Volume 15, Number 4 1996
Integrating Problem Solving, Technology,and the Experience of Mathematical Discovery in Teacher EducationSergei Abramovich and Gary Brown 323
Teaching Reinforcement of Stochastic Behaviour Using Monte Carlo SimulationWilliam P. Fox, Paul E. Grim, and Daniel L Hogan, Jr. 339
Group Interaction and Student Questioning Patterns in anInstructional Telecommunications Course for TeachersMichael Waugh 353
Guided Discovery, Visualization, and Technology Applied to the New Curriculum for Secondary Mathematics
Karan B. Smith 383
Computer Inclination of Students and Their Teachers in the Context of Computer Literacy EducationUri Zoller and David Ben-Chaim 401
The Impact of Using Computers and Calculators on Calculus Instruction:VariousPerceptionsJohn A Rochowicz, Jr. 423 John A Rochowicz,Jr.
SERGEI ABRAMOVICH AND GARY BROWN
Department of Mathematics Education
University of Georgia
105 Aderhold Hall, Athens, GA 30602-7124, USA1
George Pólya (1981) once stated that teacherscannot impart the experience of mathematical discovery if theythemselves have not had that experience. Meanwhile, traditionalteacher training courses have offered little if any engagementin exploratory mathematics. Yet the advent of newer software toolsinto the mathematical classroom brings about new opportunitiesfor investigation in contemporary problem solving courses. A technology-richenvironment based on these tools can significantly enhance andunexpectedly extend the discussion of traditional topics fromproblem solving; and it can provide an open ended and egalitarianclassroom atmosphere that stimulates students to come up withtheir own questions thus bringing about powerful instances oflearning. This paper shows how the generic software triple-a spreadsheet,a relation grapher, and a dynamic geometry-can contribute to teachertraining through an exploratory problem-solving course.
WILLIAM P. FOX, PAUL E. GRIM, AND DANIEL L. HOGAN,JR.
Department of Mathematical Sciences
United States Military Academy
West Point, NY 10996-1786, USA
This paper highlights a distinctive problem areathat was discovered in a majority of undergraduates attendingthe United States Military Academy and other major universitiesmajoring in Industrial Engineering, Operations Research, SystemsEngineering, and Applied Mathematics. None of these undergraduatemath or engineering majors have a firm understanding of the fundamentalsin using and interpreting computer simulations. A proposed blockof instruction is explained that would give these students thebasis of understanding required to begin more advanced coursesin simulation theory or applications. The proposed block consistsof an introduction to simulation, concentrating on the algorithmsused to logically represent the system to be modeled. These algorithmsare eventually coded in the language of the students choice. Theresults of each exercise are used to emphasize a particular facetof Monte Carlo simulation modeling. Students complete the blockwith a project that will demonstrate their understanding of thefundamental concepts used in Monte Carlo simulations.
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Group Interactionand Student Questioning Patterns in an Instructional TelecommunicationsCourse for Teachers
MICHAEL WAUGH
Department of Curriculum and Instruction
University of Illinois at Urbana-Champaign
1310 South Sixth Street, Champaign, IL 61820, USA
The purpose of this study was to examine group interactionsand students' questioning patterns in a university course thatwas conducted largely through using an electronic network as aninstructional medium. Twenty-one students, two instructors, 12"electronic visitors" and approximately 30 other individualsexchanged electronic communications using the FrEdMail and Internetnetworks. These communication exchanges occurred during the springsemester of 1993 as part of a university course designed to teachteachers how to use an electronic network as an instructionalmedium.
The "public" electronic communication amongthese individuals occurred using an electronic mail (email) reflectormechanism. All messages sent to this email reflector and all "private"messages sent by the students, visitors and others to the courseinstructors, and all messages exchanged between instructors formone of the datasets analyzed. In addition, selected student'slogbooks were analyzed to help develop an estimate of the totalamount of electronic mail generated between the students and theirremote project partners. Further, a sample of seven students wererandomly selected and their email communications were analyzedto identify the frequency and type of questions they asked duringthe course.
Based on the messages that students generated tothe instructors and class group and evidence provided by studentlogs, it is estimated that the average student generated between24 and 36 messages during the semester and some type of questionwas generated in approximately half of those messages. The courseinstructors addressed approximately 33% of their messages to individualstudents while course students and "electronic visitors"together were responsible for 57% of the messages addressed tothe whole group. These findings are interpreted as indicatingthe high levels of interactivity and individualized instructionthat are possible through using electronic networks for instruction.
In addition, some differences in types of questionsgenerated by students were identified and these are interpretedas being related to the students' level of networking experience.The data collected in the study also revealed that the most commontype of question asked by the participants sought informationregarding the technical aspects of electronic networking.
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Guided Discovery,Visualization, and Technology Applied to the New Curriculum for Secondary Mathematics
KARAN B. SMITH
Department of Mathematical Sciences
The University of North Carolina at Wilmington
601 South College Road, Wilmington, North Carolina28403-3297, USA
Linear programming has recently been integrated intothe high school mathematics curriculum. Graphical problem solvingoffers methods for teaching systems of constraints and objectiveswhich emphasize visualization and student discovery. Activitieswhich highlight major concepts of linear programming are presented.These activities demonstrate how technology allows students tosolve linear programming problems using exploration prior to learningalgorithmic methods. They have been used with preservice teachers,offering them experience with the new curriculum and use of technology.
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ComputerInclination of Students and Their Teachers in the Context of ComputerLiteracy Education
URI ZOLLER AND DAVID BENCHAIM
Department of Science Education
Haifa UniversityOranim, The School of Education
of the Kibbutz Movement, Kiryat Tivon 36006, Israel
The computer inclination (CI) of 501 11th-gradestudents and 53 of their teachers was assessed using the instrumentSurvey of Attitudes Toward Learning About and Working With Computersand structured interviews. Regardless of whether students or teacherswere previously exposed to computers, significant differenceswere found between the CIs of (a) students and teachers, (b) femaleand male students and teachers, (c) students in the science, socialstudies and technology tracks, and (d) teachers of science andsocial studies. CI means for all groups were found to be positive,more so for teachers compared to students. Although the exposurefactor accounts for 620% of the variance in the CI, ourresults suggest that other factors may have a substantial effect.It is argued that both students' and teachers' views concerningthe integration of computers in science teaching and the differencesin their computer inclination should be taken into considerationin the design and implementation of science courses. The externalvalidity of several commonly accepted CIrelated generalizationsin the context of computer literacy education is questioned.
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The Impactof Using Computers and Calculators on Calculus Instruction: VariousPerceptions
JOHN A. ROCHOWICZ, JR.
Department of Mathematics
Alvernia College, 400 Saint Bernardine Street
Reading, PA 19607, USA
Currently many students are unprepared to study calculus,see no relevance in the topics taught, and fail the calculus course(Anderson & Loftsgaarden, 1988). Although the use of computersand calculators for calculus instruction requires a great amountof effort on the part of the teacher, the potential exists fora learning environment that is more motivational, meaningful,and relevant. This computing technology use for calculus instructionis somewhat limited, though, and its use could be more extensive(Anderson & Loftsgaarden, 1988). With an increased knowledgeconcerning the impact of using computers and calculators in acalculus course, faculty should be more motivated to try new anddifferent ways of implementing technology in their instruction.This paper presents calculus instructors' perceived impact ofusing computers and calculators on specific topics of calculus,student motivation, student learning, and the role of the teacher.
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