using data-collection devices to enhance students...

504

Using Data-Collection Devices to Enhance Students’ Understanding

hile working with high school students at a Mathe-matics, Physics, and Advanced Technology Explo-ration Day, we observed an activity in which stu-dents tried to reproduce a distance-time graph bywalking. They used a Calculator-Based Ranger(CBR) to collect data about their distance from amotion detector and to generate a distance-timegraph in real time. During the activity, the studentsclearly did not understand the distance informationthat the given graph was conveying. See figure 1.Instead of moving back and forth along a straightline to produce a graph that matched the distance-time information given, students typically walkedin a path that resembled the shape of the original

graph. Some walked completely out of the probe’sdetecting range, as shown in figure 2.

These students were demonstrating a commonmisconception about motion and distance, graph-shape-and-path-of-motion confusion (Goldberg andAnderson 1989; McDermott, Rosenquist, and vanZee 1987). They thought that the graph should looklike the physical event being observed.

Although researchers agree that studying graphscan lead to a deeper understanding of physical con-cepts (Mokros and Tinker 1987; Brasell 1987a,1987b; Linn 1987; Goldberg and Anderson 1989;and McDermott, Rosenquist, and van Zee 1987),students often have problems with graphing andmodeling (Dunham and Osborne 1991; Leinhardt,Zaslavsky, and Stein 1990; Goldberg and Anderson1989). From research, we identified several areas ofdifficulties:

• Connecting graphs with physical concepts• Connecting graphs with the real world• Transitioning between graphs and physical

events• Building graphical concepts through student

discourse

W

MATHEMATICS TEACHER

Students typically

walked in apath that

resembled theshape of the

originalgraph Edited by Thomas Dick

[email protected] State UniversityCorvallis, OR 97331-4605

Penelope H. [email protected] CollegeAllentown, PA 18104

Douglas A. Lapp, [email protected], teaches atCentral Michigan University, Mount Pleasant, MI 48859.His interests are in the use of multiple representationsinvolving technology for teaching calculus concepts.Vivian F. Cyrus, [email protected], teaches atMorehead State University, Morehead, KY 40351. Herinterests include integrating technology into the classroomand working with secondary teachers.

Douglas A. Lapp and Vivian Flora Cyrus

Fig. 1Distance-time graph for student investigation

Probe

Fig. 2Path of walker

Copyright © 2000 The National Council of Teachers of Mathematics, Inc. www.nctm.org. All rights reserved. This material may not be copied or distributed electronically or in any other format without written permission from NCTM.

Vol. 93, No. 6 • September 2000 505

In the presence of data-collection devices, thesefour areas can interact with one another to encour-age graphical understanding. Such devices helpdevelop graphical meaning through interactionsamong the student, the technology, the physical sit-uation, and the interviewer, according toNemirovsky, Tierney, and Wright (1998). Despitemisconceptions—or alternative conceptions—aboutgraphs that were revealed by students’ initial ex-periences with data collection, repeated activitieswith the devices can improve students’ under-standing about physical phenomena (Nemirovsky,Tierney, and Wright 1998; Hale 2000; Monk andNemirovsky 1994; Thornton and Sokoloff 1990;Brasell 1987a, 1987b; Beichner 1990).

This article explores the extent to which graph-ing technology coupled with data-collection devicescan benefit mathematics and science classrooms.Before we continue with an examination of theresearch, we give a brief description of thesedevices.

DATA-COLLECTION DEVICESMicrocomputer-Based Laboratory (MBL), Calculator-Based Laboratory (CBL), and Calculator-BasedRanger (CBR) are devices that collect data withvarious probes and then store the data into a com-puter or calculator. The data can be analyzed anddisplayed in different formats, and the student cangraph as data are collected or at a later time. Fig-ure 3 shows the setup of a CBL device to collectvoltage data for a decaying capacitor over time.

cost, coupled with probes for graphing calculatorsrather than computers, have made them moreattractive for use in mathematics and science class-rooms. Because these tools have been around for awhile in computer or graphing-calculator form, weasked ourselves what we have learned about usingthese devices in the classroom.

CONNECTING GRAPHS WITH PHYSICAL CONCEPTSOne advantage of an MBL is its ability to displaygraphical representations of data in real time. Towhat extent does this feature play a role in concep-tual understanding? Is the simultaneous display ofthe graphical representation with the physicalevent the main feature that makes MBLs effective?Brasell (1987a) suggests that the immediacy ofgraph production is probably the most importantfeature of MBL activities. She discovered that adelay of even twenty seconds between the conclu-sion of the physical event and the graph displaymakes a difference in the students’ ability to linkthe graph and the physical concept.

Beichner (1989, 1990) suggests that simultaneityis not the only factor affecting the link between agraph and its physical event. He used a video re-creation of an event along with the graphical repre-sentation so that the student saw the moving objectand its graph at the same time. Although Brasell(1987a, 1987b) reported that significant differencesin students’ ability to link a graph with its physicalevent were caused almost entirely by simultaneousgraph production, Beichner found no significantdifferences while using reanimation. Beichner con-cluded that the student’s ability to control theenvironment plays a vital role in his or her under-standing of the physical event. Besides the pres-ence of technology, some affective aspect of theexperimentation process may drive the student toseek closure on an issue and thus actively pursuean understanding.

Nakhleh and Krajcik (1991, p. 19) observed that“students using MBL activities appeared to con-struct more powerful and more meaningful chemi-cal concepts.” They cited chemistry students’ con-cept maps that showed stronger connections amongthe concepts of acid, base, and pH. AlthoughNakhleh and Krajcik cautioned that students needcareful task analysis, directed teaching, and classdiscussion to counteract the formation of inappro-priate concepts, they speculated that on-screengraphs allowed MBL students to focus more onwhat was happening in an activity. The MBL main-tained the graph as a constant reference while stu-dents used their short-term memory to make pre-dictions and construct possible explanations for thegraph. This finding is consistent with that ofBrasell (1987b).

Immediacy of graph production is probablythe mostimportant feature ofMBL activities

Fig. 3Capacitor-decay setup with CBL2

Early forms of data-collection devices wereexpensive and were tied exclusively to computers.However, their increased availability and decreased

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506 MATHEMATICS TEACHER

Applying concepts learned with the MBL alsoseems to give students a sense of confidence in theirwork. Mokros (1986) reported that a group offemales who had constructed a velocity-time graphfor an accelerating cart knew that the slope of theresulting graph had to be positive. However, whena teacher stated that the graph was incorrect andthat the line should be horizontal, they argued thattheir graph was correct and that the slope had tobe nonzero for the speed to go up. These studentshad resolved the issue of slope-height confusion, inwhich students believe that the fastest rate ofchange of a graph occurs when the graph is at itshighest point (Nemirovsky, Tierney, and Wright1998; Mokros and Tinker 1987; McDermott, Rosenquist, and van Zee 1987).

To connect graphs with physical concepts, stu-dents need to see a variety of graphs representingdifferent physical events (McDermott, Rosenquist,and van Zee 1987). For example, when studentstake readings to study the relationship betweentime and the temperature of a cooling body, theysee a graph of a decreasing exponential function.See figure 4. Similarly, the relationship betweentime and voltage of a decaying capacitor yieldsanother graph of a decreasing exponential function.Observing isomorphic concepts, especially thosethat are prevalent in nature, may aid in theabstraction of mathematical concepts.

graph increased, the bicyclist was going up the hill(Linn 1987, p. 8).

Linn’s students had resolved graph-shape-and-path-of-motion confusion.

Bassok and Holyoak (1989) found that isomor-phic concepts in the mathematics classroom helpedstudents transfer these mathematical conceptsfrom algebra to physics. When linear functionswere studied in a general sense in mathematics,students tended to transfer that understanding intothe physics context. However, when physics contentisomorphic to that in the mathematics curriculumwas addressed in the physics classroom, transfer ofconcepts from physics to mathematics did not occur.For example, when physics students studiedHooke’s law, which states that the force on a springis proportional to the length of its stretch, theyobserved a linear, that is, a mathematical, relation-ship; yet they did not typically notice the connec-tion with physics content when they then experi-enced linear functions in mathematics. Using MBLactivities to link concepts from such other disci-plines as physics may improve the link with mathe-matics as well.

CONNECTING GRAPHS WITH THE REAL WORLDStudents may have difficulty distinguishingbetween the functional relationship of two vari-ables and the visual stimuli received when observ-ing the actual physical event. The most commonmisconceptions here are graph-as-a-picture confu-sion, where students do not see a graph as a rela-tionship between variables but rather as one object(Dunham and Osborne 1991; Mokros and Tinker1987), and graph-shape-and-path-of-motion confu-sion, mentioned previously. Students often believethat the shape of the graph should resemble theshape of the physical setup of the experiment(McDermott, Rosenquist, and van Zee 1987;Clement 1989; Monk 1990, 1994). If a ball is givenan initial velocity on a level “frictionless table,” asshown in figure 5, the student expects the graph of

Fig. 4Exponential model for two different physical events

Using MBLs, Linn (1987) observed the transferof relationships just described. Students in herstudy gained considerable understanding of graph-ing by observing the relationships of heat energyand temperature. They extended their understand-ing to interpreting motion graphs, although theyhad not studied kinematics or motion within thegraphing environment. For example,

As a result of studying graphs about heat and temper-ature, students could correctly interpret a graphshowing the speed of a bicycle when the bicycleascended a hill and then descended the hill. Prior toinstruction, many students assumed that when the

Fig. 5Ball rolling at constant velocity on tabletop

Studentsneed to see

a variety ofgraphs to

connect themwith physical

concepts


position versus time to also be horizontal ratherthan a straight line with nonzero slope, as shown infigure 6. Choosing the appropriate graph toexplore can be important in counteracting this mis-conception. For example, if the student used MBLor CBR to examine a velocity-time graph of thissame event, the graph would be “flat,” as shown infigure 7, thereby reinforcing the misconception.Thoughtful use of examples and nonexamples isbeneficial.

abstract representation of the history of these events.Thus, MBL tools provide an ideal medium to supportthe development of physical intuition through directinquiry.

Monk and Nemirovsky (1994) meticulouslydescribe one student’s experience with a physicalevent and the graph corresponding to the event.The student’s understanding of rate of changeevolves as he interacts with the device and graph ina real-time graphing environment. In this instance,the real-time graphing facilitates the deepening ofgraphical understanding.

TRANSITIONING BETWEEN GRAPHS AND PHYSICAL EVENTSA vital skill in science is the ability to leap backand forth between a graph and the physical eventthat the graph describes. The question is, How canwe, in practice, help students make the leap fromthe physical event to the graph and back? Bruner(1966) suggests a progression from enactive to icon-ic to symbolic representations, that is, the studentmoves from physically modeling the problem withmaterials (enactive) to diagramming or graphing(iconic) to putting the problem into an abstractmathematical form (symbolic). A CBR or any formof MBL equipped with a motion probe makes thisprogression possible.

Brasell (1987b) and Mokros (1986) began withenactive representations using MBL activities toreproduce the motion for a given graph. Mokrosused the roles of “dancer” and “choreographer” withstudents. The choreographer’s job was to explain tothe dancer what he or she had to do to reproducethe graph given by the teacher. Students had totranslate the graphical representation into a seriesof verbal directions and thereby exhibit an under-standing of the various aspects of the graph. Inboth studies, students were significantly more suc-cessful in transferring between a physical eventand its graph after using an MBL in real-timemode.

Although linking a physical event with itsgraph is important, the student also needs to beflexible when interpreting graphs. Consider themotion experiments represented in the graphs infigure 8. Here different physical events producedthe visually similar position-time, velocity-time,and acceleration-time graphs. Dealing with anapparent conflict between similar graphs arisingfrom different physical events can reinforce theway that information is obtained from each graph.To find velocity, the student must calculate slopeat a given point on the first graph, whereas thestudent simply reads the second graph’s value at agiven time. Alternatively, the student mustapproximate area under the curve to find velocityfrom the third graph.

Fig. 6Distance-versus-time graph of rolling ball on tabletop

Fig. 7Velocity-versus-time graph of rolling ball on tabletop

Real-time data collection seems to be the mosteffective way to connect a graph with the real-worldexperiences of the student (Brasell 1987b; Nakhlehand Krajcik 1991; Laws 1989). If this theory is cor-rect, then the immediacy of the graph productioncould help students see real-world relationshipsrather than simply take visual information andremember a picture of the event. Laws (1989, p. 6)states that

MBL stations give students immediate feedback bypresenting data graphically in a manner that studentscan learn to interpret almost instantly. This providesa powerful link between real events that can be per-ceived through the senses and the graph as an

A studentneeds to beflexible wheninterpretinggraphs

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Likewise, students should see a variety of graphsof the same event to experience differences in theway that information is presented. For example,students created the distance-time, velocity-time,and acceleration-time graphs in figure 9 by walk-ing back and forth in front of a CBR. The event inthis instance was obviously the same, since theexperiment was conducted only once, but thegraphs are visually different because of the infor-mation displayed. This sort of experience forces stu-dents to confront many of the previously mentionedgraphical misconceptions.

converge on a misconception. However, she suggeststhat using whole-class discussion following an explo-ration can promote further discourse while repair-ing any misconceptions. Incomplete understandingis a part of constructing concepts; eliminating it fromthe learning process is not necessarily desirable.Nakhleh and Krajcik (1991) claim that the highrates of appropriate and inappropriate conceptuallinks exhibited by students in their study indicatethat the students were positively engaged in restruc-turing their knowledge. Monk and Nemirovsky (1994)suggest that students’ misconceptions are not simplyreplaced by correct conceptions but that studentsrefine their conceptions in a gradual and continu-ous way. In some studies (Nemirovsky, Tierney, andWright 1998; Monk and Nemirovsky 1994), thisgradual development is accomplished, in part, bystudent-interviewer discourse.

SUGGESTIONS FOR CLASSROOM USETwo practices that offer promise in connectinggraphs with physical events are prediction andduplication activities. Students benefit fromexplaining what they think will happen before theyconduct an experiment. Students also apparentlymake connections if they are challenged to repro-duce a given motion graph by acting it out and see-ing the results in real time. Hale (2000, p. 416)reports a typical student’s perspective with Ben’scomment, “Doing that one lab where we actuallyhad to come up with the scenarios and then kind ofplay them out to see whether they worked—thathelped out the most I think.”

Engaging students in activities that demonstratethe relationship among different types of graphs isalso beneficial. Letting students deal with differentgraphical representations of the same event canhelp develop understanding of how information isconveyed by various types of graphs.

CONCLUSIONSWhat, then, are the reasons for success with MBLs?Mokros and Tinker (1987) give several reasons whyMBL technology is useful in connecting graphs andphysical events: MBLs use multiple modalities,pair events in real time with their symbolic repre-sentations, provide scientific experiences similar tothose of scientists in actual practice, and eliminatethe drudgery of graph production. Thornton andSokoloff (1990) warn that the tools themselves arenot enough but that gains in learning appear to beproduced by a combination of the MBL devices andappropriate curricular material that guides the stu-dents to examine appropriate phenomena. They, aswell as Mokros and Tinker, suggest that encourag-ing collaboration is an added benefit of MBLs.

For motion phenomena, using simultaneousgraph production to link a graph with a physical

Fig. 9Same physical event producing different graphical feedback

BUILDING GRAPHICAL CONCEPTSTHROUGH STUDENT DISCOURSECoupling CBL technology with student communica-tion can aid in developing mathematical and scien-tific concepts. Svec (1995, p. 23) concluded that“activities which emphasize qualitative under-standing, requiring written explanations, coopera-tive learning, eliciting and addressing students’prior knowledge and employing the learning cycleare more effective for engendering conceptualchange.” Cooper (1995) found that students need tohave time to rehearse their developing communica-tion skills as part of their investigation so that theycan effectively construct physics concepts.

Hale (1996) examined how students constructedand repaired conceptual understanding using dis-course within a CBL environment. One drawbackthat Hale found for using CBL in cooperative groupswas that sometimes, through discourse, groups would

Studentsrefine their

conceptionsin a gradual

and continuous

way

Fig. 8Different physical events producing the same graphical feedback


concept seems to be essential. However, futureresearch needs to address this issue for such otherphysical phenomena as temperature. We mightexpect that simultaneous graph production is notnecessary in some settings, because the humansenses cannot easily distinguish among varyingstates for all phenomena. For example, the averageperson perceives differences in velocity more easilythan differences in temperature. Two people walk-ing at, say, 2 MPH and 4 MPH can easily be distin-guished; however, the difference in temperaturebetween an object with a temperature of 2˚C andanother object with a temperature of 4˚C is verydifficult to distinguish.

Although the literature suggests benefits fromusing MBL technology, we must also consider prob-lems that may arise if we do not pay attention tohow the technology is implemented. Some studiesindicate that without proper precautions, technolo-gy can become an obstacle to understanding (Lapp1997; Bohren 1988; Nachmias and Linn 1987).Future research also should address how studentsview the authority of technology in problem solving.

Research suggests that we can be optimisticabout the benefits of MBL and CBL use in forminggraphical concepts. However, it is too early to drawfinal conclusions. Further study is needed beforethe research community can make any definitivestatements on the pedagogical advantages of data-collection devices.

REFERENCESBassok, Miriam, and Keith Holyoak. “Interdomain

Transfer between Isomorphic Topics in Algebra andPhysics.” Journal of Experimental Psychology:Learning, Memory, and Cognition 15 (January 1989):153–66.

Beichner, Robert J. “The Effect of SimultaneousMotion Presentation and Graph Generation in aKinematics Lab.” (Ph.D. diss., State University ofNew York at Buffalo, 1989.) Dissertation AbstractsInternational 50 (1989): 06A.

———. “The Effect of Simultaneous Motion Presenta-tion and Graph Generation in a Kinematics Lab.”Paper presented at the annual meeting of theNational Association for Research in Science Teach-ing, Atlanta, Ga., April 1990.

Bohren, Janet L. “A Nine-Month Study of Graph Con-struction Skills and Reasoning Strategies Used byNinth Grade Students to Construct Graphs of Sci-ence Data by Hand and with Computer GraphingSoftware.” (Ph.D. diss., Ohio State University, 1988.)Dissertation Abstracts International 49 (1988): 08A.

Brasell, Heather. “The Effects of Real-Time Laborato-ry Graphing on Learning Graphic Representations ofDistance and Velocity.” Journal of Research in Sci-ence Teaching 24 (April 1987a): 385–95.

———. “The Role of Microcomputer-Based Laborato-ries in Learning to Make Graphs of Distance andVelocity.” Report No. IR 012 831. Paper presented atthe annual meeting of the American Educational

Research Association, Washington, D.C., April1987b. (ERIC Document Reproduction no.ED287447)

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Clement, John. “The Concept of Variation and Mis-conceptions in Cartesian Graphing.” Focus on Learn-ing Problems in Mathematics 11 (winter-spring1989): 77–87.

Cooper, Sister Marie Anselm. “An Evaluation of theImplementation of an Integrated Learning Systemfor Introductory College Physics.” (Ph.D. diss., Rutgers University, 1995.) Dissertation AbstractsInternational 57 (1995): 02A.

Dunham, Penelope H., and Alan Osborne. “LearningHow to See: Students’ Graphing Difficulties.” Focuson Learning Problems in Mathematics 13 (fall 1991):35–49.

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Hale, Patricia L. “Building Conceptions and RepairingMisconceptions in Student Understanding of Kine-matic Graphs: Using Student Discourse in Calculator-Based Laboratories.” (Ph.D. diss., Oregon StateUniversity, 1996.) Dissertation Abstracts Interna-tional 57 (1996): 08A.

———. “Connecting Research to Teaching: Kinematicsand Graphs: Students’ Difficulties and CBLs.” Math-ematics Teacher 93 (May 2000): 414–18.

Lapp, Douglas A. “A Theoretical Model for StudentPerception of Technological Authority.” Paper pre-sented at the Third International Conference onTechnology in Mathematics Teaching, Koblenz,Germany, 29 September–2 October 1997.

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McDermott, Lillian C., Mark L. Rosenquist, andEmily H. van Zee. “Student Difficulties in Connect-ing Graphs and Physics: Examples from Kinemat-ics.” American Journal of Physics 55 (June 1987):503–13.

Mokros, Janice R. “The Impact of Microcomputer-Based Science Labs on Children’s Graphing Skills.”Report No. SE 046 290. Paper presented at the1986 annual meeting of the National Associationfor Research in Science Teaching. San Francisco,March 1986. (ERIC Document Reproduction no.ED264128)

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Problemsmay arise if we do notpay attentionto how thetechnology isimplemented


Mathematics Education I, edited by Ed Dubinsky,Alan H. Schoenfeld, and James Kaput, pp. 139–68.Vol. 4, CBMS Issues in Mathematics Education.Providence, R.I.: American Mathematical Societyand the Mathematical Association of America, 1994.

Nachmias, Rafi, and Marcia C. Linn. “Evaluations ofScience Laboratory Data: The Role of Computer-Presented Information.” Journal of Research in Science Teaching 24 (May 1987): 491–506.

Nakhleh, Mary B., and Joseph S. Krajcik. “The Effectof Level of Information as Presented by DifferentTechnologies on Students’ Understanding of Acid,Base, and pH Concepts.” Report No. SE 052102.Paper presented at the annual meeting of theNational Association for Research in Science Teach-ing, Lake Geneva, Wis., April 1991. (ERIC Docu-ment Reproduction no. ED347062)

Nemirovsky, Ricardo, Cornelia Tierney, and TracyWright. “Body Motion and Graphing.” Cognition andInstruction 16 (spring 1998): 119–72.

Svec, Michael T. “Effect of Micro-Computer BasedLaboratory on Graphing Interpretation Skills andUnderstanding of Motion.” Report No. SE 056282.Paper presented at the annual meeting of theNational Association for Research in Science Teach-ing, San Francisco, Calif., April 1995. (ERIC Docu-ment Reproduction no. ED383551)

Thornton, Ronald K., and David R. Sokoloff. “LearningMotion Concepts Using Real-Time Microcomputer-Based Laboratory Tools.” American Journal ofPhysics 58 (September 1990): 858–67. ¿

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———. “Students’ Understanding of a Function Givenby a Physical Model.” Paper presented at the Confer-ence on the Learning and Teaching of the Concept ofFunction at Purdue University, West Lafayette, Ind.,October 1990.

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