Date of Award

Spring 1971

Degree Type

Master's Essay - Restricted

Degree Name

Master of Science (MS)


Mathematical and Statistical Sciences


In this paper, a teaching-learning situation for a first year course in geometry which would be relevant to the individual needs and abilities of each student is developed. It is the writer's desire to find a way to have the student become more involved in learning and to place more emphasis on thinking in such a way that mathematics will become more important to him, that he can see a value in it and that he can find success in learning it. The area of geometry was chosen because it is an important branch of mathematics for an individual to study in preparing for his future. Because geometry is the study of shape, size and position, the content of geometry is useful to many people, from the housewife to the guided missile technician. It has value for practically all, for the language of geometry is widely used in communications with other people, and the methods for discovering or proving relationships about terms, ideas or various figures offer challenging opportunities for careful, critical thinking. For the specific unit of instruction, the concept of critical thinking with respect to developing a "proof" has been chosen because it seems to be the key to success in studying geometry and all other mathematics. The ability to write a valid proof is the whole basis of a first course in geometry, for it is the application of undefined terms, definitions, postulates and individual ideas. Although this paper is written for an essay in mathematics, much of the justification for the chosen topic, namely the relevance of mathematics for today's adolescent, comes from educational sources. The principal reason for selecting a topic of this nature is because of its pertinence to the writer. As a member of the staff of Oconomowoc Junior High School, the writer is directly involved with a project which calls for the development of a "model" junior high school. Specifically the writer is interested in the development of a mathematics program of instruction for such a school.