1. Introduction
    1. 1.
    2. Relationship of This Study to Physics and Physics Education
    3. A field which has not traditionally been associated with physics is the area of auditory display, or methods of displaying data with sound instead of by the more common visual sense. Many diverse subject areas, such as medicine, geological surveys, and fluid dynamics, are developing methods of auditory display techniques to represent data. [Kra94] These techniques often rely upon sophisticated tonal patterns and wave compression that takes much training on the part of the person using the display for interpretation.

      As many areas of physics utilize the display of data to a high degree, incorporating auditory display techniques provides an alternate method of portraying this data. In addition, the technique of auditory display may be of particular use to some people, especially those who are not able to receive information through standard graphical presentations. The studies described herein are an attempt to look at some of the most basic auditory display techniques, to see if this form of data representation is useful for answering interpretative questions about data presented as graphical information, and to discover possible improvements to these displays.

      This study on the interpretation of physics concepts presented in a graphical manner, and alternative methods for display of the information, required input from many different areas. Most notably, the subject matter developed in the field of physics education research. While this is not as broad an area as education research as a whole, it still involves many distinct areas. Those areas most directly related to this study are the overlapping areas of physics misconceptions, which may or may not include graphs, and graphical interpretation, which may or may not include physics.

      Interest in physics education research is high enough to warrant several publications and journals solely dedicated to this sub-field. Most notably are the American Journal of Physics and The Physics Teacher, both published by the American Physics Association. Of course, articles and research are not solely restricted to these examples, and often relevant information is found in other education and human factors journals.

      This study will not describe new fundamental phenomena, or characterization of processes of nature as is the case with many physics studies. Its purpose is, rather, intended to provide answers as to how data gathered in such studies can be presented in an effective manner, so that the information is readily accessible to all people, even to the beginning student in physics. All subject material portrayed in the applied tests has been chosen so that it relates to various mathematical techniques and physical phenomena that are of particular interest to beginning students.

      The techniques employed in the experimental design, and data analysis are those often found in studies pertaining to behavioral sciences. [Kir68] This study is largely about how people answer questions given some differentiating factor. In the case of the current study, the differentiation is due to the type of graph of the data. The subject material, however, has been drawn from typical graphical problems and information that first year physics students will generally encounter.

      When performing a study about graphical problems in physics, it is useful to examine both general problem areas that students have with physics, often reveled in misconceptions students have about the subject matter, and how students interpret graphical information. Fortunately, much work has already been performed investigating these problem areas.

      Often cited studies on the issue of misconceptions in physics are the Force Concept Inventory (FCI) [Hes92a] and the Mechanics Baseline Test. [Hes92b] These studies provide useable instruments that have been tested on large numbers of students. These tests provide extensive baseline data that can be used to asses the effectiveness of physics instruction in introductory physics. Other studies [Tro81; Tru96] also demonstrate the results from the FCI and Baseline studies. While these studies probe a wide range of problems that plague physics students, they often employ graphical information in parts of the tests.

      There have been many studies looking specifically at the nature of how students read and interpret graphs. While physics is the primary concern of this research, the question of how students relate to graphs does not lie solely within this domain. Enough studies have been performed in the area of mathematics to warrant at least one very comprehensive review paper. [Lei90] The field of Economics is also a popular area for research in graphical comprehension. [Coh94; Pri74] Thus, while a study working in the area of physics is useful, results may be able to be indirectly applied to other disciplines.

    4. Description of Problems That Student Have With Graphs
    5. The effectiveness, ubiquity, and importance of graphs for the physics student are apparent by the number of studies that have been devoted to finding out why students may have problems analyzing information from graphs [Mcd87; Pet92; Pri74] and by reviewing typical current general physics textbooks. [Hal93]

      Although many techniques of information design have evolved during the last 500 years (since the Italian Renaissance) [Tuf90], one of the more common and important methods of describing a single data set is through the use of the two dimensional line graph. While a large amount of information in current science text books and literature is displayed as descriptive diagrams, when large data sets or functions are to be analyzed, the line graph is a very tractable form of presentation.

      The ability to interpret graphical information is a prime concern in physics as graphs are widely used to give quick summaries of data sets, allow for pattern recognition, and portray information in new forms. With the ability to interpret the information contained within graphs, students have a greater chance to confront any discrepancies between what they think is correct and the data that is displayed. Understanding of physics comes from the ability to reconcile models of what is believed to be happening in an event, and the data produced by that event. Graphs provide methods of displaying data so that relationships between data components are more tractable to one who has the ability to correctly interpret the graph.

      The primary impetus for research in the area of learning and teaching graphical information stems perhaps from the realization that many college physics students have a great deal of confusion and misconceptions about physics. Student misconceptions have been shown to be of significant influence on student understanding of physics by such studies as the "Force Concept Inventory" [Hes92] as well as others. Since a significant method of communication in physics is through the use of graphical information, problems in conceptual understanding of physics may be a result of problems in understanding, and an inability to interpret, the graphical information which is presented.

      If misconceptions of physics arise due to the misinterpretation of the data or of the graph of the data, perhaps an alternate method of presenting that data should be considered. Various studies on alternate methods of presenting data, and for giving students a more direct understanding of what is being implied in graphs, have generally focused on the use of microcomputer based laboratories (MBLs.) [Lin87; Mok87; Bra87; Tho90] These studies usually center around how the immediacy of the graphing of the physical process aids in learning of the process being taught, or more generally, that students learn the course material during the lab. Unfortunately, it is often not well demonstrated that there are significant gains in using MBL over non-computer techniques, but it is demonstrated that learning does take place.

    6. Situations Where Auditory Graphs Are Useful
    7. While visual forms of information display have been developed so that their content can be readily and concisely discerned, there is some difficulty when someone is unable to view the graph in question. The inability to see a graph can be for several reasons: the display item (paper, computer screen, etc.) is unavailable or not within the visual periphery, the focus of attention is directed elsewhere (medical procedures, driving, etc.), or the person reading the graph has some visual disability.

      In all these cases, an alternate form of display is beneficial. One alternative solution is for the data or graph to be displayed in a haptic (tactile) format such as a raised line image. When data is presented in a descriptive diagram or picture format, tactile representation of the images and contained information can prove useful, but much time and effort is generally required when exploring each image by touch. In addition, for initial explanation of the image, some method of tutoring and initial orientation is required. This can be accomplished by the use of a personal assistant, although methods of creating computer annotated images are also being developed. [Gar98] However, auditory graphs provide an alternate method of data display and act as a replacement for the common line graph. Tactile images have the disadvantage of generally being slow and difficult to produce, create a permanent record of each graph, and are of use in limited situations.

    8. Description of Auditory Graphs
    9. Auditory display techniques are those methods that utilize sound to convey information which can be as simple as sounding an alerting bell to displaying complex relationships between variable quantities. When the sounds represent data, the process is often referred to as sonification of the data, or simply sonification. Comprehensive descriptions of various methods and developments using auditory displays can be found in conference proceedings of the International Conference on Auditory Display (ICAD) and associated texts. [Kra94] Recent research has begun to focus on the use of auditory displays to represent graphical information. Preliminary studies have been done by Flowers, & Hauer. [Flo95] The study designed in this paper is an attempt to extend the information and implications of those results.

      Recent studies [Flo95; Flo97] have demonstrated the ability of students to understand the general trends of auditory graphs. These are graphs where the data has been sonified, or converted into sounds. The most common method is to present the data so that each data point corresponds to a tone whose pitch is mapped to the dependent variable, and the independent variable is the temporal axis. Thus the graphs are a series of sounds played in time. However, it should be noted that this is a new field of research, and other auditory display techniques are being investigated. Alternate method include modifying the tonal qualities of the sound, repetition rates, or spatial locations. [Kra94]

      All of the graphs presented in this study utilize a sonified format using the pitch mapping method, with the y axis represented as pitch, and the x axis as time. There are some differences in the exact mapping methods used in the studies, and will be described in more detail in the chapters concerning those studies. The main differences in the methods are between using linear and chromatic mapping for pitch, and using tone indicators for derivative information. Also, the graphs portrayed in the studies to be discussed, were typically presented with only positive values for the y axis.

    10. Uses of Results of This Research
    11. It is possible that students who have difficulty interpreting graphical information presented as visual plots, may find auditory displays of the data more understandable. This greater understanding could then lead to the ability to overcome, or at least be lead away from some misconceptions associated with graphed information. The primary focus of this study however, is to demonstrate that simple auditory display methods can be used to impart enough information so that people can make informed and consistent decisions based on what was heard, with the intent that auditory graphs can act as a practical replacement for visual graphs.

      In the process of searching for a fairly intuitive method of auditory graph utilization, it is possible to develop graphs that are advantageous over previous methods. In fact, some of this has been noticed. From information gained in the pilot testing phases, the auditory graphs were able to be adjusted and elements added to provide more coherent graphs. These additions can then be utilized in software development, such as the Auditory Graphing Calculator, which uses auditory graphs, to provide a better interface with users.

      With accessible software, people can then take advantage of the power of auditory graphing techniques, with the minimum amount of training for the maximum amount of comprehension.

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Chapter 2

Copyright 1999 Steven Sahyun