Journal of Computers in Mathematics and Science Teaching

Volume 16, Number 2/3 1997

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Contents

The Use of Spreadsheets for ConstructingStatistical Understanding

Introducing Robotics at the UndergraduateLevel

Teachers’ Perceptions of the Impact ofGraphing Calculators in the

Mathematics Classroom

Graphing Calculators in High SchoolMathematics

Effect of Feedback on Learning to MatchAlgebraic Rules to Expressions With an Intelligent LearningEnvironment

Academic Support in Mathematics in a ThirdWorld Environment

On Learning Quantification

The Impact of Model-Centered Instruction onStudent Learning:

The Area and Volume Units

Variations in Concerns and Attitudes ofScience Teachers in an

Educational Technology DevelopmentProgram

edited by Joseph S. Krajcik

Cooperative Learning and Technology

REBECCA DENNING AND PHILIP J. SMITH

Cooperative learning has been used as an educational technique forsome time, and recently researchers have been exploring technology asa mechanism to further this educational method. While some designershave developed cooperative activities around existing software suchas spreadsheets, word processors, and hypermedia/multimedia programs,others have developed new educational software, usually specific to acontent or skill area and/or a particular learning episode to supportappropriate student interactions. This review describes severalexamples of the use of technology to support cooperative learningepisodes and examines the underlying design concepts and principlesembedded in these applications.

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MATHEW MITCHELL

This paper describes an attempt to systematically incorporate"active learning" into the structure of an elective course designedto instruct students in computer-based approaches to statistics.Active learning was implemented primarily by having students createeducational worksheets which would instruct a novice about specificstatistical concepts. This format led participants to become involvedin the process of mathematical storytelling. The in-built features ofthe spreadsheet program that were important to the goals of thecourse included (a) ability to create multiple representations ofstatistical measures, (b) ability to create number playgrounds asmini-simulations, (c) ability to incorporate story lines, (d) theopportunity for creativity, and (e) the power of open-ended softwareprograms. The student-developed educational worksheets displayed awide variety of key features including (a) storytelling, (b) posingchallenges, (c) artistic impact, (d) incorporating better visualrepresentations, (e) including interactivity, and (f) choosing moresophisticated examples. This approach to statistics instructionappeared to result in both high student learning and high studentmotivation to learn.

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SAM R. THANGIAH AND SHARAD W. JOSHI

 There is a need at the undergraduate level to exposestudents to the complexities of programming robots to accomplishtasks in real time. This paper outlines how a course in robotics canbe taught at the undergraduate level with specific experiments thatcan be used for incremental learning in programming a mobile robot.The experiments can be conducted using either a commerciallyavailable robot or by simulating the actions of a robot. In addition,we detail the caveats of teaching such a course.

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LINDA M. SIMONSEN

THOMAS P. DICK

The National Council of Teachers of Mathematics (NCTM) Standardsstates that at the high school level, graphing calculators must beavailable to all students at all times. The purpose of this study wasto compile teachers’ impressions of the barriers and/or incentivesassociated with the use of graphing calculators on classroomdynamics, curriculum and evaluation, training, support, and overallattitude. Hewlett-Packard (HP) gave 30 HP-48S graphing calculatorsand an overhead projection device to 36 high schools across theUnited States. Each school was also given a mandatory 1-dayinservice, as well as an optional 1-week summer workshop, on how touse the calculator and integrate it into the classroom. A year later,each of the schools was contacted and asked if a teacher wouldparticipate in a telephone interview which contained primarilyopen-ended questions. Twenty-seven teachers, representing a widerange of high school mathematics classes, participated in theaudiotaped interviews. Recurring themes that emerged from theinterviews were organized into these categories: (a) advantages ofcalculator use, (b) disadvantages of calculator use, (c) classroomdynamics, (d) curriculum and evaluation, and (e) professional supportand development. The results demonstrated that the teachers’perceptions of the advantages appeared to be instructionally related,whereas the perceptions of the disadvantages appeared to be primarilylogistical in nature. The dynamics of a classroom tended to shift tomore discussion, inquiry, and cooperative learning. There wasconsiderable reluctance to deviate from stringent curriculumrequirements that are reinforced by standardized tests. This studygave teachers a chance to share their knowledge, experiences, andinsights, which in turn will help guide the design of curriculummaterials, inservice programs, and support systems to best equipteachers to handle the demands and opportunities that technologypresents.

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ELAINE SIMMT

 This paper reports on a research study which examined howsome teachers used graphing calculators in their instruction ofmathematics and how their views of mathematics were manifested in theways they choose to use this technology. Six teachers were observedin their classrooms as they taught lessons on the quadratic functionusing graphing calculators and were interviewed regarding theirbeliefs, attitudes, and conceptions about mathematics and mathematicseducation. The study suggests that teachers used the graphingtechnology as an extension to the way they always taught the unit.Graphing calculators were primarily used as a device to providegraphical images from which the students were expected to observe andmake generalizations about transformations of the quadratic function.The teachers’ philosophies varied considerably and the manifestationof these philosophies was evidenced, not so much in their choice ofactivities, which included the use of graphing calculators, but inhow the teachers followed up those activities with questions andsummary notes. Although all of the teachers were provided with thesame technology and the same curricular constraints, each of theteachers brought forth the mathematics curriculum within the contextof his or her personal philosophies of mathematics and mathematicseducation.

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A. NGUYEN-XUAN

JEAN-FRANCOIS NICAUD

JEAN-MICHEL GÉLIS

This paper presents a comparative study of the effects of feedbackon students who learned to solve algebraic factorization problemswith an intelligent learning environment (ILE). Two experiments oflearning by solving problems were conducted in exactly the sameexperimental conditions, except that some of the system’s commentsregarding errors made by the students and the system’s promptsregarding one particular factorization rule were modified between thefirst and second experiments. The students’ actions and theinteraction of the students and the system were recorded. a handanalysis of the individual protocols was then made to ascertain towhat extent the students had learned to match formal rules offactorization to algebraic expressions. The results showed that whenthe same error comments were used in both experiments, similaritieswere observed in the learning paths of the respective student groups.Small changes in the comments led to small changes in the learningpaths, and significant changes in the prompts given by the system(when asked for help) and in the error comments led to significantchanges in the learning process.

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J.C. ENGELBRECHT

As part of the academic support programme, a computerised bridgingcourse in mathematics was developed at the University of Pretoria.The didactical approach of the system is that of criterion-referencedinstruction, or mastery learning, in which the progress of thestudent strictly depends on proven mastery of the concepts. Eachuniversity topic is preceded by modules on the school mathematicsnecessary for understanding the particular concepts and techniquesinvolved. A description of the content and didactical approach usedin the course is given. The course was in use at the University ofPretoria during 1991 and 1992 and the performance of the students wasmeasured against those of a control group of similar students. Theaverage performance of students in the bridging course wassignificantly better than students in the control group, forengineering as well as for non-engineering students. Furthermore,students experienced the course positively.

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ED DUBINSKY

This paper reports on a study of students learning the concept ofuniversal and existential quantification in undergraduate mathematicscourses in which the instruction was based on previous research intowhat it means to understand this concept. Following a theoreticalanalysis of the epistemology of quantification obtained in previouswork, instruction is designed in which students constructmathematical concepts on a computer, using the mathematicalprogramming language ISETL. The intention is that, as a result ofmaking the computer constructions, students will tend to makeeffective mathematical constructions in their minds.

The 36 students in the study were sophomores and juniors withjoint majors in mathematics and computer science and who were takinga course in discrete mathematics. The two groups were at twodifferent universities and the same instruction, with minorvariations, was given to both groups. Instruments used for assessingstudent learning consisted of written questions on which studentswere to work individually to provide written responses. The questionswere given in class without warning. Results suggest that when thepedagogical approach described in this paper is used, students candevelop some understanding of quantification and the ability to workwith it, even when the particular problems they are given aredifficult.

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KALYANI RAGHAVAN, MARY L. SARTORIS, AND ROBERT GLASER

The Model-based Analysis and Reasoning in Science (MARS) projectis involved in developing computer-supported, model-centeredcurriculum modules for middle school science. MARS instructionfocuses on a variety of physical, pictorial, and symbolicrepresentations of theoretical entities, providing tangible objectsthat students can use to think and talk about abstract concepts andlinks between concepts. This article examines the impact of the firsttwo units of a sixth-grade curriculum module, implemented in a publicschool during the 1993-1994 school year. After briefly describing theunderlying rationale and content of the entire nine-unit module, thearticle focuses on the units on area and volume. Descriptions of thecontent and context of the two units are followed by a detailedanalysis of implementation data, which include student test responsesand classwork, videotapes of classroom interactions, and audiotapesof individual student interviews. MARS students’ test performance iscompared with that of a traditional class, and student work samplesand videotape transcripts are used to illustrate specificobservations related to curricular impact. In addition, a scoringscheme, developed to assess understanding and use of target concepts,is described. The article concludes with a discussion of implicationsand suggestions for curriculum refinement.

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PAUL GERMANN AND CRAIG M. SASSE

This study monitored change in concerns and beliefs of elementaryand secondary teachers involved in a 2-year program to integrate theuse of computers with science teaching. Some of the first cadre ofteachers who participated in the program the first year returned thesecond year to extend their knowledge of computers and to serve asmentors. The Stages of Concern Questionnaire measured self-,management, and impact concerns. The teachers’ perceivedself-efficacy was measured by the Microcomputer Utilization inTeacher Efficacy Beliefs Instrument. Concern profiles for cadre 1teachers during the first year showed a decrease in self- andmanagement concerns and an increase in impact concerns. Instead ofcontinuing to move toward adoption stages during the second year,they reverted to relatively high self-concerns and lower impactconcerns. Concern profiles of cadre 2 teachers in the second yearwere similar to those of cadre 1 teachers during their first year.Self-efficacy of both cadres increased from pretest to posttest.Major barriers to adoption were time to prepare and the availabilityof computers and software. Results indicate that learning about theuse of computers in science teaching is not a single innovation but abundle of applications.

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