1. Review of Studies Concerning Physics, Graph Concepts in Physics, and Computer Aids in Graphing.
    1. 4.
    2. Hestenes, Wells, & Swackhamer
    3. An important study was conducted by Hestenes, Wells, & Swackhamer [Hes92a] concerning a method to probe student beliefs on the concept of force and how they compare to the Newtonian concept. The FCI was a multiple choice test instrument that provided choices between correct and common-sense alternatives to Newtonian concept questions regarding aspects of force. This was a test that has been given to many high school and college students and generated much literature. The primary uses for the FCI are as a diagnostic tool for student misconceptions and for evaluating instruction on Newtonian concepts.

      The "Force Concept Inventory" (FCI) is important because several of the questions in this well researched test served as the basis for questions asked in the Auditory graph tests. Not all of the questions could be utilized due to the nature of the display format, and the FCI only covered material relating to the concept of force whereas the conducted study had a more general basis of questioning. More will be mentioned of how this test was adapted in the section on Experimental Design. A similar article by Hestesnes and Wells [Hes92b] called the Mechanics Baseline Test" was also used for inspiration and adaptation to questions used in the auditory graph study.

    4. Trowbridge, & McDermott
    5. There are several studies that try to characterize how students conceptualize motion and the role that graphed information plays in their understanding. The first, is by Trowbridge & McDermott [Tro80] which looked only at how students understand velocity of simple observed motions. This paper described a guided interview process with over 300 subjects. The subjects were asked a series of questions relating to demonstrations about the motion of simple objects. In several of the questions, subjects were asked to compare the speed of two objects. When responding to one of the questions, some students would spontaneously draw graphs to aid as a communication device. However, it was observed that students were unable to correctly incorporate their graphing skills into a successful understanding of velocity. From student responses to interview questions, it was stated that students have a disparity between what their graphs illustrate, and what they think their graphs illustrate. It is this disparity that provided an expanded study with additional research.

    6. McDermott, Rosenquist, & van Zee
    7. The expanded study by McDermott, Rosenquist, & van Zee [Mcd87], looked not only at velocity, but at kinematics as a whole, and how students had trouble connecting physical concepts and graphical information. Their descriptive study with several hundred students, involved identifying areas in which students have difficulty in their interpretation of graphical information. Their data was derived primarily from responses to questions given to the students, presumably as part of an exam, and was mainly a categorization of the more prevalent difficulties observed.

      There are two main areas of difficulty that were identified: connecting graphs to physical concepts, and connecting graphs to real world phenomena. In the first category, the problems that were identified were difficulty discriminating between the slope and height, interpretations of changes in slope and height, relating graphs between position, velocity and acceleration coordinates, matching narrative information with relevant features of a graph, and interpretation of the integral, or area under the graph. In the relation of graphs to the real world, students drew graphs relating to the motion of a ball on various tracks. From these graphs common problems were: an inability to represent continuous motion with continuous lines, separating the shape of the graph from the path of the motion, representing negative velocity, representing constant acceleration, and distinguishing among different types of motion graphs (x, v, a vs. t).

    8. Beichner
    9. A more complete study on the subject of students’ interpretation of kinematics graphs was performed by Beichner. [Bei94]

      While the primary purpose of this article was to report on a study aimed at uncovering student problems with interpreting kinematics graphs, a secondary purpose was the proposition of a model for creating research oriented multiple choice tests which could be used as diagnostic tools and for formative and summative evaluations of instruction. Parts of the multiple choice test that was developed in the Beichner study was used as question templates for the current research

      The test evolved in several parts. Draft versions of the test were administered to 134 community college students who had been taught kinematics. The results were used to modify several of the questions, and the revisions were given to 15 high school, community college, four year college, and university faculty science educators. These individuals completed, commented on the appropriateness of the objectives, criticized items, and matched items to objectives in an effort to establish content validity. The final tests were then given to 165 juniors and seniors from three high schools, and 57 four-year college physics students.

      The test instrument consisted of 21 multiple-choice questions divided into seven testing objectives. The objectives were chosen upon examination of commonly used test banks, introductory physics books and informal interviews with science teachers. The test was designed to focus on interpretation skills. Three test items were written for each objective, most test items were written by the author although some items were adapted from previously used tests. The test questions and results of student performance was appended at the end of the paper.

      All of the statistical procedures indicated that the test was valid and reliable. Results of data analysis also indicated several other results. First, calculus based physics students did significantly better on the test (mean of 9.8 vs. 7.4) than algebra/trigonometry based physics students (t = 4.87, p < 0.01). Second, college students were not significantly better than their high school counterparts (t = 1.50, p < 0.13). Third, the mean for males of 9.5 was significantly better than the 7.2 mean for females (t = 5.66, p < 0.01).

      The developed instrument appeared to be generalizable to a wide range of students studying kinematics, from high school to university courses, across the country. The results allowed for objective grading and the ability to provide statistical analysis from large numbers of subjects.

      In a later study, Beichner [Bei96] investigated the impact of students analyzing video motion on their ability to interpret kinematics graphs. In this study it was found that the greatest impact to student's ability to interpret graphical information comes from hands-on involvement in data acquisition. The study demonstrated a strong correlation between the amount of exposure to video graphing labs and students' scores on a multiple choice test on graphs, indicating a better understanding of kinematics graphs.

      As the current studies utilized computer portrayal of graphical information, a brief discussion of some of the research investigating how computers have played a role in graphing may be warranted. These studies were also valuable as they also provided a basis from which to draw material for questions used in the current studies.

    10. Mokros, & Tinker
    11. A set of studies by Mokros & Tinker [Mok87] demonstrated that middle school students can learn to communicate with graphs in the context of appropriate microcomputer-based laboratory (MBL) investigations. The first preliminary study attempted to locate graph-related misconceptions, the second investigated children’s graphing skills, and the longitudinal study examined MBL intervention.

      In the first study, 25 seventh and eight grade students in a suburban school participated. The students were given a carefully constructed set of graphing problems in an interview setting. The problems were developed from the results of a pilot test to ensure appropriateness in terms of language, difficulty level, and coverage of various problem types. The interviews consisted of six graphing items and lasted 20 to 40 minutes. A protocol summary was completed for each student’s performance. The findings of this study were that students exhibited two major types of errors, which have also been observed in college populations: graph as picture confusion, and a weaker indication of confusion with relating slope and height.

      The second study investigated the ways in which students learn graphing skills through MBL. Data was collected through the use of intensive observational examinations consisting of narrative records for individual lab groups. Student interactions were recorded through an event sampling process and subjected to quantitative analysis. The study utilized an MBL course unit consisting of five days of activities on position and velocity plotting. The observations and scores from a nine question quiz in the second preliminary study indicated that after five days, students had developed graph interpretation skills.

      The longitudinal study was designed to provide more evidence about the impact of MBL on graphing skills. This study involved a pretest, treatment, posttest design, with each test comprising two components: a multiple-choice test of graphing skills and an interview where the students talked through their thought process. In the longitudinal study, scores on the 16 graphing items showed a small (\delta = 15%), but significant, change. This research showed that students can learn graphing concepts over a long time frame when using MBL’s.

    12. Brasell
    13. A study by Brasell [Bra87] not only extends Mokros and Tinker to high school students but also assesses the effect of a very brief exposure of a kinematics unit on the ability to translate between a physical event and the corresponding graphical representation. The study also evaluated the effect of real-time graphing in comparison to delayed graphing of data on student learning.

      The sample was drawn from entire physics classes (of seven to 17 students each) in seven rural schools in north Florida providing a total of 93 students. The students were mostly seniors and were familiar with the concepts included in the experimental activities. It is suspected that the choice of the students was a matter of convenience as the author is from the University of Florida.

      The experiment was conducted over a three day period, one day for the pre-test and orientation, one for the treatment, and one for post-testing and discussion. The treatment consisted of several groups: a Test only, a standard Microcomputer-based lab (MBL) display where data was displayed as it was acquired, a delayed MBL group where a 20 second delay was introduced between acquisition and display, and a pencil and paper graphing group that plotted their own graphs on paper. The MBL groups used curriculum units designed for the software. The paper and pencil group graphed complex motion described on a worksheet. Each class at each school had one group of students for each treatment to provide a balanced design. Students were randomly assigned to each group on a class-wise basis.

      Pre- and post-tests were described as consisting of content-specified, multiple choice items requiring students to translate between a verbal description of a physical event and the graphic representation of it. The pretest had been developed and used by a previous researcher (Thornton, ‘86) for use with humanities college students. The post-test was conceptually similar, but altered in format. Due to the change, direct change in performance measurements were not made as they would not have been valid, but were utilized as a covariant. SAT scores were recorded and used as a covariant. It was stated that neither the pre- nor posttests were checked for reliability. Validity of the tests was not mentioned. Analysis of covariance was used to reduce error variance of posttest scores.

      Factorial analysis of covariance was utilized. The pre- and posttests were divided into two sub-tests, one for distance and another for velocity. It was found that overall scores for standard MBL treatment were significantly higher, F(3, 68) 6.59, p < 0.001, than scores from the other treatments. While it was shown that scores for both sections were higher, only the distance sub-test scores were significant, F(3,68) = 6.47, p < 0.001. The velocity sub-test was not considered a significant difference, F(3, 68) = 1.80, p = 0.156. A table of the results was provided, and data was also presented in a graph of the mean error rates for the different groups.

      Brasell stated that 90% of the difference in the mean scores was due to the real-time nature of graphing provided by MBL. At no time was the performance of the delayed MBL graphing significantly superior to that of students in the control groups. It was found that even a short delay in displaying graphs dramatically reduced the effectiveness of the MBL on graphing skills. It was suggested that one of the effects of the delayed graphing was that students appeared less motivated, less actively engaged, less eager to experiment, and more concerned with the procedure, rather than the concepts.

    14. Linn, Layman, & Nachmias
    15. A study on the cognitive consequences of microcomputers on graphing skill development was attempted by Linn, Layman, and Nachmias. [Lin87] In their study, they explored how student's graphing skills changed after exposure to MBL intervention. Their study centered on an "ideal" chain of cognitive accomplishments. These were: graph features, graph templates or sequences of activities that are used repetitively to comprehend the graph, graph design skills which augment and consolidate the templates for new problems, and graph problem-solving skills. They found that the MBL intervention increased student's ability to identify trends and locate extrema, but did not compare their results to non MBL methods. Exposure to the MBL graphs acted as a basis on which students built their graphing models.

    16. Thornton, & Sokoloff
    17. A study that did attempt to compare the effectiveness of MBL techniques was conducted by Thornton and Sokoloff. [Tho90] The purpose of their study was to evaluate the effectiveness of curricula that take advantage of Microcomputer-based laboratories which present data in immediately understandable graphical forms over non-computer based courses. The ability to learn basic kinematics concepts was evaluated with pre- and post-testing as well as by observations.

      The sample was drawn from more than 1500 college and university physics students taking non-calculus and calculus based General Physics courses at the University of Oregon and Tufts University over a three year period. The research design consisted of testing students enrolled in a laboratory course involving micro-computers to display the graphical information and comparing the results from their post-test scores to those of students who were not enrolled in the lab. Data was collected by a 50 item multiple choice pre- and post-tests. It was not mentioned if the same test was given at both universities.

      The data which is reported showed dramatic reduction (up to 40%) in the error rates when compared to the non-MBL group. While the results of this study show improvement in the ability to answer multiple choice questions for students who are in the MBL’s, it was not clearly demonstrated that MBL’s would be better than traditional labs. For example, those who did not participate in the micro-computer lab, did not participate in any lab experience, hence were not as practiced as the MBL group. Another explanation is that those students not taking the lab may not be as comfortable, practiced, or competent with physics as the MBL group, which would also cause a difference in scores.

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Copyright 1999 Steven Sahyun