Volume 17, Number 2/3 1998
Contents
Using the Internet to Learn Mathematics
Sue Gerber, Thomas J. Shuell, and Carol Ann Harlos 113Abstracts
Using the Internet to Learn Mathematics
Sue Gerber and Thomas J. Shuell
Center for Educational Resources and Technologies Graduate School of Education, 222 Baldy Hall State University of New York at Buffalo Buffalo, NY 14260-1000, USAShuell@acsu.buffalo.edu
Carol Ann Harlos
Buffalo Public Schools Buffalo, NY 14202, USAStudents using the Internet to obtain data for a regularly assigned eighth-grademathematics project was studied for two purposes: (a) exploring ways in which the Internetmight be used in conjunction with such a project and (b) investigating how students goabout learning in this type of instructional environment. The four students from each oftwo classes who used the Internet were observed for 5 weeks, and field notes wererecorded. The remaining students in the classes worked on the same project but obtainedtheir data elsewhere. All students responded to questionnaires before and after theproject was completed, and the Internet students were interviewed at the end of theproject. Results are discussed in terms of four themes: (a) students’ understandingof the Internet, (b) approaches used in searching the Internet for relevant data, (c) howstudents made sense of their data once they were obtained, and (d) the effect of theproject on students’ appreciation for and understanding of mathematics as beingrelevant in ways other than those traditionally used in the classroom.
SAM-Net (SCIENCE and MATH on the Net): Connecting Students and Teachers to ScientificResearch Through Scientific Communication and Electronic Networking
Laura M. Bartolo
Libraries and Media Services Kent State University Kent, OH 44242, USAlbartolo@lms.kent.edu
Peter Palffy-Muhoray
Liquid Crystal Institute Kent State University Kent, OH 44242, USAmpalffy@cpip.kent.edu
Scientific research has always relied on communication between scientists for gatheringand providing access to data, for exchanging information, for collaborating on projects,and for disseminating results. Moreover the rapid expansion of national and worldwidescientific electronic networks and the resources residing on them are changing theenvironment in which scientific communication and research take place. Introducingstudents and teachers to the social structure of scientific communication as part of ahands-on, minds-on approach can help increase students’ knowledge and interest in thesciences. The National Science Foundation (NSF) and U.S. Congress have called uponscientific research centers and universities to play an active role in precollege scienceeducation. The NSF Science and Technology Center for Advanced Liquid Crystalline OpticalMaterials (ALCOM) with the Libraries and Media Services and Department of Mathematics andComputer Science at Kent State University in Ohio have developed SCIENCE and MATH on theNet (SAM-Net), a science education networking project designed for middle and secondaryscience and math teachers, school librarians, and their students, available through theWorld WideWeb(http://olbers.kent.edu/alcomed/ Sam_Net/samnet.shtml) via the Internet. Thisarticle describes SAM-Net which incorporates scientific communication, electronicnetworking, and scientific research as practiced by scientists into a K-12 scienceeducation program.
Image Processing for Teaching: Transforming a Scientific Research Tool Into anEducational Technology
Richard Greenberg
Lunar and Planetary Laboratory University of Arizona Tucson, AZ 85721-0092, USAgreenberg@lpl.arizona.edu
As a technology designed for scientific research in a wide range of fields, theemergence of digital image processing provided the potential to offer all studentsopen-ended opportunities for exploration, discovery, and quantitative analysis, thussupporting constructivist ideas about learning that were developing in the same timeframe. By adopting implementation strategies that put an emphasis on the challenges ofeducation, rather than on re-inventing or modifying the technology, the Image Processingfor Teaching (IPT) project has provided this powerful medium to excite students aboutscience and mathematics, as they use research-quality software on microcomputers. Thecomponents of this dissemination project have been widespread teacher education,curriculum-based materials development, and substantial follow-up support and outreach.IPT materials are developed by educators and scientists for integration into thecurriculum in all areas of science and mathematics for elementary school through collegelevels.
Sergei Abramovich
University of Illinois at Chicago M/C 249, Chicago, IL 60607-7045, USAsergei@math.uic.edu
Wanda Nabors
University of Georgia 105 Aderhold Hall Athens, GA 30602-7124, USAIn this paper the authors suggest that using iconic and computing features of aspreadsheet enhances the transition from natural language sentences to pictorial andnumerical representations of algebraic word problems. The capability of a spreadsheet tosymbolize and generalize numerical inputs interactively enables one to move from rulesthat structure relations among numbers to symbolic representations of these rules in theform of algebraic equations. The use of a relation grapher enhances the learningenvironment by providing an alternative representation of equations and their solutions.The authors argue that an enactive approach to modeling word problems, enhanced andextended by the use of the software, may result in much more impressive work on the partof the students and could lead to deeper concepts learned. The paper presents workperformed in a lab setting with preservice and inservice teachers enrolled in contemporarygeneral mathematics and problem-solving courses.
Brian Hudson
Mathematics Education Centre School of Education, Sheffield Hallam University 25 Broomgrove Road, Sheffield S10 2NA, UKB.G.Hudson@shu.ac.uk
This paper is based on a study which aimed to investigate the potential ofcollaborative learning in mathematics using multimedia. The specific context in which thiswas undertaken involved the use of the multimedia package World of Number which wassponsored by the U.K. government's National Curriculum Council. The classroom research wascarried out during the spring term of 1994 with a year-9 top set (13-/14-year-olds). Thesoftware uses video clips of motion, several of which are sporting events from the SeoulOlympics, together with options to choose different axes and different graph optionsinvolving distance, speed, acceleration, and time. Data was collected by video recordingthe work of groups working on the multimedia-based activities, and the analysis wasinformed by a socio-cultural perspective and ethnographic research methods. The aim of theanalysis was to illuminate the "sense-generating" classroom activity andstudents' mathematical meaning-making within this context. The classroom interaction wasfound to be supported, not only by language mediated by the multimedia system, but byother non-verbal tools, for example the students' own sketches and their gestures.Suggestions for future directions for further research and development are made.
Sharon Dugdale
Division of Education University of California Davis, CA 95616-8579, USAssdugdale@ucdavis.edu
Spreadsheets have become popular tools for exploring mathematical patterns and buildingconceptual understanding of variables and functional relationships. This investigation ofnumber sequences and series combines the calculational and graphical capabilities of aspreadsheet to engage students in analyzing functions and generalizing results ofmathematical inquiry. Based on a family of recursively defined functions, the project issufficiently open-ended to support a focus on familiar sequences and series and therelationships among them, as well as to stimulate investigation of more novel patterns.Examples of students’ work illustrate multiple paths of inquiry, generalization, andmathematical reasoning. Given suitable introductory activities and grade-level appropriatequestions and discussion, this project supports effective investigation of patterns andfunctions for students from middle grades through precalculus.
Renata Briano and Vittorio Midoro
Istituto per le Tecnologie Didattiche/CNR via De Marini 6, 16149 Genova, Italybriano@itd.ge.cnr.it / midoro@itd.ge.cnr.it
In the field of environmental science education the teacher’s role is not so muchto facilitate the process of transferring codified concepts, but rather to create alearning environment in which the students carry out activities that will lead to anunderstanding of the issue addressed. This paper, making reference to two experimentalprojects related to the issue of flooding in an Italian basin, describes an innovativeapproach to environmental science education. In this approach, teachers use thedevelopment of a hypermedia system as a means of supporting student’s cooperativelearning. This research has shown both how cooperative production of a learningenvironment can be a way of re-evaluating the work performed by teachers and howcooperative creation of a product can represent a good learning strategy for students inthe field of environmental science.
David Mioduser
School of Education Tel-Aviv University Ramat-Aviv, 69978, Israelmiodu@ccsg.tau.ac.il
Richard L. Venezky
Department of Educational Studies University of DelawareNewark, DE 19716, USA
Brian Gong
Learning Result Services Kentucky Department of EducationFrankfort, KY 40601, USA
The Weather Lab is a computer-based tool for assessing a student’s knowledge andunderstanding of weather phenomena. The student is involved in generating weatherforecasts or in manipulating weather components (e.g., temperature or pressure measures)affecting the final formulation of a forecast. The Weather Lab is conceived as aninstruction-based assessment tool, implying this:
1. Function: It is part of the instruction, and not a post-instruction testing device.It is aimed at informing instruction and triggering student reflections on her or hislearning.
2. Focus: It is focused on the student’s knowledge at different levels of ability(e.g., knowledge of facts, understanding of relationships, manipulation of weathervariables, and forecasting).
3. Targets for the assessment information: The collected information is used forgenerating feedback loops within the system, between the system and the student, andbetween the system and the teacher, affecting actual instructional decision-making atthese three different levels.
4. Assessment strategy and methods: The student/system interaction proceeds as acase-based, problem-solving dialog. The student may explore changes in weather variablesaffecting weather outcomes or generate forecasts for particular weather situations. Eachinteraction is assessed and evaluation information is delivered to the above mentionedtargets.
5. Use of technology: The accumulated experience in tutoring systems developmentsupports the building of sophisticated procedures aimed at representing and usingsubject-matter expertise knowledge, modeling the student performance, and generatingdialog situations.
Vishakha Parvate and K.S.R. Anjaneyulu
National Centre for Software Technology Gulmohar Cross Road, No. 9 Mumbai, Indiavis@asterix.cs.unipune.ernet.in
anji@saathi.ncst.ernet.in
Parvati Rajan
Shreemati Nathibai Damodar Thackersey Women’s University Sir Vithaldas Vidyavihar, Juhu Road Santacruz (W), Mumbai, IndiaWe have designed and implemented Mathemagic, a remedial teaching system for high schoolmathematics. The representation of a domain in Mathemagic contains a concept network withprerequisite links, a set of diagnostic questions, and a set of remediation problems. Theproblems have to be provided to the system in a predefined structure with their solution,concepts involved and all the information needed by the methods from which the student hasto choose one for problem solving. Competence factors (CFs) are used to evaluate, duringthe diagnostic phase, the degree of students’ mastery for each concept (“overlaymodel”) with positive and negative CFs being given for each diagnostic question(several questions for a concept). Based on the concepts needing remediation, problems areselected and ordered. The student has a choice of five interaction modes for solving theproblem. A preliminary study with the system shows that it can provide effectiveremediation to students. The contributions of this work are (a) using the competencefactor approach as a means to model the student’s understanding, (b) coming up with amethodology for focused remediation which is even applicable to other domains, (c)providing the user with multiple interaction modes for the same problem, and (d)integrating all of these into a practical system.
Edited by David A. Smith
Duke University, Durham, NC, USAAssisted by David J. DeVries
Georgia College & State UniversityEditorial Notes: This new Journal of Computers in Mathematics and Science Teaching(JCMST) column is an intellectual successor to the “Learning Software” columnthat appeared three times a year in UME Trends from 1989 to 1996. The initials stand forUndergraduate Mathematics Education, and UME Trends was a bimonthly newsletter that beganas a National Science Foundation-supported calculus reform project and ended as apublication of the Mathematical Association of America. Its editor throughout was EdDubinsky of Georgia State University
To explain what this column is about, I will paraphrase the introduction to“Learning Software”: “Learning: The Web” is a deliberate doubleentendre. On the one hand, it means the reader is learning about resources available onthe World Wide Web. On the other hand, it means the subject matter will be resources forlearning. That is, I intend to concentrate on Web sites that provide innovativeenvironments in which students can be expected to learn.
This column will be different from “Learning Software” in at least two ways.First, there is the obvious difference that the subject matter is now Web resources ratherthan software packages. Second, reflecting the scope of this journal, the contents will bebroadened to include natural sciences and computer science, not just mathematics.
On the other hand, there are at least two key features of “Learning Software”that will be retained. First, the learning experience cannot be just reading the column.It is even harder with Web sites than it was with software to convey in a static printmedium any real sense of how the learning can take place. At best, this column willstimulate readers to find and experience a subject Web site on their own. (The technicalterm is “check it out.”) Second, I do not intend to write all the columnsmyself. Contributions that are consistent with the second paragraph are eagerly solicited,as are comments, suggestions, corrections, criticisms, or any other kind of feedback. Sendcommunications to das@math.duke.edu.
DAS