Computer algebra systems in mathematics education: A case study examining the introduction of computer algebra systems to secondary mathematics teachers.

摘要

Computers are now routinely used as tools in mathematics instruction. Although some colleges have begun to use Computer Algebra Systems in calculus courses, their existence is unknown to many mathematics educators. How are CASs integrated into secondary mathematics instruction? As part of this study, the researcher taught a CAS course for secondary teachers providing them with hands-on CAS experience, focusing on pedagogical issues involving their use, and involving these teachers in developing and presenting CAS based curriculum topics.;This study contains a comprehensive description of the course and materials used to create a core of secondary teachers knowledgeable in the use of CASs. It also contains the sample lessons developed by these teachers. Answers to questions examining pedagogical and curricular implications of using CASs in secondary mathematics classrooms are answered based on the teachers' CAS lessons, their reactions to their fellow classmates' lessons, outside readings, and their responses to questions presented in a culminating paper.;Some results from this research support those found in the college level calculus studies--teachers' believe that the use of CASs: (1) reduces the time needed for tedious paper and pencil computations, (2) allows more time to concentrate on understanding the underlying concepts or processes, and (3) provides time to explore additional examples or topics. In addition to calculus, teachers believe that CASs can be used effectively with topics from arithmetic, algebra, geometry, trigonometry, and statistics. However, it was found that teachers feel that CASs are of little use in the area of formal proofs. All teachers agree that the use of CASs is appropriate at the senior high school level, but some question their use at the middle or junior high school levels.;They also believe that CASs allow implementation of changes suggested in the NCTM's Standards by emphasizing underlying concepts, developing problem solving techniques, allowing assignment of long term complex real world problems, and fostering effective mathematical communication.;Given the availability of sufficient hardware and software, this research shows that secondary teachers can integrate the use of CASs into traditional mathematics instruction.