This chapter presents a summary of the study with conclusions based on the findings. Recommendations for further research also are included.

    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. The study took place in a private four-year university in Ponce, Puerto Rico during the Spring of 1995. The participants enrolled in the Mathematical Reasoning Skill course, MRSG 1010, were divided by the registrar into three groups. The major topics covered in the course were The Nature of Patterns and Inductive Reasoning, Linear Equations, The Nature of Statistics, The Nature of Financial Management, and the Nature of Graphs and Systems. The Mathematical Reasoning Skill Course was selected because it was developed to promote mathematical reasoning and the development of problem solving skills.

    Two groups were designated Computer 1 (C1, Instructor A), and Computer 2 (C2, Instructor B). The third group was designated Non-Computer (NC, Instructor A). The only planned difference in the treatment was that the Computer groups worked problems involving the concepts and skills from the mathematical reasoning course using the computer; while the Non-Computer group did not use the computer in the study of the same mathematical content. The Computer groups received instruction in the use of the software Lotus 1-2-3.

    To achieve the purpose of the study, the investigator reviewed relevant literature to determine the results of related studies. Another important activity was the development of the Mathematical Reasoning and Problem Solving Skill Tests. These instruments were used as the pretest and posttest of the study to assess achievement of mathematical and problem solving skills of students who received instruction on heuristic strategies in a one semester course.
The investigator selected and developed the instructional materials for the study, and selected the self-assessment instruments. The instructional materials included activities that promote the use of tables to find a pattern, and to make a guess, or the use of a graph that could lead to the problem's solution. The self-assessment instruments used in this study were the Student Attitude Questionnaire, Fennema-Sherman Mathematics Attitudes Scales, and Perception Toward the Computer scale. Except for the Perception Toward the Computer Scale, all the instruments were administered at the beginning and at the end of the study.

Among the questions to be addressed in this study were:

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

    The investigator developed instructional materials for all the topics discussed in the course; however, computer activities are time consuming and only half of the instructional materials were used during the project. In addition, students were learning to use application software which took up part of the computer laboratory meeting period. The computer classes appeared not to be long enough for students to learn efficiently to use the computer. Time devoted to computer instruction, however, reduced substantially students' opportunities to learn mathematical content.

    The results from the interviews showed that the students who participated in the study preferred to use the computer for certain topics and not for others. The topics where they would like to use the computer were statistics, problem solving and linear equations in two variables. The reasons for this selection was that the computer facilitated the computational work and that problems from other topics were easier with paper and pencil or calculators. Other information obtained from the interviews revealed that students value computers as a useful tool for problem solving. They also are conscious that knowing how to use a specific software would help them in other academic subjects.

    The Perception Toward the Computer Scale gathered information about the attitudes that college students have in relation to computers. Subjects rated computers as powerful, useful, effective, interesting and difficult. The students in the Computer groups scored higher in all of these characteristics.

    The results from the Student Attitude Questionnaire showed that the computer is not necessarily the reason for difference in problem solving attitudes. Variables, such as the student ability can have causal effect on mathematical problem solving attitudes and achievement.

    Fennema-Sherman Mathematics Attitudes Scales showed no significant difference in the attitudes of the students before and after the treatment. The results, although surprising for the investigator, suggested that the students at this college already had positive attitudes toward the usefulness of mathematics and confidence in learning mathematics. Ninety four percent (94%) of the students in the Computer groups selected "strongly agree" or "agree" to the statement "I am sure that I can learn mathematics." Ninety five percent (95%) percent chose the same answers to the statement "I have a lot of self-confidence when it comes to math." These results can be attributed to the fact that subjects participating in studies often provide answers they believe the investigator prefers.

    The results of this investigation suggest that teachers should consider certain factors when deciding to implement technology in the teaching of mathematical reasoning and problem solving skills. Mathematical problem solving involves a mental process that could be classified as complex. Working with the mathematics, while learning how to use the computer, complicates the learning process. Other factors that should be taken into consideration are the time available for class demonstration and practice; the level of students' development; students' knowledge of the hardware and software to be used and the ability of the students to learn to use these resources.

    The facts that the students chose problem solving as a topic for which they would like to use computers, and that ninety two percents (92%) of the students said that the computer is a useful tool when solving problems, give support to the idea that computers can facilitate certain aspects of mathematics instruction. The investigator recommends further research on the effectiveness of computers when teaching mathematical reasoning and problem solving skills. A recommendation for future study is to investigate the effect of a computer-based curriculum on mathematical reasoning and problem solving skills at the college level with students who already have applied computers in other mathematics courses, or students who know how to use a spreadsheet.

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