. Responses were coded and the results were compared within each population between the two different problem sets and between populations. The results of the study show that while teachers and mathematicians agree, for the most part, about what attributes make a good mathematics problem, neither of those populations agreed with the students. The results from this study may be useful for teachers as they write or evaluate problems to use in their classes.

Thesis (Ph.D.)--University of Melbourne, Dept. of Learning and Educational Development, 2004. / Typescript (photocopy). Includes bibliographical references (leaves 247-265).

Thesis (M. Ed.)--University of Hong Kong, 1998. / Includes bibliographical references (leaf 123-130).

Thesis (M.Ed.)--University of Hong Kong, 1998. / Includes bibliographical references (leaves 123-130). Also available in print.

This thesis describes a class of problems in which interactions occur when plans to achieve members of a set of simultaneous goals are concatenated in the hope of achieving the whole goal. They will be termed "interaction problems". Several well known problems fall into this class. Swapping the values of two computer registers is a typical example. A very simple 3 block problem is used to illustrate the interaction difficulty. It is used to describe how a simple method can be employed to derive enough information from an interaction which has occurred to allow problem solving to proceed effectively. The method used to detect interactions and derive information from them, allowing problem solving to be re-directed, relies on an analysis of the goal and subgoal structure being considered by the problem solver. This goal structure will be called the "approach" taken by the system. It specifies the order in which individual goals are being attempted and any precedence relationships between them (say because one goal is a precondition of an action to achieve another). We argue that the goal structure of a problem contains information which is simpler and more meaningful than the actual plan (sequence of actions) being considered. We then show how an analysis of the goal structure of a problem, and the correction of such a structure in the light of any interaction, can direct the search towards a successful solution. Interaction problems pose particular difficulties for most current problem solvers because they achieve each part of a composite goal independently and assume that the resulting plans can be concatenated to achieve the overall goal. This assumption is beneficial in that it can drastically reduce the search necessary in many problems. However, it does restrict the range of problems which can be tackled. The problem solver, INTERPLAN, to be described as a result of this investigation, also assumes that subgoals can be solved independently, but when an interaction is detected it performs an analysis of the goal structure of the problem to re-direct the search. INTERPLAN is an efficient system which allows the class of interaction problems to be coped with. INTERPLAN uses a data structure called a "ticklist" as the basis of its mechanism for keeping track of the search it performs. The ticklist allows a very simple method to be employed for detecting and correcting for interactions by providing a summary of the goal structure of the problem being tried.