Capitulo 1

Chapter I
INTRODUCTION
Need for the Study

The 1980s were the decade in which computers began to influence all levels of education. The number of computers available for students' use changed from 800,000 to 1.7 million during the 1980s (U.S. Congress, Office of Technology Assessment, 1988). Today there are two million computers in American schools, which represent about one computer for every twenty five students. Many higher education institutions utilized newly available technology to enrich the curriculum and assist the teaching-learning process. Infusions of technology resulted in recommendations from accrediting agencies to develop formal evaluation procedures to assess the outcomes of technological innovations in the teaching-learning process and to determine their effectiveness in relation to the human and fiscal resources expended.

Reports such as Everybody Counts (National Research Council, 1989) and Moving Beyond the Myths (National Research Council, 1991) supported the position that the society has much to gain from the increasing role of technology in mathematics education. The role of technology in mathematics education presented in Everybody Counts was:

School mathematics can become more like the mathematics people actually use, both on the job and in scientific application.
Weakness in algebraic skills need no longer prevent students from understanding ideas in more advanced mathematics.
Mathematics learning can become more active and dynamic, hence more effective.
Students can explore mathematics on their own, to ask and answer countless "what if" questions. Although calculators and computers will not necessarily cause students to think for themselves, they can provide an environment in which student-generated mathematical ideas can thrive.
Time invested in mathematics study can build long lasting intuition and insight, not just short lived strategies for calculation. (pp. 62-63)

The National Council of Teachers of Mathematics publication Curriculum and Evaluation Standards for School Mathematics (NCTM,1989) established priorities for curricula as the basis for improving mathematics teaching. The document explicitly recommended the integration of technology within the mathematics program at all grade levels. It also urged changes in the methods and the strategies that educators use in the teaching of mathematics. NCTM Standards proposed that:

appropriate calculators should be available to all students at all times;
a computer should be available in every classroom for demonstration purposes;
every student should have access to a computer for individual and group work;
students should learn to use the computer as a tool for processing information and performing calculations to investigate and solve problems. (p. 8)

Problem solving and technology related studies have been the focus of a considerable amount of research over the past 25 years. Lester (1994) asserted that there is a need to provide teachers with well-documented information about problem solving. He suggested three issues related to problem solving instruction that need more investigation: (1) The Role of the Teacher in a Problem-Centered Classroom; (2) What Actually Takes Place in Problem-Centered Classrooms?; (3) Research Should Focus on Groups and Whole Classes Rather than Individuals.

Schroeder and Lester (1989) indicated that there is an urgent need to provide teachers with information about “teaching via problem solving.” Kaput and Thompson (1994) urged that educators should assume responsibilities for shaping the roles of new technologies in school mathematics and researchers should turn issues raised by new technologies into research-able questions.
Clearly, there seems to be a need in mathematics education to find some effective uses for technology. It appears, also, that more research is necessary about the effect of a technology-based curriculum on mathematical reasoning skills and students' attitudes toward their own problem solving abilities.

Purpose of the Study

The purpose of this study is to prepare computer-based instructional materials for use in a mathematical reasoning and problem solving skills course at the college level, and to test the effects of these materials in a college setting. Among the questions to be addressed in this study are:

Within what topics of a mathematics reasoning skill course can a technology-based methodology be used?
What is the effect of a technology-based curriculum on students' achievement in a mathematical reasoning skill course given the fact that additional time was devoted to learning to use a computer?
What attitudes toward computers do students at the college level have?
Does the use of technology improve students' attitude toward the usefulness of mathematics?
Does the use of technology increase students' confidence in learning mathematics?
Does the use of technology affect students' attitude toward their own problem solving abilities?

Procedure of the Study

The study took place in a private four-year university in Ponce, Puerto Rico, during the Spring of 1995 (See Appendix A for the consent forms). Three groups participated in the study. The students were divided into three sections by the registrar. Two of the groups were designated Computer I (C1, Instructor A), and Computer 2 (C2, Instructor B). The third group was designated Non-computer (NC, Instructor A). The investigator taught Computer 1 and Non-Computer groups. A mathematics department colleague taught group Computer 2.

The students in the computer groups received three sessions of instruction in the use of Lotus 1-2-3. Additional instruction was given as needed for the purpose of the project. The instructional content was textbook oriented and was identical for both treatment C1, C2 and comparison NC groups.

The following procedures were followed to achieve the purpose of the study. First, a review of relevant literature to obtain information about investigations related to the study was undertaken. Based upon this review instruments for evaluating achievement of problem solving skills were developed. Instruments to assess students' attitudes toward the usefulness of mathematics and confidence of learning mathematics; their own problem solving abilities; and computers were chosen.

The investigator and a mathematics colleague constructed two measures, the pretest and the posttest, (See Appendix B). The problems on the two examinations were matched in that the strategies that can be used to solve a pretest problem can also help to solve a posttest problem.

The Fennema-Sherman Mathematics Attitudes Scales, (See Appendix C) instruments were used to measure attitudes toward the learning of mathematics by males and females (Fennema & Sherman, 1976) and to asses the students' attitudes toward the usefulness of mathematics and their confidence of learning mathematics. The Student Attitude Questionnaire (See Appendix D), developed for the Mathematical Problem-Solving Project at Indiana University (Moses, 1976) was selected to assess problem solving abilities. The students' attitudes toward computers (See Appendix E) were assessed using instruments developed by the Office of Planning, Development and Evaluation in the university where the study was conducted. Permission for the use of the instruments was requested and received (See Appendix A).

The study required other activities. There was a review of the software available in the Mathematics and Computer Assisted Instruction Laboratories. The investigator developed and selected from the literature reviewed computer-based activities for the mathematical reasoning skill course. She also organized the computer-based curriculum project, including the curricular materials and the schedule for computer laboratory visits. Other activities were the administration of the pretest, the posttest, and the self-assessment instruments. The investigator and the colleague working in the study interviewed a selected sample from the treatment groups to get student's thoughts and feelings about the treatment.

Plan of the Report

The plan of the report follows the sequence established in the procedure of the study. The review of literature is presented in Chapter II. The review includes studies involving problem solving, the use of computers in mathematics, and the use of computers to provide concrete experience as an aid to problem solving.

Information about the subjects of the study, treatment groups and comparison group, the course, the environment, the instructional materials and the instruments appears in Chapter III. The analysis of the data is presented in Chapter IV, and the Summary, Conclusions and Recommendations in Chapter V.

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