Computers in Physics Using Education Research to Develop Waves Courseware Diane J. Grayson and Denis Donnelly Citation: Computers in Physics 10, 30 (1996); doi: 10.1063/1.4822353 View online: http://dx.doi.org/10.1063/1.4822353 View Table of Contents: http://scitation.aip.org/content/aip/journal/cip/10/1?ver=pdfcov Published by the AIP Publishing Articles you may be interested in The development of mathematics courseware for learning line and angle AIP Conf. Proc. 1660, 050021 (2015); 10.1063/1.4915654 Accelerating Learning with Distance Education and Open Courseware Comput. Sci. Eng. 14, 4 (2012); 10.1109/MCSE.2012.70 Pathway — Using a State‐of‐the‐Art Digital Video Database for Research and Development in Teacher Education AIP Conf. Proc. 818, 15 (2006); 10.1063/1.2177012 University of Minnesota Physics Education Research and Development Phys. Teach. 40, 447 (2002); 10.1119/1.1558126 Using physics courseware Phys. Teach. 27, 188 (1989); 10.1119/1.2342714
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COMPUTERS IN EDUCATION
USING EDUCATION RESEARCH TO DEVELOP WAVES COURSEWARE
Diane J. Grayson Department Editor: Denis Donnelly
[email protected] Figure 1. Motion graphs for an asymmetric, triangular pulse: (a) y versus x, (b) y versus t, (c) v versus t, and (d) v versus x.
The topic of waves forms the foundation of many branches of physics, such as acoustics, opties, and quantum mechanics. Thus it is essential that students of physics acquire a good understanding of waves if they wish to understand many other aspects of physics. Unfortunately, this topic presents a serious obstacle to many students, who often find it abstract and too mathematical. In order to help make the topic more accessible to students, Aronsl recommends that waves be introduced from a kinematical perspective by first considering graphical representations of single, transverse pulses. In this way, students are provided with a bridge from a more familiar and more concrete domain, kinematics, to a less familiar and more abstract domain, waves. Moreover, this approach to waves provides a context in which students can apply, reinforce, and extend graphing skills initially learned in kinematics. From a kinematical perspective, transverse displacement (y) of a point on a string is analogous to displacement in one dimension, and the (transverse) velocity of that point can be found by taking the slope of a graph of (transverse) displacement versus time. However, the string is not a single particle, nor is it a rigid body that moves as a whole. Rather, it consists of many pieces that do not move together. Thus, transverse displacement depends not only on the time of observation but also on which piece of the string is observed. Consequently, a new variable, position along the string (x), is needed. The motion of a pulse on a string thus provides a context in which to introduce the notion of a function of two independent variables. Another important aspect of waves is the need to distinguish between the motion of the pulse and the motion of particles of the medium as the pulse passes through them. This distinction can be highlighted by plotting an x versus t Diane J. Grayson is an assistant professor in the physics deparhnent at the University of Natal, South Africa. E-mail:
[email protected]
graph for a point of constant phase on the pulse in addition to a y versus t graph for a particular particle of the medium. The approach described above is embodied in the computer program Pulses on a String: Graphical Representations. As the name suggests, the program is designed to help students learn to produce and interpret various graphical representations of transverse pulses. The program displays successive "snapshots" of a pulse as it propagates along a string. This enables a student to follow in detail the changes in position with time of either particular bits of string or of a point of constant phase on the pulse itself. This type of detailed analysis is not possible in the laboratory because the motions happen too quickly. Thus the study of pulses lends itself well to computer-based activities.2 In the process of creating Pulses on a String, we also developed a model for instructional-software development that could be useful to others who are concerned with producing software that is both pedagogically sound and instructionally effective. The model involves first identifying student conceptual difficulties and then engaging in repeated cycles of program development and student use of the program, during which detailed observations of student/program interaction are made and student input solicited regarding pos sible improvements to the program. The software-development process is thus both interactive and iterative. Moreover, the resulting program is well-suited to the intended users, both because specific conceptual difficulties they are likely to encounter are addressed and because students play an active role in determining the final form of the program. This article presents the results of the research relevant to the program design, a description of the program, a discussion of the use of the program with several populations of students and some of the program changes that resulted, and a summary of the model for software development that emerged.
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Research on student conceptual difficulties Numerous studies have shown that students often hold alternative conceptions that are scientifically unacceptable, even after instruction.3 An implication of such studies is that if instruction does not specifically address students' alternative conceptions, then the students may never develop scientifically acceptable concepts. Thus it is important for an instructor, or software author in the case of instructional software, to be cognizant of specific conceptual difficulties students are likely to have with the subject matter.4 In the case of a computer program, the author can design the program in such a way as to confront and address particular conceptual difficulties in order to foster conceptual change. If this is not done, students' difficulties may remain intact even after use of the computer program, as often happens with traditional modes of instruction.5 Alternatively, the program may be confusing to students if the ideas presented conflict with their own conceptions.
It is important for an instructor, or software author in the case of instructional software, to be cognizant of specific conceptual difficulties students are likely to have with the subject matter. In order to identify conceptual difficulties with the content addressed by Pulses on a String: Graphical Representations, individual interviews were conducted with 18 students enrolled in an introductory university physics course. The interviews were conducted a few weeks after the students had studied waves, and a few months after they had studied motion graphs. Students were shown a sketch of an idealized, asymmetric triangular pulse, which they were told was moving to the right along a string. The sketch represented the shape of the string at one instant—that is, it was like a snapshot of the string. A set of y—x axes was overlaid on the sketch to act as a reference, where y is the transverse position and x is the lateral position. Thus the snapshot of the string indicates the shape of the y versus x graph (see Fig. la). The student was then asked to sketch graphs of y versus t for one bit of string, labeled A, transverse velocity v versus t for the same bit of string, and v versus x for the moment at which the snapshot was taken. Students can obtain the graphs by thinking qualitatively about the motion. As the pulse passes through the bit of string at A, point A moves upwards (+y direction) rapidly but for a short time (since the leading edge of pulse is short), then moves downwards (—y direction) slowly and for a longer time (as the longer trailing edge passes through). This motion is represented on a y versus t graph as a short steep section, followed by a longer, shallower section (see Fig. lb). On the v versus t graph, there is a short section of large, constant positive velocity followed by a longer section of smalt, constant negative velocity as the bit of string at A moves back to
its original position (Fig. 1c). The v versus x graph represents the transverse velocity of all the bits of string at the moment the snapshot was taken (Fig. 1d). At this instant, all the bits of string along the leading edge of the pulse (large x values) would be moving up (+y direction) with a large constant velocity, and all the bits of string on the trailing edge (smalt x values) would be moving down (—y direction) with a smaller constant velocity. As an example of the sort of difficulty that was observed, only 22% (4 out of 18) of the students were able to sketch the v versus x graph correctly. More than a quarter of the students interviewed obtained the shape of the v versus x graph by taking the slope of the y versus x graph. While it is legitimate to find the shape of the v versus t graph from the slope of the y versus t graph (since v = dy/dt), the slope of a y versus x graph does not represent a velocity. The next section includes a discussion of how the program tries to address this particular problem. The other main problem observed for all of the graphs was the drawing of curved graphs rather than straight line segments. The student comment "I'm just used to drawing sine waves because nothing very much except for a sawtooth shows up like that" suggests that this occurred because the students were remembering the sine curves they had encountered in their study of waves, rather than thinking physically about what was happening and then translating that physical reasoning into graphs.
Preliminary program design The approach to the plotting of y versus t and v versus t graphs was based on a series of paper-and-pencil exercises that formed part of a teaching module on waves developed by the Physics Education Group.6 In these tasks, students made numerous drawings of a triangular pulse on a string to represent the position of the pulse and the velocity of the string particles at successive times. These exercises helped students to develop an understanding of the motions involved but were slow and tedious. Moreover, great accuracy was required in order to generate meaningful graphs, and extensive individual interaction with tutors was needed for students to interpret their graphs. Pulses on a String was designed to remove the tedious and time-consuming aspects of the tasks without removing the requirement that the student do the thinking.7 In addition, the program allows for more exploration than the paper-and-pencil exercises in that students can study curved pulses as well as straight-sided pulses. Pulses on a String was written on a Macintosh computer, which has very good graphics capabilities, and so the program is heavily graphics-oriented. In addition, the programming language used, cT,8 made it feasible to accept and interpret verbal responses from students. The core of the program is a drawing editor developed by Bruce Sherwood9 and modified by David Trowbridge 1° in the development of his program Graphs and Tracks: Part IL The authorll further modified the drawing editor and wrote the plotting routines, sketching features, introductory drawing tutorial, help sequences, and discussion sequences. The program begins with an introduction that instructs the student on use of the various drawing features that are
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COMPUTERS IN EDUCATION d
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Figure 2. Screen display from Pulses on a String showing the sample y versus x graph, the graphing palette, and the doek.
Figure 3. Screen display shows how the y versus t graph is plotted.
After students either choose the sample pulse or draw their own pulse shapes, they are free to plot any of the types of graphs available in any order. Clook In the original version of the program r-5-707.1 MOVE these were y versus t and v versus t right graphs for one bit of string (x-value) and v versus x graph for the whole string at Time bobrees one time. (Note that the option to plot snapshots is: 0.50 5 an x versus t graph shown in Fig. 2 was added only after the program had been used with students.) The program disA point el» appesred on the v vs. t plays successive positions of the pulse lams. The Moe of the tremor'e quickly and accurately and does the acvelocity, v, is the longth of the error', (Ay) divided b the time tual plotting of points, but the student hely*. n snapshots (At). must indicate the values to be plotted. In Berild up your v va. t greph by the original version, when the student moving the putte end dressing from the old string pealtion (detted line) finished plotting points, the program %the tev ens (»lid line). connected the student's points together - - ----- t- - - • ••• • • • • - I -You con delete á point bv going to the --- 1* " 1- • O 1 2 3 4 dot-to-dot. Delete menu. • • The manner in which each graph is • Whea looke ere dem platting points held down the SHIFT key and generated emphasizes the physical beclick . havior of the string. For example, when Figure 4. Screen display shows how the v versus t graph is plotted. the program plots the y versus t or v versus t graphs for one bit of string, a slit encloses that bit of string to show that its motion is needed later on in the main program. Following the introductransverse. The program displays the current position of the tion, the student proceeds to the main program, in which a pulse as a solid line and the position a short time earlier as a sample pulse in the form of an asymmetric triangle is disdashed line. To plot a y versus t graph, the student clicks on played. Arons recommends this pulse shape because it rethe height of the string inside the slit, thus indicating its quires students to differentiate between graphs with time as current transverse position, and the program plots a point on abscissa and those with position as abscissa. Moreover, the straight segments mean that the transverse velocities on each the y versus t axes below (see Fig. 3). To plot a v versus t graph, the student points to the old position of the bit of string portion of the pulse are constant. However, students may of interest and drags it to its new position, thus indicating the choose to create their own pulse shape by using a combination of line segments or curved shapes provided in a graphing displacement that occurs during the time between the two snapshots. The program then divides this displacement by the palette. A set of coordinate axes is overlaid on the pulse to time between snapshots to obtain the transverse velocity. An form a graph of y versus x. Thus the y versus x graph is arrow appears on the pulse and a point is plotted on the v essentially like taking a snapshot of the pulse at a certain time. The time is indicated by a digital doek displayed next to the versus t axes below (see Fig. 4). The student conceptual difficulties identified with the v graphing palette (see Fig. 2). Options Plot Help Delete Discussion Show
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versus x graph were addressed in the original version of the program by having the student use essentially the same method to plot the v versus x graph and the v versus t graph. The student would indicate a displacement Ay, which the computer then divides by a time At. The only difference in the two plotting procedures was that for the v versus x graph, instead of following one point on the string over time, the student would indicate the motion of a number of points during one time interval. It was hoped that in this way students would see that velocity is always a displacement divided by a time (not dy/dx). Help sequences are available for each type of graph and may be called up from a menu at almost any point in the program. Each help sequence leads the student step-by-step through the plotting of a sample graph. The purpose of each step of the procedure is explained along the way, and the computer checks student responses to make sure each instruction has been correctly executed.
The manner in which each graph is generated emphasizes the physical behavior of the string. A pedagogical concern that influenced the program design was that students often treat instructional computer programs as video games.11 There is nothing wrong with a program having the appeal of a game, but there is a danger that students may just move objects around on the screen without being cognitively engaged. Two features of the program were designed to try to avert this "video-game syndrome." First, at the beginning of each plotting routine, students are required to use shapes from the graphing palette to sketch how they predict the graph will look on a set of axes displayed below the original pulse. The sketch appears with dashed lines and remains on the screen while the actual points are plotted on the same set of axes. This enables students to compare their predicted and plotted graphs. The second feature designed to promote cognitive engagement is a set of discussion sequences, which become available once a graph has been plotted. Each discussion sequence comprises a structured series of questions that require the student to type in verbal responses. The program is sensitive to the specific answers given and can vary the questions somewhat according to student responses. The discussion sequences are intended to focus students' attention on the salient features of their graphs and on the interrelationships among them. Students have a high level of control in terms of the shape of pulse they can choose to study, the sequences they wish to work through, and the order in which they wish to do the work.
The topic for the course was kinematics. Only a few of the teachers were qualified to teach physics; the rest were trained as teachers of biology, chemistry, mathematics or physical science. In practice, such teachers tend to have similar conceptual difficulties to those of undergraduate physics students. This fact, together with the teachers' awareness of learning processes, makes them a good group of people on which to field-test new instructional materials. Pulses on a String was used with the teachers very early on in its development, when it was still quite buggy and fragile. It was so fragile, in fact, that a staff member sat behind each pair of teachers working at a computer in order to get the program going again when it crashed.12 In addition, the staff member made detailed notes about what the teachers did and in what sequence and what responses they gave to questions in the discussion sequences. Much useful information came out of these direct observations. Before using the program, the teachers were given an assignment that was intended to influence their thinking as they worked through it. They were asked to think about what concepts from kinematics could be applied to the topic of pulses on a string and what concepts were new. They were also asked to comment on the program, what they liked and did not like, what was helpful and not helpful, and to suggest improvements. The assignment was written up in the form of a short paper. From their written papers handed in after using the program, it was clear that the teachers readily grasped the analogies between one-dimensional kinematics and the kinematics of pulses. The teachers seemed to understand the extension from one to two variables and why it is necessary in the case of transverse pulses. In terms of teaching strategy, the teachers found that the program' s operational approach to the plotting of points helped them to understand where the graph shapes came from. In addition, they appreciated making the link between waves and kinematics and applying their graphing skills in a new context. A number of teachers commented that the help and discussion sequences were useful to them. The discussion sequences in particular helped them to understand the relationships among the various gráphs. The teachers were tested before and after using the program, and a question on the material was included in the final examination several weeks later. The questions asked on these tests were similar to the original interview questions. Teachers were presented with a sketch of a y versus x graph and asked to sketch graphs of y versus t and v versus t for a point Table I. Results of a pretest, posttest, and examination question indicating percentage of in-service teachers who correctly sketched various graphs given a graph of y versus x. The number of correct answers is shown in parentheses. The total number of teachers in the group was 19.
Graph Type vs t
Preset 89(17)
Posttest 95 (18)
Final Exam 100 (19)
Use of the program with students: First trial
V vs t
84(16)
89(17)
89(17)
The program was first tried with 19 in-service teachers enrolled in an intensive six-week summer course in physics.
V vs x
53 (10)
84 (16)
79 (15)
y
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COMPUTERS IN EDUCATION
on the string and v versus x for one time. The results are given in Table I. Improvements from the pretest to the posttest on the y versus t and v versus t graphs were marginal, as the percentages of correct answers were high from the start. However, the number of people who could correctly sketch a v versus x graph given a y versus x graph showed a marked gain from pretest to posttest. This gain was still observable several weeks later when the final examination was administered. Many students answered the posttest and examination questions by referring explicitly to approaches used in the program. Modifications to the program as a result of student use Since the version of Pulses on a String used by the teachers was in an early stage of development, it had numerous bugs, which the teachers helped to document. They also made useful technical suggestions, such as recommending a larger font for the text. Other suggestions incorporated into the program were options to delete incorrectly plotted points or incorrectly sketched shapes and an option to view again any graph that has already been plotted. The teachers also provided information about their interactions with the program through the user interface. They pointed out where the wording of instructions was unclear, where alternative acceptable responses needed to be added to the discussion sequences, and which parts of the program were clumsy or difficult to use. A pedagogical issue that arose was what to show on the screen when the student finished plotting points. In the version used by the teachers, the program just connected the user' s points together dot-to-dot. Several problems were observed with this approach; the most serious was that some users were careless about plotting the graphs. The problem became quite acute with velocity graphs, where small errors in the value of Ay became magnified when Ay was divided by a small time interval. If the students were not careful about how far they dragged the mouse, the supposedly constant velocity sections ended up rather wiggly! Several teachers commented that they were confused when this happened to them, particularly when they later tried to respond to questions in the discussion section. However, it did not seem desirable to take control away from the student in the plotting of points. It was thus decided to let students generate the points, accurately or inaccurately, but when they indicated they were done, have the computer plot the correct graph as a solid line without removing either their plotted points or Table II. Results of a pretest and posttest indicating percentage of students who correctly sketched various graphs given a graph of y versus x. The number of correct answers is shown in parentheses. The total number of students in the group was 12. Graph Type
Preset
Posttest
y vs t
92(11)
100 (12)
v vs t
67 (8)
100 (12)
V vs x
33(4)
75 (9)
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Figure 5. Screen display from Pulses on a String showing the correct graph displayed as a solid line, in addition to the student' s plotted points and predicted graph (dashed line).
their predicted graph (see Fig. 5). Another pedagogical issue that arose was whether to distinguish between the average velocity indicated by the student (displacement/small time interval) and the instantaneous velocity (slope of they versus t graph). Several teachers felt that it was important to raise this issue, and so a discussion sequence was added to address the point. Several teachers suggested that the program should allow them to plot an x versus t graph as well as y versus t in order to highlight the distinction between the lateral motion (x-direction) of the pulse and the transverse motion (y-direction) of the bits of string. This idea had already been considered, and with encouragement from the teachers a fourth graph was added to the list of graphs that could be plotted. Use of the program with students: Second trial Pulses on a String was next used with 12 students from the introductory physics course who had studied kinematics but not waves. The students worked individually with the program, while the author observed them and took notes. Part of the reason for conducting observations of individual student use was to determine the extent to which the program could be used by a student alone. Thus instances were noted in which intervention was needed because instructions were not clear or the program crashed. Program bugs were also noted. In addition, observations were made of how students interacted with the program, including the options they selected, the order in which they were chosen, and the specific verbal responses they gave to questions in the discussion sequences. A pretest and posttest were administered immediately before and after using the program, respectively (see Table II). These tests resembled the program tasks in that the student was shown a y versus x graph for a single pulse and asked to sketch graphs of y versus t and v versus t for a particular bit of string and v versus x for a particular time. As with the in-service teachers, the v versus x graph posed the most problems, with only one third of the students drawing the graph correctly on the pretest. However, on the posttest, three-quarters of the students drew a correct v versus x graph. Information garnered from watching individual students work with the program was used to make further modifications. In particular, various bugs were fixed, instructions were clarified, and the program as a whole was made more robust
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(less amenable to crashes). Students tended not to choose the discussion sequences unless specifically instructed to do so. Thus the program was modified to make the associated discussion sequence appear automatically after the first graph is plotted. It was hoped that after working through one discussion "involuntarily," students would then choose to work through later ones. Use of the program with students: Third trial Pulses on a String was next used with a class of 23 in-service teachers enrolled in a six-week summer physics course, one year after the first usage.13 These teachers had just completed a month-long section on kinematics and were beginning a study of waves. As with the first group of teachers, they were given a written assignment prior to using the program; this assignment required them to connect concepts addressed by the program with concepts from kinematics. Since the program was now much more robust than the original version, little instructor intervention was needed. As before, the teachers' papers provided information on how they interacted with the program. The most striking difference between the papers submitted by these teachers and those from the first group was the strong emphasis placed on the two different motions: transverse motion of the bits of string (y-direction) and lateral motion of the pulse (x-direction). This distinction was clearly made by nearly everyone. Indeed, it was often one of the first things mentioned in their papers. For example, one teacher wrote: "My biggest confusion with graphing pulses on a string was: why use so many graphs to describe a single simple motion? As I looked closer, I realized we are not looking at a single motion but two separate motions—a motion in the y-direction and the motion along the string." Part of the reason why these teachers focused so clearly on the two orthogonal motions may be the addition of the x versus t graph to the program. Plotting this additional graph and working through the associated discussion on the relationship between the two position-time graphs (x versus t and y versus t) helped to highlight the two distinct motions. The teachers also distinguished between the two velocities involved, the transverse velocity (of the bits of string) and the propagation velocity (of the pulse). Another major change that was made to the program between use with the two groups of teachers was having the computer draw in the correct graph when the user had finished plotting a graph (rather than connecting the points together dot-to-dot). Although most people did not comment on this feature, or even question it, some did comment that this feature was helpful to them. A few teachers commented that they felt there should be some explanation of what the computer was doing when it drew in the correct graph, rather than just having the graph appear on the screen. This really became an issue in the case of the velocity graphs. The student plotted average velocity, whereas the computer displayed instantaneous velocity. As mentioned earlier, the discussion sequence on average and instantaneous velocities was designed to address this difference. For some teachers, the discussion proved adequate for the purpose, but others wanted to see some explanation of why
Table III. Results of a pretest and posttest indicating percentage of in-service teachers who correctly sketched various graphs given a graph of y versus x. The number of correct answers is shown in parentheses. The total number of teachers in the group was 23. vs 1
Preset 78(18)
Posttest 87 (20)
v vs t
52(12)
87 (20)
V VS x
26 (6)
65(15)
x VS t
57(13)
78 (18)
Graph Type y
the computer-drawn line and the student-plotted points were different when the correct graph was first displayed. As with the first group of teachers, these teachers readily made the connections between the kinematics of pulses and the one-dimensional kinematics they had studied previously. They found the sequence of topics (from one-dimensional kinematics to pulses) logical and helpful. They also were able to make the extension from a function of one variable to a function of two variables. The teachers were nearly unanimous in finding the discussion sequences helpful in focusing their attention on the important aspects of their graphs and the interrelationships among them. Most teachers found the program reacted adequately to their responses, although some wanted greater flexibility in handling user responses. The discussion on the v versus t and v versus x graph had been altered to include questions about whether the velocity could be found from the slope of the y versus t and y versus x graphs in order to reinforce the fact that the slope of the y versus x graph does not represent velocity. On a posttest administered several days after the program was used, no one tried to obtain the shape of the v versus x graph from the slope of the y versus x graph. As before, there were marked improvements in the number of people who could draw correctly the various graphs from pretest to posttest (see Table III). In particular, the number of people who drew a correct v versus x graph increased from 26% on the pretest to 65% on the posttest. About one-third (8) of the teachers sketched the position of the pulse at a little later time on their written posttests, following the method used by the program. As a result of use with this group of teachers, further minor modifications were made to the program. For example, several people suggested that the "snapshot" of the motion should be distinguished from the graph of y versus x. To this end, the program was modified to look more like the original interview task. Instead of showing a graph of y versus x initially, the program now displays a snapshot of a pulse on a string with no axes shown and explains that axes can be overlaid on the string to act as a reference. At this point, the student presses a key and only then is the set of y—x axes superimposed on the pulse.
Use of the program with students: Fourth trial Pulses on a String was used six months later (about 18 months after the first use) with a class of 24 undergraduate students enrolled in a preparatory physics class. For these
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students, the program fonned part of a course on waves that integrated laboratory and computer-based activities. By this time the program was fairly stable, robust, and comprehensible to students, so little intervention was needed from an instructor during program use. Unlike the teachers, these students were not required to write a paper after using the program. Moreover, no immediate follow-up activity took place after they used the program. The next encounter with the concepts addressed by the program occurred two weeks later in the form of a posttest. The results did not improve from pretest to posttest. In particular, the number of correct v versus x graphs on the posttest was exactly the same as the number on the pretest (10 out of 24, or 42%). One possible explanation for this is that for learning to occur, program use must be accompanied by some sort of reinforcing activity, such as an assignment or posttest administered soon after using the program.14
An interactive, iterative process Pulses on a String was tried out in various incarnations with about 100 students in all. Successive use of the program with students led to ongoing program development. This cycle of observing students use the program and soliciting their feedback, followed by modification of the program, was repeated several times over.15
As the program got more sophisticated and more poweiful, it also became bigger and more difficult to modify. It is important to note that as the program got more sophisticated and more powerful, it also became bigger and more difficult to modify. This point highlights the importance of using the program with students early on in the development process—as Chabay and Sherwood put it, "long before you have talked yourself into believing that your program is wonderful and finished, because after that point it will be much more difficult to accept contrary evidence!"16 Use of Pulses on a String: Graphical Representations with four groups of users suggests that understanding of graphical representations of pulses can be enhanced substantially by working with the program. Moreover, use of the program with people who had studied kinematics but not waves suggests that this approach to the introduction of waves provides a useful bridge between the two domains. Written comments made by the teachers illustrate that it also promotes a phenomenological understanding of wave motion and helps users distinguish the motion of the wave from motion of the medium. However, the posttest results from the last group of students suggest that use of the program alone may not be sufficient—some sort of immediate reinforcing activity seems to be needed. The following steps can be extracted and generalized as desirable components in a model for instructional software
development: 1.Select topic (content area) and target group; 2. Identify student conceptual difficulties; 3. Write preliminary version of program;17 4. Try it out with students—observe what they do and how they interact with the program, test what they learn, and solicit students' comments and suggestions; 5. Modify program on the basis of step 4; 6. Try it out with students; 7. Repeat steps 5 and 6 until the program is reasonably robust and fairly stable. While most of the steps listed above are common practice, two aspects of the model are particularly worth emphasizing. First, for instruction of any sort to be most effective (computer-based instruction included), student preconceptions and conceptual difficulties should be identified and explicitly addressed, hence the value of incorporating a research component into the development process. Second, in this model the users who try out the program are in a sense co-designers of the program. The early use of Pulses on a String in the classroom not only allowed for identification of bugs but also raised a number of design and pedagogical issues. A number of the changes or additions resulted from suggestions from the students themselves, changes that might not have occurred to the author. Thus, in this model, program development is an interactive process. Cycling through the loop of student use and program modification several times also makes the development process iterative. The resulting program almost certainly will be different from what the author originally envisaged. Moreover, it it likely to be wellmatched to the students for whom it is intended.
Acknowledgements The work described in this paper was carried out at the University of Washington in Seattle. I would like to thank members of the Physics Education Group for various forms of assistance. I would particularly like to thank Arnold Arons and Lillian McDermott for valuable discussions and guidance in the design of the program, David Trowbridge for extensive programming assistance, and Peter Shaffer and Mark Somers for assistance in the data collection. I would also like to thank David Treagust and Mario Zadnik for helpful suggestions on an earlier version of this paper. This work was conducted with partial support by the National Science Foundation under Grants No. DPE 8470081 and MDR 8950322. References 1. A. B. Arons, A Guide to Introductory Physics Teaching (Wiley, New York, 1990), p. 201-204. 2. Other programs on waves have been written. Examples are Making Waves by Joseph Snir of the Laboratory for Research and Development of Computers for Learning, University of Haifa, Israel, and Standing Waves by Eric Lane of the University of Iowa, published by CONDUIT. However, at the time Pulses on a String was written, no other software was known to the author that dealt with the kinematics of pulses. Subsequently a program called WaveMaker by Freeman Deutsch of the Harvard-Smithsonian Center for Astrophysics has become available; it
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shows both a simulation of pulses along a beaded string and motion graphs. For more information, see D. Donnelly, Comput. Phys. 5, 636 (1991). See, for example, Lillian C. McDermott and Peter S. Shaffer, Am. 1. Phys. 60, 994 (1992); D. Hestenes, M. Wells, andG. Swackhamer, Phys. Teach. 30,141 (1992). Lillian C. McDermott, Am. 1. Phys. 59, 301 (1991). See, for example, Rosalind Driver, Inti. 1. of Science Educ. 11, Special Issue, 481 (1989). James Evans, Mark Rosenquist, and Lillian McDermott, Waves (University of Washington, Seattle: ASUW Publishing, 1984). Lillian C. McDermott, Am. 1. Phys. 58, 452 (1990). cT is a derivative of the language called Tutor that was part ofthe PLATO system originally developed for mainframe computers. It is published by Falcon Software Inc., P.O. Box 200, Wentworth, NH 03282. For more information see Bruce Sherwood and David Anderson, Comput. Phys. 7, 136 (1993). Bruce Sherwood developed a drawing editor called draw. t. He is at the Center for Design of Educational Computing (CDEC), Carnegie Mellon University, Pittsburgh, PA. David Trowbridge, in Proceedings ofthe Conference on Computers in Physics Instruction, edited by E. F. Redish and 1. S. Risley (Addison-Wesley, Redwood City, CA, 1990), pp. 282-290. Diane J. Grayson, Ph.D. dissertation, University of Washington, 1990. We found that it was highly desirable for students to work together in pairs on a computer task. This way students can discuss what they are doing with one another, and they tend to think more carefully about the actual tasks they are performing. When students work alone, it is easy for the program to be treated as a video game, with little intellectual engagement on the part of the student. As with the first group, this group of teachers comprised not just physics teachers but also biology, mathematics, physical-science, and chemistry teachers. It should also be noted that since these students were in a preparatory physics course, they were the least wellprepared academically of the four group of students who used the program. This procedure is analogous to the procedure used by the Physics Education Group at the University of Washington to develop written curriculum materials. See Refs. 4 and 7. Ruth W. Chabay and Bruce A. Sherwood, in ComputerAssisted Instruction and Intelligent Tutoring Systems: Shared Goals and Complementary Approaches, edited by 1. H. Larkin and R.W. Chabay (Lawrence Erlbaum Associates, Hillsdale, NJ, 1992), pp. 151-186. Before beginning the coding process it is, of course, essential to create some sort of flow charts or sketches of screen displays on paper. However, Chabay and Sherwood (Ref. 16) suggest that as much of the work as possible should be done in an interactive manner on the computer itself. I agree, since what works on paper and what works on the computer are often quite different.
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